Table of Contents
Resources:
- Variational Bayes and The Mean-Field Approximation (blog)
- Variational Inference: Mean Field Approximation (Lecture Notes)
- Graphical Models, Exponential Families, and Variational Inference (M Jordan)
- Why is the Variational Bound Tight: the variational bound compared to the original error surface (reddit!)
Inference and Approximate Inference
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Inference:
Inference usually refers to computing the probability distribution over one set of variables given another.Goals:
- Computing the likelihood of observed data (in models with latent variables).
- Computing the marginal distribution over a given subset of nodes in the model.
- Computing the conditional distribution over a subsets of nodes given a disjoint subset of nodes.
- Computing a mode of the density (for the above distributions).
Approaches:
- Exact inference algorithms:
- Brute force
- The elimination algorithm
- Message passing (sum-product algorithm, belief propagation)
- Junction tree algorithm
- Approximate inference algorithms:
- Loopy belief propagation
- Variational (Bayesian) inference \(+\) mean field approximations
- Stochastic simulation / sampling / MCMC
Inference in Deep Learning - Formulation:
In the context of Deep Learning, we usually have two sets of variables:
(1) Set of visible (observed) variables: \(\: \boldsymbol{v}\)
(2) Set of latent variables: \(\: \boldsymbol{h}\)Inference in DL corresponds to computing the likelihood of observed data \(p(\boldsymbol{v})\).
When training probabilistic models with latent variables, we are usually interested in computing
$$p(\boldsymbol{h} \vert \boldsymbol{v})$$
where \(\boldsymbol{h}\) are the latent variables, and \(\boldsymbol{v}\) are the observed (visible) variables (data).
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The Challenge of Inference:
Motivation - The Challenge of Inference:
The challenge of inference usually refers to the difficult problem of computing \(p(\boldsymbol{h} \vert \boldsymbol{v})\) or taking expectations wrt it.
Such operations are often necessary for tasks like Maximum Likelihood Learning.Intractable Inference:
In DL, intractable inference problems, usually, arise from interactions between latent variables in a structured graphical model.
These interactions are usually due to:- Directed Models: “explaining away” interactions between mutual ancestors of the same visible unit.
- Undirected Models: direct interactions between the latent variables.
In Models:
- Tractable Inference:
- Many simple graphical models with only one hidden layer have tractable inference.
E.g. RBMs, PPCA.
- Many simple graphical models with only one hidden layer have tractable inference.
- Intractable Inference:
- Most graphical models with multiple hidden layers with hidden variables have intractable posterior distributions.
Exact inference requires an exponential time.
E.g. DBMs, DBNs. - Even some models with only a single layer can be intractable.
E.g. Sparse Coding
- Most graphical models with multiple hidden layers with hidden variables have intractable posterior distributions.
Computing the Likelihood of Observed Data:
We usually want to compute the likelihood of the observed data \(p(\boldsymbol{v})\), equivalently the log-likelihood \(\log p(\boldsymbol{v})\).
This usually requires marginalizing out \(\boldsymbol{h}\).
This problem is intractable (difficult) if it is costly to marginalize \(\boldsymbol{h}\).- Data Likelihood: (intractable)
\(p_{\theta}(\boldsymbol{v})=\int_\boldsymbol{h} p_{\theta}(h) p_{\theta}(v \vert h) dh\) - Marginal Likelihood (evidence): is the data likelihood \(p_{\theta}(\boldsymbol{v})\) (intractable)
\(\int_\boldsymbol{h} p_{\theta}(h) p_{\theta}(v \vert h) dh\) - Prior:
\(p(\boldsymbol{h})\) - (Conditional) Likelihood:
\(p_{\theta}(\boldsymbol{v} \vert h)\) - Joint:
\(p_{\theta}(\boldsymbol{v}, \boldsymbol{h})\) - Posterior: (intractable)
\(p_{\theta}(\boldsymbol{h} \vert \boldsymbol{v})=\frac{p_{\theta}(\boldsymbol{v}, \boldsymbol{h})}{p_{\theta}(\boldsymbol{v})}=\frac{p_{\theta}(\boldsymbol{v} \vert h) p_{\theta}(h)}{\int_{\boldsymbol{h}} p_{\theta}(h) p_{\theta}(x \vert h) d h}\)
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Approximate Inference:
Approximate Inference is an important and practical approach to confronting the challenge of (intractable) inference.
It poses exact inference as an optimization problem, and aims to approximate the underlying optimization problem.
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Inference as Optimization:
Exact inference can be described as an optimization problem.- Inference Problem:
- Compute the log-likelihood of the observed data, \(\log p(\boldsymbol{v} ; \boldsymbol{\theta})\).
Can be intractable to marginalize \(\boldsymbol{h}\).
- Compute the log-likelihood of the observed data, \(\log p(\boldsymbol{v} ; \boldsymbol{\theta})\).
- Inference Problem as Optimization - Core Idea:
- Choose a family of distributions over the latent variables \(\boldsymbol{h}\) with its own set of variational parameters \(\boldsymbol{v}\): \(q(\boldsymbol{h} \vert \boldsymbol{v})\).
- Find the setting of the parameters that makes our approximation closest to the posterior distribution over the latent variables \(p(\boldsymbol{h} \vert \boldsymbol{v})\).
I.E. Optimization - Use learned \(q\) in place of the posterior (as an approximation).
- Optimization - Fitting \(q\) to the posterior \(p\):
- Optimize \(q\) to approximate \(p(\boldsymbol{h} \vert \boldsymbol{v})\)
- Similarity Measure: use the KL-Divergence as a similarity measure between the two distributions
$$D_{\mathrm{KL}}(q \| p) = \mathrm{E}_ {h \sim q}\left[\log \frac{q(h)}{p(h\vert {v})}\right] =\int_{h} q(h) \log \left(\frac{q(h)}{p(h\vert {v})}\right) dh$$
- Intractability: minimizing the KL Divergence (above) is an intractable problem.
Because the expression contains the intractable term \(p(\boldsymbol{h}\vert \boldsymbol{v})\) which we were trying to avoid.
- Evidence Lower Bound:
- We rewrite the KL Divergence expression in terms of log-likelihood of the data:
$$\begin{aligned} D_{\mathrm{KL}}(q \| p) &=\int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h \vert v)} dh \\ &=\int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh+\int_{\boldsymbol{h}} q(h) \log p(v) dh \\ &=\int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh+\log p(\boldsymbol{v}) \end{aligned}$$
where we’re using Bayes theorem on the second line and the RHS integral simplifies because it’s simply integrating over the support of \(q\) and \(p\) is not a function of \(h\).
Thus,$$\log p(\boldsymbol{v}) = D_{\mathrm{KL}}(q \| p) - \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh$$
- Notice that since the KL-Divergence is Non-Negative:
$$\begin{align} D_{\mathrm{KL}}(q \| p) &\geq 0 \\ D_{\mathrm{KL}}(q \| p) - \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh &\geq - \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh \\ \log p(\boldsymbol{v}) &\geq - \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh \end{align} $$
Thus, the term \(- \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh\) provides a lower-bound on the log likelihood of the data.
- We rewrite the term as:
$$\mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q) = - \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh$$
the Evidence Lower Bound (ELBO) AKA Variational Free Energy.
Thus,$$\log p(\boldsymbol{v}) \geq \mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q)$$
- The Evidence Lower Bound can also be defined as:
$$\begin{align} \mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q) &= - \int_{\boldsymbol{h}} q(h) \log \frac{q(h)}{p(h, v)} dh \\ &= \log p(\boldsymbol{v} ; \boldsymbol{\theta})-D_{\mathrm{KL}}(q(\boldsymbol{h} \vert \boldsymbol{v}) \| p(\boldsymbol{h} \vert \boldsymbol{v} ; \boldsymbol{\theta})) \\ &= \mathbb{E}_ {\mathbf{h} \sim q}[\log p(\boldsymbol{h}, \boldsymbol{v})]+H(q) \end{align} $$
The latter being the canonical definition of the ELBO.
- We rewrite the KL Divergence expression in terms of log-likelihood of the data:
- Inference with the Evidence Lower Bound:
- For an appropriate choice of \(q, \mathcal{L}\) is tractable to compute.
- For any choice of \(q, \mathcal{L}\) provides a lower bound on the likelihood
- For \(q(\boldsymbol{h} \vert \boldsymbol{v})\) that are better approximations of \(p(\boldsymbol{h} \vert \boldsymbol{v}),\) the lower bound \(\mathcal{L}\) will be tighter
I.E. closer to \(\log p(\boldsymbol{v})\). - When \(q(\boldsymbol{h} \vert \boldsymbol{v})=p(\boldsymbol{h} \vert \boldsymbol{v}),\) the approximation is perfect, and \(\mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q)=\log p(\boldsymbol{v} ; \boldsymbol{\theta})\).
- Maximizing the ELBO minimizes the KL-Divergence \(D_{\mathrm{KL}}(q \| p)\).
- Inference:
We can thus think of inference as the procedure for finding the \(q\) that maximizes \(\mathcal{L}\):- Exact Inference: maximizes \(\mathcal{L}\) perfectly by searching over a family of functions \(q\) that includes \(p(\boldsymbol{h} \vert \boldsymbol{v})\).
- Approximate Inference: approximate inference uses approximate optimization to find \(q\).
We can make the optimization procedure less expensive but approximate by:- Restricting the family of distributions \(q\) that the optimization is allowed to search over
- Using an imperfect optimization procedure that may not completely maximize \(\mathcal{L}\) but may merely increase it by a significant amount.
- Core Idea of Variational Inference:
We don’t need to explicitly compute the posterior (or the marginal likelihood), we can solve an optimization problem by finding the right distribution \(\) that best fits the Evidence Lower Bound.
Learning and Inference wrt the ELBO - Summary:
The ELBO \(\mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q)\) is a lower bound on \(\log p(\boldsymbol{v} ; \boldsymbol{\theta})\):- Inference: can be viewed as maximizing \(\mathcal{L}\) with respect to \(q\).
- Learning: can be viewed as maximizing \(\mathcal{L}\) with respect to \(\theta\).
Notes:
- The difference between the ELBO and the KL divergence is the log normalizer (i.e. the evidence), which is the quantity that the ELBO bounds.
- Maximizing the ELBO is equivalent to Minimizing the KL-Divergence.
- Inference Problem:
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Expectation Maximization:
The Expectation-Maximization Algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models with unobserved latent variables.It is based on maximizing a lower bound \(\mathcal{L}\).
It is not an approach to approximate inference.
It is an approach to learning with an approximate posterior.The EM Algorithm:
The EM Algorithm consists of alternating between two steps until convergence:- The E(xpectation)-step:
- Let \(\theta^{(0)}\) denote the value of the parameters at the beginning of the step.
- Set \(q\left(\boldsymbol{h}^{(i)} \vert \boldsymbol{v}\right)=p\left(\boldsymbol{h}^{(i)} ; \boldsymbol{\theta}^{(0)}\right)\) for all indices \(i\) of the training examples \(\boldsymbol{v}^{(i)}\) we want to train on (both batch and minibatch variants are valid).
By this we mean \(q\) is defined in terms of the current parameter value of \(\boldsymbol{\theta}^{(0)}\);
if we vary \(\boldsymbol{\theta},\) then \(p(\boldsymbol{h} \vert \boldsymbol{v} ; \boldsymbol{\theta})\) will change, but \(q(\boldsymbol{h} \vert \boldsymbol{v})\) will remain equal to \(p\left(\boldsymbol{h} \vert \boldsymbol{v} ; \boldsymbol{\theta}^{(0)}\right)\).
- The M(aximization)-step:
- Completely or partially maximize
$$\sum_i \mathcal{L}\left(\boldsymbol{v}^{(i)}, \boldsymbol{\theta}, q\right)$$
with respect to \(\boldsymbol{\theta}\) using your optimization algorithm of choice.
- Completely or partially maximize
Relation to Coordinate Ascent:
The algorithm can be viewed as a Coordinate Ascent algorithm to maximize \(\mathcal{L}\).
On one step, we maximize \(\mathcal{L}\) with respect to \(q,\) and on the other, we maximize \(\mathcal{L}\) with respect to \(\boldsymbol{\theta}\).
Stochastic Gradient Ascent on latent variable models can be seen as a special case of the EM algorithm where the M-step consists of taking a single gradient step.Other variants of the EM algorithm can make much larger steps. For some model families, the M-step can even be performed analytically, jumping all the way to the optimal solution for \(\theta\) given the current \(q\).
As Approximate Inference - Interpretation:
Even though the E-step involves exact inference, the EM algorithm can be viewed as using approximate inference.
The M-step assumes that the same value of \(q\) can be used for all values of \(\theta\).
This will introduce a gap between \(\mathcal{L}\) and the true \(\log p(\boldsymbol{v})\) as the M-step moves further and further away from the value \(\boldsymbol{\theta}^{(0)}\) used in the E-step.
Fortunately, the E-step reduces the gap to zero again as we enter the loop for the next time.Insights/Takeaways:
- The Basic Structure of the Learning Process:
We update the model parameters to improve the likelihood of a completed dataset, where all missing variables have their values provided by an estimate of the posterior distribution.This particular insight is not unique to the EM algorithm. For example, using gradient descent to maximize the log-likelihood also has this same property; the log-likelihood gradient computations require taking expectations with respect to the posterior distribution over the hidden units.
- Reusing \(q\):
We can continue to use one value of \(q\) even after we have moved to a different value of \(\theta\).
This particular insight is used throughout classical machine learning to derive large M-step updates.
In the context of deep learning, most models are too complex to admit a tractable solution for an optimal large M-step update, so this second insight, which is more unique to the EM algorithm, is rarely used.
Notes:
- The Expectation-Maximization Algorithm and Derivation (Blog!)
- The EM algorithm enables us to make large learning steps with a fixed \(q\)
- The E(xpectation)-step:
- MAP Inference:
MAP Inference is an alternative form of inference where we are interested in computing the single most likely value of the missing variables, rather than to infer the entire distribution over their possible values \(p(\boldsymbol{h} \vert \boldsymbol{v})\).
In the context of latent variable models, we compute:$$\boldsymbol{h}^{* }=\underset{\boldsymbol{h}}{\arg \max } p(\boldsymbol{h} \vert \boldsymbol{v})$$
As Approximate Inference:
It is not usually thought of as approximate inference, since it computes the exact most likely value of \(\boldsymbol{h}^{* }\).
However, to develop a learning process wrt maximizing the lower bound \(\mathcal{L}(\boldsymbol{v}, \boldsymbol{h}, q),\) then it is helpful to think of MAP inference as a procedure that provides a value of \(q\).
In this sense, we can think of MAP inference as approximate inference, because it does not provide the optimal \(q\).
We can derive MAP Inference as a form of approximate inference by restricting the family of distributions \(q\) may be drawn from.
Derivation:- We require \(q\) to take on a Dirac distribution:
$$q(\boldsymbol{h} \vert \boldsymbol{v})=\delta(\boldsymbol{h}-\boldsymbol{\mu})$$
- This means that we can now control \(q\) entirely via \(\boldsymbol{\mu}\).
- Dropping terms of \(\mathcal{L}\) that do not vary with \(\boldsymbol{\mu},\) we are left with the optimization problem:
$$\boldsymbol{\mu}^{* }=\underset{\mu}{\arg \max } \log p(\boldsymbol{h}=\boldsymbol{\mu}, \boldsymbol{v})$$
- which is equivalent to the MAP inference problem:
$$\boldsymbol{h}^{* }=\underset{\boldsymbol{h}}{\arg \max } p(\boldsymbol{h} \vert \boldsymbol{v})$$
The Learning Procedure with MAP Inference:
We can, thus, justify a learning procedure similar to EM, where we alternate between:- Performing MAP inference to infer \(\boldsymbol{h}^{* }\), and
- Updating update \(\boldsymbol{\theta}\) to increase \(\log p\left(\boldsymbol{h}^{* }, \boldsymbol{v}\right)\).
As Coordinate Ascent:
As with EM, this is a form of coordinate ascent on \(\mathcal{L},\) where we alternate between using inference to optimize \(\mathcal{L}\) with respect to \(q\) and using parameter updates to optimize \(\mathcal{L}\) with respect to \(\boldsymbol{\theta}\).Lower Bound (ELBO) Justification:
The procedure as a whole can be justified by the fact that \(\mathcal{L}\) is a lower bound on \(\log p(\boldsymbol{v})\).
In the case of MAP inference, this justification is rather vacuous, because the bound is infinitely loose, due to the Dirac distribution’s differential entropy of negative infinity.
Adding noise to \(\mu\) would make the bound meaningful again.MAP Inference in Deep Learning - Applications:
MAP Inference is commonly used in deep learning as both a feature extractor and a learning mechanism.
It is primarily used for sparse coding models.MAP Inference in Sparse Coding Models:
Summary:
Learning algorithms based on MAP inference enable us to learn using a point estimate of \(p(\boldsymbol{h} \vert \boldsymbol{v})\) rather than inferring the entire distribution.
- We require \(q\) to take on a Dirac distribution:
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Variational Inference and Learning:
Main Idea - Restricting family of distributions \(q\):
The core idea behind variational learning is that we can maximize \(\mathcal{L}\) over a restricted family of distributions \(q\).
This family should be chosen so that it is easy to compute \(\mathbb{E}_ {q} \log p(\boldsymbol{h}, \boldsymbol{v})\).
A typical way to do this is to introduce assumptions about how \(q\) factorizes.
Mainly, we make a Mean-Field Approximation to \(q\).Mean-Field Approximation:
Mean-Field Approximation is a type of Variational Bayesian Inference where we assume that the unknown variables can be partitioned so that each partition is independent of the others.
The Mean-Field Approximation assumes the variational distribution over the latent variables factorizes as:$$q(\boldsymbol{h} \vert \boldsymbol{v})=\prod_{i} q\left(h_{i} \vert \boldsymbol{v}\right)$$
I.E. it imposes the restriction that \(q\) is a factorial distribution.
More generally, we can impose any graphical model structure we choose on \(q,\) to flexibly determine how many interactions we want our approximation to capture.
This fully general graphical model approach is called structured variational inference (Saul and Jordan, 1996).The Optimal Probability Distribution \(q\):
The beauty of the variational approach is that we do not need to specify a specific parametric form for \(q\).
We specify how it should factorize, but then the optimization problem determines the optimal probability distribution within those factorization constraints.
The Inference Optimization Problem:- For discrete latent variables: we use traditional optimization techniques to optimize a finite number of variables describing the \(q\) distribution.
- For continuous latent variables: we use calculus of variations to perform optimization over a space of functions and actually determine which function should be used to represent \(q\).
- Calculus of Variations removes much of the responsibility from the human designer of the model, who now must specify only how \(q\) factorizes, rather than needing to guess how to design a specific \(q\) that can accurately approximate the posterior.
Calculus of variations is the origin of the names “variational learning” and “variational inference”, but the names apply in both discrete and continuous cases.
KL-Divergence Optimization:
- The Inference Optimization Problem boils down to maximizing \(\mathcal{L}\) with respect to \(q\).
- This is equivalent to minimizing \(D_{\mathrm{KL}}(q(\boldsymbol{h} \vert \boldsymbol{v}) \| p(\boldsymbol{h} \vert \boldsymbol{v}))\).
- Thus, we are fitting \(q\) to \(p\).
- However, we are doing so with the opposite direction of the KL-Divergence. We are, unnaturally, assuming that \(q\) is constant and \(p\) is varying.
- In the inference optimization problem, we choose to use \(D_{\mathrm{KL}}\left(q(\boldsymbol{h} \vert \boldsymbol{v}) \| p(\boldsymbol{h} \vert \boldsymbol{v})\right)\) for computational reasons.
- Specifically, computing \(D_{\mathrm{KL}}\left(q(\boldsymbol{h} \vert \boldsymbol{v}) \| p(\boldsymbol{h} \vert \boldsymbol{v})\right)\) involves evaluating expectations with respect to \(q,\) so by designing \(q\) to be simple, we can simplify the required expectations.
- The opposite direction of the KL divergence would require computing expectations with respect to the true posterior.
Because the form of the true posterior is determined by the choice of model, we cannot design a reduced-cost approach to computing \(D_{\mathrm{KL}}(p(\boldsymbol{h} \vert \boldsymbol{v}) \| q(\boldsymbol{h} \vert \boldsymbol{v}))\) exactly.
- Three Cases for Optimization:
- If \(q\) is high and \(p\) is high, then we are happy (i.e. low KL divergence).
- If \(q\) is high and \(p\) is low then we pay a price (i.e. high KL divergence).
- If \(q\) is low then we dont care (i.e. also low KL divergence, regardless of \(p\)).
- Optimization-based Inference vs Maximum Likelihood (ML) Learning:
- ML-Learning: fits a model to data by minimizing \(D_{\mathrm{KL}}\left(p_{\text {data }} \| p_{\text {model }}\right)\).
It encourages the model to have high probability everywhere that the data has high probability, - Optimization-based Inference:
It encourages \(q\) to have low probability everywhere the true posterior has low probability.
- ML-Learning: fits a model to data by minimizing \(D_{\mathrm{KL}}\left(p_{\text {data }} \| p_{\text {model }}\right)\).
Variational (Bayesian) Inference:
Variational Bayesian Inference AKA Variational Bayes is most often used to infer the conditional distribution over the latent variables given the observations (and parameters).
This is also known as the posterior distribution over the latent variables:$$p(z \vert x, \alpha)=\frac{p(z, x \vert \alpha)}{\int_{z} p(z, x \vert \alpha)}$$
which is usually intractable.
Notes:
- KL Divergence Optimization:
Optimizing the KL-Divergence given by:$$D_{\mathrm{KL}}(q \| p) = \mathrm{E}_ {z \sim q}\left[\log \frac{q(z)}{p(z\vert x)}\right] =\int_{z} q(z) \log \left(\frac{q(z)}{p(z\vert x)}\right) dz$$
- Three Cases for Optimization:
- If \(q\) is high and \(p\) is high, then we are happy (i.e. low KL divergence).
- If \(q\) is high and \(p\) is low then we pay a price (i.e. high KL divergence).
- If \(q\) is low then we dont care (i.e. also low KL divergence, regardless of \(p\)).
- Three Cases for Optimization:
Variational Inference and Learning
- Variational Inference - Discrete Latent Variables:
Variational Inference with Discrete Latent Variables is relatively straightforward.
Representing \(q\):
We define a distribution \(q\) where each factor of \(q\) is just defined by a lookup table over discrete states.
In the simplest case, \(h\) is binary and we make the mean field assumption that \(q\) factorizes over each individual \(h_{i}\).
In this case we can parametrize \(q\) with a vector \(\hat{h}\) whose entries are probabilities.
Then \(q\left(h_{i}=1 \vert \boldsymbol{v}\right)=\hat{h}_ {i}\).
Optimizing \(q\):
After determining how to represent \(q\) we simply optimize its parameters.
For discrete latent variables this is just a standard optimization problem e.g. gradient descent.
However, because this optimization must occur in the inner loop of a learning algorithm, it must be very fast1.
A popular choice is to iterate fixed-point equations; to solve:$$\frac{\partial}{\partial \hat{h}_ {i}} \mathcal{L}=0$$
for \(\hat{h}_ {i}\).
We repeatedly update different elements of \(\hat{\boldsymbol{h}}\) until we satisfy a convergence criterion.Application - Binary Sparse Coding:
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Variational Inference - Continuous Latent Variables:
Variational Inference and Learning with Continuous Latent Variables requires the use of the calculus of variations for maximizing \(\mathcal{L}\) with respect to \(q(\boldsymbol{h} \vert \boldsymbol{v})\).In most cases, practitioners need not solve any calculus of variations problems themselves. Instead, there is a general equation for the mean field fixed-point updates.
The General Equation for Mean-Field Fixed-Point Updates:
If we make the mean field approximation$$q(\boldsymbol{h} \vert \boldsymbol{v})=\prod_{i} q\left(h_{i} \vert \boldsymbol{v}\right)$$
and fix \(q\left(h_{j} \vert \boldsymbol{v}\right)\) for all \(j \neq i,\) then the optimal \(q\left(h_{i} \vert \boldsymbol{v}\right)\) may be obtained by normalizing the unnormalized distribution:
$$\tilde{q}\left(h_{i} \vert \boldsymbol{v}\right) = \exp \left(\mathbb{E}_{\mathbf{h}_{-i} \sim q\left(\mathbf{h}_ {-i} \vert \boldsymbol{v}\right)} \log \tilde{p}(\boldsymbol{v}, \boldsymbol{h})\right) = e^{\mathbb{E}_{\mathbf{h}_ {-i} \sim q\left(\mathbf{h}_ {-i} \vert \boldsymbol{v}\right)} \log \tilde{p}(\boldsymbol{v}, \boldsymbol{h})}$$
as long as \(p\) does not assign \(0\) probability to any joint configuration of variables.
- Carrying out the expectation inside the equation will yield the correct functional form of \(q\left(h_{i} \vert \boldsymbol{v}\right)\).
- The General Equation yields the mean field approximation for any probabilistic model.
- Deriving functional forms of \(q\) directly using calculus of variations is only necessary if one wishes to develop a new form of variational learning.
- The General Equation is a fixed-point equation, designed to be iteratively applied for each value of \(i\) repeatedly until convergence.Functional Form of the Optimal Distribution/Solution:
The General Equation tells us the functional form that the optimal solution will take, whether we arrive there by fixed-point equations or not.
This means we can take the functional form from that equation but regard some of the values that appear in it as parameters, which we can optimize with any optimization algorithm we like.
For examples of real applications of variational learning with continuous variables in the context of deep learning, see Goodfellow et al. (2013d).
- Interactions between Learning and Inference:
Using approximate inference as part of a learning algorithm affects the learning process, and this in turn affects the accuracy of the inference algorithm.
Analysis:- The training algorithm tends to adapt the model in a way that makes the approximating assumptions underlying the approximate inference algorithm become more true.
- When training the parameters, variational learning increases
$$\mathbb{E}_ {\mathbf{h} \sim q} \log p(\boldsymbol{v}, \boldsymbol{h})$$
- For a specific \(v\) this:
- increases \(p(\boldsymbol{h} \vert \boldsymbol{v})\) for values of \(\boldsymbol{h}\) that have high probability under \(q(\boldsymbol{h} \vert \boldsymbol{v})\) and
- decreases \(p(\boldsymbol{h} \vert \boldsymbol{v})\) for values of \(\boldsymbol{h}\) that have low probability under \(q(\boldsymbol{h} \vert \boldsymbol{v})\).
- This behavior causes our approximating assumptions to become self-fulfilling prophecies.
If we train the model with a unimodal approximate posterior, we will obtain a model with a true posterior that is far closer to unimodal than we would have obtained by training the model with exact inference.
Computing the Effect (Harm) of using Variational Inference:
Computing the true amount of harm imposed on a model by a variational approximation is thus very difficult.- There exist several methods for estimating \(\log p(\boldsymbol{v})\):
We often estimate \(\log p(\boldsymbol{v} ; \boldsymbol{\theta})\) after training the model and find that the gap with \(\mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q)\) is small.- From this, we can conclude that our variational approximation is accurate for the specific value of \(\boldsymbol{\theta}\) that we obtained from the learning process.
- We should not conclude that our variational approximation is accurate in general or that the variational approximation did little harm to the learning process.
- To measure the true amount of harm induced by the variational approximation:
- We would need to know \(\boldsymbol{\theta}^{* }=\max_{\boldsymbol{\theta}} \log p(\boldsymbol{v} ; \boldsymbol{\theta})\).
- It is possible for \(\mathcal{L}(\boldsymbol{v}, \boldsymbol{\theta}, q) \approx \log p(\boldsymbol{v} ; \boldsymbol{\theta})\) and \(\log p(\boldsymbol{v} ; \boldsymbol{\theta}) \ll \log p\left(\boldsymbol{v} ; \boldsymbol{\theta}^{* }\right)\) to hold simultaneously.
- If \(\max_{q} \mathcal{L}\left(\boldsymbol{v}, \boldsymbol{\theta}^{* }, q\right) \ll \log p\left(\boldsymbol{v} ; \boldsymbol{\theta}^{* }\right),\) because \(\boldsymbol{\theta}^{* }\) induces too complicated of a posterior distribution for our \(q\) family to capture, then the learning process will never approach \(\boldsymbol{\theta}^{* }\).
- Such a problem is very difficult to detect, because we can only know for sure that it happened if we have a superior learning algorithm that can find \(\boldsymbol{\theta}^{* }\) for comparison.
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Learned Approximate Inference:
Motivation:
Explicitly performing optimization via iterative procedures such as fixed-point equations or gradient-based optimization is often very expensive and time consuming.
Many approaches to inference avoid this expense by learning to perform approximate inference.Learned Approximate Inference:
Learns to perform approximate inference by viewing the (multistep iterative) optimization process as a function \(f\) that maps an input \(v\) to an approximate distribution \(q^{* }=\arg \max_{q} \mathcal{L}(\boldsymbol{v}, q)\), and then approximates this function with a neural network that implements an approximation \(f(\boldsymbol{v} ; \boldsymbol{\theta})\).Wake-Sleep:
Motivation:- One of the main difficulties with training a model to infer \(h\) from \(v\) is that we do not have a supervised training set with which to train the model.
- Given a \(v\) we do not know the appropriate \(h\).
- The mapping from \(v\) to \(h\) depends on the choice of model family, and evolves throughout the learning process as \(\theta\) changes.
Wake-Sleep Algorithm:
The wake-sleep algorithm (Hinton et al., 1995b; Frey et al., 1996) resolves this problem by drawing samples of both \(h\) and \(v\) from the model distribution.- For example, in a directed model, this can be done cheaply by performing ancestral sampling beginning at \(h\) and ending at \(v\).
The inference network can then be trained to perform the reverse mapping: predicting which \(h\) caused the present $\boldsymbol{v}$.
DrawBacks:
The main drawback to this approach is that we will only be able to train the inference network on values of \(\boldsymbol{v}\) that have high probability under the model.
Early in learning, the model distribution will not resemble the data distribution, so the inference network will not have an opportunity to learn on samples that resemble data.Relation to Biological Dreaming:
Generative Modeling - Application:
Learned approximate inference has recently become one of the dominant approaches to generative modeling, in the form of the Variational AutoEncoder (Kingma, 2013; Rezende et al., 2014).
In this elegant approach, there is no need to construct explicit targets for the inference network.
Instead, the inference network is simply used to define \(\mathcal{L},\) and then the parameters of the inference network are adapted to increase \(\mathcal{L}\).
Mathematics of Approximate Inference
Directional Derivative
The Calculus of Variations (Blog!)
-
Calculus of Variations:
Method for finding the stationary functions of a functional \(I[f]\) (function of functions) by solving a differential equation.
Formally, calculus of variations seeks to find the function \(y=f(x)\) such that the integral (functional):
$$I[y]=\int_{x_{1}}^{x_{2}} L\left(x, y(x), y^{\prime}(x)\right) d x$$
$$\begin{array}{l}{\text {where}}\\{x_{1}, x_{2} \text { are constants, }} \\ {y(x) \text { is twice continuously differentiable, }} \\ {y^{\prime}(x)=d y / d x} \\ {L\left(x, y(x), y^{\prime}(x)\right) \text { is twice continuously differentiable with respect to its arguments } x, y, y^{\prime}}\end{array}$$
is stationary.
Euler Lagrange Equation - Finding Extrema:
Finding the extrema of functionals is similar to finding the maxima and minima of functions. The maxima and minima of a function may be located by finding the points where its derivative vanishes (i.e., is equal to zero). The extrema of functionals may be obtained by finding functions where the functional derivative is equal to zero. This leads to solving the associated Euler–Lagrange equation.The Euler Lagrange Equation is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary:
$$\frac{\partial L}{\partial f}-\frac{d}{d x} \frac{\partial L}{\partial f^{\prime}} = 0$$
It is defined in terms of the functional derivative:
$$\frac{\delta J}{\delta f(x)} = \frac{\partial L}{\partial f}-\frac{d}{d x} \frac{\partial L}{\partial f^{\prime}} = 0$$
Shortest Path between Two Points:
Find path such that the distance \(AB\) between two points is minimized.
Using the arc length, we define the following functional:$$\begin{align} I &= \int_{A}^{B} dS \\ &= \int_{A}^{B} \sqrt{dx^2 + dy^2} \\ &= \int_{A}^{B} \sqrt{1 + \left(\dfrac{dy}{dx}\right)^2} dx \\ &= \int_{x_1}^{x_2} \sqrt{1 + \left(\dfrac{dy}{dx}\right)^2} dx \end{align} $$
- Now, we formulate the variational problem:
Find the extremal function \(y=f(x)\) between two points \(A=(x_1, y_1)\) and \(B=(x_2, y_2)\) such that the following integral is minimized:$$I[y] = \int_{x_{1}}^{x_{2}} \sqrt{1+\left[y^{\prime}(x)\right]^{2}} d x$$
where \(y^{\prime}(x)=\frac{d y}{d x}, y_{1}=f\left(x_{1}\right), y_{2}=f\left(x_{2}\right)\).
- Solution:
We use the Euler-Lagrange Equation to find the extremal function \(f(x)\) that minimizes the functional \(I[y]\):$$\frac{\partial L}{\partial f}-\frac{d}{d x} \frac{\partial L}{\partial f^{\prime}}=0$$
where \(L=\sqrt{1+\left[f^{\prime}(x)\right]^{2}}\).
- Since \(f\) does not appear explicity in \(L,\) the first term in the Euler-Lagrange equation vanishes for all \(f(x)\)
$$\frac{\partial L}{\partial f} = 0$$
- Thus,
$$\frac{d}{d x} \frac{\partial L}{\partial f^{\prime}}=0$$
- Substituting for \(L\) and taking the derivative:
$$\frac{d}{d x} \frac{f^{\prime}(x)}{\sqrt{1+\left[f^{\prime}(x)\right]^{2}}}=0$$
for some constant \(c\).
- If the derivative \(\frac{d}{dx}\), above, is zero, then
$$\frac{f^{\prime}(x)}{\sqrt{1+\left[f^{\prime}(x)\right]^{2}}}=c$$
for some constant \(c\).
- Square both sides:
$$\frac{\left[f^{\prime}(x)\right]^{2}}{1+\left[f^{\prime}(x)\right]^{2}}=c^{2}$$
where \(0 \leq c^{2}<1\).
- Solving:
$$\left[f^{\prime}(x)\right]^{2}=\frac{c^{2}}{1-c^{2}}$$
\(\implies\)
$$f^{\prime}(x)=m$$
is a constant \(m\).
- Integrating:
$$f(x)=m x+b$$
is an equation of a (straight) line, where \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \quad\) and \(\quad b=\frac{x_{2} y_{1}-x_{1} y_{2}}{x_{2}-x_{1}}\).
In other words, the shortest distance between two points is a straight line.
We have found the extremal function \(f(x)\) that minimizes the functional \(A[y]\) so that \(A[f]\) is a minimum.
- Since \(f\) does not appear explicity in \(L,\) the first term in the Euler-Lagrange equation vanishes for all \(f(x)\)
- Now, we formulate the variational problem:
-
Mean Field Methods:
-
Mean Field Approximations:
-
To achieve this speed, we typically use special optimization algorithms that are designed to solve comparatively small and simple problems in few iterations. ↩


{%extends "hr-home.html"%} {%block content%}
| ID | Gender | First Name | Last Name | Department | Title | Manager | ManagerID |
| {{ employee['EmployeeID'] }} | {{ employee['Gender'] }} | {{ employee['FirstName'] }} | {{ employee['LastName'] }} | {{ employee['DeptName'] }} | {{ employee['TitleName'] }} | {{ employee['ManagerName'] }} | {{ employee['ManagerID'] }} | {% endfor %} {% endif %}


Gecode::Int::Regular::Dom< View >::LayeredGraph< View > Class Template Reference
List of all members.
Detailed Description
template<class View>
template<class View>
class Gecode::Int::Regular::Dom< View >::LayeredGraph< View >
LayeredGraph as data structure used for propagation in regular
Definition at line 79 of file dom.icc.
Constructor & Destructor Documentation
|
|
Construct layered graph.
Definition at line 180 of file dom.icc. |
|
|
Release layered graph.
Definition at line 383 of file dom.icc. |
Member Function Documentation
|
|
Prune initially for view sequence x.
Definition at line 236 of file dom.icc. |
|
|
Prune incrementally for view sequence x.
Definition at line 280 of file dom.icc. |
|
|
Return memory required for layered graph.
Definition at line 389 of file dom.icc. |
The documentation for this class was generated from the following file:


Pirates Coach Talks Lorch And Discipline
by Soccer LadumaFor Rulani Mokwena, the best player in the country remains none other than Thembinkosi Lorch despite the Orlando Pirates talisman going through a bit of a tough spell and being sent off midweek, which effectively ended his game time in 2019.
Many have argued the holder of the Footballer of the Season award has been a shadow of a player that cleaned up at the Premier Soccer League event in May this year, but his club coach continues to back him.
Read: Pitso: Do I Want To Risk That?
“Unfortunately we forget that he is still the reigning Footballer of the Season and sometimes I think we put undue pressure because of social media,” Mokwena told the media.
“So the expectations are based more on that. I always tell him that he’s still the best player in the country. Who has the award of Footballer of the Season at home? It’s Thembinkosi Lorch. He has got nothing to prove to anybody.”
Lorch was red carded for retaliation in Pirates’ 3-2 Absa Premiership victory against Polokwane City on Tuesday night and has also had close calls in previous matches where he was lucky to have still been on the pitch.
Read: PSL Give Downs Major TKO Boost
There were also suggestions that no move to Europe materialised even though Pirates received numerous offers from both French and Belgian clubs during the most recent transfer window that slammed shut on September 2.
“Some of the incidents, like you mention, are difficult to assess because like the (Polokwane) incident, he was fouled. With a little bit more emotional intelligence he could have avoided the situation. But it’s different to the Chiefs one (his stamp on Billiat) or the previous match. We can’t be too critical of Nyoso. He is still the best player in the country. If someone wants to argue I will talk stats. The award is at his house,” said Mokwena.
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nips nips2006 nips2006-128 nips2006-128-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Matthias Hein, Markus Maier
Abstract: We consider the problem of denoising a noisily sampled submanifold M in Rd , where the submanifold M is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graph-based diffusion process of the point sample. We analyze this diffusion process using recent results about the convergence of graph Laplacians. In the experiments we show that our method is capable of dealing with non-trivial high-dimensional noise. Moreover using the denoising algorithm as pre-processing method we can improve the results of a semi-supervised learning algorithm. 1
[1] M. Belkin and P. Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comp., 15(6):1373–1396, 2003.
[2] C. M. Bishop, M. Svensen, and C. K. I. Williams. GTM: The generative topographic mapping. Neural Computation, 10:215–234, 1998.
[3] O. Chapelle, B. Sch¨ lkopf, and A. Zien, editors. Semi-Supervised Learning. MIT Press, Cambridge, o 2006. in press, http://www.kyb.tuebingen.mpg.de/ssl-book.
[4] P. Grassberger and I. Procaccia. Measuring the strangeness of strange attractors. Physica D, 9:189–208, 1983.
[5] A. Grigoryan. Heat kernels on weighted manifolds and applications. Cont. Math., 398:93–191, 2006.
[6] T. Hastie and W. Stuetzle. Principal curves. J. Amer. Stat. Assoc., 84:502–516, 1989.
[7] M. Hein, J.-Y. Audibert, and U. von Luxburg. From graphs to manifolds - weak and strong pointwise consistency of graph Laplacians. In P. Auer and R. Meir, editors, Proc. of the 18th Conf. on Learning Theory (COLT), pages 486–500, Berlin, 2005. Springer.
[8] M. Hein, J.-Y. Audibert, and U. von Luxburg. Graph Laplacians and their convergence on random neighborhood graphs, 2006. accepted at JMLR, available at arXiv:math.ST/0608522.
[9] M. Hein. Geometrical aspects of statistical learning theory. PhD thesis, MPI f¨ r biologische Kyberu netik/Technische Universit¨ t Darmstadt, 2005. a
[10] D. Keysers, W. Macherey, H. Ney, and J. Dahmen. Adaptation in statistical pattern recognition using tangent vectors. IEEE Trans. on Pattern Anal. and Machine Intel., 26:269–274, 2004.
[11] C. Lange and K. Polthier. Anisotropic smoothing of point sets. Computer Aided Geometric Design, 22:680–692, 2005.
[12] O. Scherzer and J. Weickert. Relations between regularization and diffusion imaging. J. of Mathematical Imaging and Vision, 12:43–63, 2000.
[13] G. Taubin. A signal processing approach to fair surface design. In Proc. of the 22nd annual conf. on Computer graphics and interactive techniques (Siggraph), pages 351–358, 1995.
[14] J. B. Tenenbaum, V. de Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500):2319–2323, 2000.
[15] D. Zhou, O. Bousquet, T. N. Lal, J. Weston, and B. Sch¨ lkopf. Learning with local and global consistency. o In S. Thrun, L. Saul, and B. Sch¨ lkopf, editors, Adv. in Neur. Inf. Proc. Syst. (NIPS), volume 16. MIT o Press, 2004.


Refined Words
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Sweet Uncertainty
Broaden My Narrow Vision
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James Orduno Computer Science Student and Technology aficionado
Currently
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Education
2008-12
San Francisco State University Bachelor’s degree in Urban Studies and Planning
2017-18
SoftStack Factory Meanstack Coding Bootcamp
Technical skills
- HTML and CSS
- Javascript
- Angular2
- Ionic
Projects
CV
I created a this web page to show off my CV.
Trackdom
Angular 2 App for tracking things you’ve watched, read, played
SS Calculator
Ionic 3 App to calculate Social Security Retirement Benefits
Achievements
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Roasted Bean Coffe House
Worked for two summers on the Roasted Bean Coffe House as a barista.


Located on the northern tip of the island.
Position 12°13.7' S, 049°22.3' E (entrance to the bay)
This is a port of entry.
See Noonsite/Madagascar/Formalities page for details of clearance.
Last updated November 2015.
Be aware that your electronic chart position may be not correct. Some can be over half a mile out! Eyeball navigation is essential.
It is easy to enter the large bay through it's eastern channel, but it is can be very hard to leave. The current, wind, and waves entering the bay will test most sailors trying to exit the bay. However, if you can pick your weather window a difficult departure can be avoided.
Anchoring in here should be done with extreme care as there are a number of unmarked wrecks, particularly after last cyclones in 2008 and 2009.
Last updated November 2015.


Since the first mobile crushing station off the assembly line, from the mobile tire station, crawler mobile station to the K series of mobile tire stations.From rugged utility lines to rounded streamlined aesthetic design, from custom non-standard models to multi-combination of the standard configuration models.kefid is always innovating according to market trends and customer needs, and relying on its high-end configuration, stable performance is gradually becoming the ideal choice for customers worldwide in the field of mobile crushing equipment.
1.Highly efficient and flexible processing capacity
Optimized modes of grates pre-screening on vibrating feeder, adjustable installation angle on vibrating screen and speed-adjustable mode on trailer belts maximize the processing capacity in crushing sand and gravel.
2.Optimal emission reduction and noise reduction
The design of water-spray dustproof device, rubber skin in the position of discharging opening and material receiving are added to effectively reduce the noise and dust emissions, so as to minimize the impact on the environment.
3.Most humanized structure design
The humanity design, which includes the maintenance of lifting frame, hooks and operation system, tools of maintenance, toolbox and centralized lubrication, the electrical signal over-loaded alarm system and hydraulic controlling system, reduces the risk to a minimum.
4.The latest modular design
The material for the production are upgraded from Q235A steel to Q345B steel with higher strength, combined with interchangeable system of main machines and the versatility of one trailer, so it is suitable to deal with changeful stone material processing requirements in remote areas.
5.Most flexible solution configuration
According to different crushing process requirements can be composed of different models, with high flexibility to meet the various needs of customers.
Equipment:YG1349EW8+Y3S2160HP220 mobile crushers
Material: limestone
Output size: 0-10mm，10-25mm，25-50mm
Material: limestone
Output size: 0-5mm、5-10mm、10-20mm
Equipment: KE860-1+KH300-2+KV9532-2 mobile crushers
Material: Iron ore
Output size: 0-10mm，10-25mm，25-50mm
Equipment: YG1349EW8、Y3S2160HP220 (EC) mobile crushers
Material: limestone
Output size: 0-5mm，5-20mm，20-40mm
Equipment: YG938E69+Y3S1860F1214 mobile crushers
Material: hard rock
Output size: 0-10mm，10-19mm，19-25mm，25-34mm
Equipment: YG1142E710、Y4S1860CSB160 mobile crushers
Material: river stone
Output size: 0-10mm，10-20mm，20-40mm
Equipment: KS1860-1 mobile crushers


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Honeycomb will provide you a platform to share your travel experience!
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You can find information about your destination and other travellers' experiences here!
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Bloominglabs is Indiana's first hackerspace (also known as a makerspace). We are a group of group of people who have rented a shared workshop where we can build projects both collectively and individually. Our space is located at 1609 S. Rogers Street, Building 4 (our building has our gear logo painted on the wall). We are open to the public on Wednesday evenings from 7pm until 10pm and are family friendly.
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.


https://localhost:44392/api/about
https://localhost:44392/api/about?culture=de-CH
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--- layout: post title: '"Isolinux.bin missing or corrupt" when booting from USB' date: 2011-01-22 10:43:44.000000000 +01:00 categories: - linux tags: [] status: publish type: post published: true meta: _edit_last: '1' _wp_old_slug: '' author: ---
I was trying it out to boot from USB using fedora for a friends laptop. On booting I saw the above error.
And found the answer at:
http://chakra-project.org/bbs/viewtopic.php?pid=15013#p15013
dd if=[name of iso] of=/dev/sdc
NOT /dev/sdc1 and before removing the usb stick type into terminal:
sync
eject /dev/sdc
sdc being whatever your usb stick device is
this will ensure that all the data is written to the stick before removal.
Voila! It worked. Like the next comment says in the above post, indeed, so stupid of me :P


Plain of Tears [ar31], plain, in Mandoria, peasants: 135
Last updated Turn #127
Plain of Tears [ar31], plain, in Mandoria, peasants: 135
------------------------------------------------------------------------
0: Garrison [cn8t], garrison, uncontrolled, with five peasants guards
0: Plain of Tears [ar31].
9: None of them [s9n], refugee, arrived from the east.
11: None of them [s9n], refugee, went west.
30: The population grows by one peasant.
Routes leaving Plain of Tears:
North, plain, to Plain of Tears [aq31], 7 days
Garrison [bl5x], garrison, uncontrolled, with six peasants
East, plain, to Plain of Tears [ar32], 7 days
Garrison [bj6y], garrison, uncontrolled, with ten peasants
South, plain, to Plain of Tears [as31], 7 days
Garrison [jo3e], garrison, uncontrolled, with seven peasants
West, plain, to Plain of Tears [ar30], 7 days
Seen here:
Garrison [cn8t], garrison, uncontrolled, with five peasants


Template functions that return simple types have the form
template<class type-parameter [, class type-parameter]... >
ret-type function-name (parameter-list)
Each type-parameter is a name that may be used inside the function definition wherever a type is required. Each of these names should be used in the function parameter-list to name the type of one or more parameters.
If the types do not all appear in the argument list, then the caller must qualify the function-name with the actual types that cannot be inferred. For example,
template<class T> T zero() { return 0; }
defines zero
to be a template function with a single type parameter, which is used to
name the return type. In calling this function, we must supply the return type explicitly:
double x = zero<double>();
The typename
keyword must be used to qualify declarations that use types that are
defined by the template type parameters. For example,
typename T::size_type name;
declares name
to have type size_type
, which must be defined as a type inside T
.
The implementation automatically instantiates a separate instance of the template function for each set of types used in a call to the function.
Iterators: A key contribution of the C++ standard library is the idea that algorithms can achieve data-structure independence by using iterators as the glue between algorithms and containers. Furthermore, the realization that algorithms can be factored based on the operations that are required for the iterators that they use means that it is easy to match a container with the algorithms that can be used on it.
There are five iterator categories. In general, the later categories subsume the operations in the earlier ones:
Input iterator: Sequential access in one direction, input only Output iterator: Sequential access in one direction, output only Forward iterator: Sequential access in one direction, input and output Bidirectional iterator: Sequential access in both directions, input and output Random-access iterator: Efficient access to any element, input and output
8-0. Compile, execute, and test the programs in this chapter.
8-1. Note that the various analysis
functions we wrote in §6.2/110 share the same behavior;
they differ only in terms of the functions they call to calculate the final grade. Write a template
function, parameterized by the type of the grading function, and use that function to
evaluate the grading schemes.
8-2. Implement the following library algorithms, which we used in Chapter 6 and described in §6.5/121. Specify what kinds of iterators they require. Try to minimize the number of distinct iterator operations that each function requires. After you have finished your implementation, see §B.3/321 to see how well you did.
equal(b, e, d) search(b, e, b2, e2) find(b, e, t) find_if(b, e, p) copy(b, e, d) remove_copy(b, e, d, t) remove_copy_if(b, e, d, p) remove(b, e, t) transform(b, e, d, f) partition(b, e, p) accumulate(b, e, t)
8-3. As we learned in §4.1.4/58, it can be expensive to return (or pass) a container by value. Yet
the median
function that we wrote in §8.1.1/140 passes the vector
by value. Could we
rewrite the median
function to operate on iterators instead of passing the vector
? If we
did so, what would you expect the performance impact to be?
8-4. Implement the swap
function that we used in §8.2.5/148. Why did we call swap
rather than
exchange the values of *beg
and *end
directly? Hint: Try it and see.
8-5. Reimplement the gen_sentence
and xref
functions from Chapter 7 to use output iterators
rather than writing their output directly to a vector<string>
. Test these new versions by
writing programs that attach the output iterator directly to the standard output, and by storing
the results in a list<string>
and a vector<string>
.
8-6. Suppose that m
has type map<int, string>
, and that we encounter a call to
copy(m.begin(), m.end(), back_inserter(x))
. What can we say about the type of
x
? What if the call were copy(x.begin(), x.end(), back_inserter(m))
instead?
8-7. Why doesn't the max
function use two template parameters, one for each argument type?
8-8. In the binary_search
function in §8.2.6/148, why didn't we write (begin + end) / 2
instead of the more complicated begin + (end - begin) /2
?


Mashup: React-Router and Animation in React
Monday, July 27, 2015 at 7:00pm
July's meetup will be two talks mashed together. Jason Hansen will be talking about using React-Router to manage state in your applications, which will lead nicely into Charlie King talking about different approaches for animation in React.
Reflux Deep Dive
Monday, August 17, 2015 at 7:00pm
In the never-ending search for the perfect Flux framework, Mike Groseclose is going to deep dive in to Reflux and tell us all about it.
Tucson ReactJS meetups use the great downtown warehouse space provided by Elegant Thought, LLC. Drinks and light snacks will be provided by the organizers!
Elegant Thought


Hi, I'm Sebastian.
I'm a 26 years old Production Coordinator with 3+ years of experience in 3D animation studios and video game companies from Buenos Aires, Argentina.
Graduated as Image and Sound Designer from Universidad de Palermo, I moved to Toronto, Ontario, in May 2018 with an open work permit and am currently seeking for job opportunities.
I'm an ambitious and passionate professional, who’s fully dedicated to the audiovisual industry, from film to video games and TV series. I have a solid foundation on CGI, having learnt through formal education and by myself. This allows me to interact smoothly from a technical and creative point of view in any production.
I study everyday of my life to have a broad set of skills, from technical aspects to production, marketing, team management and product development. My main goal is always focused on managing and delivering products and projects with the highest quality standards, whilst getting things done.


A collection of methods for displaying debug information about game objects. If your game is running in WebGL then Debug will create a Sprite that is placed at the top of the Stage display list and bind a canvas texture to it, which must be uploaded every frame. Be advised: this is very expensive, especially in browsers like Firefox. So please only enable Debug in WebGL mode if you really need it (or your desktop can cope with it well) and disable it for production! If your game is using a Canvas renderer then the debug information is literally drawn on the top of the active game canvas and no Sprite is used.


Game of thrones script generator
by Ashish Choure
I have trained RNN model with all game of thrones seasons script using GRU. Enter any word or dialog to continue with. The model will generate rest of the script
Enter any word or partial sentence to start
Generate


{% extends "html/_layouts/base.html" %} {% block content %} {% include "html/_includes/form.html" %} {% endblock %}


A magic member.
TODO: resolve class imports for types
Public Properties | |
| string | $docblock = '' |
| string | $fqn = '' |
| int | $logLevel = LOG_USER |
| string | $name = '' |
Public Static Methods | |
| static self[] | fromDocBlock (AbstractRefClass $owner, string &$docblock) |
| Extracts magic members of the called type from a root entity's docblock. More... | |
Public Methods | |
| string | __toString () |
| string | getVisibility () |
Magic members are always public . More... | |
| Public Methods inherited from MemberInterface | |
| bool | isStatic () |
| Public Methods inherited from XMLWriterInterface | |
| void | write (RefXML $xml) |
| Reflector writes itself to the XML. More... | |
Protected Methods | |
| void | setDocBlock (string $docblock) |
| Cleans up a fragmented magic member comment from the parser and sets it as the docblock. More... | |
| Protected Methods inherited from DocBlockTrait | |
| void | writeDocBlock (RefXML $xml, string $docblock) |
| Writes the docblock. More... | |
| void | writeDocBlock_Prune (&$docblock) |
| void | writeDocBlock_Tags (RefXML $xml, string &$docblock) |
| void | writeDocBlock_Tags_internal (RefXML $xml, string &$docblock) |
| void | writeDocBlock_Tags_see (RefXML $xml, string &$docblock) |
| void | writeDocBlock_Tags_todo (RefXML $xml, string &$docblock) |
Additional Inherited Members | |
| Protected Properties inherited from DocBlockTrait | |
| string[] | $warnings = [] |
| string __toString | ( | ) |
<ClassFQN>::<identifier>
Implements MemberInterface.
|
staticabstract |
Extracts magic members of the called type from a root entity's docblock.
| AbstractRefClass | $owner | |
| string | $docblock | Extracted magic members are removed. |
|
final |
|
protected |
Cleans up a fragmented magic member comment from the parser and sets it as the docblock.
| string | $docblock |


Sweet Free Stuff
///////////////////////////////////////////
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Fill out the form at the bottom of the page. FREE Hitch ‘N’ Fish Sticker
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Posted: 29 Aug 2014 11:21 AM PDT
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Load the coupon to your shoppers card today only (8/29,) and use by
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SweetFreeStuff.com.
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Posted: 29 Aug 2014 11:13 AM PDT
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Connect your Facebook, Twitter or Instagram and get a free sample of
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Free 2014 National POW/MIA Recognition Day Poster - Click the Order Poster
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Posted: 28 Aug 2014 10:05 PM PDT
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Before Change
pdb_ch = pdb.upper() + "_" + ch.upper()
index = clusters.index(pdb_ch)
maxlen = clusters.index("\n")
end = clusters.find("\n", index)
start = clusters.rfind("\n", index-maxlen, end)+1
cluster = clusters[start:end]
return [tuple(item.split("_")) for item in cluster.split()]
def fetchPDBClusters(sqid=None):
After Change
clusters = PDB_CLUSTERS[sqid]
pdb_ch = (pdb.upper(), ch)
for cluster in clusters:
if pdb_ch in cluster:
return cluster
return
def fetchPDBClusters(sqid=None):
Retrieve PDB sequence clusters. PDB sequence clusters are results of


| Interface and Description |
|---|
| org.apache.cayenne.dba.DbAdapterFactory
since 3.1 in favor of
DbAdapterFactory configured via
dependency injection. |
| org.apache.cayenne.cache.QueryCacheFactory
since 3.1 QueryCacheFactory is unused and replaced by corresponding
Provider implementation for various types of QueryCache. |
| org.apache.cayenne.conf.ResourceFinder
since 3.1 deprecated in favor of injectable
org.apache.cayenne.resource.ResourceLocator.
|
| org.apache.cayenne.xml.XMLSerializable
since 3.1 this XML serialization package is deprecated and will be removed
in the following releases. It has a number of functional and performance
limitations that make it impossible to evolve further. A replacement may be
provided in an undefined future. For now we recommend the users to
implement XML serialization of persistent objects based JAXB, XStream or
other similar frameworks.
|
| Class and Description |
|---|
| org.apache.cayenne.map.AshwoodEntitySorter
since 3.1 moved to "org.apache.cayenne.ashwood" package.
|
| org.apache.cayenne.conn.ContainerPoolFactory
since 3.1. This class does not belong in Cayenne, as Cayenne no longer
attempts to provide appserver pieces. End users should not need this class
and should use their container's preferred approach to map a DataSource
instead.
|
| org.apache.cayenne.DataObjectUtils
since 3.1
Cayenne class is used instead |
| org.apache.cayenne.remote.hessian.service.HessianServlet
since 3.1 use
ROPHessianServlet . |
| org.apache.cayenne.cache.MapQueryCacheFactory
since 3.1 MapQueryCacheFactory and QueryCacheFactory are unused. Analog of
MapQueryCacheFactory is DI-friendly
MapQueryCacheProvider . |
| org.apache.cayenne.cache.OSQueryCacheFactory
since 3.1 OSQueryCacheFactory and QueryCacheFactory are unused.
|
| org.apache.cayenne.access.QueryLogger
since 3.1 replaced by injectable
JdbcEventLogger . |
| org.apache.cayenne.util.ResourceLocator
since 3.1 deprecated in favor of injectable
org.apache.cayenne.resource.ResourceLocator.
|
| org.apache.cayenne.conf.WebApplicationContextFilter
since 3.0
CayenneFilter should be used. |
| org.apache.cayenne.xml.XMLDecoder
since 3.1 this XML serialization package is deprecated and will be removed
in the following releases. It has a number of functional and performance
limitations that make it impossible to evolve further. A replacement may be
provided in an undefined future. For now we recommend the users to
implement XML serialization of persistent objects based JAXB, XStream or
other similar frameworks.
|
| org.apache.cayenne.xml.XMLEncoder
since 3.1 this XML serialization package is deprecated and will be removed
in the following releases. It has a number of functional and performance
limitations that make it impossible to evolve further. A replacement may be
provided in an undefined future. For now we recommend the users to
implement XML serialization of persistent objects based JAXB, XStream or
other similar frameworks.
|
| org.apache.cayenne.util.ZipUtil
since 3.1. This class is unused and will be removed in the future
versions..
|
| Field and Description |
|---|
| org.apache.cayenne.query.PrefetchSelectQuery.parentQuery
since 3.1 unused
|
Copyright © 2001–2014 Apache Cayenne. All rights reserved.


Zabeg za Oblaka Marathon
Zlatoust RUS
Website: en.cloudrace.ru/about-marathon
Race Winners
(18 runnings)
02 Sep
2007
22 Jul
2006
04
Sep
2005
11 Sep
2004
20
Jul
2003
14
Sep
2002
02 Sep
2001
02 Sep
2000
Note: 1999 was the inaugural year. In English, the race name is "Above the
Clouds." A shorter race was held for 1991-1993. In 1991, the race
was held over two days (28-29 Sep) with 15 km the first day and 4 km the second
day. On 12 Sep 1992 and 18 Sep 1993, the entire 19 km was run. The
race is off-road, starting at the Taganay National Park main entrance and
including an ascent of Mount Kruglitsa (1178 m). The course has been
changed several times. The orienteering club of Zlatoust is the organizer
for this race. In 2004, the race was run short due to rain on Mount
Kruglitsa making footing dangerous. The recent course has 1400m of climb.
28 Aug
2016
3:22:20
Yevgeniy Markov-2
3:55:55
Antonina Ogorodinkova (RUS)
30
Aug
2015
3:25:55
Aleksey Malikhin (RUS)
4:23:42
Nataliya
Neshcheret (RUS)
31
Aug
2014
3:26:59
Yevgeniy Markov (RUS)
5:01:04
Natalya
Larshina (RUS)
25
Aug 2013
3:43:55
Dmitriy Gaukov-2
5:14:34
Yulia Baigeldyeva (RUS)
25 Aug
2012
3:33:08
Igor Zaitsev (RUS)
5:23:20
Olga Pashagina (RUS)
28 Aug
2011
3:33:50
Anton Azanov (RUS)
5:50:12
Yuliya Kitabova-2
29 Aug
2010
3:33:02
Dmitriy Gaukov (RUS)
5:57:53
Yuliya Kitabova (RUS)
12 Sep
2009
3:44:41
Vladimir Rodikin (RUS)
6:42:00
Natasha Kostileva-4
30 Aug
2008
4:12:50
Vasiliy Baklanov (RUS)
6:30:45
Natalya Kostileva-3
3:47:50
Andrey Ivanov (RUS)
6:54:59
Natalya Kostileva-2
3:44:32
Erik Khasnov (RUS)
7:00:05
Natalya Kostileva (RUS)
3:41:33
Vadim Nesterov-2
4:17:20
Yekaterina Suleimanova
(RUS)
---
Aleksey Vasilyev (RUS)
---
Anna Kharitonova (RUS)
3:17:39
Semen Kotov (RUS)
4:29:29
Yuliya Gubajdullina
(RUS)
---
n/a
---
n/a
3:34:13
Igor Grachev (RUS)
---
n/a
3:23:16
Aleksandr Kirilin (RUS)
4:28:18
Marina Myschlyanova
(RUS)
04
Sep 1999
3:25:30
Vadim Nesterov (RUS)
---
Tatyana Teslenko (RUS)
Most Wins (1999/date)
Men
2
Vadim Nesterov (RUS)
1999,2005
Dmitriy Gaukov (RUS)
2010,2013
Yevgeniy Markov (RUS)
2014,2016
Women
2
Yuliya Kitabova (RUS)
2010-11
Prize Money
(ADR qualified runners)
No information on prize money has been received for this race.
Race Time Bias
(sec/km)
Insufficient information to calculate the race time bias.
Competitive Level
(1990-date)
Insufficient information to calculate the competitive level.
Quality Performances
Men No men under 2:20 Women No women under 2:50
Last Updated on 05 Nov 2016
Contributors: Klaas Loonstra (23), Pavel Kazakov


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Details: {{errorMessage}}
Please try again, or contact your administrator for further support.


Thread to be used for evaluating a function and returning the result
through a pipe.
| NEW(f) @public |
| $setProc(f) @public |
Set the function to be invoked by start().
|
| $eval(f) pipe<Titem> @public |
Start the thread and return the pipe to read the result from.
|
| $getPipe() pipe<Titem> @public |
Return the pipe to read the result from.
|
| |
| eval(f) pipe<Titem> @public |
Quick way to evaluate a function in a thread.
|
| |
| Inherited from THREAD.ThreadBase: |
| string | $name @public | optional name, NIL when not set
|
| THREAD.State | $state @public | state of the thread
|
| Type | $type @public | type of thread
|
| |
| NEW() @public |
Create a new thread.
|
| $setName(name) @file |
Set the name of the thread.
|
| $start() @public |
Start executing the thread.
|
| $wait() @public |
Wait in the current thread for the thread of this object to finish.
|
| $kill() @public |
Kill the thread, stop its execution.
|
| $remove() @public |
Not Implemented Yet
|
| |


New weights
Layer 1: sin() cos() tanh() linear()
Layer 2: sin() cos() tanh() linear()
Layer 3: sin() cos() tanh() linear()
Layer 4: sin() cos() tanh()
Click the button or press space to generate a 1920x1080 wallpaper. Once generation is done (may take a while!), the image will appear below. It will look like a thumbnail, but it's actually full-res and can be saved.
Generate wallpaper


three.js
- cameras
O
orthographic
P
perspective
Click to play
(W, A, S, D = Move, SPACE = Jump, MOUSE = Look around)


| Event | Location | Date |
|---|---|---|
| Devoxx Belgium | Antwerp, Belgium | Nov. 7-11, 2016 |
| DEVintersection Europe | Amsterdam, Netherlands | Nov 14-16, 2016 |
| dotJS | Paris, France | Dec. 5, 2016 |
| NG-BE | Ghent, Belgium | Dec. 9, 2016 |
| Event | Location | Date |
|---|---|---|
| Devoxx Belgium | Antwerp, Belgium | Nov. 7-11, 2016 |
| DEVintersection Europe | Amsterdam, Netherlands | Nov 14-16, 2016 |
| dotJS | Paris, France | Dec. 5, 2016 |
| NG-BE | Ghent, Belgium | Dec. 9, 2016 |


The bind() method creates a new function that, when called, has its this keyword set to the provided value, with a given sequence of arguments preceding any provided when the new function is called.
The **bind()**
method creates a new function that, when called, has its this
keyword set
to the provided value, with a given sequence of arguments preceding any provided when the new function is called.
The source for this interactive example is stored in a GitHub repository. If you'd like to contribute to the interactive examples project, please clone https://github.com/mdn/interactive-examples and send us a pull request.
let boundFunc = func.bind(thisArg[, arg1[, arg2[, …argN]]])
thisArg
The value to be passed as the this
parameter to the target function func
when the bound
function is called. The value is ignored if the bound function is constructed using the new
operator. When using bind
to create a function (supplied as a callback) inside a
setTimeout
,
any primitive value passed as thisArg
is converted to object. If no arguments are provided to
bind
, or if the thisArg
is null
or undefined
, the
this
of the executing scope is treated as the thisArg
for the new function.
arg1, arg2, ...argN
Optional
Arguments to prepend to arguments provided to the bound function when invoking func
.
A copy of the given function with the specified this
value, and initial arguments (if provided).
The bind()
function creates a new bound function, which is an exotic function
object (a term from ECMAScript 2015) that wraps the original function object. Calling the bound function
generally results in the execution of its wrapped function.
A bound function has the following internal properties:
[[BoundTargetFunction]]
The wrapped function object
**[[BoundThis]]**
The value that is always passed as this
value when calling the wrapped function.
**[[BoundArguments]]**
A list of values whose elements are used as the first arguments to any call to the wrapped function.
**[[Call]]**
Executes code associated with this object. Invoked via a function call expression. The arguments to the internal
method are a this
value and a list containing the arguments passed to the function by a call
expression.
When a bound function is called, it calls internal method [[Call]]
on
[[BoundTargetFunction]]
, with following arguments Call(boundThis, ...args)
. Where
boundThis
is [[BoundThis]]
, args
is [[BoundArguments]]
, followed
by the arguments passed by the function call.
A bound function may also be constructed using the new
operator. Doing so acts as though the target function had instead been constructed. The provided this
value is ignored, while prepended arguments are provided to the emulated function.
Because older browsers are generally also slower browsers, it is far more critical than most people recognize to create performance polyfills to make the browsing experience in outdated browsers slightly less horrible.
Thus, presented below are two options for Function.prototype.bind()
polyfills:
new
operator.
new
operator on
bound functions.Generally, in most code it's very rare to see new
used on a bound function, so it is generally best to
go with the first option.
if (!Function.prototype.bind) (function(){
var slice = Array.prototype.slice;
Function.prototype.bind = function() {
var thatFunc = this, thatArg = arguments[0];
var args = slice.call(arguments, 1);
if (typeof thatFunc !== 'function') {
throw new TypeError('Function.prototype.bind - ' +
'what is trying to be bound is not callable');
}
return function(){
var funcArgs = args.concat(slice.call(arguments))
return thatFunc.apply(thatArg, funcArgs);
};
};
})();
You can partially work around this by inserting the following code at the beginning of your scripts, allowing use
of much of the functionality of bind()
in implementations that do not natively support it.
if (!Function.prototype.bind) (function(){
var ArrayPrototypeSlice = Array.prototype.slice;
Function.prototype.bind = function(otherThis) {
if (typeof this !== 'function') {
throw new TypeError('Function.prototype.bind - what is trying to be bound is not callable');
}
var baseArgs= ArrayPrototypeSlice.call(arguments, 1),
baseArgsLength = baseArgs.length,
fToBind = this,
fNOP = function() {},
fBound = function() {
baseArgs.length = baseArgsLength;
baseArgs.push.apply(baseArgs, arguments);
return fToBind.apply(
fNOP.prototype.isPrototypeOf(this) ? this : otherThis, baseArgs
);
};
if (this.prototype) {
fNOP.prototype = this.prototype;
}
fBound.prototype = new fNOP();
return fBound;
};
})();
Some of the many differences (there may well be others, as this list does not seriously attempt to be exhaustive) between this algorithm and the specified algorithm are:
Array.prototype.slice()
,
Array.prototype.concat()
,
Function.prototype.call()
and Function.prototype.apply()
,
built-in methods to have their original values.
caller
and arguments
properties that throw a TypeError
upon get, set, or deletion. (This could be added if the implementation supports Object.defineProperty
,
or partially implemented [without throw-on-delete behavior] if the implementation supports the __defineGetter__
and __defineSetter__
extensions.)prototype
property. (Proper bound
functions have none.)length
property does not agree with that mandated by ECMA-262: it creates functions with length
of
0
. A full implementation—depending on the length of the target function and the number of
pre-specified
arguments—may return a non-zero length.
name
property is not derived from the original function name. According to ECMA-262, name of the returned bound
function
should be "bound" + name of target function (note the space character).If you choose to use this partial implementation, you must not rely on those cases where behavior deviates from ECMA-262, 5th edition! Thankfully, these deviations from the specification rarely (if ever) come up in most coding situations. If you do not understand any of the deviations from the specification above, then it is safe in this particular case to not worry about these noncompliant deviation details.
If it's absolutely necessary and performance is not a concern, a far slower (but more specification-compliant solution) can be found at https://github.com/Raynos/function-bind.
The simplest use of bind()
is to make a function that, no matter how it is called, is called with a
particular this
value.
A common mistake for new JavaScript programmers is to extract a method from an object, then to later call that
function and expect it to use the original object as its this
(e.g., by using the method in
callback-based code).
Without special care, however, the original object is usually lost. Creating a bound function from the function, using the original object, neatly solves this problem:
pre data-role="codeBlock" data-info="js" class="language-javascript">this.x = 9;
const module = {
x: 81,
getX: function() { return this.x; }
};
module.getX();
const retrieveX = module.getX;
retrieveX();
const boundGetX = retrieveX.bind(module);
boundGetX();
The next simplest use of bind()
is to make a function with pre-specified initial arguments.
These arguments (if any) follow the provided this
value and are then inserted at the start of the
arguments passed to the target function, followed by whatever arguments are passed bound function at the time it is
called.
function list() {
return Array.prototype.slice.call(arguments);
}
function addArguments(arg1, arg2) {
return arg1 + arg2
}
const list1 = list(1, 2, 3);
const result1 = addArguments(1, 2);
const leadingThirtysevenList = list.bind(null, 37);
const addThirtySeven = addArguments.bind(null, 37);
const list2 = leadingThirtysevenList();
const list3 = leadingThirtysevenList(1, 2, 3);
const result2 = addThirtySeven(5);
const result3 = addThirtySeven(5, 10);
setTimeout()
By default within window.setTimeout()
,
the this
keyword will be set to the window
(or
global
) object. When working with class methods that require this
to refer to class
instances, you may explicitly bind this
to the callback function, in order to maintain the instance.
function LateBloomer() {
this.petalCount = Math.floor(Math.random() * 12) + 1;
}
LateBloomer.prototype.bloom = function() {
window.setTimeout(this.declare.bind(this), 1000);
};
LateBloomer.prototype.declare = function() {
console.log(`I am a beautiful flower with ${this.petalCount} petals!`);
};
const flower = new LateBloomer();
flower.bloom();
Warning: This section demonstrates JavaScript capabilities and documents some edge cases of the
bind()
method.
The methods shown below are not the best way to do things, and probably should not be used in any production environment.
Bound functions are automatically suitable for use with the new
operator to construct new instances created by the target function. When a bound function is used to construct a
value, the provided this
is ignored.
However, provided arguments are still prepended to the constructor call:
pre data-role="codeBlock" data-info="js" class="language-javascript">function Point(x, y) {
this.x = x;
this.y = y;
}
Point.prototype.toString = function() {
return `${this.x},${this.y}`;
};
const p = new Point(1, 2);
p.toString();
const YAxisPoint = Point.bind(null, 0);
const emptyObj = {};
const YAxisPoint = Point.bind(emptyObj, 0);
const axisPoint = new YAxisPoint(5);
axisPoint.toString();
axisPoint instanceof Point;
axisPoint instanceof YAxisPoint;
new YAxisPoint(17, 42) instanceof Point;
Note that you need not do anything special to create a bound function for use with new
.
The corollary is that you need not do anything special to create a bound function to be called plainly, even if you
would rather require the bound function to only be called using new
.
YAxisPoint(13);
`${emptyObj.x},${emptyObj.y}`;
If you wish to support the use of a bound function only using new
,
or only by calling it, the target function must enforce that restriction.
bind()
is also helpful in cases where you want to create a shortcut to a function which requires a
specific this
value.
Take Array.prototype.slice()
,
for example, which you want to use for converting an array-like object to a real array. You could create a shortcut
like this:
const slice = Array.prototype.slice;
slice.apply(arguments);
With bind()
, this can be simplified.
In the following piece of code, slice()
is a bound function to the apply()
function of Function.prototype
,
with the this
value set to the slice()
function of Array.prototype
. This means that additional apply()
calls can be eliminated:
const unboundSlice = Array.prototype.slice;
const slice = Function.prototype.apply.bind(unboundSlice);
slice(arguments);
| Specification |
|---|
| [ECMAScript (ECMA-262) |
| The definition of ‘Function.prototype.bind' in that specification.](https://tc39.es/ecma262/#sec-function.prototype.bind) |
The compatibility table on this page is generated from structured data. If you'd like to contribute to the data, please check out https://github.com/mdn/browser-compat-data and send us a pull request.
Update compatibility data on GitHub
| Desktop | Mobile | Server | |
|---|---|---|---|
| Chrome | Edge | Firefox | |
| — | — | — | — |
bind |
Chrome Full support 7 | Edge Full support 12 | Firefox Full support 4 |
Our team will review your report. Once we verify the information you have supplied we will update this browser compatability table accordingly.
You can join the GitHub repository to see updates and commits for this table data:
https://github.com/mdn/browser-compat-data
Our goal is to provide accurate, real values for all our compatibility data tables. Notifying MDN of inaccurate
data or supplying new data pushes us further towards our goal of providing 100% real values to the developer
community.
Thank you for helping.
Please select the browser or browsers which are affected.
Briefly outline the issue you are highlighting. Minimum 10 and maximum 1,000 characters.
Browser documentation and release notes are good supporting items to accompany your message. A demo hosted on services like Codepen or JSBin are perfect for providing real examples of your findings.
Connection error:Sorry, we can't seem to reach the server. We are working to fix the problem. Please try again later.
Full support
Full support


Usage of the Bloom filter allows to speed up password check for large dictionaries and has some other benefits. The idea to use Bloom filter for that purpose is came from the descrip‐ tion of the OPUS project OPUS: Preventing Weak Password Choices Purdue Technical Report CSD-TR 92-028 writen by Eugene H. Spafford. You can obtain this article from: http://www.cerias.purdue.edu/homes/spaf/tech-reps/9128.ps It has very nice description of Bloom filter and it's advantages for password checking systems. In simple words, apgbfm generates n hash values for every word and sets corresponding bits in filter file to 1. To check the word apgbfm gener‐ ates the same hash functions for that word and if all n corresponding bits in filter file are set to 1 then it suppose that word exists in dicionary. apgbfm uses SHA-1 as a hash function. apgbfm can be used as standalone utility, not only with apg, or apgd. WARNING !!! Filter file format can be changed in the future. I'll try to make file formats compatible but i can not guaranty this.  OPTIONS -f filter use filter as the name for Bloom filter filename. -i filter print information about filter. -n numofwords create new empty filter for numofwords number of words. Useful when you want to fill filter dynamicaly. -d dictfile create new filter from dictfile. It may take a lot of time to gen‐ erate filter from a big dictionary. In that dictionary you may place words (one per line) that should not appear as generated passwords. For example: user names common words, etc. You even can use one of the dictionaries that come with dictionary password crackers. This check is case sensitive. For example, if you want to reject word 'root', you should insert in dictfile words: root, Root, RoOt, ... , ROOT. To indicate that program is working apg‐ bfm prints dot for every 100 words added in dictionary. -a word add word to the filter. -A dictfile add all words from dictfile to the filter. To indicate that pro‐ gram is working apgbfm prints dot for every 100 words added in dictionary. -c word check word for appearance in the filter. -C dictfile check every word from dictfile for appearance in the filter. -q quiet mode. -s create new filter in case-insensitive mode. -v print version information. -h print help information. EXIT CODE On successful completion of its task, apgbfm will complete with exit code 0. An exit code of -1 indicates an error occurred. Textual errors are written to the standard error stream. FILES None. BUGS None. If you've found one, please send bug description to the author. This man page is Alpha too. SEE ALSO apg(1) AUTHOR Adel I. Mirzazhanov<EMAIL_ADDRESS>Project home page: http://www.adel.nursat.kz/apg/ Automated Password Generator 2003 Jun 19 APGBFM(1)


Foundation JS ->
- Modals
- Toggler
- Smooth Scroll To (menu links)
WayPoints ->
- is element in viewport Event
- sticky
owl.carousel ->
- Good For Partners Carousel
paroller ->
Slick ->
- Slick.js
- Almost any image carousel or slider
Scroll Reveal ->
- Scroll Reveal.js
- Awesome on scroll reveal animations!
- NOTE: Might have some issues with some jQuery version
Animate.css ->
Hamburgers Menu.css ->
Canvas BG Effects ->
Cinemagraphs ->
ShuffleJS ->
Material Image Lightbox ->
CSS Shake Effect ->
Image Galleries ->
HTML MASKS ->
CANVAS CHARTS ->
Shuffle Letters ->
Materialize Css ->
- Toasts For messages
- Waves on buttons
Odomoteter ->


This is a data story about the famous tv mediums. They have a rich history about making money and having an insane amount of followers. This data story takes a deep dive about their technique and how succesful they are.
You can find the project here
You can find more on the Github


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