In this project, you'll build your first neural network and use it to predict daily bike rental ridership. We've provided some of the code, but left the implementation of the neural network up to you (for the most part). After you've submitted this project, feel free to explore the data and the model more.
%matplotlib inline
%config InlineBackend.figure_format = 'retina'
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
A critical step in working with neural networks is preparing the data correctly. Variables on different scales make it difficult for the network to efficiently learn the correct weights. Below, we've written the code to load and prepare the data. You'll learn more about this soon!
data_path = 'Bike-Sharing-Dataset/hour.csv'
rides = pd.read_csv(data_path)
rides.head()
This dataset has the number of riders for each hour of each day from January 1 2011 to December 31 2012. The number of riders is split between casual and registered, summed up in the cnt
column. You can see the first few rows of the data above.
Below is a plot showing the number of bike riders over the first 10 days or so in the data set. (Some days don't have exactly 24 entries in the data set, so it's not exactly 10 days.) You can see the hourly rentals here. This data is pretty complicated! The weekends have lower overall ridership and there are spikes when people are biking to and from work during the week. Looking at the data above, we also have information about temperature, humidity, and windspeed, all of these likely affecting the number of riders. You'll be trying to capture all this with your model.
rides[:24*10].plot(x='dteday', y='cnt')
Here we have some categorical variables like season, weather, month. To include these in our model, we'll need to make binary dummy variables. This is simple to do with Pandas thanks to get_dummies()
.
dummy_fields = ['season', 'weathersit', 'mnth', 'hr', 'weekday']
for each in dummy_fields:
dummies = pd.get_dummies(rides[each], prefix=each, drop_first=False)
rides = pd.concat([rides, dummies], axis=1)
fields_to_drop = ['instant', 'dteday', 'season', 'weathersit',
'weekday', 'atemp', 'mnth', 'workingday', 'hr']
data = rides.drop(fields_to_drop, axis=1)
data.head()
To make training the network easier, we'll standardize each of the continuous variables. That is, we'll shift and scale the variables such that they have zero mean and a standard deviation of 1.
The scaling factors are saved so we can go backwards when we use the network for predictions.
quant_features = ['casual', 'registered', 'cnt', 'temp', 'hum', 'windspeed']
# Store scalings in a dictionary so we can convert back later
scaled_features = {}
for each in quant_features:
mean, std = data[each].mean(), data[each].std()
scaled_features[each] = [mean, std]
data.loc[:, each] = (data[each] - mean)/std
We'll save the data for the last approximately 21 days to use as a test set after we've trained the network. We'll use this set to make predictions and compare them with the actual number of riders.
# Save data for approximately the last 21 days
test_data = data[-21*24:]
# Now remove the test data from the data set
data = data[:-21*24]
# Separate the data into features and targets
target_fields = ['cnt', 'casual', 'registered']
features, targets = data.drop(target_fields, axis=1), data[target_fields]
test_features, test_targets = test_data.drop(target_fields, axis=1), test_data[target_fields]
We'll split the data into two sets, one for training and one for validating as the network is being trained. Since this is time series data, we'll train on historical data, then try to predict on future data (the validation set).
# Hold out the last 60 days or so of the remaining data as a validation set
train_features, train_targets = features[:-60*24], targets[:-60*24]
val_features, val_targets = features[-60*24:], targets[-60*24:]
Below you'll build your network. We've built out the structure. You'll implement the forward pass and backward pass through the network. You'll also set the hyperparameters: the learning rate, the number of hidden units, and the number of training passes.
The network has two layers, a hidden layer and an output layer. The hidden layer will use the sigmoid function for activations. The output layer has only one node and is used for the regression. The output of the node is continuous (number of rides) and the same as the input of the node. That is, the activation function is $f(x)=x$. A function that takes the input signal and generates an output signal, but takes into account the threshold, is called an activation function. We work through each layer of our network calculating the outputs for each neuron. All of the outputs from one layer become inputs to the neurons on the next layer. This process is called forward propagation.
We use the weights to propagate signals forward from the input to the output layers in a neural network. We use the weights to also propagate error backwards from the output back into the network to update our weights. This is called backpropagation.
Hint: You'll need the derivative of the output activation function ($f(x) = x$) for the backpropagation implementation. If you aren't familiar with calculus, this function is equivalent to the equation $y = x$. What is the slope of that equation? That is the derivative of $f(x)$.
Below, you have these tasks:
self.activation_function
in __init__
to your sigmoid function.train
method.train
method, including calculating the output error.run
method.class NeuralNetwork(object):
def __init__(self, input_nodes, hidden_nodes, output_nodes, learning_rate):
# Set number of nodes in input, hidden and output layers.
self.input_nodes = input_nodes
self.hidden_nodes = hidden_nodes
self.output_nodes = output_nodes
# Initialize weights
self.weights_input_to_hidden = np.random.normal(0.0, self.input_nodes**-0.5,
(self.input_nodes, self.hidden_nodes))
self.weights_hidden_to_output = np.random.normal(0.0, self.hidden_nodes**-0.5,
(self.hidden_nodes, self.output_nodes))
self.lr = learning_rate
#### Set self.activation_function to sigmoid function ####
#
# Note: in Python, you can define a function with a lambda expression,
# as shown below.
self.activation_function = lambda x : 1 / (1 + np.exp( -x )) # Replace 0 with your sigmoid calculation.
### If the lambda code above is not something you're familiar with,
# You can uncomment out the following three lines and put your
# implementation there instead.
#
#def sigmoid(x):
# return 0 # Replace 0 with your sigmoid calculation here
#self.activation_function = sigmoid
def train(self, features, targets):
''' Train the network on batch of features and targets.
Arguments
---------
features: 2D array, each row is one data record, each column is a feature
targets: 1D array of target values
'''
n_records = features.shape[0]
delta_weights_i_h = np.zeros(self.weights_input_to_hidden.shape)
delta_weights_h_o = np.zeros(self.weights_hidden_to_output.shape)
## Training ##
for X, y in zip(features, targets):
### Forward pass ###
#### Hidden layer ####
hidden_inputs = np.dot(X, self.weights_input_to_hidden) # signals into hidden layer
hidden_outputs = self.activation_function(hidden_inputs) # signals from hidden layer
#### Output layer ####
final_inputs = np.dot(hidden_outputs, self.weights_hidden_to_output) # signals into final output layer
# Note: The output node is a regression node, so activation function is the identity f(x)=x
final_outputs = final_inputs # signals from final output layer
### Backward pass ###
#### Output layer ####
error = y - final_outputs # Output layer error is the difference between desired target and actual output.
# Note: The derivative of f(x)=x is 1
output_error_term = error * 1.0
# print("DEBUG: error={}".format(error))
#### Hidden layer ####
# The shape of the hidden layer's error is the same as the shape of the hidden layer output
hidden_error = output_error_term * self.weights_hidden_to_output
# The shape of hidden error term should be such that X.T * delta_h should have the shape of i2h
# Note: Efficiency shortcut using the fact that sig_prime(x) = sig(x) * (1-sig(x))
hidden_error_term = (hidden_outputs * (1-hidden_outputs)) * hidden_error.T
### Weight step ###
# Input to hidden)
delta_weights_i_h += X[:, None] * hidden_error_term
# Hidden to output)
delta_weights_h_o += output_error_term * hidden_outputs[:, None]
## Weight update ##
self.weights_hidden_to_output += self.lr * delta_weights_h_o / n_records # update hidden-to-output weights with gradient descent step
self.weights_input_to_hidden += self.lr * delta_weights_i_h / n_records # update input-to-hidden weights with gradient descent step
def run(self, features):
''' Run a forward pass through the network with input features
Arguments
---------
features: 1D array of feature values
'''
## Forward pass ##
# Hidden layer
hidden_inputs = features.dot(self.weights_input_to_hidden) # signals into hidden layer
hidden_outputs = self.activation_function(hidden_inputs) # signals from hidden layer
# Output layer
final_inputs = hidden_outputs.dot(self.weights_hidden_to_output) # signals into final output layer
final_outputs = final_inputs # signals from final output layer
return final_outputs # Note: If 'features' is a pd.DF, so is 'final_outputs'!
def MSE(y, Y):
return np.mean((y - Y)**2)
Run these unit tests to check the correctness of your network implementation. This will help you be sure your network was implemented correctly befor you starting trying to train it. These tests must all be successful to pass the project.
import unittest
# seed the random module for repeatability
np.random.seed(41)
inputs = np.array([[0.5, -0.2, 0.1]])
targets = np.array([[0.4]])
test_w_i_h = np.array([[0.1, -0.2],
[0.4, 0.5],
[-0.3, 0.2]])
test_w_h_o = np.array([[0.3],
[-0.1]])
class TestMethods(unittest.TestCase):
##########
# Unit tests for data loading
##########
def test_data_path(self):
# Test that file path to dataset has been unaltered
self.assertTrue(data_path.lower() == 'bike-sharing-dataset/hour.csv')
def test_data_loaded(self):
# Test that data frame loaded
self.assertTrue(isinstance(rides, pd.DataFrame))
##########
# Unit tests for network functionality
##########
def test_activation(self):
network = NeuralNetwork(3, 2, 1, 0.5)
# Test that the activation function is a sigmoid
self.assertTrue(np.all(network.activation_function(0.5) == 1/(1+np.exp(-0.5))))
def test_train(self):
# Test that weights are updated correctly on training
network = NeuralNetwork(3, 2, 1, 0.5)
network.weights_input_to_hidden = test_w_i_h.copy()
network.weights_hidden_to_output = test_w_h_o.copy()
network.train(inputs, targets)
self.assertTrue(np.allclose(network.weights_hidden_to_output,
np.array([[ 0.37275328],
[-0.03172939]])))
self.assertTrue(np.allclose(network.weights_input_to_hidden,
np.array([[ 0.10562014, -0.20185996],
[0.39775194, 0.50074398],
[-0.29887597, 0.19962801]])))
def test_run(self):
# Test correctness of run method
network = NeuralNetwork(3, 2, 1, 0.5)
network.weights_input_to_hidden = test_w_i_h.copy()
network.weights_hidden_to_output = test_w_h_o.copy()
self.assertTrue(np.allclose(network.run(inputs), 0.09998924))
suite = unittest.TestLoader().loadTestsFromModule(TestMethods())
unittest.TextTestRunner().run(suite)
Here you'll set the hyperparameters for the network. The strategy here is to find hyperparameters such that the error on the training set is low, but you're not overfitting to the data. If you train the network too long or have too many hidden nodes, it can become overly specific to the training set and will fail to generalize to the validation set. That is, the loss on the validation set will start increasing as the training set loss drops.
You'll also be using a method know as Stochastic Gradient Descent (SGD) to train the network. The idea is that for each training pass, you grab a random sample of the data instead of using the whole data set. You use many more training passes than with normal gradient descent, but each pass is much faster. This ends up training the network more efficiently. You'll learn more about SGD later.
This is the number of batches of samples from the training data we'll use to train the network. The more iterations you use, the better the model will fit the data. However, if you use too many iterations, then the model with not generalize well to other data, this is called overfitting. You want to find a number here where the network has a low training loss, and the validation loss is at a minimum. As you start overfitting, you'll see the training loss continue to decrease while the validation loss starts to increase.
This scales the size of weight updates. If this is too big, the weights tend to explode and the network fails to fit the data. A good choice to start at is 0.1. If the network has problems fitting the data, try reducing the learning rate. Note that the lower the learning rate, the smaller the steps are in the weight updates and the longer it takes for the neural network to converge.
The more hidden nodes you have, the more accurate predictions the model will make. Try a few different numbers and see how it affects the performance. You can look at the losses dictionary for a metric of the network performance. If the number of hidden units is too low, then the model won't have enough space to learn and if it is too high there are too many options for the direction that the learning can take. The trick here is to find the right balance in number of hidden units you choose.
There are three hyperparameters to tweak in this NN model (value set in brackets):
[2, 3, 4, 5, 6, 7, 8, 9, 10]
).[0.001, 0.005, 0.01, 0.05, 0.1, 0.5]
).[100, 500, 1000, 5000, 10000, 50000, 100000, 500000]
).
The code cell below will explore this parameter space and record the training and validation loss for each parameter combination. The value sets for learning rate and training iterations were picked to be logarithmic to cover larger swaths of the parameter space.import sys
from tqdm import tnrange, tqdm_notebook
### Set the hyperparameters here ###
# iterations = [1000, 5000]
# learning_rate = [0.01, 0.1]
# hidden_nodes = [2, 3, 4]
# output_nodes = 1
iterations = [100, 500, 1000, 5000, 10000, 50000, 100000, 500000] # 8
learning_rate = [0.001, 0.005, 0.01, 0.05, 0.1, 0.5] # 6
hidden_nodes = [2, 3, 4, 5, 6, 7, 8, 9, 10] # 9
output_nodes = 1
N_i = train_features.shape[1]
all_losses = {}
for hh in tqdm_notebook(hidden_nodes, desc='Hidden nodes'):
for ll in tqdm_notebook(learning_rate, desc='Learning rate'):
for it in tqdm_notebook(iterations, desc='Iterations'):
# TODO: Mini-batch, weight-update variations, different neurons
network = NeuralNetwork(N_i, hh, output_nodes, ll)
losses = {'network':network, 'train':[], 'validation':[]}
for ii in tnrange(it):
# Go through a random batch of 128 records from the training data set
batch = np.random.choice(train_features.index, size=128)
# Note: ix[] is deprecated, using iloc[]
X, y = train_features.loc[batch].values, train_targets.iloc[batch]['cnt']
network.train(X, y) # TODO: Mini-batch, weight-update variations, different neurons
# Note: Because train_features is a pd.DF, so is the result of NN.run(), and this screws up np.mean()
train_loss = MSE(network.run(train_features.values).T, train_targets['cnt'].values)
val_loss = MSE(network.run(val_features.values).T, val_targets['cnt'].values)
sys.stdout.write("\rProgress ({0:2d}, {1:5.3f}, {2:6d}): {3:5.1f}% ... Training loss: {4:5.3f} ... Validation loss: {5:5.3f}".format(\
hh, ll, it,
100 * ii/float(it),
train_loss,
val_loss))
sys.stdout.flush()
losses['train'].append(train_loss)
losses['validation'].append(val_loss)
all_losses[(hh, ll, it)] = losses
The above exploration of the trainging parameter space ran for 1 week w/o interruption on a 2014 Macbook Pro, clearly not the best device for training even simple NNs :D
# How many datapoints do we have?
len(all_losses)
# Final validation loss achieved for a parameter combination
all_losses[(2, .001, 100)]['validation'][-1]
# This takes too long and runs up the NotebookApp.iopub_data_rate_limit config variable
# Jupyter notbook has to be started with this variable set to a large number (see Note)
# Since all_losses cannot be pickled (due to the presence of a lambda function in
# NeuralNetwork - should have read ahead), the notebook cannot be restarted and rerun
sorted(all_losses.items(), key=lambda x: x[1]['validation'][-1])
Circumventing the rate limit in Jupyter notebook https://github.com/jupyter/notebook/issues/2287.
# A much, much faster way to achieve the same sorting operation :)
validation_losses = {param: losses['validation'][-1] for param, losses in all_losses.items()}
# Not run
validation_losses
# Parameter combinations for the 20 lowest validation losses
sorted(validation_losses.items(), key=lambda x: x[1])[:20]
# Network parameters for the 20 middle validation losses
sorted(validation_losses.items(), key=lambda x: x[1])[206:226]
# Network parameters for the 20 highest validation losses
sorted(validation_losses.items(), key=lambda x: x[1])[-20:]
# Network parameters for every 22nd validation loss
sorted(validation_losses.items(), key=lambda x: x[1])[::22]
list_valid_losses = list(sorted(validation_losses.values(), reverse=True))
plt.plot(list_valid_losses, label='Validation loss')
plt.legend()
range_loss = 1.9490 - 0.1304
print(range_loss)
# IDIOT: Used a function name for a variable name :(
reset_selective range
Note: This training used stochastic gradient descent and each parameter set was run only once, so the results should be considered random and interpreted only in general terms.
Note: The last value of the validation loss is taken to represent the parameter set but this is not necessarily the lowest value achieved by the set. There can be overfitting causing the validation loss to start growing after achieving its minimum.
Of the 432 parameter combinations, the lowest validation loss of 0.1304 is achieved for hidden, learning rate, iterations = 3, 0.1, 100000 and the highest loss of 1.9490 is achieved for hidden, learning rate, iterations = 3, 0.001, 100. The range of 1.8186 is not very significant, indicating that this model, that is, the model's structure, is at the limit of its abilities to capture the patterns of the dataset. Clearly, any further tweaking of the hyperparameters is not going to yield significantly better predictions.
The expected inverse relationship between learning rate and training iterations is clearly visible from the data: we get nearly the same validation loss for parameter sets (n, 10^(-x), 10^x). There is a similar but less clear inverse relationship between number of hidden nodes and number of iterations.
The prevalence of n=3|4
and lr=0.1
in the top 20 suggests that these are very reasonable values for the two hyperparameters. The higher numbers of iterations are likely to mitigate the randomization effect of SGD.
Below are shown the training dynamics for a sampling of the parameter sets. Discussion in the comments.
# Training dynamics for the top parameter set (n=3, lr=0.1, iter=100,000)
losses100k = all_losses[(3, 0.1, 100000)]
losses50k = all_losses[(3, 0.1, 50000)]
losses10k = all_losses[(3, 0.1, 10000)]
plt.plot(losses100k['train'], label='Training loss (100k)')
plt.plot(losses100k['validation'], label='Validation loss (100k)')
plt.plot(losses50k['train'], label='Training loss (50k)')
plt.plot(losses50k['validation'], label='Validation loss (50k)')
plt.plot(losses10k['train'], label='Training loss (10k)')
plt.plot(losses10k['validation'], label='Validation loss (10k)')
plt.legend()
_ = plt.ylim()
print(validation_losses[(3, 0.1, 100000)])
print(validation_losses[(3, 0.1, 50000)])
print(validation_losses[(3, 0.1, 10000)])
Clearly, the number of iterations is excessive. There is little decrease in validation loss between 50K and 100K. On the other hand, 10K is clearly not enough.
The apparent thickness of the lines is actually oscillation due to SGD.
# Training dynamics for the top parameter set (n=3, lr=0.1, iter=100,000)
losses500k = all_losses[(10, 0.1, 500000)]
losses100k = all_losses[(10, 0.1, 100000)]
losses50k = all_losses[(10, 0.1, 50000)]
plt.plot(losses500k['train'], label='Training loss (500k)')
plt.plot(losses500k['validation'], label='Validationv loss (500k)')
plt.plot(losses100k['train'], label='Training loss (100k)')
plt.plot(losses100k['validation'], label='Validation loss (100k)')
plt.plot(losses50k['train'], label='Training loss (50k)')
plt.plot(losses50k['validation'], label='Validation loss (50k)')
plt.legend()
_ = plt.ylim()
print(validation_losses[(10, 0.1, 500000)])
print(validation_losses[(10, 0.1, 100000)])
print(validation_losses[(10, 0.1, 50000)])
print(validation_losses[(10, 0.1, 10000)])
This is a parameter set with a high probability of overfitting, with n=10
and iter=500000
. The dip around 20k, also evident at 50k, is clearly one indication of overfitting. The gradual decrease to the last value at 500k is another.
# let's try one more from among the top performing parameter sets
losses500k = all_losses[(4, 0.005, 500000)]
plt.plot(losses500k['train'], label='Training loss (500k)')
plt.plot(losses500k['validation'], label='Validation loss (500k)')
plt.legend()
_ = plt.ylim()
# let's try one more from among the top performing parameter sets
losses50k = all_losses[(4, 0.005, 50000)]
plt.plot(losses50k['train'], label='Training loss (50k)')
plt.plot(losses50k['validation'], label='Validation loss (50k)')
plt.legend()
_ = plt.ylim()
print(validation_losses[(4, 0.005, 500000)])
print(validation_losses[(4, 0.005, 100000)])
print(validation_losses[(4, 0.005, 50000)])
print(validation_losses[(4, 0.005, 10000)])
This set does not overfit, due to the reasonable number of nodes and the very low learning rate. In addition, the oscillations caused by SGD are almost nonexistent, again due to the low learning rate.
On the flip side, the low learning rate clearly requires a large number of iterations to approach the overall validation loss minimum.
# let's try one more from among the top performing parameter sets
losses = all_losses[(10, 0.5, 5000)]
plt.plot(losses['train'], label='Training loss')
plt.plot(losses['validation'], label='Validation loss')
plt.legend()
_ = plt.ylim()
print(validation_losses[(4, 0.5, 5000)])
print(validation_losses[(4, 0.5, 10000)])
print(validation_losses[(4, 0.5, 50000)])
This set does not overfit, due to the low number of iterations. The validation loss is decent but can be improved by a larger number of iterations. The number has to be tuned well to avoid the inevitable overfitting at this high learning rate.
The high learning rate causes oscillations with an amplitude of 0.1.
Here, use the test data to view how well your network is modeling the data. If something is completely wrong here, make sure each step in your network is implemented correctly.
fig, ax = plt.subplots(figsize=(8,4))
network = all_losses[(3, 0.1, 100000)]['network']
mean, std = scaled_features['cnt']
predictions = network.run(test_features).T*std + mean
ax.plot(predictions.values.T, label='Prediction')
ax.plot((test_targets['cnt']*std + mean).values, label='Data')
ax.set_xlim(right=len(predictions))
ax.legend()
dates = pd.to_datetime(rides.iloc[test_data.index]['dteday'])
dates = dates.apply(lambda d: d.strftime('%b %d'))
ax.set_xticks(np.arange(len(dates))[12::24])
_ = ax.set_xticklabels(dates[12::24], rotation=45)
fig, ax = plt.subplots(figsize=(8,4))
network = all_losses[(10, 0.1, 500000)]['network']
mean, std = scaled_features['cnt']
predictions = network.run(test_features).T*std + mean
ax.plot(predictions.values.T, label='Prediction')
ax.plot((test_targets['cnt']*std + mean).values, label='Data')
ax.set_xlim(right=len(predictions))
ax.legend()
dates = pd.to_datetime(rides.iloc[test_data.index]['dteday'])
dates = dates.apply(lambda d: d.strftime('%b %d'))
ax.set_xticks(np.arange(len(dates))[12::24])
_ = ax.set_xticklabels(dates[12::24], rotation=45)
fig, ax = plt.subplots(figsize=(8,4))
network = all_losses[(4, 0.005, 500000)]['network']
mean, std = scaled_features['cnt']
predictions = network.run(test_features).T*std + mean
ax.plot(predictions.values.T, label='Prediction')
ax.plot((test_targets['cnt']*std + mean).values, label='Data')
ax.set_xlim(right=len(predictions))
ax.legend()
dates = pd.to_datetime(rides.iloc[test_data.index]['dteday'])
dates = dates.apply(lambda d: d.strftime('%b %d'))
ax.set_xticks(np.arange(len(dates))[12::24])
_ = ax.set_xticklabels(dates[12::24], rotation=45)
fig, ax = plt.subplots(figsize=(8,4))
network = all_losses[(10, 0.5, 5000)]['network']
mean, std = scaled_features['cnt']
predictions = network.run(test_features).T*std + mean
ax.plot(predictions.values.T, label='Prediction')
ax.plot((test_targets['cnt']*std + mean).values, label='Data')
ax.set_xlim(right=len(predictions))
ax.legend()
dates = pd.to_datetime(rides.iloc[test_data.index]['dteday'])
dates = dates.apply(lambda d: d.strftime('%b %d'))
ax.set_xticks(np.arange(len(dates))[12::24])
_ = ax.set_xticklabels(dates[12::24], rotation=45)
fig, ax = plt.subplots(figsize=(8,4))
network = all_losses[(3, 0.001, 100)]['network']
mean, std = scaled_features['cnt']
predictions = network.run(test_features).T*std + mean
ax.plot(predictions.values.T, label='Prediction')
ax.plot((test_targets['cnt']*std + mean).values, label='Data')
ax.set_xlim(right=len(predictions))
ax.legend()
dates = pd.to_datetime(rides.iloc[test_data.index]['dteday'])
dates = dates.apply(lambda d: d.strftime('%b %d'))
ax.set_xticks(np.arange(len(dates))[12::24])
_ = ax.set_xticklabels(dates[12::24], rotation=45)
The above test set predictions are done using the networks for the first three parameter sets for which the training dynamics were examined in the previous section. There is little visible difference in their predictions. The all are successful and unsuccessful in the same regions of the test set. (See the OPTIONAL part for further discussion.)
Just for sport, the last prediction plot is from a barely trained network. It's predictions are still very close to the mean of the training set values.
Answer these questions about your results. How well does the model predict the data? Where does it fail? Why does it fail where it does?
Note: You can edit the text in this cell by double clicking on it. When you want to render the text, press control + enter
The prediction for the first 10-11 days seems very good, but it becomes unsatisfactory for the remaining 9-10 days. Possible reasons:
Using the mplot3d
toolkit.
Now try to visualize parts of the parameter space. The space has 3 dimensions:
The dependent variables are:
'''
======================
3D surface (color map)
======================
A series of plots to visualize the parameter space.
'''
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np
fig, axes = plt.subplots(3, 2,
sharex='all', sharey='all',
subplot_kw=dict(projection='3d'),
figsize=(24, 16))
plt.suptitle('Validation loss for hyperparameter space for NN')
# Make data.
X = np.array([100, 500, 1000, 5000, 10000, 50000, 100000, 500000])
Y = np.array([2, 3, 4, 5, 6, 7, 8, 9, 10])
X, Y = np.meshgrid(X, Y)
Z001 = np.zeros( (9, 8) )
Z005 = np.zeros( (9, 8) )
Z01 = np.zeros( (9, 8) )
Z05 = np.zeros( (9, 8) )
Z1 = np.zeros( (9, 8) )
Z5 = np.zeros( (9, 8) )
for i in range(9):
for j in range(8):
Z001[i, j] = validation_losses[(Y[i, j], 0.001, X[i, j])]
Z005[i, j] = validation_losses[(Y[i, j], 0.005, X[i, j])]
Z01[i, j] = validation_losses[(Y[i, j], 0.01, X[i, j])]
Z05[i, j] = validation_losses[(Y[i, j], 0.05, X[i, j])]
Z1[i, j] = validation_losses[(Y[i, j], 0.1, X[i, j])]
Z5[i, j] = validation_losses[(Y[i, j], 0.5, X[i, j])]
# Plot the surfaces
# 0,0
surf00 = axes[0,0].plot_surface(X, Y, Z001, cmap=cm.coolwarm, linewidth=0, antialiased=False)
axes[0,0].set_zlim(0.13, 1.95) # Customize z axis
axes[0,0].zaxis.set_major_locator(LinearLocator(10))
axes[0,0].zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
axes[0,0].set_title('Learning rate, 0.001')
fig.colorbar(surf00, ax=axes[0,0], shrink=0.5, aspect=5) # Add colorbar
# 0,1
surf01 = axes[0,1].plot_surface(X, Y, Z005, cmap=cm.coolwarm, linewidth=0, antialiased=False)
axes[0,1].set_zlim(0.13, 1.95) # Customize z axis
axes[0,1].zaxis.set_major_locator(LinearLocator(10))
axes[0,1].zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
axes[0,1].set_title('Learning rate, 0.005')
fig.colorbar(surf01, ax=axes[0,1], shrink=0.5, aspect=5) # Add colorbar
# 1,0
surf10 = axes[1,0].plot_surface(X, Y, Z01, cmap=cm.coolwarm, linewidth=0, antialiased=False)
axes[1,0].set_zlim(0.13, 1.95) # Customize z axis
axes[1,0].zaxis.set_major_locator(LinearLocator(10))
axes[1,0].zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
axes[1,0].set_title('Learning rate, 0.01')
fig.colorbar(surf10, ax=axes[1,0], shrink=0.5, aspect=5) # Add colorbar
# 1,1
surf11 = axes[1,1].plot_surface(X, Y, Z05, cmap=cm.coolwarm, linewidth=0, antialiased=False)
axes[1,1].set_zlim(0.13, 1.95) # Customize z axis
axes[1,1].zaxis.set_major_locator(LinearLocator(10))
axes[1,1].zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
axes[1,1].set_title('Learning rate, 0.05')
fig.colorbar(surf11, ax=axes[1,1], shrink=0.5, aspect=5) # Add colorbar
# 2,0
surf20 = axes[2,0].plot_surface(X, Y, Z1, cmap=cm.coolwarm, linewidth=0, antialiased=False)
axes[2,0].set_zlim(0.13, 1.95) # Customize z axis
axes[2,0].zaxis.set_major_locator(LinearLocator(10))
axes[2,0].zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
axes[2,0].set_title('Learning rate, 0.1')
fig.colorbar(surf20, ax=axes[2,0], shrink=0.5, aspect=5) # Add colorbar
# 2,1
surf21 = axes[2,1].plot_surface(X, Y, Z5, cmap=cm.coolwarm, linewidth=0, antialiased=False)
axes[2,1].set_zlim(0.13, 1.95) # Customize z axis
axes[2,1].zaxis.set_major_locator(LinearLocator(10))
axes[2,1].zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
axes[2,1].set_title('Learning rate, 0.5')
fig.colorbar(surf21, ax=axes[2,1], shrink=0.5, aspect=5) # Add colorbar
# Draw
plt.show()
The lower learning rates cause more gently sloping and smoother surfaces. The higher learning rates show a sharper drop in the beginning but various wavy artifacts along both horizontal axes (iterations and number of hidden nodes).


| Title | Author | Categories | Tags | Messages | Date | ||
|---|---|---|---|---|---|---|---|
| Hello world! | |
admin | Uncategorized | Phone, fashion, Marketing | 5 | Published 2018/02/08 | |
| Hello world! | |
admin | Uncategorized | Phone, fashion, Marketing | 5 | Published 2018/02/08 | |
| Hello world! | |
admin | Uncategorized | Phone, fashion, Marketing | 5 | Published 2018/02/08 | |
| Hello world! | |
admin | Uncategorized | Phone, fashion, Marketing | 5 | Published 2018/02/08 | |
| Hello world! | |
admin | Uncategorized | Phone, fashion, Marketing | 5 | Published 2018/02/08 |


|
QuantumLibrary
|
Exposes methods to access and manipulate a non-coroutine promise (i.e. used in a thread) More...
#include <quantum_ithread_promise.h>
Public Types | |
| using | ContextTag = ThreadContextTag |
| using | Ptr = std::shared_ptr< IThreadPromise< PROMISE, T > > |
| using | Impl = PROMISE< T > |
Public Member Functions | |
| IThreadPromise (Impl *derived) | |
| Constructor. More... | |
| virtual ThreadFuturePtr< T > | getIThreadFuture () const =0 |
| Get the associated thread future. More... | |
| template<class V , class = NonBufferType<T,V>> | |
| int | set (V &&value) |
| Set the promised value. More... | |
| template<class V , class = BufferType<T,V>> | |
| void | push (V &&value) |
| Push a single value into the promise buffer. More... | |
| template<class V = T, class = BufferRetType<V>> | |
| int | closeBuffer () |
| Close a promise buffer. More... | |
| Public Member Functions inherited from Bloomberg::quantum::Traits::DerivedFrom< PROMISE< T >, IThreadPromise< PROMISE, T >, IPromiseBase > | |
| virtual | ~DerivedFrom ()=default |
| operator IPromiseBase * () | |
| operator IPromiseBase & () | |
Exposes methods to access and manipulate a non-coroutine promise (i.e. used in a thread)
| PROMISE | The derived promise (concrete type). |
| T | The type of value contained in this promise. |
| using Bloomberg::quantum::IThreadPromise< PROMISE, T >::ContextTag = ThreadContextTag |
| using Bloomberg::quantum::IThreadPromise< PROMISE, T >::Impl = PROMISE<T> |
| using Bloomberg::quantum::IThreadPromise< PROMISE, T >::Ptr = std::shared_ptr<IThreadPromise<PROMISE, T> > |
|
inline |
Constructor.
| [in] | derived | A pointer to the concrete implementation of this class. |
| int Bloomberg::quantum::IThreadPromise< PROMISE, T >::closeBuffer | ( | ) |
Close a promise buffer.
| BUF | Represents a class of type Buffer. |
|
pure virtual |
Get the associated thread future.
Implemented in Bloomberg::quantum::Promise< T >.
| void Bloomberg::quantum::IThreadPromise< PROMISE, T >::push | ( | V && | value | ) |
Push a single value into the promise buffer.
| [in] | value | Value to push at the end of the buffer. |
| int Bloomberg::quantum::IThreadPromise< PROMISE, T >::set | ( | V && | value | ) |
Set the promised value.
| V | The type of the value. Must be implicitly deduced by the compiler and should always be == T. |
| [in] | value | A reference to the value (l-value or r-value). |


MERS-CoV SARS-CoV- cells HTCC virus using HTCC- OpenUrl presence Vero control CrossRef cultures protein PBS coronavirus performed respiratory entry data inhibition values &; Figure HAE human incubated interaction presented replication confocal polymer standard triplicate, assay average errors viruses DPP PBS. analyzed <; Cell HTCCs RT-qPCR. View Virus cell coronaviruses incubation obtained results untreated °C. Download Fisher Next, Science Scientific, Spike airway collected min showed syndrome μg/ml) (LRV) (for Cells FREE Following GFP Log Med Poland) Poland). Removal Replication Text Value antiviral associated compared cultured day different epithelium evaluated fully immunostained inhibitors inoculated microscopy. new novel observed plasmid sample. Abstract Coronavirus East However, Huh Open Web absence according apical based chitosan data-hide-link-title=""> data-icon-position="" described drug effect emerging figure fixed given infected infection pathogenic polymers previously promising receptor replication. study tab used viability vitro vivo °C, (Thermo ACE DNA Fluorescence HTCC-, HTCC. MERS-CoV-N Middle PFA Pre-cooled VSV-G Virol XTT activity acute analysis assessed blocks concentration coronaviruses. demonstrated effective efficiently experiments, exposed hampered highly ice-cold inhibitor inhibitory internalization lentiviral measured mock particles polymeric post-inoculation prepared presented. selected shown shown. signal significant specific statistically surface viral virions


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{% include "app/header.html" %}
League of
Downing
Players
Champions
Items
About
Search
Search
{% include "app/footer.html" %}


--- layout: post title: Backbone.js RESTful URL calls in Rails date: 2013-10-08 14:47:37.000000000 -04:00 type: post published: true status: publish categories: - Backbone - Rails tags: [] meta: _edit_last: '2' bwps_enable_ssl: '' _css_code: "div#social a img {\r\n padding: 0px;\r\n margin: 10px 3px 0 0;\r\n}" author: login<EMAIL_ADDRESS>email<EMAIL_ADDRESS>display_name: Aimee Knight first_name: Aimee last_name: Knight ---
Just some notes written down for my own reference. Enjoy them if you wish!
{% highlight javascript %} var BookModel = Backbone.Model.extend({ urlRoot: '/books' }); var BookCollection = Backbone.Collection.extend({ model: BookModel, url: '/books' }); {% endhighlight %}
Create (POST)
{% highlight javascript %} var brandNewBook = new BookModel({ title: '1984', author: 'George Orwel' }); brandNewBook.save(); {% endhighlight %}Backbone sees I'm trying to create a new book and makes the following POST request received by the Rails router:
POST /books HTTP/1.1
Host: example.com
{"title":"1984","author":"George Orwel"}
Read (GET) -- collection
{% highlight javascript %} BookCollection().fetch(); {% endhighlight %}Backbone sees I'm trying to read a collection of books and makes the following GET request received by the Rails router:
GET /books HTTP/1.1
Host: example.com
Read (GET) -- object
{% highlight javascript %} new BookModel({ id: 42 }).fetch(); {% endhighlight %}Backbone sees I'm trying to read a single book and makes the following GET request received by the Rails router:
GET /books/42 HTTP/1.1
Host: example.com
Update (PUT)
{% highlight javascript %} brandNewBook.set('author', 'George Orwell'); brandNewBook.save(); {% endhighlight %}Backbone knows 'brandNewBook' is in the database so it updates the book with a PUT request received by the Rails router:
PUT /books/84 HTTP/1.1
Host: example.com
{"title":"1984","author":"George Orwell"}
Destroy (DELETE)
{% highlight javascript %} brandNewBook.destroy(); {% endhighlight %}Backbone sees I'm trying to destroy a single book and makes the following DELETE request received by the Rails router:
DELETE /books/84 HTTP/1.1
Host: example.com


The aim of this colloquium is to relax the "one proof and one joke" requirement of a good seminar talk to merely "one joke". The audience is very forgiving. It consists mainly of the local PhD students and the most curious of the staff. We hope though, that students from nearby universities will come as well when the talk iterests them. In short, everyone is welcome. The expectation is that we learn about a fascinating maths topic from a person who knows it better than we do. We aim to have young researchers speak as we hope for a serving of unrefined idealism (topic motivation), wild speculations (conjectures), and mediocre substance (the maths). And while we are sure that seasoned researchers can often deliver all three, we don't want to disappointed. So, as a speaker, feel free to do talk (in a colloquium style) about anything, as long as it really interests you! Some suggestions:
The colloquium is organized by the OU PhD students and for now, we also come up with suggestions for inviting speakers. However, with time, we hope to get input from students and potential audience outside of The Open University as well. So, if you want to hear a particular talk, please let us know -- we will be in touch to discuss the idea of inviting the speaker.
We are grateful to receive support from The Open University Maths & Stats department. This allows us to get some cookies and reimburse speakers' travel expenses.


'They've Taken The Ball Away From Me' – Hurt Barca Star Opens Up
by Kurt BuckerfieldHaving fallen down the pecking order at Spanish giants FC Barcelona despite his years of consistency, one of the club's midfielders has expressed his sadness at seemingly not being in the manager's plans.
13 Players Who've Scored 50 Free-Kicks Or More
In previous seasons, Ivan Rakitic was one of the Blaugrana's most relied-upon players, but his time as one of the first names on the teamsheet appear to be over.
The 31-year-old has played just 255 minutes of football in this campaign so far, with manager Ernesto Valverde preferring the likes of Arthur, Arturo Vidal, Frenkie de Jong and Sergio Busquets to him in midfield.
Asked in a recent interview about how things have gone for him this season, Rakitic likened his situation to a child having their favourite toy taken away from them.
"How can I enjoy myself? Playing football. Playing football," he told Universo Valdano.
"How does my youngest daughter feel if I take her toy from her? She's sad.
"I feel the same: they have taken the ball from me and I am sad."
Earn Airtime & Data With Soccer Laduma’s Social Media App - Download Now
However, the Croatian also explained that he respects Valverde's decision.
"I understand and respect the decisions made by the coach (Ernesto Valverde) and the club, but I think I've given a lot in the last five and a bit years here, and the only thing I want is to be able to keep enjoying myself.
"That's the most important thing for me."
Rakitic has started just once match for Barca so far this season, and has been tipped to leave the club in the January transfer window.


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This is the sample-view.html template.
Today is {{sc.today}}.
{{sc.time}}
This project includes things I often use when creating small design prototypes with Angular JS. Components and references include:
See the angular-handy project on GitHub for more information.
| Id | Title | User Id |
|---|---|---|
| {{item.id}} | {{item.title}} | {{item.userId}} |


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What I do
I'm a computer programmer currently working for an international Internet-based retailer in London. Previously I worked for a small indie video game company doing pretty much everything except washing the pots and a large computer graphics IP company in the south of England.


Stack Web Services
Stack Web Services is an independent software vendor (ISV) that focuses mostly on:
- network infrastructure (e-mail & dns)
- remote server management (control & health monitoring)
- highly concurrent network applications
- scalable webservices
For more information, please contact us: info@stackwebservices.com.


application module¶
-
class
application.
BrowseListHandler
(app)[source]¶ Bases:
object
-
browse_link_clicked
(item)[source]¶ Adds items relative to the clicked browse item, to the tree view.
- self : instance
- Class instance.
- item : QStandardItem
- The item clicked
-
change_type
(type)[source]¶ Changes the model shown to the user for browsing the meta-data.
- self : instance
- Class instance.
- type : int
- The index corresponding to the new browse model
-
change_type_order
(index)[source]¶ Changes the order of the browse model.
- self : instance
- Class instance.
- index : int
- The index corresponding to the new type order
-
generate_browse_models
(list, model)[source]¶ Takes an input list and an empty model, and fills said model.
- self : instance
- Class instance.
- list : str[]
- The input list of items for the model
- model : QStandardItemModel
- An empty model for QStandardItems
-
-
class
application.
BrowseTreeViewHandler
(main)[source]¶ Bases:
object
-
add_tracks_tree
(extension_type, tracklist, index)[source]¶ Adds a tracklist to the tree view.
- self : instance
- Class instance.
- extension_type : str
- The requested format for the audio association.
- tracklist : dict
- The tracklist for the performance.
- index : QModelIndex
- The index in the treeview (i.e. the performance), clicked.
-
expand_tree_item
(index)[source]¶ Expands a performance, adding its tracklist as children in the tree.
- self : instance
- Class instance.
- index : QModelIndex
- The index in the treeview (i.e. the performance), clicked.
-
play_tree_item
(index)[source]¶ Called when an item in the browse tab treeview is double-clicked, starting audio playback
- self : instance
- Class instance.
- index : QModelIndex
- The row index clicked by the user.
-
-
class
application.
SearchHandler
(main)[source]¶ Bases:
object
-
change_condition_or
(customConditions)[source]¶ Adjusts a search FILTER from “ALL” or “OR”.
- customConditions : str[]
- A list of custom conditions returned by the class instance.
-
ensure_matching_parentheses
(customConditions)[source]¶ Performs validation on SPARQL filter queries to ensure that our query is valid.
- customConditions : str[]
- A list of custom conditions returned by the class instance.
-
generate_mapped_locations
()[source]¶ A user may request all performances within a specified radius of a given location.
We calculate the desired locations using point-to-point distance calculations, relative to the location map keys.
- countries : str[]
- A list of performance countries.
-
-
class
application.
TableHandler
(prog)[source]¶ Bases:
object
-
add_table_item
(i, c, itemText)[source]¶ Adds an item to the table view.
- self : instance
- Class instance.
- i : int
- Row index.
- c : int
- Row index.
- itemText : str
- Table item text.
-
fill_table
(results)[source]¶ Starts a thread to fill the table with the data returned from a search.
- self : instance
- Class instance.
- results : dict
- Dictionary of results returned from the SPARQL query.
-
generate_table_end
()[source]¶ Perform post-processing on table after all the data has been entered.
- self : instance
- Class instance.
-
generate_table_start
(c, col, columnNames)[source]¶ Adds an item to the table view.
- self : instance
- Class instance.
- c : int
- Number of rows for the table.
- col : int
- Number of columns for the table.
- columnNames : str[]
- List of column names.
-
get_table_container
()[source]¶ Returns the table element instance widget.
- self : instance
- Class instance.
-
on_table_scroll
(value)[source]¶ Starts a new thread for replacing URIs with location labels.
- self : instance
- Class instance.
- value : int
- The desired row index.
-
-
class
application.
TreePropertiesView
(app)[source]¶ Bases:
PyQt5.QtWidgets.QTreeView
-
class
application.
mainWindow
(dialog)[source]¶ Bases:
UI.UI
-
auto_comp
(inputList)[source]¶ Creates and returns an auto-completer with the input list.
- self : instance
- Class instance.
- inputList : str[]
- The input list providing the model for the auto-completer.
-
check_lastfm_status
()[source]¶ Checks whether we have an existing Last.FM session, and if not, initiates authentication with the API.
- self : instance
- Class instance.
Called when the user requests a context menu from the tree view.
- self : instance
- Class instance.
- pos : QStandardItem
- The item the user right clicked on
-
set_tooltips
()[source]¶ Sets up help tooltips which appear when the user hovers over a particular widget.
- self : instance
- Class instance.
Processes use of the menu in the tree view.
- self : instance
- Class instance.
index : int
-


Plugin Information |
|---|
View AsakusaSatellite on the plugin site for more information. |
This plugin notifies AsakusaSatellite of build results.
Features
- Notify AsakusaSatellite of build results
Setup
At (your project) > Configure > AsakusaSatellite, set room information at your AsakusaSatellite.
- appkey: secret key of your AsakusaSatellite acount. You can get this key at your acount page at AsakusaSatellite.
- baseUrl: a Base URL of AsakusaSatellite
- roomNumber: a room id. Typically, URL of rooms are such as baseUrl/chat/room/roomNumber
- message: a message template. You can use following variables
- ${project}: a project name
- ${number}: a build number
- ${result}: a build result
- ${url}: a url of build result
- ${changeset}: change set of this build
Version History
Version 0.1 (22 October, 2012)
- Initial release
Attachments:
jenkins_as_notifier.png (image/png)
as_api.png (image/png)
jenkins_as_notifier2.png (image/png)
jenkins_message.png (image/png)
as_api.png (image/png)
jenkins_as_notifier2.png (image/png)
jenkins_message.png (image/png)


This class is used to make an object for Tasklist.
Get the task list created time.
Task list created time.
# File projects/model/Tasklist.rb, line 88 def getCreatedTime return @createdTime end
Get the task list created time format.
Task list created time format.
# File projects/model/Tasklist.rb, line 108 def getCreatedTimeFormat return @createdTimeFormat end
Get the task list created time long.
Task list created time long.
# File projects/model/Tasklist.rb, line 128 def getCreatedTimeLong return @createdTimeLong end
Get the flag for the task list.
Task list flag.
# File projects/model/Tasklist.rb, line 228 def getFlag return @flag end
Get the task list id.
Task list id.
# File projects/model/Tasklist.rb, line 28 def getId return @id end
Get the milestone for the task list.
Milestone object.
# File projects/model/Tasklist.rb, line 268 def getMilestone return @milestone end
Get the task list name.
task list name.
# File projects/model/Tasklist.rb, line 48 def getName return @name end
Get the sequence of the task list.
Sequence of the task list.
# File projects/model/Tasklist.rb, line 168 def getSequence return @sequence end
Get the status of the task list.
Status of the task list.
# File projects/model/Tasklist.rb, line 248 def getStatus return @status end
Get the task URL.
Task URL.
# File projects/model/Tasklist.rb, line 208 def getTaskURL return @taskUrl end
Get the task list URL.
Task list URL.
# File projects/model/Tasklist.rb, line 188 def getURL return @url end
Get whether the task list is completed or not.
true, if the task list is completed else returns false.
# File projects/model/Tasklist.rb, line 68 def isCompleted return @completed end
Get whether the task list rolled or not.
true, if the task list is rolled else returns false.
# File projects/model/Tasklist.rb, line 148 def isRolled return rolled end
Set whether the task list is completed or not.
Whether the task list is completed or not.
# File projects/model/Tasklist.rb, line 58 def setCompleted(completed) @completed = completed end
Set the task list created time.
Task list created time.
# File projects/model/Tasklist.rb, line 78 def setCreatedTime(createdTime) @createdTime = createdTime end
Set the task list created time format.
Task list created time format.
# File projects/model/Tasklist.rb, line 98 def setCreatedTimeFormat(createdTimeFormat) @createdTimeFormat = createdTimeFormat end
Set the task list created time long.
Task list created time long.
# File projects/model/Tasklist.rb, line 118 def setCreatedTimeLong(createdTimeLong) @createdTimeLong = createdTimeLong end
Set the flag for the task list.
Flag for the task list.
# File projects/model/Tasklist.rb, line 218 def setFlag(flag) @flag = flag end
Set the task list id.
ID of the task list.
# File projects/model/Tasklist.rb, line 18 def setId(id) @id = id end
Set the milestone for the task list.
Milestone object.
# File projects/model/Tasklist.rb, line 258 def setMilestone(milestone) @milestone = milestone end
Set the task list name.
Name of the task list.
# File projects/model/Tasklist.rb, line 38 def setName(name) @name = name end
Set whether the task list is rolled or not.
Whether the task list is rolled or not.
# File projects/model/Tasklist.rb, line 138 def setRolled(rolled) @rolled = rolled end
Set the sequence of the task list.
Sequence of the task list.
# File projects/model/Tasklist.rb, line 158 def setSequence(sequence) @sequence = sequence end
Set the status of the task list.
Status of the task list.
# File projects/model/Tasklist.rb, line 238 def setStatus(status) @status = status end
Set the task URL.
URL for the task.
# File projects/model/Tasklist.rb, line 198 def setTaskURL(taskUrl) @taskUrl = taskUrl end
Set the task list URL.
URL for the task list.
# File projects/model/Tasklist.rb, line 178 def setURL(url) @url = url end
Convert the Tasklist object into HashMap.
HashMap object.
# File projects/model/Tasklist.rb, line 278 def toParamMAP requestBody = Hash.new if milestone != nil requestBody["milestone_id"] = milestone.getId end if name != nil requestBody["name"] = name end if flag != nil requestBody["flag"] = flag end if status != nil requestBody["status"] = status end return requestBody end


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