class: title-slide, center   3  # A Quick Introduction to tidymodels ## Feature Engineering --- # Loading ```r library(tidymodels) ``` ``` ## ── Attaching packages ──────────────────────────────────────────────────── tidymodels 0.1.1 ── ``` ``` ## ✓ broom 0.7.0 ✓ recipes 0.1.13 ## ✓ dials 0.0.9 ✓ rsample 0.0.8 ## ✓ dplyr 1.0.2 ✓ tibble 3.0.3 ## ✓ ggplot2 3.3.2 ✓ tidyr 1.1.2 ## ✓ infer 0.5.2 ✓ tune 0.1.1 ## ✓ modeldata 0.0.2 ✓ workflows 0.2.0 ## ✓ parsnip <IP_ADDRESS>00 ✓ yardstick 0.0.7 ## ✓ purrr 0.3.4 ``` ``` ## ── Conflicts ─────────────────────────────────────────────────────── tidymodels_conflicts() ── ## x purrr::discard() masks scales::discard() ## x dplyr::filter() masks stats::filter() ## x dplyr::lag() masks stats::lag() ## x recipes::step() masks stats::step() ``` --- # Previously ```r data(ames, package = "modeldata") ames <- ames %>% mutate(Sale_Price = log10(Sale_Price)) set.seed(4595) data_split <- initial_split(ames, strata = "Sale_Price") ames_train <- training(data_split) ames_test <- testing(data_split) lm_mod <- linear_reg() %>% set_engine("lm") perf_metrics <- metric_set(rmse, rsq, ccc) ``` --- layout: false class: inverse, middle, center # Feature Engineering --- # Preprocessing and Feature Engineering This part mostly concerns what we can _do_ to our variables to make the models more effective. This is mostly related to the predictors. Operations that we might use are: * transformations of individual predictors or groups of variables * alternate encodings of a variable * elimination of predictors (unsupervised) In statistics, this is generally called _preprocessing_ the data. As usual, the computer science side of modeling has a much flashier name: _feature engineering_. --- # Reasons for Modifying the Data * Some models (_K_-NN, SVMs, PLS, neural networks) require that the predictor variables have the same units. **Centering** and **scaling** the predictors can be used for this purpose. * Other models are very sensitive to correlations between the predictors and **filters** or **PCA signal extraction** can improve the model. * As we'll see in an example, changing the scale of the predictors using a **transformation** can lead to a big improvement. * In other cases, the data can be **encoded** in a way that maximizes its effect on the model. Representing the date as the day of the week can be very effective for modeling public transportation data. --- # Reasons for Modifying the Data * Many models cannot cope with missing data so **imputation** strategies might be necessary. * Development of new _features_ that represent something important to the outcome (e.g. compute distances to public transportation, university buildings, public schools, etc.) --- layout: false class: inverse, middle, center # Preprocessing Categorical Predictors --- # Dummy Variables One common procedure for modeling is to create numeric representations of categorical data. This is usually done via _dummy variables_: a set of binary 0/1 variables for different levels of an R factor. For example, the Ames housing data contains a predictor called `Alley` with levels: 'Gravel', 'No_Alley_Access', 'Paved'. Most dummy variable procedures would make _two_ numeric variables from this predictor that are 1 when the observation has that level, and 0 otherwise.

Data

Dummy Variables

  	  No_Alley_Access 	  Paved

  Gravel 	  0 	  0

  No_Alley_Access 	  1 	  0

  Paved 	  0 	  1

 --- # Dummy Variables If there are _C_ levels of the factor, only _C_-1 dummy variables are created since the last can be inferred from the others. There are different contrast schemes for creating the new variables. How do you create them in R? The formula method does this for you1. Otherwise, the traditional method is to use `model.matrix()` to create a matrix. However, there are some caveats to this that can make things difficult. We'll show another method for making them shortly. .footnote[[1] _Almost always_ at least. Tree- and rule-based model functions do not. Examples are `randomforest`, `ranger`, `rpart`, `C50`, `Cubist`, `klaR::NaiveBayes` and others.] ??? Caveats include new (unseen) levels of a predictor value. --- # Infrequent Levels in Categorical Factors .pull-left[ One issue is: what happens when there are very few values of a level? Consider the Ames training set and the `Neighborhood` variable. If these data are resampled, what would happen to Landmark and similar locations when dummy variables are created? ] .pull-right[  ] ??? Bring up the idea that these issues are model-dependent and something like trees wouldn't care. Mention the alley variable and how almost all properties have no alley access. Talk about near-zero-variance predictors. --- # Infrequent Levels in Categorical Factors A _zero-variance_ predictor that has only a single value (zero) would be the result. Many models (e.g. linear/logistic regression, etc.) would find this numerically problematic and issue a warning and `NA` values for that coefficient. Trees and similar models would not notice. There are two main approaches to dealing with this: * Run a filter on the training set predictors prior to running the model and remove the zero-variance predictors. * Recode the factor so that infrequently occurring predictors (and possibly new values) are pooled into an "other" category. However, `model.matrix()` and the formula method are incapable of helping you. --- # Recipes  Recipes are an alternative method for creating the data frame of predictors for a model. They allow for a sequence of _steps_ that define how data should be handled. Recall the previous part where we used the formula `Sale_Price ~ Longitude + Latitude`? These steps are: .pull-left-a-little[ * Assign `Sale_Price` to be the outcome * Assign `Longitude` and `Latitude` as predictors ] .pull-right-a-lot[ To start using a recipe, these steps can be done using ```r # recipes loaded by tidymodels mod_rec <- recipe(Sale_Price ~ Longitude + Latitude, ames_train) ``` This starts a recipe for data processing (but does not execute it yet) ] --- # Recipes and Categorical Predictors  To deal with the dummy variable issue, we can expand the recipe with more steps: .pull-left[ ```r mod_rec <- recipe( Sale_Price ~ Longitude + Latitude + Neighborhood, data = ames_train ) %>% # Lump factor levels that occur in # <= 5% of data as "other" step_other(Neighborhood, threshold = 0.05) %>% # Create dummy variables for _any_ factor variables step_dummy(all_nominal()) ``` ] .pull-right[ ```r mod_rec ``` ``` ## Data Recipe ## ## Inputs: ## ## role #variables ## outcome 1 ## predictor 3 ## ## Operations: ## ## Collapsing factor levels for Neighborhood ## Dummy variables from all_nominal() ``` ] Note that we can use standard `dplyr` selectors as well as some new ones based on the data type (`all_nominal()`) or by their role in the analysis (`all_predictors()`). --- # Using Recipes

  --- # Preparing the Recipe  Now that we have a preprocessing _specification_, let's run it on the training set to _prepare_ the recipe: ```r mod_rec_trained <- prep(mod_rec, training = ames_train, verbose = TRUE) ``` ``` ## oper 1 step other [training] ## oper 2 step dummy [training] ## The retained training set is ~ 0.23 Mb in memory. ``` Here, the "training" is to determine which levels to lump together and to enumerate the factor levels of the `Neighborhood` variable. --- # Preparing the Recipe  ```r mod_rec_trained ``` ``` ## Data Recipe ## ## Inputs: ## ## role #variables ## outcome 1 ## predictor 3 ## ## Training data contained 2199 data points and no missing data. ## ## Operations: ## ## Collapsing factor levels for Neighborhood [trained] ## Dummy variables from Neighborhood [trained] ``` --- # Getting the Values - Training  Now that the recipe has been prepared, we can extract the processed training set from it, with all of the steps applied. To do that, we use `juice()`. ```r # Extracts processed version of `ames_train` juice(mod_rec_trained) ``` ``` ## # A tibble: 2,199 x 11 ## Longitude Latitude Sale_Price Neighborhood_Co… Neighborhood_Ol… Neighborhood_Ed… Neighborhood_So… ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 -93.6 42.1 5.24 0 0 0 0 ## 2 -93.6 42.1 5.39 0 0 0 0 ## 3 -93.6 42.1 5.28 0 0 0 0 ## 4 -93.6 42.1 5.29 0 0 0 0 ## 5 -93.6 42.1 5.33 0 0 0 0 ## 6 -93.6 42.1 5.28 0 0 0 0 ## 7 -93.6 42.1 5.37 0 0 0 0 ## 8 -93.6 42.1 5.28 0 0 0 0 ## 9 -93.6 42.1 5.25 0 0 0 0 ## 10 -93.6 42.1 5.26 0 0 0 0 ## # … with 2,189 more rows, and 4 more variables: Neighborhood_Northridge_Heights <dbl>, ## # Neighborhood_Gilbert <dbl>, Neighborhood_Sawyer <dbl>, Neighborhood_other <dbl> ``` This is what you'd pass on to `fit()` your model. --- # Getting the Values - Testing  After model fitting, you'll eventually want to make predictions on _new data_. But first, you have to reapply all of the pre-processing steps on it. To do that, use `bake()`. ```r bake(mod_rec_trained, new_data = ames_test) ``` ``` ## # A tibble: 731 x 11 ## Longitude Latitude Sale_Price Neighborhood_Co… Neighborhood_Ol… Neighborhood_Ed… Neighborhood_So… ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> ## 1 -93.6 42.1 5.33 0 0 0 0 ## 2 -93.6 42.1 5.02 0 0 0 0 ## 3 -93.6 42.1 5.27 0 0 0 0 ## 4 -93.6 42.1 5.60 0 0 0 0 ## 5 -93.6 42.1 5.28 0 0 0 0 ## 6 -93.6 42.1 5.17 0 0 0 0 ## 7 -93.6 42.1 5.02 0 0 0 0 ## 8 -93.7 42.1 5.46 0 0 0 0 ## 9 -93.7 42.1 5.44 0 0 0 0 ## 10 -93.7 42.1 5.33 0 0 0 0 ## # … with 721 more rows, and 4 more variables: Neighborhood_Northridge_Heights <dbl>, ## # Neighborhood_Gilbert <dbl>, Neighborhood_Sawyer <dbl>, Neighborhood_other <dbl> ``` This is what you'd pass on to `predict()`. --- # How Data Are Used  Note that we have: ```r recipe(..., data = data_set) prep(..., training = data_set) bake(..., new_data = data_set) ``` * `recipe()` - `data` is used _only_ to determine column names and types. A 0-row data frame could even be used. * `prep()` - `training` is the entire training set, used to estimate parameters in each step (like means or standard deviations). * `bake()` - `new_data` is data to apply the pre-processing to, using the _same estimated parameters_ from when `prep()` was called on the training set. --- # Ongoing use of `juice()` We've found that the difference in `juice()` and `bake()` is not obvious. For the next version of `recipes`, we'll focus on using: ```r bake(recipe, new_data = NULL) ``` instead of ```r juice(recipes) ``` `juice()` won't be going away but we'll not talk about it in training any more. --- layout: false class: inverse, middle, center # Interaction Effects --- # Interactions  An **interaction** between two predictors indicates that the relationship between the predictors and the outcome cannot be describe using only one of the variables. For example, let's look at the relationship between the price of a house and the year in which it was built. The relationship appears to be slightly nonlinear, possibly quadratic: .pull-left[ ```r price_breaks <- (1:6)*(10^5) ames_train %>% ggplot(aes(x = Year_Built, y = Sale_Price)) + geom_point(alpha = 0.4) + geom_smooth(method = "loess") ``` ] .pull-right[  ] --- # Interactions  However... what if we separate this trend based on whether the property has air conditioning or not. .pull-left[ ```r ames_train %>% group_by(Central_Air) %>% count() %>% ungroup() %>% mutate(percent = n / sum(n) * 100) ``` ``` ## # A tibble: 2 x 3 ## Central_Air n percent ## <fct> <int> <dbl> ## 1 N 141 6.41 ## 2 Y 2058 93.6 ``` ```r ames_train %>% ggplot(aes(x = Year_Built, y = Sale_Price)) + geom_point(alpha = 0.4) + facet_wrap(~ Central_Air, nrow = 2) + geom_smooth(method = "lm") ``` ] .pull-right[  ] --- # Interactions It appears as though the relationship between the year built and the sale price is somewhat _different_ for the two groups. * When there is no AC, the trend is perhaps flat or slightly decreasing. * With AC, there is a linear increasing trend or is perhaps slightly quadratic with some outliers at the low end. ```r mod1 <- lm(Sale_Price ~ Year_Built + Central_Air, data = ames_train) mod2 <- lm(Sale_Price ~ Year_Built + Central_Air + Year_Built:Central_Air, data = ames_train) anova(mod1, mod2) ``` ``` ## Analysis of Variance Table ## ## Model 1: Sale_Price ~ Year_Built + Central_Air ## Model 2: Sale_Price ~ Year_Built + Central_Air + Year_Built:Central_Air ## Res.Df RSS Df Sum of Sq F Pr(>F) ## 1 2196 42.741 ## 2 2195 41.733 1 1.0075 52.993 4.64e-13 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ``` --- # Interactions in Recipes  We first create the dummy variables for the qualitative predictor (`Central_Air`) then use a formula to create the interaction using the `:` operator in an additional step: ```r interact_rec <- recipe(Sale_Price ~ Year_Built + Central_Air, data = ames_train) %>% step_dummy(Central_Air) %>% step_interact(~ starts_with("Central_Air"):Year_Built) interact_rec %>% prep(training = ames_train) %>% juice() %>% # select a few rows with different values slice(153:157) ``` ``` ## # A tibble: 5 x 4 ## Year_Built Sale_Price Central_Air_Y Central_Air_Y_x_Year_Built ## <int> <dbl> <dbl> <dbl> ## 1 1915 5.17 1 1915 ## 2 1912 5.20 1 1912 ## 3 1920 5.09 1 1920 ## 4 1963 5.04 0 0 ## 5 1930 4.74 0 0 ``` --- layout: false class: inverse, middle, center # Skipping Steps --- # Steps that require the outcome .left-narrow[ If we have a step that requires the outcome data, what do we do when predicting new samples (where the outcome is unknown or absent)? Instead of pre-logging, suppose that we had used: ```r step_log(Sale_Price, base = 10) ``` When running the recipe on new data **this would fail** since there is no `Sale_Price` column. ] .left-wide[  ] --- # Steps that require the outcome If a simple transformation (like `log()`) is used on the outcome, we suggest pre-transforming the data prior to the recipe. tidymodels packages tend to isolate the prediction data from the outcome columns (even when they exist).
 _However_, there are other types of operations where we shouldn't (or can't) apply to the data being predicted. For example, **down-sampling** is a method to deal with class imbalances where the data used for modeling are reduced to equal class frequencies. It is very important that down-sampling is **not** applied to the prediction data (or test set). --- # Only down-sample the modeling data  --- # Skipping steps So we need a way to apply all of the steps when creating the data that will be used for modeling (i.e., `juice()`) but _not_ for new data (i.e., `bake()`). All recipes steps have an optional `skip` argument that defaults to `FALSE`. * In most cases, we apply steps to all data (`skip = FALSE`). * For down-sampling and similar cases, `skip = TRUE` will do the appropriate thing. The steps have the appropriate default value for `skip` (unless you have an atypical application). --- layout: false class: inverse, middle, center # Principal Component Analysis --- # A Bivariate Example .pull-left[ .font120[ The plot on the right shows two **predictors** from a real _test_ set where the objective is to predict the two classes. The predictors are strongly correlated and each has a right-skewed distribution. There appears to be some class separation but only in the bivariate plot; the individual predictors show poor discrimination of the classes. Some models might be sensitive to highly correlated and/or skewed predictors. Is there something that we can do to make the predictors _easier for the model to use_? ***Any ideas***? ] ] .pull-right[  ] ??? Skewed, positive data => ratios (to me) Mention the use of logistic regression and ROC curve results. These data are in the github repo --- # A Bivariate Example .pull-left[ .font110[ We might start by estimating transformations of the predictors to resolve the skewness. The Box-Cox transformation is a family of transformations originally designed for the outcomes of models. We can use it here for the predictors. It uses the data to estimate a wide variety of transformations including the inverse, log, sqrt, and polynomial functions. Using each factor in isolation, both predictors were determined to need inverse transformations (approximately). The figure on the right shows the data after these transformations have been applied. A logistic regression model shows a substantial improvement in classifying using the altered data. ] ] .pull-right[  ] ??? The reason to show the _test data_ (or some other data) is to emphasize that we can visually overfit by reapplying the model to the data (as before). Ordinarily, we would not use the test set in this way. When there is enough data, use a random sample (like a validation set) to evaluate the changes. --- # More Recipe Steps  The package has a [rich set](https://tidymodels.github.io/recipes/reference/index.html) of steps that can be used including transformations, filters, variable creation and removal, dimension reduction procedures, imputation, and others. There are also packages like [`embed`]( https://tidymodels.github.io/embed), [`textrecipes`]( https://tidymodels.github.io/textrecipes), and [`themis`]( https://tidymodels.github.io/themis) that extend recipes with new steps. For example, in the previous bivariate data problem, the Box-Cox transformation was conducted using: ```r data(bivariate) bivariate_rec <- recipe(Class ~ ., data = bivariate_train) %>% step_BoxCox(all_predictors()) bivariate_rec <- prep(bivariate_rec, training = bivariate_train) inverse_test_data <- bake(bivariate_rec, new_data = bivariate_test) ``` ??? Show `tidy` method to get the lambda values --- # Correlated Predictors In the Ames data, there are potential clusters of _highly correlated variables_: * proxies for size: `Lot_Area`, `Gr_Liv_Area`, `First_Flr_SF`, `Bsmt_Unf_SF`, `Full_Bath` etc. * quality fields: `Overall_Qual`, `Garage_Qual`, `Kitchen_Qual`, `Exter_Qual`, etc. It would be nice if we could combine/amalgamate the variables in these clusters into a single variable that represents them. Another way of putting this is that we would like to create artificial features of the data that account for a certain amount of _variation_ in the data. There are a few different methods that can accomplish this; we will focus on principal component analysis (PCA). Another, regularization, will be discussed later. --- # PCA Signal Extraction Principal component analysis (PCA) is a multivariate statistical technique that can be used to create artificial new variables from an existing set. Conceptually, PCA determines which variables account for the most correlation in the data and creates a new variable that is a linear combination of all the predictors. * This is called the _first principal component_ (aka `PC1`). * This linear combination emphasizes the variables that are the most correlated. The variables constructing `PC1` are then _removed from the data_. The second PCA component is the linear combination that accounts for the most left-over correlation in the data (and so on). --- # PCA Signal Extraction The main takeaways: * The components account for as much as the variation in the original data as possible. * Each component is uncorrelated with the others. * The new variables are _linear combinations_ of all of the input variables and are effectively unitless (It is generally a good idea to center and scale your predictors because of this). For our purposes, we would use PCA on the _predictors_ to: * Reduce the number of variables exposed to the model (but this is not feature selection). * Combat excessive correlations between the predictors (aka multicollinearity). In this way, the procedure is often called _signal extraction_ but this is poorly named since there is no guarantee that the new variables will have an association with the outcome. ??? No feature selection due to linear combinations --- # Back to the Bivariate Example - Transformed Data  --- # Back to the Bivariate Example -  We can build on our transformed data recipe and add normalization: ```r bivariate_pca <- recipe(Class ~ A + B, data = bivariate_train) %>% step_BoxCox(all_predictors()) %>% step_normalize(all_predictors()) %>% # center and scale step_pca(all_predictors()) %>% prep(training = bivariate_train) pca_test <- bake(bivariate_pca, new_data = bivariate_test) # Put components axes on the same range pca_rng <- extendrange(c(pca_test$PC1, pca_test$PC2)) pca_test %>% ggplot(aes(x = PC1, y = PC2, color = Class)) + geom_point(alpha = .2, cex = 1.5) + theme(legend.position = "top") + scale_colour_calc() + xlim(pca_rng) + ylim(pca_rng) + xlab("Principal Component 1") + ylab("Principal Component 2") ``` ??? Order matters; Box-Cox before centering; YJ transformation --- # Back to the Bivariate Example .pull-left[ .font120[ Recall that even after the Box-Cox transformation was applied to our previous example, there was still a high degree of correlation between the predictors. After the transformation, the predictors were centered and scaled, then PCA was conducted. The plot on the right shows the results. Since these two predictors are highly correlated, the first component captures 91.7% of the variation in the original data. However... ...recall that PCA does not guarantee that the components are associated with the outcome. In this example, the _least important_ component has the association with the outcome. ] ] .pull-right[  ] --- class: middle, center # PCA does a _rotation_ of the data so that the _variation_ in one dimension is maximized. # The rotation also makes the new variables _uncorrelated_. --- class: middle, center  --- layout: false class: inverse, middle, center # Recipe and Models --- # Longitude  .pull-left[ ```r ggplot(ames_train, aes(x = Longitude, y = Sale_Price)) + geom_point(alpha = .5) + geom_smooth( method = "lm", formula = y ~ splines::bs(x, 5), se = FALSE ) ``` Splines add nonlinear versions of the predictor to a linear model to create smooth and flexible relationships between the predictor and outcome. This "basis expansion" technique will be seen again in the regression section of the workshop. ] .pull-right[  ] --- # Latitude  .pull-left[ ```r ggplot(ames_train, aes(x = Latitude, y = Sale_Price)) + geom_point(alpha = .5) + geom_smooth( method = "lm", formula = y ~ splines::ns(x, df = 5), se = FALSE ) ``` ] .pull-right[  ] --- # Linear Models Again  .pull-left-a-little[ * We'll add neighborhood in as well and a few other house features. * Our plots suggests that the coordinates can be helpful but probably require a nonlinear representation. We can add these using _B-splines_ with 5 degrees of freedom. ] .pull-right-a-lot[ * Two numeric predictors are very skewed and could use a transformation (`Lot_Area` and `Gr_Liv_Area`). ```r ames_rec <- recipe( Sale_Price ~ Bldg_Type + Neighborhood + Year_Built + Gr_Liv_Area + Full_Bath + Year_Sold + Lot_Area + Central_Air + Longitude + Latitude, data = ames_train ) %>% step_BoxCox(Lot_Area, Gr_Liv_Area) %>% step_other(Neighborhood, threshold = 0.05) %>% step_dummy(all_nominal()) %>% step_interact(~ starts_with("Central_Air"):Year_Built) %>% step_ns(Longitude, Latitude, deg_free = 5) ``` ] --- # Combining the Recipe with a Model  - `prep()`/`juice()`/`fit()` ```r ames_rec <- prep(ames_rec) lm_fit <- lm_mod %>% # Sale_Price is already on the log scale: fit(Sale_Price ~ ., data = juice(ames_rec)) glance(lm_fit$fit) ``` ``` ## # A tibble: 1 x 12 ## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual ## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int> ## 1 0.802 0.799 0.0800 303. 0 29 2448. -4834. -4657. 13.9 2169 ## # … with 1 more variable: nobs <int> ``` - `bake()`/`predict()` ```r ames_test_processed <- bake(ames_rec, ames_test, all_predictors()) # but let's not do this # predict(lm_fit, new_data = ames_test_processed) ``` --- # That Modeling Process Again .pull-left[ We are * estimating transformations on some variables, * making nonlinear features for the geocoding variables, and * estimating new encodings for some factor variables. These should definitely be included in our overall modeling process. ] .pull-right[  ] --- # Workflows  The `workflows` package enables a handy type of object that can bundle pre-processing and models together. - You don’t have to keep track of separate objects in your workspace. - The recipe prepping and model fitting can be executed using a single call to `fit()` instead of `prep()`/`juice()`/`fit()`. - The recipe baking and model predictions are handled with a single call to `predict()` instead of `bake()`/`predict()`. - Workflows _will_ be able to add post-processing operations in upcoming versions. An example of post-processing would be to modify (and tune) the probability cutoff for two-class models. --- # Workflows  ```r ames_wfl <- workflow() %>% add_recipe(ames_rec) %>% add_model(lm_mod) ames_wfl ``` ``` ## ══ Workflow ══════════════════════════════════════════════════════════════════════════════════ ## Preprocessor: Recipe ## Model: linear_reg() ## ## ── Preprocessor ────────────────────────────────────────────────────────────────────────────── ## 5 Recipe Steps ## ## ● step_BoxCox() ## ● step_other() ## ● step_dummy() ## ● step_interact() ## ● step_ns() ## ## ── Model ───────────────────────────────────────────────────────────────────────────────────── ## Linear Regression Model Specification (regression) ## ## Computational engine: lm ``` --- # 1-Step fitting and predicting  The `fit()` method for a workflow automatically does the `prep`/`juice`/`fit` sequence with one call: ```r ames_wfl_fit <- fit(ames_wfl, ames_train) ``` The workflow `predict()` method does the `bake`/`predict` sequence: ```r predict(ames_wfl_fit, ames_test) %>% slice(1:5) ``` Some other notes about workflows: * `add_formula()` and `add_variables()` can be used as simple alternatives to `add_recipe()` (see [this blog post](https://www.tidyverse.org/blog/2020/09/workflows-0-2-0/)). * A _secondary formula_ can be given to `add_model()` that will be directly passed to the model. This is helpful when recipes are used with GAMs or mixed-models. * There are `remove_*()` and `update_*()` functions too. --- layout: false class: inverse, middle, center # Encoding predictors --- # Encoding predictors There is some heterogeneity in how different modeling functions handle predictors: * _Most_ create dummy variables from categorical (i.e. factor) predictors. * Tree-based methods (and some others) do not touch the predictors; no dummy variables are used. * At least one model (`kernlab::svm()`) makes a one-hot-encoding for dummy variables. When using `parsnip`, in most cases the data are handed as-is to the underlying modeling function. There are exceptions. * For example, when using `fit(formula, data)` with a `glmnet` model, `parsnip` will make indicators for you. With `workflows`, we attempt to emulate what the underlying package would do with the data. In many cases, we pass the data as-is to the model function when that is appropriate. When in doubt, check the `parsnip` help pacakge for the model. --- layout: false class: inverse, middle, center # A Quick Knowledge Check --- # Match tasks to packages .pull-left[ * Fit a K-NN model * Extract holidays from dates * Make a training/test split * Bundle a recipe and model * Is high in vitamin A * Compute R2 * Bin a predictor (but seriously,...don't) ] .pull-right[ * `workflows` * `yardstick` * `carrot` * `recipes` * `parsnip` * `rsample` * `ggvis` ]


[gecode-users] Re:gecode with linear programming
j.brongniart at laposte.net
j.brongniart at laposte.net
Tue Jun 20 09:11:24 CEST 2006
> On 6/19/06, j.brongniart at laposte.net
<j.brongniart at laposte.net> wrote:
> > Hi,
> >
> > First, sorry for my english...
> >
> > I have to implement a hybrid "Constraint Programming"/"Linéar
> > Programming" algorithm and I want to known if it exist such a
> > solution using gecode (Or maybe someone known a open-source
> > project doing that) ?
> >
thanks for your propositions, I look at that
Accédez au courrier électronique de La Poste : www.laposte.net
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['https://rickandmortyapi.com/api/character/23', 'https://rickandmortyapi.com/api/character/204', 'https://rickandmortyapi.com/api/character/320']


If you are a data science guy or girl, you'd know what machine learning is. However, this project is built for everyone inlcuding people from non-tech background. I wanted to make this project interactive so everyone can find it intiutive or 😉 less boring.
First, I'd like to give an overview about Titanic.
Read here ...


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SPAWN
Section: Maintenance Commands (8)Index Return to Main Contents
NAME
spawn - Postfix external command spawnerSYNOPSIS
spawn [generic Postfix daemon options] command_attributes...
DESCRIPTION
The spawn(8) daemon provides the Postfix equivalent of inetd. It listens on a port as specified in the Postfix master.cf file and spawns an external command whenever a connection is established. The connection can be made over local IPC (such as UNIX-domain sockets) or over non-local IPC (such as TCP sockets). The command's standard input, output and error streams are connected directly to the communication endpoint.This daemon expects to be run from the master(8) process manager.
COMMAND ATTRIBUTE SYNTAX
The external command attributes are given in the master.cf file at the end of a service definition. The syntax is as follows:
- user=username (required)
- user=username:groupname
- The external command is executed with the rights of the specified username. The software refuses to execute commands with root privileges, or with the privileges of the mail system owner. If groupname is specified, the corresponding group ID is used instead of the group ID of username.
- argv=command... (required)
- The command to be executed. This must be specified as the last command attribute. The command is executed directly, i.e. without interpretation of shell meta characters by a shell command interpreter.
BUGS
In order to enforce standard Postfix process resource controls, the spawn(8) daemon runs only one external command at a time. As such, it presents a noticeable overhead by wasting precious process resources. The spawn(8) daemon is expected to be replaced by a more structural solution.DIAGNOSTICS
The spawn(8) daemon reports abnormal child exits. Problems are logged to syslogd(8).SECURITY
This program needs root privilege in order to execute external commands as the specified user. It is therefore security sensitive. However the spawn(8) daemon does not talk to the external command and thus is not vulnerable to data-driven attacks.
CONFIGURATION PARAMETERS
Changes to main.cf are picked up automatically as spawn(8) processes run for only a limited amount of time. Use the command "postfix reload" to speed up a change.
The text below provides only a parameter summary. See postconf(5) for more details including examples.
In the text below, transport is the first field of the entry in the master.cf file.
RESOURCE AND RATE CONTROL
- transport_time_limit ($command_time_limit)
-
The amount of time the command is allowed to run before it is
terminated.
Postfix 2.4 and later support a suffix that specifies the time unit: s (seconds), m (minutes), h (hours), d (days), w (weeks). The default time unit is seconds.
MISCELLANEOUS
- config_directory (see 'postconf -d' output)
- The default location of the Postfix main.cf and master.cf configuration files.
- daemon_timeout (18000s)
- How much time a Postfix daemon process may take to handle a request before it is terminated by a built-in watchdog timer.
- export_environment (see 'postconf -d' output)
- The list of environment variables that a Postfix process will export to non-Postfix processes.
- ipc_timeout (3600s)
- The time limit for sending or receiving information over an internal communication channel.
- mail_owner (postfix)
- The UNIX system account that owns the Postfix queue and most Postfix daemon processes.
- max_idle (100s)
- The maximum amount of time that an idle Postfix daemon process waits for an incoming connection before terminating voluntarily.
- max_use (100)
- The maximal number of incoming connections that a Postfix daemon process will service before terminating voluntarily.
- process_id (read-only)
- The process ID of a Postfix command or daemon process.
- process_name (read-only)
- The process name of a Postfix command or daemon process.
- queue_directory (see 'postconf -d' output)
- The location of the Postfix top-level queue directory.
- syslog_facility (mail)
- The syslog facility of Postfix logging.
- syslog_name (see 'postconf -d' output)
- The mail system name that is prepended to the process name in syslog records, so that "smtpd" becomes, for example, "postfix/smtpd".
SEE ALSO
postconf(5), configuration parameters master(8), process manager syslogd(8), system logging
LICENSE
The Secure Mailer license must be distributed with this software.
AUTHOR(S)
Wietse Venema IBM T.J. Watson Research P.O. Box 704 Yorktown Heights, NY 10598, USA
Index
- NAME
- SYNOPSIS
- DESCRIPTION
- COMMAND ATTRIBUTE SYNTAX
- BUGS
- DIAGNOSTICS
- SECURITY
- CONFIGURATION PARAMETERS
- RESOURCE AND RATE CONTROL
- MISCELLANEOUS
- SEE ALSO
- LICENSE
- AUTHOR(S)
This document was created by man2html, using the manual pages.
Time: 05:34:30 GMT, December 24, 2015


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--- layout: archive-full permalink: /ietf2 regenerate: true hero-image: images/new-design/SR-Background-Image-2.png title: "IETF" type: "IETF" description: "Segment Routing is being standardized by the IETF. The architecture and use-cases are handled in the SPRING working group. Protocol extensions are handled in their specific protocol working group (ISIS, OSPF, IDR, PCEP, 6MAN)." --- {% include base_path %} {% assign articles = site.data.ietf2["list_rfcs"] %}


Ruby on Rails Guides Guidelines¶ ↑
This guide documents guidelines for writing Ruby on Rails Guides. This guide follows itself in a graceful loop, serving itself as an example.
After reading this guide, you will know:
-
About the conventions to be used in Rails documentation.
-
How to generate guides locally.
Markdown¶ ↑
Guides are written in GitHub Flavored Markdown. There is comprehensive documentation for Markdown, as well as a cheatsheet.
Prologue¶ ↑
Each guide should start with motivational text at the top (that's the little introduction in the blue area). The prologue should tell the reader what the guide is about, and what they will learn. As an example, see the Routing Guide.
Headings¶ ↑
The title of every guide uses an h1
heading; guide sections
use h2
headings; subsections use h3
headings;
etc. Note that the generated HTML output will use heading tags starting
with <h2>
.
Guide Title =========== Section ------- ### Sub Section
When writing headings, capitalize all words except for prepositions, conjunctions, internal articles, and forms of the verb “to be”:
#### Middleware Stack is an Array #### When are Objects Saved?
Use the same inline formatting as regular text:
##### The `:content_type` Option
API Documentation Guidelines¶ ↑
The guides and the API should be coherent and consistent where appropriate. In particular, these sections of the API Documentation Guidelines also apply to the guides:
HTML Guides¶ ↑
Before generating the guides, make sure that you have the latest version of Bundler installed on your system. As of this writing, you must install Bundler 1.3.5 on your device.
To install the latest version of Bundler, run gem install
bundler
.
Generation¶ ↑
To generate all the guides, just cd
into the
guides
directory, run bundle install
, and
execute:
bundle exec rake guides:generate
or
bundle exec rake guides:generate:html
To process my_guide.md
and nothing else use the
ONLY
environment variable:
touch my_guide.md bundle exec rake guides:generate ONLY=my_guide
By default, guides that have not been modified are not processed, so
ONLY
is rarely needed in practice.
To force processing all the guides, pass ALL=1
.
It is also recommended that you work with WARNINGS=1
. This
detects duplicate IDs and warns about broken internal links.
If you want to generate guides in a language other than English, you can
keep them in a separate directory under source
(eg.
source/es
) and use the GUIDES_LANGUAGE
environment variable:
bundle exec rake guides:generate GUIDES_LANGUAGE=es
If you want to see all the environment variables you can use to configure the generation script just run:
rake
Validation¶ ↑
Please validate the generated HTML with:
bundle exec rake guides:validate
Particularly, titles get an ID generated from their content and this often
leads to duplicates. Please set WARNINGS=1
when generating
guides to detect them. The warning messages suggest a solution.
Kindle Guides¶ ↑
Generation¶ ↑
To generate guides for the Kindle, use the following rake task:
bundle exec rake guides:generate:kindle


If you think adventure is dangerous, try routine, it's lethal
Completed courses:
Programming Basics with C#
Programming Fundamentals
Software Technologies
C# Advanced
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DB Basics - MS SQL
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ReactJs


{% extends "base.html" %}{% load i18n %} {% block title %}Forums: Home{% endblock %} {% block content %} The Best Forums Get your discussion on.
Get your discussion on.
This is the home page


"Point light" fragment shader.

- Parameters
-
| NdotH | angle between the half and normal directions |
| alpha | the roughness squared |
- Returns
- the distribution term
◆ F()
| vec3 GLSL::Frag::Point_light::F |
( |
vec3 |
F0, |
|
|
float |
VdotH |
|
) |
| |
|
inline |
Fresnel approximation.
- Parameters
-
| F0 | fresnel based coefficient |
| VdotH | angle between the half and view directions |
- Returns
- the Fresnel term
◆ G()
| float GLSL::Frag::Point_light::G |
( |
float |
NdotL, |
|
|
float |
NdotV, |
|
|
float |
alpha |
|
) |
| |
|
inline |
Geometric term of GGX BRDF, G.
- Parameters
-
| NdotL | dot product of the light direction with the surface normal |
| NdotV | dot product of the view direction with the surface normal |
| alpha | squared roughness |
- Returns
- the value of G
◆ G1()
| float GLSL::Frag::Point_light::G1 |
( |
float |
NdotX, |
|
|
float |
halfAlpha |
|
) |
| |
|
inline |
Geometric half-term of GGX BRDF.
- Parameters
-
| NdotX | dot product of either the light or the view direction with the surface normal |
| halfAlpha | half squared roughness |
- Returns
- the value of the half-term
◆ ggx()
| vec3 GLSL::Frag::Point_light::ggx |
( |
vec3 |
n, |
|
|
vec3 |
v, |
|
|
vec3 |
l, |
|
|
vec3 |
F0, |
|
|
float |
roughness |
|
) |
| |
|
inline |
Evaluate the GGX BRDF for a given normal, view direction and material parameters.
- Parameters
-
| n | the surface normal |
| v | the view direction |
| l | the light direction |
| F0 | the Fresnel coefficient |
| roughness | the surface roughness |
- Returns
- the BRDF value
◆ main()
| void GLSL::Frag::Point_light::main |
( |
| ) |
|
|
inline |
Compute the lighting contribution of a point light using the GGX BRDF.
◆ positionFromDepth()
| vec3 GLSL::Frag::Point_light::positionFromDepth |
( |
float |
depth, |
|
|
vec2 |
uv |
|
) |
| |
|
inline |
Estimate the position of the current fragment in view space based on its depth and camera parameters.
- Parameters
-
| depth | the depth of the fragment |
| uv | the uv coordinates of the fragment |
- Returns
- the view space position
◆ shadow()
| float GLSL::Frag::Point_light::shadow |
( |
vec3 |
lightToPosDir | ) |
|
|
inline |
Compute the shadow multiplicator based on shadow map.
- Parameters
-
| lightToPosDir | direction from the light to the fragment position, in world space. |
- Returns
- the shadowing factor
The documentation for this class was generated from the following file:
- resources/common/shaders/lights/point_light.frag


--- layout: page title: About header-img: "img/about-bg.png" ---
M. is enrolled in Flatiron’s part time Full-Stack Engineer program. Their background is in Microbiology and Spanish. When not practicing coding they enjoy reading, taking long walks in the woods, and cuddling their 80 pound lap dog.


Martin Scorsese's "The Age of Innocence" did not sweep at the Oscars back in 1994 as I had expected. "Schindler's List" and "The Piano" stole some of its thunder, not to mention the similar tale of repression, "The Remains of the Day." This film was also a major departure for Scorsese, who is known mostly for the whirling intensity of "Mean Streets" and "GoodFellas."  Good question, yet Scorsese has proven to be diverse in the past, from filming concert footage of the Band to dealing with a feminist heroine like Alice from "Alice Doesn't Live Here Anymore." "The Age of Innocence" is ironically among Scorsese's greatest films, a sumptuous, delicate tale of repression and repressed emotional violence.
Daniel Day-Lewis stars as a New York lawyer, Newland Archer, who romantically yearns for the sexy, open-hearted Countess Olenska (Michelle Pfeiffer) despite his plans to marry her cousin, the childlike, innocent May Welland (Winona Ryder). But problems arise such as Olenska's unsettled scandalous divorce, and Newland's inability to cope with his deep feelings because of the strict class order of practically all of New York. People seem to repress their feelings because of fear of being ousted from family and friends - Olenska comes dangerously close to being one of these people. As a tearful Olenska says in one scene, "Does nobody want to hear the truth Mr. Archer? Everyone asks you to pretend."  I suppose there is no need to."
I wasn't sure how Scorsese would direct this tale, or why he wanted to do it. This is a director who seems to deal with characters that let go of their emotions rather than keeping them bottled up. A tale of this kind is often handled by the Merchant Ivory production team or David Lean. I think it is finally the elements of tragic love, repressed feelings, and internal emotional violence that attracted Scorsese to the project, and he fuses these elements flawlessly. There are the minute, carefully chosen details such as the three-course dinners, manners of etiquette, and paintings that illustrate the bravado of certain characters, such as Beaufort (Stuart Wilson), a playboy that shames the family - his selection of nude paintings directly reflects his character. Not to mention the grandly ostentatious gossip-mongerer Mrs. Mingott (Miriam Margoyles), and her plethora of paintings of dogs and a savage "Last of the Mohicans" painting.
Scorsese brings this world alive as he did with the world of gangsters in "GoodFellas" - you almost feel as if you went back in time to a more innocent era. The cinematography by Michael Ballahaus captures every single nuance and is particularly attentive to subtle details, even in human behavior. There are throwaway moments that capture glimpses of character, such as May Welland making a quick glance at Newland when he says his goodbyes to Countess Olenska at Mrs. Mingott's house. There is also the tender, touching, underplayed scene where Newland is told by his son that May knew all along about his love for the Countess. Any other director might have played up the symphonic score or used distracting close-ups, but instead Scorsese films it in one long take and as a two-shot. Less is definitely more in terms of finding the right visual cues for this story.
The actors are all perfect and understated, probably more than they ever will be. Daniel Day-Lewis astutely captures Newland's longing and growing sense of desperation for what he cannot have. Michelle Pfeiffer is both sensual and far more pragmatic than at the onset - she magnificently captures Olenska's frail side and her need to be accepted, though her behavior is unconventional. But the biggest surprise is Winona Ryder, capturing the innocence of the title - the seemingly naive May Welland who provides the emotional center. Her frozen smile of recognition is haunting in the film, suggesting that she is far more knowledgeable of her surroundings than she lets on. There are also colorful supporting turns by the aforementioned Miriam Margoyles, Richard E. Grant as the sarcastic Larry Lefferts, Alec McGowen as the expert on gossip regarding all the families, and Michael Gough as the important head of the van der Luyden family, who orchestrate a formal dinner to matriculate Ole! nska into society.
There is so much to love and take in from this film that you have to see it more than once. See it once for the beautiful settings and the extraordinary camerawork, and the second time for the finely tuned acting and the emotions that threaten to explode in every one of the characters.
For more reviews, check out JERRY AT THE MOVIES at http://buffs.moviething.com/buffs/faust/
E-mail me with any questions, comments or complaints at<EMAIL_ADDRESS>or at<EMAIL_ADDRESS>The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
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The Company is committed to safeguarding personal privacy. It recognizes that individuals have a right to control how their personal information is collected and used. Providing personal information is an act of trust and it is taken seriously. Unless given consent to do otherwise, the Company will only collect and use personal information as set out below.
The Company will not collect or monitor any personal information about an individual without their consent. The only personal information collected is what has been provided voluntarily.
The Company uses tracking technologies such as cookies or web beacons to make use of the website and services as convenient as possible. Cookies are pieces of information that a web site transfers to a computer's hard disk for record keeping purposes. Most web browsers are set to accept tracking technologies such as cookies or web beacons. These tracking technologies do not themselves personally identify users, although they do identify a user's browser. 4. Using and disclosing your personal information:
Personal Information will be used for the following primary purpose:
- To fulfill obligations under any sale and purchase contract and/or any other contract between the individual and the Company.
- To render services related to Company's business such as warranty or after sales services.
For the purpose described above, information may be shared with Company's group companies either in Australia or overseas. Also, in order to operate the web site or deliver a service, personal information may also be shared with a service provider, a non-Company group company.
The Company may contact individuals using the information, which was provided by them in order to:
- Provide information that may be of interest about upgrades, new Company products, special offers and other matters that may be of interest.
- To send newsletters.
Individuals have the right to review the information that may be recorded on the Company's database. Information may be reviewed by contacting the Company .
The Company provides links to web sites outside of the Company site. These linked sites are not under the control of Company, and the Company is not responsible for the conduct of companies linked to the Company web site, nor for the performance or otherwise of any content and/or software contained in such external websites.
Queries relating to the Privacy Policy, or any problems or complaints may be directed to the Personal Information Officer by calling the customer enquiry number [Number].


"With each bottle of Alex + Keiths, we put immense care into the user experience, tailoring the flavours to be the perfect complement to relaxing after a hard day's work." - Randy Blevins (CEO)
Starting with the iconic Alex + Keiths bottle, we use the sand from the Halifax beaches that we later smelt down into to be molded. After the bottle is done, the cap is shipped in from Nunavut.
Starting with the iconic Alex + Keiths bottle, we use the sand from the famous Halifax beaches that is later smelted down by skilled engineers into the glass material to be molded in a warehouse. After the bottle is done, the cap is shipped in from Nunavut.