class: center, middle, inverse, title-slide # Recipes for Data Processing ### Max Kuhn (RStudio) --- # `recipes` and Other Modeling Packages .pull-left[ `recipes` is part of a growing collection of R packages that use the tenets of the [tidyverse](http://www.tidyverse.org/): 1. Reuse existing data structures. 1. Compose simple functions with the pipe. 1. Embrace functional programming. 1. Design for humans. This approach is exemplified by packages such as: [`broom`](https://cran.r-project.org/package=broom), [`infer`](https://cran.r-project.org/package=infer), [`rsample`](https://tidymodels.github.io/rsample/), [`recipes`](https://tidymodels.github.io/recipes/), [`tidyposterior`](https://tidymodels.github.io/tidyposterior/), [`tidytext`](https://cran.r-project.org/package=tidytext), and [`yardstick`](https://tidymodels.github.io/yardstick/). The list of packages in the `tidymodels` org continues to grow. ] .pull-right[ The more _traditional approach_ uses high-level syntax and is perhaps the most untidy code that you will encounter. [`caret`](https://tidymodels.github.io/caret) is the primary package for _highly untidy_ predictive modeling: 1. More traditional R coding style. 1. High-level "I'll do that for you" syntax. 1. More comprehensive (for now) and less modular. 1. Contains many optimizations and is easily parallelized. Luckily, `recipes` can work with both approaches. ] --- # Example Data Set - House Prices For regression problems, we will use the Ames IA housing data. There are 2,930 properties in the data. The sale price was recorded along with 81 predictors, including: * Location (e.g. neighborhood) and lot information. * House components (garage, fireplace, pool, porch, etc.). * General assessments such as overall quality and condition. * Number of bedrooms, baths, and so on. More details can be found in [De Cock (2011, Journal of Statistics Education)](http://ww2.amstat.org/publications/jse/v19n3/decock.pdf). The raw data are at [`http://bit.ly/2whgsQM`](http://bit.ly/2whgsQM) but we will use a processed version found in the [`AmesHousing`](https://github.com/topepo/AmesHousing) package. --- # Example Data Set - House Prices <div id="htmlwidget-632d3428812d0cda0bd5" style="width:80%;height:480px;" class="leaflet html-widget"></div> <script type="application/json" 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--- # Tidyverse Syntax <img src="images/dplyr.png" class="title-hex"> Many tidyverse functions have syntax unlike base R code. For example: * vectors of variable names are eschewed in favor of _functional programming_. For example: ```r contains("Sepal") # instead of c("Sepal.Width", "Sepal.Length") ``` * The _pipe_ operator is preferred. For example ```r merged <- inner_join(a, b) # is equal to merged <- a %>% inner_join(b) ``` * Functions are more _modular_ than their traditional analogs (`dplyr`'s `filter` and `select` vs `base::subset`) --- # Some Example Data Manipulation Code <img src="images/dplyr.png" class="title-hex"><img src="images/readr.png" class="title-hex"> ```r library(tidyverse) ames <- read_delim("http://bit.ly/2whgsQM", delim = "\t") %>% rename_at(vars(contains(' ')), funs(gsub(' ', '_', .))) %>% rename(Sale_Price = SalePrice) %>% filter(!is.na(Electrical)) %>% select(-Order, -PID, -Garage_Yr_Blt) ames %>% group_by(Alley) %>% summarize(mean_price = mean(Sale_Price/1000), n = sum(!is.na(Sale_Price))) ``` ``` ## # A tibble: 3 x 3 ## Alley mean_price n ## <chr> <dbl> <int> ## 1 Grvl 124. 120 ## 2 Pave 177. 78 ## 3 <NA> 183. 2731 ``` --- # Example `ggplot2` Code <img src="images/ggplot2.png" class="title-hex"> .pull-left[ ```r library(ggplot2) ggplot(ames, aes(x = Garage_Type, y = Sale_Price)) + geom_violin() + coord_trans(y = "log10") + xlab("Garage Type") + ylab("Sale Price") ``` ] .pull-left[ <img src="Recipes_for_Data_Processing_files/figure-html/ggplot - example - disp-1.svg" width="100%" style="display: block; margin: auto;" /> ] --- # Examples of `purrr::map*` <img src="images/dplyr.png" class="title-hex"><img src="images/purrr.png" class="title-hex"> .pull-left[ ```r library(purrr) # summarize via purrr::map by_alley <- split(ames, ames$Alley) is_list(by_alley) ``` ``` ## [1] TRUE ``` ```r map(by_alley, nrow) ``` ``` ## $Grvl ## [1] 120 ## ## $Pave ## [1] 78 ``` ] .pull-right[ ```r # or better yet: map_int(by_alley, nrow) ``` ``` ## Grvl Pave ## 120 78 ``` ```r # works on non-list vectors too ames %>% mutate(Sale_Price = Sale_Price %>% map_dbl(function(x) x / 1000)) %>% select(Sale_Price, Yr_Sold) %>% head(4) ``` ``` ## # A tibble: 4 x 2 ## Sale_Price Yr_Sold ## <dbl> <int> ## 1 215 2010 ## 2 105 2010 ## 3 172 2010 ## 4 244 2010 ``` ] # 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), etc. 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 an 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 or the week can be very effective for modeling public transportation 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.) --- # A Bivariate Example .pull-left[ .font80[ The plot on the right shows two predictors from a real _test_ set where the object 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[ <img src="Recipes_for_Data_Processing_files/figure-html/bivariate-plot-natural-1.svg" width="90%" style="display: block; margin: auto;" /> ] ??? 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[ .font80[ 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[ <img src="Recipes_for_Data_Processing_files/figure-html/bivariate-plot-inverse-1.svg" width="90%" style="display: block; margin: auto;" /> ] ??? 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. --- layout: false class: inverse, middle, center # Preprocessing Categorical Predictors (Chapter [Five](https://bookdown.org/max/FES/encoding-categorical-predictors.html)) --- # Ames Data The `AmesHousing` package has a better version of the data that has been cleaned up and includes geocodes for the properties. Let's load that and use the `rsample` package to make a split of the data where 3/4 goes into training set: ```r library(AmesHousing) ames <- make_ames() nrow(ames) ``` ``` ## [1] 2930 ``` ```r library(rsample) # Make sure that you get the same random numbers set.seed(4595) data_split <- initial_split(ames, strata = "Sale_Price") ames_train <- training(data_split) ames_test <- testing(data_split) ``` --- # 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 zero for a level and one otherwise: <table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;"> <thead> <tr> <th style="border-bottom:hidden; padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="1"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px;">Data</div></th> <th style="border-bottom:hidden; padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #ddd; padding-bottom: 5px;">Dummy Variables</div></th> </tr> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> No_Alley_Access </th> <th style="text-align:right;"> Paved </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> Gravel </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> </tr> <tr> <td style="text-align:left;"> No_Alley_Access </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 0 </td> </tr> <tr> <td style="text-align:left;"> Paved </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 1 </td> </tr> </tbody> </table> --- # Dummy Variables If there are _C_ levels of the factor, only _C_-1 dummy variables area created since the last can be inferred from the others. There are different contrast schemes for creating the new variables. For ordered factors, [_polynomial_ contrasts](https://bookdown.org/max/FES/encoding-categorical-predictors.html#encodings-for-ordered-data) are used. How do you create them in R? The formula method does this for you¹. Otherwise, the traditional method is to use the `model.matrix` function 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::randomForest`, `ranger::ranger`, `rpart::rpart`, `C50::C5.0`, `Cubist::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[ <img src="Recipes_for_Data_Processing_files/figure-html/ames-hood-1.svg" width="100%" style="display: block; margin: auto;" /> ] ??? 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. For 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 doing either of these. --- # Other Approaches .pull-left[ .font90[ A few other approaches that might help here: * _effect_ or _likelihood encodings_ of categorical predictors estimate the mean effect of the outcome for every factor level in the predictor. These estimates are used in place of the factor levels. Shrinkage/regularization can improve these approaches. * _entity embeddings_ use a neural network to create features that capture the relationships between the categories and the categories and the outcome. An addd-on to `recipes` called `embed` can be used for these encodings. ] ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/embed-plot-1.svg" width="90%" style="display: block; margin: auto;" /> ] --- layout: false class: inverse, middle, center # Creating Recipes --- # Recipes <img src="images/recipes.png" class="title-hex"> 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. Suppose we use the formula `log10(Sale_Price) ~ Longitude + Latitude`? These steps are: * Assign `Sale_Price` to be the outcome * Assign `Longitude` and `Latitude` are predictors * Log transform the outcome To start using a recipe, the these steps can be done using ```r library(recipes) mod_rec <- recipe(Sale_Price ~ Longitude + Latitude, data = ames_train) %>% step_log(Sale_Price, base = 10) ``` This creates the recipe for data processing (but does not execute it yet) --- # Recipes and Categorical Predictors <img src="images/recipes.png" class="title-hex"> To deal with the dummy variable issue, we can expand the recipe with more steps: ```r mod_rec <- recipe(Sale_Price ~ Longitude + Latitude + Neighborhood, data = ames_train) %>% step_log(Sale_Price, base = 10) %>% # 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()) ``` 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()`). The general process for using recipes is .font120[ ``` recipe --> prep() --> bake/juice (define) --> (estimate) --> (apply) ``` ] --- # Preparing the Recipe <img src="images/recipes.png" class="title-hex"> 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, retain = TRUE, verbose = TRUE) ``` ``` ## oper 1 step log [training] ## oper 2 step other [training] ## oper 3 step dummy [training] ``` Here, the "training" is to determine which factors to pool and to enumerate the factor levels of the `Neighborhood` variable, `retain` keeps the processed version of the training set around so we don't have to recompute it. --- # 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: ## ## Log transformation on Sale_Price [trained] ## Collapsing factor levels for Neighborhood [trained] ## Dummy variables from Neighborhood [trained] ``` --- # Getting the Values <img src="images/recipes.png" class="title-hex"> Once the recipe is prepared, it can be applied to any data set using `bake`: ```r ames_test_dummies <- bake(mod_rec_trained,newdata = ames_test) names(ames_test_dummies) ``` ``` ## [1] "Sale_Price" "Longitude" "Latitude" ## [4] "Neighborhood_College_Creek" "Neighborhood_Old_Town" "Neighborhood_Edwards" ## [7] "Neighborhood_Somerset" "Neighborhood_Northridge_Heights" "Neighborhood_Gilbert" ## [10] "Neighborhood_Sawyer" "Neighborhood_other" ``` If `retain = TRUE` the training set does not need to be "rebaked". The `juice` function can return the processed version of the training data. Selectors can be used with `bake` and the default is `everything()`. --- layout: false class: inverse, middle, center # Interaction Effects --- # Interactions An interactions 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) ggplot(ames_train, aes(x = Year_Built, y = Sale_Price)) + geom_point(alpha = 0.4) + scale_x_log10() + scale_y_continuous(breaks = price_breaks, trans = "log10") + geom_smooth(method = "loess") ``` ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/year-built-plot-1.svg" width="90%" style="display: block; margin: auto;" /> ] --- # Interactions However... what if we seperate this trend based on whether the property has air conditioning (93.4% of the training set) or not (6.6%): .pull-left[ ```r library(MASS) # to get robust linear regression model ggplot(ames_train, aes(x = Year_Built, y = Sale_Price)) + geom_point(alpha = 0.4) + scale_y_continuous(breaks = price_breaks, trans = "log10") + facet_wrap(~ Central_Air, nrow = 2) + geom_smooth(method = "rlm") ``` ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/year-built-ac-plot-1.svg" width="100%" style="display: block; margin: auto;" /> ] --- # 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 as 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(log10(Sale_Price) ~ Year_Built + Central_Air, data = ames_train) mod2 <- lm(log10(Sale_Price) ~ Year_Built + Central_Air + Year_Built: Central_Air, data = ames_train) anova(mod1, mod2) ``` ``` ## Analysis of Variance Table ## ## Model 1: log10(Sale_Price) ~ Year_Built + Central_Air ## Model 2: log10(Sale_Price) ~ Year_Built + Central_Air + Year_Built:Central_Air ## Res.Df RSS Df Sum of Sq F Pr(>F) ## 1 2196 41.3 ## 2 2195 40.2 1 1.11 60.6 1.1e-14 *** ## --- ## 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 recipe(Sale_Price ~ Year_Built + Central_Air, data = ames_train) %>% step_log(Sale_Price) %>% step_dummy(Central_Air) %>% step_interact(~ starts_with("Central_Air"):Year_Built) %>% prep(training = ames_train, retain = TRUE) %>% 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 1912 12.0 1 1912 ## 2 1930 10.9 0 0 ## 3 1900 11.8 1 1900 ## 4 1959 12.1 1 1959 ## 5 1917 11.6 0 0 ``` --- layout: false class: inverse, middle, center # Adding Recipes to our `rsample` Workflows --- # Resampling Methods .pull-left[ These are [additional data splitting schemes](https://bookdown.org/max/FES/review-predictive-modeling-process.html#resampling) that are applied to the _training_ set. They attempt to simulate slightly different versions of the training set. These versions of the original are split into two model subsets: * The _analysis set_ is used to fit the model (analogous to the training set). * Performance is determined using the _assessment set_. This process is repeated many times. There are different flavors or resampling but we will focus on two methods. ] .pull-right[ <div id="htmlwidget-aef1462446d83cd57e74" style="width:100%;height:480px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-aef1462446d83cd57e74">{"x":{"diagram":"\ndigraph resampling_diag {\n \ngraph [layout = dot,bgcolor = transparent]\n\nnode [fontname = Helvetica]\n\nall [shape = circle,\n label = \"All\nData\"]\n\nte [shape = circle,\n style = filled,\n label = \"Testing\",\n fillcolor = \"#eeeeb4\"]\n\ntr [shape = circle,\n style = filled,\n label = \"Training\",\n fillcolor = \"#c8d8c2\"]\n\nr1 [shape = rectangle,\n label = \"Resample 1\"]\n\nan1 [shape = oval,\n style = filled,\n label = \"Analysis\",\n fillcolor = honeydew]\nas1 [shape = oval,\n style = filled,\n label = \"Assessment\",\n fillcolor = ivory]\n\nr2 [shape = rectangle,\n label = \"Resample 2\"]\n \nan2 [shape = oval,\n style = filled,\n label = \"Analysis\",\n fillcolor = honeydew]\n\nas2 [shape = oval,\n style = filled,\n label = \"Assessment\",\n fillcolor = ivory]\n\nr3 [shape = rectangle,\n label = \"Resample 3\"]\n \nan3 [shape = oval,\n style = filled,\n label = \"Analysis\",\n fillcolor = honeydew]\nas3 [shape = oval,\n style = filled,\n label = \"Assessment\",\n fillcolor = ivory]\n\nall -> {tr te }\ntr -> {r1 r2 r3 }\nr1 -> {as1 an1 }\nr2 -> {an2 as2 }\nr3 -> {an3 as3 }\n}\n","config":{"engine":"dot","options":{"width":"100%"}}},"evals":[],"jsHooks":[]}</script> ] --- # V-Fold Cross-Validation Here, we randomly split the training data into _V_ distinct blocks of roughly equal size. * We leave out the first block of analysis data and fit a model. * This model is used to predict the held-out block of assessment data. * We continue this process until we've predicted all _V_ assessment blocks The final performance is based on the hold-out predictions by _averaging_ the statistics from the _V_ blocks. _V_ is usually taken to be 5 or 10 and leave one out cross-validation has each sample as a block. --- # 10-Fold Cross-Validation with _n_ = 50 <img src="Recipes_for_Data_Processing_files/figure-html/cv-plot-1.svg" width="60%" style="display: block; margin: auto;" /> --- # Resampling and Preprocessing It is important to realize that almost all preprocessing steps that involve estimation should be bundled inside of the resampling process so that the performance estimates are not biased. * **Bad**: preprocess the data, resample the model * **Good**: resample the preprocessing and modeling Also: * Avoid _information leakage_ by having all operations in the modeling process occur only on the training set. * Do not reestimate anything on the test set. For example, to center new data, the training set mean is used. --- # `recipes` and `rsample` <img src="images/recipes.png" class="title-hex"><img src="images/rsample.png" class="title-hex"> Let's go back to the Ames housing data and work on building models with recipes and resampling. We'll do a 3/4 split of the data with the majority going into the training set. For resampling, 10-fold CV would leave out about 219 houses (which should be enough to compute the RMSE). .pull-left[ ```r set.seed(2453) cv_splits <- vfold_cv(ames_train, v = 10, strata = "Sale_Price") cv_splits[1:3,] ``` ``` ## # A tibble: 3 x 2 ## splits id ## * <list> <chr> ## 1 <S3: rsplit> Fold01 ## 2 <S3: rsplit> Fold02 ## 3 <S3: rsplit> Fold03 ``` ] .pull-right[ ```r cv_splits$splits[[1]] ``` ``` ## <1977/222/2199> ``` ```r cv_splits$splits[[1]] %>% analysis() %>% nrow() ``` ``` ## [1] 1977 ``` ```r cv_splits$splits[[1]] %>% assessment() %>% nrow() ``` ``` ## [1] 222 ``` ] --- # Linear Models <img src="images/recipes.png" class="title-hex"> .font80[ Let's preprocess the traning set prior to adding the data to a linear regression model. * Two numeric predictors are very skewed and could use a transformation (`Lot_Area` and `Gr_Liv_Area`). * We'll add neighborhood in as well and a few other house features. * Visualizations suggest that the coordinates can be helpful but probably require a nonlinear representation. We can add these using [_B-splines_](https://bookdown.org/max/FES/engineering-numeric-predictors.html#numeric-basis-functions) with 5 degrees of freedom. To evaluate this, we will create two versions of the recipe to evaluate this hypothesis. ] ```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_log(Sale_Price, base = 10) %>% step_YeoJohnson(Lot_Area, Gr_Liv_Area) %>% step_other(Neighborhood, threshold = 0.05) %>% step_dummy(all_nominal()) %>% step_interact(~ starts_with("Central_Air"):Year_Built) %>% step_bs(Longitude, Latitude, options = list(df = 5)) ``` --- # Longitude <img src="images/ggplot2.png" class="title-hex"> .pull-left[ ```r library(ggplot2) 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 ) + scale_y_log10() ``` Splines add nonlinear versions of the predictor to a linear model to create smooth and flexible relationships between the predictor and outcome. ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/longitude-1.svg" width="100%" style="display: block; margin: auto;" /> ] --- # Latitude <img src="images/ggplot2.png" class="title-hex"> .pull-left[ ```r ggplot(ames_train, aes(x = Latitude, y = Sale_Price)) + geom_point(alpha = .5) + geom_smooth( method = "lm", formula = y ~ splines::bs(x, 5), se = FALSE ) + scale_y_log10() ``` ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/latitude-1.svg" width="100%" style="display: block; margin: auto;" /> ] --- # Preparing the Recipes <img src="images/purrr.png" class="title-hex"><img src="images/recipes.png" class="title-hex"> Our first step is the run `prep()` on the `ames_rec` recipe but using each of the analysis sets. `rsample` has a function that is a wrapper around `prep()` that can be used to map over the split objects: ```r prepper ``` ``` ## function (split_obj, recipe, ...) ## { ## prep(recipe, training = analysis(split_obj), ...) ## } ## <bytecode: 0x7f80df049348> ## <environment: namespace:rsample> ``` ```r library(purrr) cv_splits <- cv_splits %>% mutate(ames_rec = map(splits, prepper, recipe = ames_rec, retain = TRUE)) ``` --- # Fitting the Models <img src="images/broom.png" class="title-hex"><img src="images/purrr.png" class="title-hex"><img src="images/recipes.png" class="title-hex"> The code below will use the recipe object to get the data. Since each analysis set is used to train the recipe, our previous use of `retain = TRUE` means that the processed version of the data is within the recipe. This can be returned via the `juice` function. ```r lm_fit_rec <- function(rec_obj, ...) lm(..., data = juice(rec_obj)) cv_splits <- cv_splits %>% mutate(fits = map(ames_rec, lm_fit_rec, Sale_Price ~ .)) library(broom) glance(cv_splits$fits[[1]]) ``` ``` ## r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual ## 1 0.805 0.802 0.0794 276 0 30 2218 -4374 -4200 12.3 1947 ``` --- # Predicting the Assessment Set <img src="images/recipes.png" class="title-hex"><img src="images/rsample.png" class="title-hex"> This is a little more complex. We need three elements contained in our tibble: * the split object (to get the assessment data) * the recipe object (to process the data) * the linear model (for predictions) The function is not too bad: ```r assess_predictions <- function(split_obj, rec_obj, mod_obj) { raw_data <- assessment(split_obj) proc_x <- bake(rec_obj, newdata = raw_data, all_predictors()) # Now save _all_ of the columns and add predictions. bake(rec_obj, newdata = raw_data, everything()) %>% mutate( .fitted = predict(mod_obj, newdata = proc_x), .resid = Sale_Price - .fitted, # Sale_Price is already logged by the recipe # Save the original row number of the data .row = as.integer(split_obj, data = "assessment") ) } ``` --- # Predicting the Assessment Set <img src="images/purrr.png" class="title-hex"> Since we have three inputs, we will use `purrr`'s `pmap` function to walk along all three columns in the tibble. ```r cv_splits <- cv_splits %>% mutate( pred = pmap( lst(split_obj = cv_splits$splits, rec_obj = cv_splits$ames_rec, mod_obj = cv_splits$fits), assess_predictions ) ) ``` We do get some warnings that the assessment data are outside the range of the analysis set values: ``` ## Warning in bs(x = c(-93.6235954, -93.636372, -93.627536, -93.65332, ## -93.649447, : some 'x' values beyond boundary knots may cause ill- ## conditioned bases ``` --- # Predicting the Assessment Set <img src="images/yardstick.png" class="title-hex"><img src="images/purrr.png" class="title-hex"> `yardstick::metrics` will compute a small set of summary statistics for metrics model based on the type of outcome (e.g. regression, classification, etc). ```r library(yardstick) # Compute the summary statistics map_df(cv_splits$pred, metrics, truth = Sale_Price, estimate = .fitted) %>% colMeans ``` ``` ## rmse rsq mae ## 0.0798 0.8005 0.0569 ``` These results are good but "_the only way to be comfortable with your results is to never look at them_". --- # Graphical Checks for Fit <img src="images/dplyr.png" class="title-hex"><img src="images/ggplot2.png" class="title-hex"> .pull-left[ ```r assess_pred <- bind_rows(cv_splits$pred) %>% mutate(Sale_Price = 10^Sale_Price, .fitted = 10^.fitted) ggplot(assess_pred, aes(x = Sale_Price, y = .fitted)) + geom_abline(lty = 2) + geom_point(alpha = .4) + geom_smooth(se = FALSE, col = "red") ``` ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/lm-obs-pred-show-1.svg" width="80%" style="display: block; margin: auto;" /> ] --- # `caret` and `recipes` To facilitate model tuning and other conveniences, `recipes` can be used as inputs into `train` (and, soon, the various feature selection routines). This allows for: * more extensive feature engineering and preprocessing tools. * the ability to estimate performance using columns in the data set. (Unfortunately, the recipe parameters can't be included as part of the tuning process.) The general syntax is ```r train(recipe, data, method, ...) ``` We'll use a _K_-nearest neighbors model to illustrate. --- # 8-Nearest Neighbors (Geographically) <div id="htmlwidget-056a6f4f6290e4fd42b1" style="width:100%;height:480px;" class="leaflet html-widget"></div> <script type="application/json" 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--- # Recipe for a K-NN Model Since a _distance_ will be computed, we'll need to add two intermediary steps that puts the predictors on the same scale: ```r ames_rec_norm <- 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_log(Sale_Price, base = 10) %>% step_YeoJohnson(Lot_Area, Gr_Liv_Area) %>% step_other(Neighborhood, threshold = 0.05) %>% step_dummy(all_nominal()) %>% step_center(all_predictors()) %>% step_scale(all_predictors()) %>% step_interact(~ starts_with("Central_Air"):Year_Built) %>% step_bs(Longitude, Latitude, options = list(df = 5)) ``` We will tune the model over the number of neighbors as well as how to weight the distances to the neighbors. --- # K-NN Model Code .pull-left[ ```r converted_resamples <- rsample2caret(cv_splits) ctrl <- trainControl(method = "cv", savePredictions = "final") ctrl$index <- converted_resamples$index ctrl$indexOut <- converted_resamples$indexOut knn_grid <- expand.grid( kmax = 1:9, distance = 2, kernel = c("rectangular", "triangular", "gaussian") ) knn_fit <- train( ames_rec_norm, data = ames_train, method = "kknn", tuneGrid = knn_grid, trControl = ctrl ) ``` ] .pull-right[ <br> `<=` Standardize the resamples format to go between `rsample` and `caret` <br> <br> `<=` Define the grid of parameters to tune over. <br> <br> `<=` Fit the model ] --- # K-NN Model .pull-left[ ```r ggplot(knn_fit) ``` ```r getTrainPerf(knn_fit) ``` ``` ## TrainRMSE TrainRsquared TrainMAE method ## 1 0.0809 0.794 0.0571 kknn ``` ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/ames-hood-show-1.svg" width="100%" style="display: block; margin: auto;" /> ] --- # Graphical Check for Fit <img src="images/dplyr.png" class="title-hex"><img src="images/ggplot2.png" class="title-hex"> .pull-left[ ```r knn_pred <- knn_fit$pred %>% mutate(Sale_Price = 10^obs, .fitted = 10^pred) ggplot(knn_pred, aes(x = Sale_Price, y = .fitted)) + geom_abline(lty = 2) + geom_point(alpha = .4) + geom_smooth(se = FALSE, col = "red") ``` ] .pull-right[ <img src="Recipes_for_Data_Processing_files/figure-html/knn-obs-pred-show-1.svg" width="80%" style="display: block; margin: auto;" /> ] --- # About Some of These Houses .font90[ From Dmytro Perepolkin via [`GitHub/topepo/AmesHousing`](https://github.com/topepo/AmesHousing/issues/2#issuecomment-351005269): > I did a little bit of research on [Kaggle](https://www.kaggle.com/c/house-prices-advanced-regression-techniques/discussion/23919) regarding those five houses (three "partial sale" houses in Edwards and two upscale in Northridge): >> _In fact all three of Edwards properties were sold within three months by the same company. The lots are located next to each other in Cochrane Pkwy Ames, IA. I guess the story was that developer was either in trouble or wanted to boost sales, so they were signing sales contracts on half-finished houses in a new development area at a deep discount. Those few houses are likely to have been built first out of the whole residential block that followed._ >> _Two of the upscale houses in Northridge (sold at 745 and 755 thousand, respectively) are located next to each other. Houses are, of course, eyecandies (at least to my taste). They are outliers with regards to size in their own neighborhoods!_ ] Sometimes it really pays off to be a [forensic](http://www.nytimes.com/2011/07/08/health/research/08genes.html) [statistician](https://projecteuclid.org/euclid.aoas/1267453942).