Neural Networks and Machine Learning in R
R Source Code by Leonid Shpaner
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# load the requisite libraries pack <- function(lib){ new.lib <- lib[!(lib %in% installed.packages()[, 'Package'])] if (length(new.lib)) install.packages(new.lib, dependencies = TRUE) sapply(lib, require, character.only = TRUE) } # neuralnet for neural networks, corrplot and caret for correlations # caTools for train_test split, and ggplot for plotting packages <- c('neuralnet', 'corrplot', 'caret', 'caTools', 'ggplot2', 'ggpubr', 'cowplot', 'h2o', 'lime', 'pander', 'DT') pack(packages) getwd() # establish current working directory # set new working directory working_dir = paste('C:/Users/lshpaner/OneDrive/Cornell University/Coursework/', 'Data Science Certificate Program/', 'CEEM586 - Neural Networks and Machine Learning/', sep = '') setwd(working_dir) # Read in the data election <- read.csv(paste('https://raw.githubusercontent.com/lshpaner/', 'CEEM586_Neural_Networks_and_ML/main/data/', 'ElectionData.csv', sep = ''), row.names = 1, header = TRUE, stringsAsFactors = FALSE) # remove index column to better adapt to machine learning format rownames(election) <- NULL head(election) # inspect the df election_new <- election; election_new$Clinton <- NULL # remove Clinton from df head(election) # reinspect the new df str(election_new[1, ]) # inspect the structure of the df cat('Dimensions of dataset:', dim(election_new), # dimensions of dataframe '\n', 'There are', sum(is.na(election_new)), 'NA values in the entire dataset.') ####################################### ### Exploratory Data Analysis (EDA) ### ####################################### # create function to plot correlation matrix and establish multicollinearity # takes one input (df) to pass in dataframe of interest multicollinearity <- function(df, tl.srt, tl.offset, number.cex, tl.cex) { # Examine between predictor correlations/multicollinearity corr <- cor(df, use = 'pairwise.complete.obs') corrplot(corr, mar = c(0, 0, 0, 0), method = 'color', col = colorRampPalette(c('#FC0320', '#FFFFFF', '#FF0000'))(100), addCoef.col = 'black', tl.srt = tl.srt, tl.offset = tl.offset, tl.col = 'black', number.cex = number.cex, tl.cex = tl.cex, type = 'lower') # count how many highly correlate variables exist based on 0.75 threshold highCorr <- findCorrelation(corr, cutoff = 0.75) # find correlated names highCorr_names <- findCorrelation(corr, cutoff = 0.75, names = TRUE) cat(' There are', length(highCorr_names), 'highly correlated predictors.', '\n The following variables should be omitted:', paste('\n', unlist(highCorr_names))) } ##################### ### Scatter Plots ### ##################### # create a correlation matrix between all variables by calling the function multicollinearity(election_new, tl.srt = 6, tl.offset = 1, number.cex = 0.55, tl.cex = 0.7) x1 = election$Trump; y1 = election$Clinton plot1 <- ggplot(election, aes(x = x1, y = y1)) + ggtitle('Clinton vs. Trump by Fraction of Votes') + xlab('Trump') + ylab('Clinton') + geom_point(pch = 1) + geom_smooth(method = 'lm', se = FALSE) + theme_classic() + # Add correlation coefficient stat_cor(method = 'pearson', label.x = 0.05, label.y = 0.02) x2 = election$PercentBelowPoverty; y2 = election$IncomeperCapita plot2 <- ggplot(election, aes(x = x2, y = y2)) + ggtitle('Income Per Capita vs. Percent Below Poverty') + xlab('Percent Below Poverty') + ylab('Income Per Capita') + geom_point(pch = 1) + geom_smooth(method = 'lm', se = FALSE) + theme_classic() + # Add correlation coefficient stat_cor(method = 'pearson', label.x = 0.15, label.y = 0.20) x3 = election$PercentBelowPoverty; y3 = election$HomeOwnership plot3 <- ggplot(election, aes(x = x3, y = y3)) + ggtitle('Home Ownership vs. Percent Below Poverty') + xlab('Percent Below Poverty') + ylab('Home Ownership') + geom_point(pch = 1) + geom_smooth(method = 'lm', se = FALSE) + theme_classic() + # Add correlation coefficient stat_cor(method = 'pearson', label.x = 0.15, label.y = 10) x4 = election$PercentBelowPoverty; y4 = election$PersonsPerHouse plot4 <- ggplot(election, aes(x = x4, y = y4)) + ggtitle('Persons Per House vs. Percent Below Poverty') + xlab('Percent Below Poverty') + ylab('Persons Per House') + geom_point(pch = 1) + geom_smooth(method = 'lm', se = FALSE) + theme_classic() + # Add correlation coefficient stat_cor(method = 'pearson', label.x = 0.15, label.y = 0.20) plot_grid(plot1, plot2, plot3, plot4, labels = 'AUTO', ncol = 2, align = 'v') # remove highly correlated predictors election_new$Percent.White.Not.Hispanic <- NULL election_new$Percent.foreign.born <- NULL election_new$PercentLangDiffEnglish <- NULL election_new$PercentWhite <- NULL election_new$Bachlorsorhigher <- NULL ########################### ### Partition The Data ### ########################### set.seed(222) # set seed for reproducibility #Use 70% of dataset as training set and remaining 30% as testing set sample <- sample(c(TRUE, FALSE), nrow(election_new), replace=TRUE, prob=c(0.7,0.3)) train <- election_new[sample, ] # training set test <- election_new[!sample, ] # test set cat('\n Training Dimensions:',dim(train), '\n Testing Dimensions:', dim(test), '\n', '\n Training Dimensions Percentage:', round(nrow(train)/ nrow(election_new), 2), '\n Testing Dimensions Percentage:', round(nrow(test)/ nrow(election_new), 2)) # Create a function to normalize the data by scaling it between 0 and 1 normalize <- function(x) { return ((x-min(x))/(max(x)-min(x))) } # Use the normalize function to normalize each column of train and test. # This creates a new dataframe by applying the normalize function to each row # of the dataset ‘frame’ maxmindtrain <- as.data.frame(lapply(train, normalize)) maxmindtest <- as.data.frame(lapply(test, normalize)) # Define input and output variables to create the training data data frame input_train <- train[c(1:22)] input_test <- test[c(1:22)] output_train <- train$Trump # training output output_test <- test$Trump # validation output trainingdata <- cbind(input_train, output_train) testdata <- cbind(input_test, output_test) ################################ ### Generalized Linear Model ### ################################ set.seed(222) # set the random seed for reproducibility lm.fit <- glm(Trump ~ ., data = trainingdata) summary(lm.fit) ################################### ### Simple Neural Network Model ### ################################### set.seed(222) n_train <- names(trainingdata) n_test <- names(testdata) f_train <- as.formula(paste('Trump ~', paste(n_train[!n_train %in% 'Trump'], collapse = ' + '))) f_test <- as.formula(paste('Trump ~', paste(n_test[!n_test %in% 'Trump'], collapse = ' + '))) # 2 hidden layers with 5 and 3 neurons, respectively nn_train <- neuralnet(f_train, data = trainingdata, hidden = c(5, 3), linear.output = T) nn_test <- neuralnet(f_test, data = testdata, hidden = c(5, 3), linear.output = T) plot(nn_train, rep = 'best') # plot the neural network - training data # Predict on Training Data and Test Data set.seed(222) # set the random seed for reproducibility # Compute fitted values from the training data predictions_train <- predict(nn_train, newdata = trainingdata) # Test the neural networks out of sample performance predictions_test <- predict(nn_test, newdata = testdata) # Compute mean absolute error between true and fitted values # we are wrong on average by this many fraction of votes train_mae = mean(abs(predictions_train - output_train)) test_mae = mean(abs(predictions_test - output_test)) cat('\n', 'Train MAE:', train_mae, '\n', 'Test MAE:', test_mae, '\n', 'Difference in MAE Between Train and Validation Set:', train_mae - test_mae) ################## #### Part Two #### ################## h2o.init() # Read in the data housing <- read.csv(paste('https://raw.githubusercontent.com/lshpaner/', 'CEEM586_Neural_Networks_and_ML/main/data/', 'DC_PropertieResidentialunder1mill.csv', sep = ''), header = TRUE) # examine first 10 columns of data head(housing[, 1:10]) # examine structure of dataframe str(housing[1, ]) # only look at first column ####################### #### Preprocessing #### ####################### # remove non-numeric variables s.t. amendable to ML modeling housing$CENSUS_BLOCK <- NULL housing$BATHRM <- NULL # unrounded expression of bathrooms housing$CNDTN <- NULL housing$EXTWALL <- NULL housing$ROOF <- NULL housing$INTWALL <- NULL housing$ASSESSMENT_SUBNBHD <- NULL # contains 53 levels (already as variables/columns) housing$ASSESSMENT_NBHD <- NULL housing$SQUARE <- NULL housing$QUADRANT <- NULL # remove logPrice since PRICE is the target, and we do not # need to linearize it housing$logPrice <- NULL housing$X <- NULL; housing$Y <- NULL # GPS coordiantes (x, y) --> not necessary # supply names of columns that have 0 variance names(housing[, sapply(housing, function(v) var(v, na.rm=TRUE)==0)]) # exclude zero variance columns housing <- housing[, sapply(housing, function(v) var(v, na.rm = TRUE) != 0)] # dimensions of dataset cat(' Dimensions of dataset:', dim(housing), '\n', 'There are', sum(is.na(housing)), 'NA values in the entire dataset.') # assign variable to count how many highly correlated # variables there exist based on 0.75 threshold highCorr_names <- findCorrelation(cor(housing, use = 'pairwise.complete.obs'), cutoff = 0.75, names = TRUE) highCorr <- findCorrelation(cor(housing), cutoff = 0.75) cat(' There are', length(highCorr_names), 'highly correlated predictors.'); highCorr_names # remove highly correlated predictors housing$NW <- NULL; housing$Ward6 <- NULL housing$Multi <- NULL; housing$NUM_UNITS <- NULL X_var <- colnames(housing) # independent X_var <- list(colnames(housing)) # variables X_var <- X_var[[1]][-15]; X_var <- X_var[-1]; X_var # remove from list ############################### #### Partitioning The Data #### ############################### # dataset is partitioned using a 70/30 train_test split as follows. set.seed(222) # make this example reproducible seventy_percent = 0.70*nrow(housing) # what is 70% of length of dataframe? # reassign to new var as sample of 70% of data ind <- sample(1:nrow(housing), seventy_percent) train_data <- as.h2o(housing[ind, ]) # create training set as h2o data frame test_data <- as.h2o(housing[-ind, ]) # create test set as h2o data frame cat(' Train Size:', dim(train_data), '\n Test Size:', dim(test_data), '\n Train Percentage:', round(nrow(train_data)/nrow(housing), 2), '\n Test Percentage:', round(nrow(test_data)/nrow(housing), 2)) # Estimate The Deep Neural Network dl_DC_Properties1 <- h2o.deeplearning(y = 'PRICE', x = c(X_var), training_frame = train_data, validation_frame = test_data, activation = 'Tanh', epochs = 1000, hidden = c(4, 4), standardize = TRUE, l1 = 0.0001, l2 = 0.001, adaptive_rate = TRUE, variable_importances = TRUE, nfolds = 3, reproducible = TRUE, seed = 222) # Plot and Model Summary plot(dl_DC_Properties1, metric = 'mae') # loss plotted throughout training summary(dl_DC_Properties1) # Print model summary information # Variable Importance # plot the first 10 important variables h2o.varimp_plot(dl_DC_Properties1, 10) # Retrieve the variable importance varimp <- h2o.varimp(dl_DC_Properties1) top_10 <- varimp[1:10, ] # for data exploration top_20 <- varimp[1:20, ] # top 20 variables for subsequent modeling top20_var <- top_20$variable print(top_10) # print the top 10 variables and their respective importance # Additional Exploratory Data Analysis (EDA) # The 20 most important variables are taken into consideration, but scatter # plots on the full dataset (not training) are created only for columns with # quantitative and continuous values. # plot CENSUS-TRACT VS. PRICE x5 = housing$ROOMS; y5 = housing$PRICE corrplot5 <- ggplot(housing, aes(x = x5, y = y5)) + ggtitle('Price vs. Rooms') + xlab('Rooms') + ylab('Price') + geom_point(pch = 1) + geom_smooth(method = 'lm', se = FALSE) + theme_classic() + # Add correlation coefficient stat_cor(method = 'pearson', label.x = 3, label.y = 30) # plot BATHROOMS VS. PRICE x6 = housing$BATHROOM; y6 = housing$PRICE corrplot6 <- ggplot(housing, aes(x = x6, y = y6)) + ggtitle('Price vs. Bathrooms') + xlab('Bathrooms') + ylab('Price') + geom_point(pch = 1) + geom_smooth(method = 'lm', se = FALSE) + theme_classic() + # Add correlation coefficient stat_cor(method = 'pearson', label.x = 0.5, label.y = 30) plot_grid(corrplot5, corrplot6, labels='AUTO', ncol = 2, align = 'v') # create list from top 10 variables list <- c(top_10['variable']) # subset top 10 variables into new df top_ten_housing <- housing[c(top_10[, 'variable'])] # Correlation Matrix # Since we have already determined and omitted the highly correlated predictors # from the main dataframe, this is just another sanity check to confirm that no # more of them exist. # create a correlation matrix between all variables multicollinearity(top_ten_housing, tl.srt = 45, tl.offset = 1, number.cex = 0.7, tl.cex = 0.8) # call the multicollinearity function dl_DC_Properties2 <- h2o.deeplearning(y = 'PRICE', x = c(top20_var), training_frame = train_data, validation_frame = test_data, activation = 'Tanh', # hidden_layer, node epochs = 1000, hidden = c(2,2), standardize = TRUE, l1 = 0.0001, l2 = 0.01, adaptive_rate = TRUE, variable_importances = TRUE, nfolds = 3, reproducible = TRUE, seed = 222) # training and test loss plotted plot(dl_DC_Properties2, metric = 'mae') # Re-estimate The Deep Neural Network summary(dl_DC_Properties2) # print out model summary information and statistics # Predict outputs on the test set predictions <- h2o.predict(dl_DC_Properties2, test_data) # print the predictions print(predictions) # Create data set for analysis with LIME # Pick 5 indices from the training set for_lime <- sample(1:nrow(housing[ind, ]), 5) data_for_lime <- housing[for_lime, ] dl_DC_Properties3 <- h2o.deeplearning(y = 'PRICE', x = c(top20_var), training_frame = train_data, validation_frame = test_data, activation = 'Tanh', # hidden_layer, node epochs = 1000, hidden = c(2,2), standardize = TRUE, l1 = 0.0001, l2 = 0.015, adaptive_rate = TRUE, variable_importances = TRUE, reproducible = TRUE, seed = 222) plot(dl_DC_Properties3, metric = 'mae') # training and test loss plotted summary(dl_DC_Properties3) # print out model summary information and statistics # Convert data_for_lime into an h2o data frame predict_data_for_lime <- as.h2o(data_for_lime) # Compute predictions with estimated neural network for the lime dataset predictionsforlime <- h2o.predict(dl_DC_Properties3, predict_data_for_lime) # Use lime to analyze the predictions explainer_price <- lime(data_for_lime, dl_DC_Properties3) explanation <- explain(data_for_lime, explainer_price, n_labels = 2, n_features = 4) # print explanation output pandoc.table(explanation[c(2, 3, 4, 5, 6, 11)], style = 'simple', split.table = Inf) pandoc.table(data_for_lime, style = 'simple') # table the data for lime analysis # Visualize the lime output plot_features(explanation, ncol = 1) plot_explanations(explanation) price_prediction <- as.data.frame(explanation$prediction) price_prediction <- as.numeric(unlist(price_prediction)) cat('\n', 'Mean Price Prediction:', mean(price_prediction), '\n', 'Mean Home Price:', mean(housing$PRICE, na.rm = TRUE), '\n', 'Difference:', mean(housing$PRICE, na.rm = TRUE) - mean(price_prediction), '\n', '% Difference:', 1 - mean(price_prediction)/mean(housing$PRICE, na.rm = TRUE)) plot(explanation$model_r2, main = 'Predictions: R-Squared', xlab = 'Index', ylab = 'R-Squared') # plot the model explanation |