root/MachineLearningWithMATLAB/Regression_FuelEconomy/FuelEconomyPrediction.m @ 11
| 10 | anderm8 | %% Predicting Fuel Economy
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% In this demo, we use regression trees to predict the fuel economy of
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% vehicles.
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% ---------------------------------
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%
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% Copyright 2015 The MathWorks, Inc.
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%% Loading Excel file representing Fuel Economy Data
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CarData = importCarTable('2004dat.xlsx');
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%% Categorical Variables
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% Many of the variables represent discrete items, or categories: a car or a
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% truck, front wheel or rear wheel drive, etc. To conserve memory and
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% accurately classify these, we'll convert them to |categorical| variables.
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CarData.Car_Truck = categorical(CarData.Car_Truck);
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CarData.Police = categorical(CarData.Police);
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CarData.Transmission = categorical(CarData.Transmission);
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CarData.Drive = categorical(CarData.Drive);
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CarData.AC = categorical(CarData.AC);
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CarData.City_Highway = categorical(CarData.City_Highway);
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% Not enough samples of each Manufacturer and Car Line (100s unique ones)
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% Year is all the same
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CarData.MfrName = [];
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CarData.CarLine = [];
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CarData.Year = [];
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% %% Test with 10% of the Data
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% % Several of the techniques below use random numbers. We are going
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% % to set the random number generator here to ensure repeatability.
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% rng(5)
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%% Partition Data for Cross Validation
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% cvpartition helps us create a cross-validation partition for data. We
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% create a test set (10% of data) and training set (90% of data).
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% Build cross-validation partition
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c = cvpartition(height(CarData),'holdout');
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% Extract data at indices
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mdlTrain = CarData(training(c),:);
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mdlTest = CarData(test(c),:);
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% Extract predictors and response
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X = CarData;
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X.MPG = []; % Remove mpg
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Y = CarData.MPG;
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%% Multiple Linear Regression
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% First try multiple linear regression
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% Fit linear model
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modelLR = fitlm(mdlTrain,'ResponseVar', 'MPG');
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disp(modelLR)
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% Make prediction on test set
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yfitLR = predict(modelLR,mdlTest);
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% Show Results
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showFit(mdlTest.MPG, yfitLR)
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%% Stepwise Linear Regression
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% Stepwise linear regression adds each term to see which ones decrease the
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% error the most.
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modelSW = stepwiselm(mdlTrain,'ResponseVar', 'MPG','Upper','linear');
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disp(modelSW)
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disp(mdlTrain.Properties.VariableNames(modelSW.VariableInfo.InModel).');
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% Make prediction on test set
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yfitSW = predict(modelSW,mdlTest);
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% Show Results
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showFit(mdlTest.MPG, yfitSW)
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% %% Support Vector Regression
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% % Stepwise linear regression adds each term to see which ones decrease the
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% % error the most.
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% modelsvm = fitrsvm(mdlTrain,'MPG');
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% disp(modelsvm)
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%
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% % Make prediction on test set
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% yfitsvm = predict(modelsvm,mdlTest);
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%
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% % Show Results
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% showFit(mdlTest.MPG, yfitsvm)
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%% Regression Trees: Train the Tree
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% In many cases, the form of the relationship between predictors and a
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% response is unknown. Decision trees offer a nonparametric alternative
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% for regression.
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t = fitrtree(mdlTrain,'MPG');
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t2 = prune(t,'level',250);
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% view(t2); % textual
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view(t2,'mode','graph'); % as a tree
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% Regression Trees: Evaluate the Tree
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yfitT = predict(t, mdlTest);
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% Show Results
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showFit(mdlTest.MPG, yfitT)
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%% Bagged Decision Trees
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% Bagging stands for bootstrap aggregation. Every tree in the ensemble is
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% grown on an independently drawn sample of input data. To
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% compute prediction for the ensemble of trees, fitensemble
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% takes an average of predictions from individual trees. Ensemble
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% techniques such as bagging combining many weak learners to produce a
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% strong learner.
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%
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% To use default values:
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%
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% tbfit = fitensemble(Xtrain,Ytrain,'Bag',100,'tree','type','regression');
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%
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% To determine how many trees to use in your ensemble:
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%
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% treeLoss = oobLoss(tbfit,'mode','cumulative')
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% plot(1:length(treeLoss),treeLoss)
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%
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% oobLoss (Out-of-bag regression error) computes MSE versus the number of
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% grown trees. You can use a similar technique to figure out best mininum
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% leaf size.
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ttemp = templateTree('MinLeaf',1);
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tbfit = fitensemble(mdlTrain,'MPG','Bag',100,ttemp,'type','regression');
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% Predict
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yfitTB = predict(tbfit,mdlTest);
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% Show Results
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showFit(mdlTest.MPG, yfitTB)
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%% Bagged Decision Trees: Predictor Importance
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% Predictor importance offers insight into the relative importance of each
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% predictor in the model. It is calculated by summing changes in
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% the mean squared error (MSE) due to splits on every predictor and
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% dividing the sum by the number of branch nodes.
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figure
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pI = predictorImportance(tbfit);
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barh(pI)
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set(gca,'YTick',1:numel(X.Properties.VariableNames));
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set(gca,'YTickLabel',strrep(X.Properties.VariableNames,'_','\_'));
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xlabel('Predictor Importance')
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%% Sequential Feature Selection
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% Sequential feature selection selects a subset of features from the data
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% matrix X that best predict the data in Y by sequentially selecting
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% features until there is no improvement in prediction. We are using 3
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% fold cross-validation so we can use the whole data set here without
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% having to break up a training set and a test set. Normally, you
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% may want to use a higher fold, but we are keeping it small for demo
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% purposes. We can then see which features to keep in our model.
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% Data needs to be numeric
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Xdummy = dummytable(X);
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XNumeric = table2array(Xdummy);
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gcp; % open a pool of workers
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opts = statset('display','iter','UseParallel','always','TolFun',1e-2);
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% use our cv partition object with 3-fold cross validation
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cv = cvpartition(height(X),'k',3);
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% Determine important features
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fs = sequentialfs(@featureTest,XNumeric,Y,'options',opts,'cv',cv);
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% Display
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disp(Xdummy.Properties.VariableNames(fs).')
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%% Treebagger with New Predictor Set
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% About the same answer but smaller set of predictors. Important for
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% computational speed, avoiding overtraining, and for general simplicity.
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% Could yield a more accurate result, as well.
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ttemp = templateTree('MinLeaf',1);
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tbfit = fitensemble(XNumeric(training(c),fs),Y(training(c)),...
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'Bag',100,ttemp,'type','regression');
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yfitFinal = predict(tbfit,XNumeric(test(c),fs));
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% Show results
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showFit(Y(test(c)), yfitFinal)
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%% Neural Networks
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% Use app to train data to _XNumeric_ and _Y_. Then generate the script
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% and turn it into a function:
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net = trainRegressionNetwork(XNumeric,Y);
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yfitNN = net(XNumeric.');
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% Show results
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showFit(Y,yfitNN.');
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