# Advanced Regression Technique on House Prices of Ames, Iowa

## Introduction

The main goal of this project was to predict housing prices of Ames, Iowa using supervised machine learning techniques. Dataset was retrieved from the corresponding Kaggle competition webpage. Kaggle is an online community for Data Scientist and Machine Learning practitioners, owned by Google.

Our process to devise the best model for precise predictions took mainly four steps.

- Basic EDA
- Feature Engineering
- Modeling
- Ensemble Learning Technique (Stacking) for additional accuracy
- Bayesian Optimization

## Basic EDA & Data Cleaning

The Kaggle data set was split into a training dataset containing 1,460 sales and a test dataset with 1,459 sales. There were 81 feature variables in training data set including the sale price and 80 in the test data set without the sale price. Among the variables, there were 80 variables: 20 continuous, 14 discrete, 22 categorical, and 24 ordinal.

Since we are predicting the sale price with our model, we looked into the correlation between each variable and sale price. As we examined, there were several of the variables that had a higher correlation with sale price than others, including GrLivArea and TotalBsmtSF.

Furthermore, we created a heatmap to illustrate the structure of correlations among the variables. In the chart, cells with lighter color indicate a higher correlation between two variables while the ones with darker color showed a lower correlation. The top row demonstrates the correlation between the sale price and various features in the dataset. As you can see, variables as OverallQual, GrLivArea, GarageCars are the variables are highly correlated with the sale price.

After looking into the features that are highly correlated with the sale price, we examined the sale price variable itself. As the histogram and the Q-Q plot below shows, sale price does not fulfill the assumption of normality. It is skewed to the right and such skewedness means that we cannot predict sale price with linear regression. Thus, we applied a log transformation to correct the issue.

Then, we analyzed the missing values and recognized that there were 34 different variables with missing values.

For the sake of missing value imputation, we examined deeper into each feature and found out that many of the missing values meant that there was an absence of a feature. For example, NA in BsmtQual(Basement Quality) meant that there was no basement in the house. Thus, we imputed either “None” or 0 depending on the feature type. Furthermore, we imputed either Mode for the categorical features and median for a numerical one.

Finally, we analyzed the most important indicators for sale prices and eliminated outliers from Ground Living Area in order to increase the accuracy of the prediction.

## Feature Engineering

As we examined the features, we concluded that we can combine some of the variables to extract additional insight from the data and minimize noise. Below are the features that we engineered to do so:

- Overall Grade: multiplication of Overall Quality and Overall condition
- Garage Score: multiplication of Garage Area and Garage Quality
- External Grade: multiplication of external quality and external condition
- Kitchen Score: multiplication of the number of kitchen above ground and kitchen quality
- Fireplace Score: multiplication of the number of fireplaces and fireplace quality
- Pool Score: multiplication of Pool Area and Pool Quality
- Total bath: sum of basement full bath, full bath, basement half bath, and half bath
- TotalSF, AllPorchSF: sum of the square footage of the subfeatures
- HasMasVnr: binary feature to communicate if the house has Masonry Veneer or not
- HouseCompleteorNot: binary feature to communicate if the house was complete before sale or not

After we executed feature engineering, we analyzed and made sure that the newly engineered features provide additional value in comparison to the existing ones. Below are the main features that were the best re-engineered predictors.

After feature engineering was completed, we dummified the categorical features and replaced the existing categorical features with them.

## Modeling

1. Linear Models

Since there are multiple features in this dataset, we thought that building a basic multiple linear regression model was not the best route we could take. Instead, we implemented penalized regression models. All three models(Ridge, Lasso, and ElasticNet) were built using cross-validation with 4 train fold and 1 test fold with each fold containing 20% of the train data. We chose the rmse score as a measure to find the best model and lasso performed better as it deleted the coefficients that are irrelevant. As you can see from the graph, ElasticNet has the alpha of 1 that it performs the same as lasso.

2. Tree-based Models

In order to leverage the overfitting issue, we tried three different tree-base models.

1) Random Forest & ExtraTreeRegressor

First, we implemented the Random Forest model. Since each decision tree is uncorrelated and limited to a limited number of sample, it makes a strong predictor when each of them is assembled. Such aspect of the model deals with overfitting issue because even if each decision tree is overfitted, the assembling part of the model lessens the issue. As long as there is enough number of decision trees, individual noise that overfitted individual decision tree makes are leveraged. In addition, we implemented ExtraTreeRegressor since it implements a meta estimator that fits a number of randomized decision trees on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting.

2) Gradient Boosting & XGBoost

Boosting is a method that takes a sequential format to make a better prediction. Instead of assembling prediction made by individual decision tree, boosting takes the information from the residuals of the previous tree. As a result, boosting puts more weight on the predictions that made better prediction on the ones that were predicted wrong more frequently. This makes the prediction more accurate as the number of tree in the boosting model is increased. However, such structure makes the model prone to outliers.

In addition to Gradient Boosting, we implemented XGBoost since it uses a more regularized model formalization to control over-fitting that it gives a better performance.

We did not include the parameters and hyperparameter numeric values in this post. RMSE scores for each models are as follow:

Random Forest: 0.1419

ExtraTreeRegressor: 0.1353

Gradient Boosting: 0.1232

XGBoost: 0.1219

## Ensemble Learning Technique (Stacking) for additional accuracy

Among the multiple models we have chosen to implement, we tried multiple different combinations of them to find the best predictor. In order to do so, we tried two different techniques to aggregate 4 models that had the best RMSE scores.

1. Simple Average Ensemble

This technique gets predictions from the list of model input and get the average value of the predictions. After several trials, we’ve found out that averaging ElasticNet, Gradient Boosting, XGBoost, and Lasso gave the best Kaggle score of 0.12469.

2. Stacking with Meta-Model

When you use Stacking with Meta-Model, a number of first-level individual learners are generated from the training data set by employing different learning algorithms. Those individual learners are then combined by a second-level learner which is called as meta-learner. By doing so, the accuracy of the prediction increases. When we implemented ElasticNet, Gradient Boosting, XGBoost as first-level learners and used lasso as a second-level learner, we got the best Kaggle score of 0.12320.

## Bayesian Optimization

After implementing the Stacking with Meta-Model, we examined the details of our models to locate possible improvements. Then we realized that instead of GridSearchCV, we can use Bayesian Optimization package to for hyperparameter tuning process. Bayesian optimization, in contrast to random or grid search, keep track of past evaluation results which they use to form a probabilistic model mapping hyperparameters to a probability of a score on the objective function. Such a model is called a surrogate model and Bayesian methods work by finding the next set of hyperparameters to evaluate on the actual objective function by selecting hyperparameters that perform best on the surrogate function. Thus, we used the hyperparameters tuned by the Bayesian Optimization package for XGBoost and got improved the rmse score of XGBoost from 0.1211 to 0.1191. Consequently, Kaggle score of our stacked model improved to 0.12212 which was our final submission.