Machine Learning Project -House Prices: Advanced Regression Techniques

Posted on Mar 25, 2018

In 2016, Kaggle released a competition calledย House Prices: Advanced Regression Techniques.ย The goal of the competition was to predict the final sale price of homes in Ames, Iowa. The dataset itself came with 79 explanatory variables describing just about every aspect of a residential home.

 

Workflow

I used various techniques I learned from the Bootcamp and any insight gained from investigating Kaggler's kernels to tackle the competition. Using the workflow depicted below, I was able to make predictions of my own.

Most of the work done dealt with transforming, cleaning, imputing, and aggregating data. Once complete, models were made using the following machine learning algorithms.

  • Lasso Regularization
  • Ridge Regularization
  • ElasticNet
  • Gradient Boosting Regression

 

Data Structure and Data Preprocessing

Data:

A histogram plot shows the distribution of the target variable 'SalePrice' as being was right-skewed. Before moving any further, I decided to obtain a normal distribution by way of log-transformation.

To get a better understanding of missingness with the given data sets (train and test), I determined the percentage of missing values and built bar plots.

In the train dataset, 19 out of 81 features had missing values. As for the test dataset, 33 out of 80 features had missing values.

Some of the features had outliers. Looking at the graph below, we can see that there's two homes that are very spacious yet are extremely low in price. When making my model, I must ensure that they are robust to outliers.

To check for multicollinearity, I created a correlation matrix with respect to the target variable โ€˜SalePriceโ€™.

Some variables were highly correlated, such as 'GarageArea' and 'GarageCars'. This makes sense since the size of a garage determines('GarageArea') the number of cars that fit in it ('GarageCars'). Other variables that were highly correlated show the same type of dependency.

Missingness

As you can see, the categorical features' Alley, 'PoolQC', and 'MscFeature' have over 90% of their column missing. However, looking at the data description, the NA's in categorical variables means "not present". So, for example, NA in the 'Alley' variable meant that the home has no alley.

To correct the issue, I first concatenated the train and test set. I then replaced the Na's with "None". I further researched that two of the numerical features ('MSSubClass' and 'Mosold') were actually categorical. 'MoSold' used numerical values that represented months. For example, "1" meant January, and "2" meant February. In 'MSSubClass', numerical values identified the type of dwelling involved in the sale. Both features were converted into strings. For the remaining numerical features, NA's were replaced by the value zero

Feature Engineering

Since the data has many categorical variables, I converted them into dummy/indicator variables. As for numerical features, quite a few had a highly skewed distribution which can lead to poor models. To combat this, these features were log-transformed.

Ridge Regression

Regularization reduces the magnitude of the features' coefficients to improve the accuracy of a model. By shrinking parameters, we prevent multicollinearity. With ridge regression, an L2 penalty is added to the loss functions to implement the reduction. Its' tuning parameter lambda controls the relative impact of the coefficient estimates. Using a grid of values, I determined that the best lambda (alpha in the ridge function) was 0.0005.

Lasso Regression

Lasso has an L1 penalty which allows coefficients to shrink to zero one by one to reduce their variance. Hence, lasso can be used to select essential features. In this case,101 features were chosen, and the other 119 features were eliminated. "GrLivArea" which represents the above-ground living area, seems to be the central feature in determining the sale price.

Elastic Net

Elastic net combines L1 with L2 regularization to create a linear regression model to correct overfitting. Here the alpha tuning parameter sets the ratio between them. It is also known to be robust to outliers. Elastic net performed slightly better than lasso and ridge when submitting predictions to lasso.

Gradient Boosting Regression

Gradient boosting uses weak prediction models and combines them to make a strong "learner". The loss was set to "huber" for it to be robust to outliers. My model received an R squared score of .98, which means that the explanatory variables can explain 98% of the variance in the target.

Conclusions

The advantage of ridge and lasso is that regularization helps to balance between overfitting and underfitting. Therefore, it's easy to assume that elastic net would be the top choice for modeling. However, after many submissions and fine-tuning, xgboost had the best predictions.

As the final prediction, I decided to average the predictions of lasso, elastic net, and gradientboostingregressor. Model ensembling is known to increase accuracy on a variety of machine learning tasks. That, combined with meticulously prepping the data through imputation and feature engineering before modeling, ensured good results. Furthermore, fine-tuning parameters of the model helped prevent overfitting. As a result, I was able to land in the top 16% of the 4074 Kaggle teams.

If you would like more information, visit my GitHub for more details.

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