9.1 House Price Prediction in King County

We use the house_sales_prediction dataset contained in this book in order to provide a use-case for the application of mlr3 on real-world data.

9.1.1 Exploratory Data Analysis

In order to get a quick impression of our data, we perform some initial Exploratory Data Analysis. This helps us to get a first impression of our data and might help us arrive at additional features that can help with the prediction of the house prices.

We can get a quick overview using R’s summary function:

##        id                 date               price            bedrooms    
##  Min.   :   1000102   Length:21613       Min.   :  75000   Min.   : 0.00  
##  1st Qu.:2123049194   Class :character   1st Qu.: 321950   1st Qu.: 3.00  
##  Median :3904930410   Mode  :character   Median : 450000   Median : 3.00  
##  Mean   :4580301520                      Mean   : 540088   Mean   : 3.37  
##  3rd Qu.:7308900445                      3rd Qu.: 645000   3rd Qu.: 4.00  
##  Max.   :9900000190                      Max.   :7700000   Max.   :33.00  
##    bathrooms     sqft_living       sqft_lot           floors    
##  Min.   :0.00   Min.   :  290   Min.   :    520   Min.   :1.00  
##  1st Qu.:1.75   1st Qu.: 1427   1st Qu.:   5040   1st Qu.:1.00  
##  Median :2.25   Median : 1910   Median :   7618   Median :1.50  
##  Mean   :2.12   Mean   : 2080   Mean   :  15107   Mean   :1.49  
##  3rd Qu.:2.50   3rd Qu.: 2550   3rd Qu.:  10688   3rd Qu.:2.00  
##  Max.   :8.00   Max.   :13540   Max.   :1651359   Max.   :3.50  
##    waterfront          view         condition        grade         sqft_above  
##  Min.   :0.0000   Min.   :0.000   Min.   :1.00   Min.   : 1.00   Min.   : 290  
##  1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:3.00   1st Qu.: 7.00   1st Qu.:1190  
##  Median :0.0000   Median :0.000   Median :3.00   Median : 7.00   Median :1560  
##  Mean   :0.0075   Mean   :0.234   Mean   :3.41   Mean   : 7.66   Mean   :1788  
##  3rd Qu.:0.0000   3rd Qu.:0.000   3rd Qu.:4.00   3rd Qu.: 8.00   3rd Qu.:2210  
##  Max.   :1.0000   Max.   :4.000   Max.   :5.00   Max.   :13.00   Max.   :9410  
##  sqft_basement     yr_built     yr_renovated       zipcode           lat      
##  Min.   :   0   Min.   :1900   Min.   :   0.0   Min.   :98001   Min.   :47.2  
##  1st Qu.:   0   1st Qu.:1951   1st Qu.:   0.0   1st Qu.:98033   1st Qu.:47.5  
##  Median :   0   Median :1975   Median :   0.0   Median :98065   Median :47.6  
##  Mean   : 292   Mean   :1971   Mean   :  84.4   Mean   :98078   Mean   :47.6  
##  3rd Qu.: 560   3rd Qu.:1997   3rd Qu.:   0.0   3rd Qu.:98118   3rd Qu.:47.7  
##  Max.   :4820   Max.   :2015   Max.   :2015.0   Max.   :98199   Max.   :47.8  
##       long      sqft_living15    sqft_lot15    
##  Min.   :-123   Min.   : 399   Min.   :   651  
##  1st Qu.:-122   1st Qu.:1490   1st Qu.:  5100  
##  Median :-122   Median :1840   Median :  7620  
##  Mean   :-122   Mean   :1987   Mean   : 12768  
##  3rd Qu.:-122   3rd Qu.:2360   3rd Qu.: 10083  
##  Max.   :-121   Max.   :6210   Max.   :871200
## [1] 21613    21

Our dataset has 21613 observations and 21 columns. The variable we want to predict is price. In addition to the price column, we have several other columns:

  • id: A unique identifier for every house.

  • date: A date column, indicating when the house was sold. This column is currently not encoded as a date and requires some preprocessing.

  • zipcode: A column indicating the ZIP code. This is a categorical variable with many factor levels.

  • long, lat The longitude and latitude of the house

  • ... several other numeric columns providing information about the house, such as number of rooms, square feet etc.

Before we continue with the analysis, we preprocess some features so that they are stored in the correct format.

First we convert the date column to numeric to be able to treat it as a numeric feature:

Afterwards, we convert the zip code to a factor:

And add a new column renovated indicating whether a house was renovated at some point.

Additionally we convert the price from Dollar to units of 1000 Dollar to improve readability.

We can now plot the density of the price to get a first impression on its distribution.

We can see that the prices for most houses lie between 75.000 and 1.5 million dollars. There are few extreme values of up to 7.7 million dollars.

Feature engineering often allows us to incorporate additional knowledge about the data and underlying processes. This can often greatly enhance predictive performance. A simple example: A house which has yr_renovated == 0 means that is has not been renovated yet. Additionally we want to drop features which should not have any influence (id column).

After those initial manipulations, we load all required packages and create a Task containing our data.

We can inspect associations between variables using mlr3viz’s autoplot function in order to get some good first impressions for our data. Note, that this does in no way prevent us from using other powerful plot functions of our choice on the original data. Distribution of the price:

The outcome we want to predict is the price variable. The autoplot function provides a good first glimpse on our data. As the resulting object is a ggplot2 object, we can use faceting and other functions from ggplot2 in order to enhance plots.

We can observe that renovated flats seem to achieve higher sales values, and this might thus be a relevant feature.

Additionally, we can for example look at the condition of the house. Again, we clearly can see that the price rises with increasing condition. Association between variables

In addition to the association with the target variable, the association between the features can also lead to interesting insights. We investigate using variables associated with the quality and size of the house. Note that we use $clone() and $select() to clone the task and select only a subset of the features for the autoplot function, as autoplot per default uses all features. The task is cloned before we select features in order to keep the original task intact.

9.1.2 Splitting into train and test data

In mlr3, we do not create train and test data sets, but instead keep only a vector of train and test indices.

9.1.3 A first model: Decision Tree

Decision trees cannot only be used as a powerful tool for predictive models but also for exploratory data analysis. In order to fit a decision tree, we first get the regr.rpart learner from the mlr_learners dictionary by using the sugar function lrn.

For now we leave out the zipcode variable, as we also have the latitude and longitude of each house.

The learned tree relies on several variables in order to distinguish between cheaper and pricier houses. The features we split along are grade, sqft_living, but also some features related to the area (longitude and latitude).

We can visualize the price across different regions in order to get more info:

We can see that the price is clearly associated with the zipcode when comparing then two plots. As a result, we might want to indeed use the zipcode column in our future endeavours.

9.1.4 A first baseline: Decision Tree

After getting an initial idea for our data, we might want to construct a first baseline, in order to see what a simple model already can achieve.

We use resample with 3-fold cross-validation on our training data in order to get a reliable estimate of the algorithm’s performance on future data. Before we start with defining and training learners, we create a Resampling in order to make sure that we always compare on exactly the same data.

For the cross-validation we only use the training data by cloning the task and selecting only observations from the training set.

9.1.5 Many Trees: Random Forest

We might be able to improve upon the RMSE using more powerful learners. We first load the mlr3learners package, which contains the ranger learner (a package which implements the “Random Forest” algorithm).

Often tuning RandomForest methods does not increase predictive performances substantially. If time permits, it can nonetheless lead to improvements and should thus be performed. In this case, we resort to tune a different kind of model: Gradient Boosted Decision Trees from the package xgboost.

9.1.6 A better baseline: AutoTuner

Tuning can often further improve the performance. In this case, we tune the xgboost learner in order to see whether this can improve performance. For the AutoTuner we have to specify a Termination Criterion (how long the tuning should run) a Tuner (which tuning method to use) and a ParamSet (which space we might want to search through). For now we do not use the zipcode column, as xgboost cannot naturally deal with categorical features. The AutoTuner automatically performs nested cross-validation.

We can obtain the resulting params in the respective splits by accessing the ResampleResult.

NOTE: To keep runtime low, we only tune parts of the hyperparameter space of xgboost in this example. Additionally, we only allow for \(10\) random search iterations, which is usually to little for real-world applications. Nonetheless, we are able to obtain an improved performance when comparing to the ranger model.

In order to further improve our results we have several options:

  • Find or engineer better features
  • Remove Features to avoid overfitting
  • Obtain additional data (often prohibitive)
  • Try more models
  • Improve the tuning
    • Increase the tuning budget
    • Enlarge the tuning search space
    • Use a more efficient tuning algorithm
  • Stacking and Ensembles (see Pipelines)

Below we will investigate some of those possibilities and investigate whether this improves performance.