Hello, and welcome to this lesson on univariate statistical tests for feature selection in machine learning using R. The effective management of dataset features can significantly influence the performance of your machine learning models. By carefully selecting the most relevant features, you can improve model accuracy, reduce overfitting, and decrease training time. One widely used approach for this is univariate selection for feature selection. In this lesson, we will explore how to perform univariate feature selection in R, focusing on statistical tests that help identify the most informative features in your dataset. By the end of this session, you will understand how to use univariate feature selection in R and appreciate its strengths and limitations.

Univariate statistical tests evaluate each feature independently to determine its relationship with the response variable. These tests are straightforward to apply and interpret, providing valuable insights into your data. In base R, we can use the chi-square test (chisq.test) to assess association between each feature and the target. Because the iris features are numeric, we first discretize each feature into bins, create a contingency table versus the target, compute the chi-square statistic, and then rank features by that score.

For this tutorial, we will use the built-in iris dataset in R. The iris dataset contains measurements for 150 iris flowers from three different species. It includes five attributes: Sepal.Length, Sepal.Width, Petal.Length, Petal.Width, and Species. The Species column is our target variable, while the other columns are the features.

Here's how you load and inspect the dataset in R:

This output shows that the dataset has 150 samples, each with 4 feature variables and 1 target variable (Species). In R, the iris dataset is stored as a data frame, where each column represents a variable.

Below is a small helper for scoring a single numeric feature against the categorical target with chi-square, followed by ranking and selecting the top k features.

The chi-squared statistic measures the strength of the association between each (binned) feature and the target variable. A higher chi-squared score indicates a stronger relationship.

The chi-squared statistic is calculated as follows:

While the chi-squared scores indicate the strength of the relationship, the p-value tells us about the statistical significance of this relationship. In R, you can use the chisq.test function after discretizing a continuous feature.

Here's how you can calculate the p-value for a single feature (for example, Petal.Length):

Repeat this process for each feature to obtain their respective p-values. A p-value less than 0.05 typically indicates a significant relationship between the feature and the target variable.

• If the p-value for a feature is less than 0.05, you can conclude that there is a significant association between that feature and the target variable.
• If the p-value is greater than 0.05, there is no significant association.

It's important to consider both the chi-squared scores and the p-values when interpreting your results.

While univariate feature selection is a useful method for filtering out irrelevant features, it has some limitations:

• The chi-squared test evaluates categorical variables; for numeric features you must discretize, and your binning choice can affect results.
• It evaluates each feature independently, which can result in the selection of multiple highly correlated features.
• It does not consider interactions between features, potentially leading to the selection of redundant features.

Being aware of these limitations will help you choose the most appropriate feature selection technique for your dataset.

In this lesson, you learned about the power of univariate feature selection and how it can enhance the effectiveness and efficiency of your machine learning models in R. We explored the concept of univariate selection and demonstrated how to implement it from scratch using the chi-square test to identify the most informative features.

Remember, this technique has its limitations — it is best suited for categorical data and requires discretization when features are continuous.

To reinforce your understanding, try applying univariate feature selection to other datasets in R. Practice interpreting the results. This hands-on experience will prepare you for more advanced feature selection and dimensionality reduction techniques in future lessons. Let's get started!