MLxtend: A Library with Interesting Tools for Data Science Tasks | by Esmaeil Alizadeh | Dec, 2020

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MLxtend library is developed by Sebastian Raschka (a professor of statistics at the University of Wisconsin-Madison). The library has nice API documentation as well as many examples.

You can install the MLxtend package through the Python Package Index (PyPi) by running pip install mlxtend.

In this post, I’m using the wine data set obtained from the Kaggle. The data contains 13 attributes of alcohol for three types of wine. This is a multiclass classification dataset, and you can find the description of the dataset here.

First, let’s import the data and prepare the input variables X (feature set) and the output variable y (target).

Data preprocessing

For creating counterfactual records (in the context of machine learning), we need to modify the features of some records from the training set in order to change the model prediction [2]. This may be helpful in explaining the behavior of a trained model. The algorithm used in the library to create counterfactual records is developed by Wachter et al [3].

You can create counterfactual records using create_counterfactual() from the library. Note that this implementation works with any scikit-learn estimator that supports the predict() function. Below is an example of creating a counterfactual record for an ML model. The counterfactual record is highlighted in a red dot within the classifier’s decision regions (we will go over how to draw decision regions of classifiers later in the post).

The code to create a counterfactual record in a classifier’s decision regions (Source code: author)
A counterfactual record is highlighted within a classifier’s decision region (Image by author)

An interesting and different way to look at PCA results is through a correlation circle that can be plotted using plot_pca_correlation_graph(). We basically compute the correlation between the original dataset columns and the PCs (principal components). Then, these correlations are plotted as vectors on a unit-circle. The axes of the circle are the selected dimensions (a.k.a. PCs). You can specify the PCs you’re interested in by passing them as a tuple to dimensions function argument. The correlation circle axes labels show the percentage of the explained variance for the corresponding PC [1].

Remember that the normalization is important in PCA because the PCA projects the original data on to the directions that maximize the variance.

The code to plot the PCA correlation graph (Source code: author)
PCA correlation circle diagram between the first two principal components and all data attributes (Image by author)
Correlation matrix between wine features and the first two PCs (Image by author)

You often hear about the bias-variance tradeoff to show the model performance. In supervised learning, the goal often is to minimize both the bias error (to prevent underfitting) and variance (to prevent overfitting) so that our model can generalize beyond the training set [4]. This process is known as a bias-variance tradeoff.

Note that we cannot calculate the actual bias and variance for a predictive model, and the bias-variance tradeoff is a concept that an ML engineer should always consider and tries to find a sweet spot between the two.
Having said that, we can still study the model’s expected generalization error for certain problems. In particular, we can use the bias-variance decomposition to decompose the generalization error into a sum of 1) bias, 2) variance, and 3) irreducible error [4, 5].

The bias-variance decomposition can be implemented through bias_variance_decomp() in the library. An example of such implementation for a decision tree classifier is given below.

The Bias-Variance Decomposition implementation (Source code: author)
>>> Average expected loss: 0.108 
>>> Average bias: 0.032
>>> Average variance: 0.076

MLxtend library has an out-of-the-box function plot_decision_regions() to draw a classifier’s decision regions in 1 or 2 dimensions.

Here, I will draw decision regions for several scikit-learn as well as MLxtend models. Let’s first import the models and initialize them.

Initialize all ML models (Source code: author)

Now that we have initialized all the classifiers, let’s train the models and draw decision boundaries using plot_decision_regions() from the MLxtend library.

The code to draw the decision regions of all classifiers (Source code: author)
Decision regions of all classifiers (Image by author)

Another useful tool from MLxtend is the ability to draw a matrix of scatter plots for features (using scatterplotmatrix()). In order to add another dimension to the scatter plots, we can also assign different colors for different target classes.

The code to plot the matrix of scatter plots (Source code: author)
A matrix of scatter plot of all wine attributes with different colors for wine types (Image by author)

By the way, for plotting similar scatter plots, you can also use Pandas’ scatter_matrix() or seaborn’s pairplot() function.

The bootstrap is an easy way to estimate a sample statistic and generate the corresponding confidence interval by drawing random samples with replacement. For this, you can use the function bootstrap() from the library. Note that you can pass a custom statistic to the bootstrap function through argument func. The custom function must return a scalar value.

>>> Mean: 5.03
>>> Standard Error: +/- 0.11
>>> CI95: [4.8, 5.26]

In this post, we went over several MLxtend library functionalities, in particular, we talked about creating counterfactual instances for better model interpretability and plotting decision regions for classifiers, drawing PCA correlation circle, analyzing bias-variance tradeoff through decomposition, drawing a matrix of scatter plots of features with colored targets, and implementing the bootstrapping. The library is a nice addition to your data science toolbox, and I recommend giving this library a try.

You can find the Jupyter notebook for this blog post on GitHub.

Thanks for reading!

You can download the one-page summary of this post at https://ealizadeh.com.

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