Introduction

A common problem with machine learning models is their interpretability and explainability.
We create a dataset and we train a model to achieve a task, then we would like to understand how the model obtains those results. This is often quite difficult to understand, especially with very complex models.

In this blog post, I would like to present a very useful library called SHAP. In particular, I will write about its amazing tools and I will explain to you how to interpret the results in a learning to rank scenario.

Tree SHAP gives an explanation to the model behavior, in particular how each feature impacts on the model’s output.

Tree SHAP is an algorithm that computes SHAP values for tree-based machine learning models.
SHAP (SHapley Additive exPlanations) is a game-theoretic approach to explain the output of any machine learning model. It connects optimal credit allocation with local explanations using the classic Shapley values from game theory and their related extensions [1, 2].

Tree SHAP allows us to give an explanation to the model behavior, in particular to how each feature impact on the model’s output. Here each output/prediction is seen as a sum of the contribution of each individual feature.

It provides several tools in order to deeply inspect the model predictions, in particular through detailed plots.
These plots give us a [4]:

  • Global interpretability: through summary plots. These reflect the general behavior of the features in the model and allow us to understand which are the features that most impact the final output and of how much.
  • Local interpretability: through force/dependence plots. These show the specific behavior of the features in a single model prediction, allowing us to understand all their single impacts on the final output.
  • It can be used for several machine learning models: SHAP provides several explainers that cover most of the machine learning methods. These are a collection of classes, where each class represents an explainer for a specific machine learning algorithm. The explainer is the object that allows us to understand the model behavior.

Plots

Tree SHAP provides us with several different types of plots, each one highlighting a specific aspect of the model. The available plots are:

  • Summary plot
  • Force plot
  • Dependence plot
  • Decision plot

These plots are generated after the computation of the SHAP values. These values measure how and how much each feature impacts the model.
In particular, they are computed through a method that looks at the marginal contribution of each feature. What this method does, to evaluate the impact of a feature is to see how the output of the model changes after the feature removal. To evaluate the change it averages the results of the differences in predictions over all possible orderings of the other features [1, 4].

Interpretation

Suppose to be in a learning to rank scenario.

We have to manage a book catalog in an e-commerce website. Each book has many different features such as publishing year, target age, genre, author, and so on.
A user can visit the website, make a query through some filters selection on the books’ features, and then inspect the obtained search result page.
In order to train our model, we collect all the interactions that users have with the website products (e.g. views, clicks, add to cart, sales..) and create a data set consisting of <query, document> pairs (e.g. the filters selected and the features of the product viewed/clicked/sold/…).

We obtain something like this, where s_feature indicates the selected feature from the website filters and book_feature the feature of the product with which the user interacted:

Interactionss_genres_price_rangebook_genrebook_authorbook_price
interaction_1thriller[15-20]thrillerBrown18
interaction_2mystery[5-10]mysteryChristie8
interaction_3fantasy[10-15]fantasyAsimov15

In order to use them, these features need to be manipulated.
In particular the categorical features need to be encoded. We do this using the one-hot encoding, that creates a column for each value of each categorical features. In this way we will obtain something like this for the genre column:

Interactionsis_genre_thrilleris_genre_mysteryis_genre_fantasy
interaction_1TrueFalseFalse
interaction_2FalseTrueFalse
interaction_3FalseFalseTrue

Now we are ready to explain the Tree SHAP plots.

summary plot

The first plot I would like to analyze is the summary plot.
This can give us global information on the interpretability of the model.

As we can see from the picture below, the plot represents:

  • the most important feature of the model on the y-axis in a descending order (at the top the most important one).
  • the SHAP value on the x-axis.
  • the feature value with colors. A high value is represented with red, while a low value with blue.
  • also here each point represent a prediction result.

From the example we can see that:

  • the higher the total number of reviews the higher the positive impact on the relevance
  • the higher the review average the higher the positive impact on the relevance
  • if it is an ebook it is more relevant in most of the cases
  • it the book genre is fantasy it has a negative impact on the relevance

There are also features for which there isn’t a clear behavior with respect to their values, for example the book sales, the book price and the publishing year.
From the plot we can also see how much each feature impact the model looking at the x-axis with the SHAP value.

Another type of summary plot is the bar one:

This represents the same concept of the other using a bar representation with the mean(|SHAP value|) in the x-axis.

FOrce plot

The second plot I would like to analyze is the force plot.

This plot allow us to give explainability to a single model prediction.
Suppose to take an interaction like:

Interactionis_publishing_year_2020is_for_age_40is_ebookis_new_arrivals
interaction_4FalseFalseFalseFalse

The corresponding plot will be:

From the plot we can see:

  1. The model output value: -4.54
  2. The base value: this is the value that would be predicted if we didn’t know any features for the current output [1].
  3. The impact of each feature on the output.

In particular, we can see some red and blue arrows associated with each feature.
Each of this arrow shows:

  • how much the feature impacts the model: the bigger the arrow, the bigger the impact.
  • how the feature impacts the model: a red arrow increases the model output value while a blue arrow decreases the model output value.

In the plot we represent, the fact that the book has not been published in year 2020 and doesn’t have a target age range of [30-50] impact positively on the output, while not being an ebook, not being a new arrival and not having a legend genre, impact negatively.

Since we are talking about learning to rank, the model output represents the SHAP score of the book. The scores of all the books in answer to a specific query are used to rank the products. Therefore if our model predicts:

InteractionsquerybookSHAP score (model output)
interaction_5q1book_1-2.91
interaction_6q1book_2-4.54
interaction_7q1book_3-1.85

We will have, for the query q1, the ranking:

  1. book_3 (-1.85)
  2. book_1 (-2.91)
  3. book_2 (-4.54)

Since -4.54 < -2.91 < -1.85 .

An interesting aspect of this plot emerges from the comparison of the outputs for a specific query.
Looking at how each book is scored inside a query, we can detect the differences between products in terms of features’ values.

If we want a global representation of the previous predictions, we can use a variant of the force plot:

Here we can see the predictions made before (one for each interaction) place vertically (rotated of 90°) and side by side.

dependence plot

Another plot useful for the local interpretability is the dependence plot.
This plot compares a chosen feature with another one and shows if these two features have an interaction effect.

As a first example, I reported here the dependence plot between age and education-num for a model trained on the classic UCI adult income dataset (which is classification task to predict if people made over 50k in the 90s)[5].

Figure from [5]

Here each point corresponds to a prediction. In the x-axis we have the Age while in the y-axis we have the predicted SHAP value (how much knowing that feature’s value changes the output of the model for that sample’s prediction).
The color represents the Education-Num, therefore we can see if having a specific age AND having a specific education-num impact positively or negatively on the output.
From the plot we can deduce that 20-year-olds with a high level of education are less likely make over 50k than 20-year-olds with a low level of education, while 50-year-olds with a high level of education are more likely make over 50k than 50-year-olds with a low level of education. This suggests an interaction effect between Education-Num and Age [5].

This kind of relationships aren’t always present between features as we can see, from our book scenario, for the features book_price and is_genre_fantasy:

decision plot

The last plot I would like to present is the decision plot.

This plot shows how the prediction changes during the decision process. In the y-axis we have the features ordered by importance as for the summary plot. In the x-axis we have the output of the model.

Moving from the bottom of the plot to the top, SHAP values for each feature are added to the model’s base value. This shows how each feature contributes to the overall prediction [5].

Here each line represent a single prediction, so suppose to consider this one:

If we just plot the correspondent line we will have:

Here the value of each features is reported in parenthesis.
From the graph we can see that is_for_age_40-50 False, is_author_Asimov True, is_publishing_year_2020 True, is_book_genre_in_cart 6 and book_reviews 992 impact positively to the model, while the other features impact negatively.

Pros

What I would like to highlight with this post is the usefulness of this tool.
Tree SHAP allows us to:

  • Interpret how the model makes a specific decision through the force and decision plots.
  • Compare the predictions belonging to a common query printing all the related force plots. Therefore to make a query analysis.
  • Understand the relative importance of the features through the summary plot.
  • See how the value for each feature impact the model, if positively or negatively, through the summary plot.
  • Understand if we have a training set and a model that reflects our scenario.
  • Analyze if we correctly store the interactions used or if there are any anomalies.
  • Identify which features to prioritize for improvements based on their importance.

To be aware of

When using this tool we have to be aware of a couple of things:

  1. The measure of the importance of the features is executed considering the totality of the interactions as a unique set. The interactions aren’t considered grouped by query. Therefore we can’t directly see the importance of the features within each query, but we have to extrapolate all the interactions with the same query before and then execute the plot just on them.
  2. The output of the model is not the relevance label. The output is just a measure of the relevance of that product for that query, but it is a value generated from the library that doesn’t reflect the relevance labels we use in training/testing. Despite this, the score represents the same concept if we look at the relative relevance between products. A product with a score of 2 for the query one is more relevant with respect to another product with a score of 0 for the same query.
  3. From what we said from the previous point, we have to pay attention on how we interpret the score. A negative value doesn’t directly means that the document is not relevant. We always have to consider it in relation to the other products in the same query.

Future Works

We have added to our to-do list also the integration of the TreeSHAP library in Solr.
Since Solr allows to use a learning to rank model for the re-ranking of the documents, it could be very useful to analyze directly the models behavior inside the platform.

You can find the first opened jira issues here:


References:

[1] Lundberg, Scott M., and Su-In Lee. “A unified approach to interpreting model predictions.” Advances in neural information processing systems. 2017.
[2] SHAP GitHub: https://github.com/slundberg/shap
[3] Why Tree SHAP: https://towardsdatascience.com/interpretable-machine-learning-with-xgboost-9ec80d148d27
[4] SHAP values: https://towardsdatascience.com/explain-your-model-with-the-shap-values-bc36aac4de3d
[5] Dependence plot: https://slundberg.github.io/shap/notebooks/plots/dependence_plot.html

Other useful links:

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