Interview Prep
Career
GenAI
Prompt Engg
ChatGPT
LLM
Langchain
RAG
AI Agents
Machine Learning
Deep Learning
GenAI Tools
LLMOps
Python
NLP
SQL
AIML Projects

Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Accumulated Local Effects (ALE) – Feature Effects Global Interpretability

Aman
Aman Last Updated : 29 Dec, 2020
6 min read

This article was published as a part of the Data Science Blogathon.

This article happens to be a continuation of my last article on ‘Global Model Interpretability Techniques for Black Box Models’. Here we will discuss the feature importance technique – Accumulated Local Effects (ALE).

Introduction

With the availability of larger and richer data sets in many domains, black box supervised learning models like complex trees, random forests, boosted trees, nearest neighbors, support vector machines, etc. are gaining more importance as compared to the more transparent and more interpretable linear and logistic regression models to capture non-linear phenomena. Even if the purpose is purely predictive, understanding the effects of the predictors may still be quite important.

If the effect of a predictor violates intuition (e.g. if it appears from the supervised learning model that the risk of experiencing a cardiac event decreases as patients age), then this is either an indication that the fitted model is unreliable or that a surprising new phenomenon has been discovered. In addition, predictive models must be transparent in many regulatory environments, e.g. to demonstrate to regulators that consumer credit risk models do not penalize credit applicants based on age, race, etc.

When fitting black box supervised learning models, visualizing the main effects of the individual predictor variables and their low-order interaction effects is often important, and partial dependence (PD) plots are the most popular approach for accomplishing this.

However, they suffer from a stringent assumption: features have to be uncorrelated. In real-world scenarios, features are often correlated, whether because some are directly computed from others, or because observed phenomena produce correlated distributions. Hence, we need an unbiased technique, which ignores correlation among the features to a great extent. Accumulated Local Effects (ALE) can handle correlated predictors. 

 

PDP vs  M-plot vs Accumulated Local Effects (ALE)

In this article, we will explain a house price prediction example. For constructing a Partial Dependence Plot the following steps are to be followed:

  • Select feature
  • Define grid
  • Per grid value:
    • Replace feature with grid value
    • Average predictions
  • Draw the curve

For example, if we want to find the feature effects of sqft_living variable in comparison to the number of rooms, for the calculation of the first grid value of the PDP – say 40 m2 – we replace the sqft_living area for all instances by 40 m2, even for the houses with up to 8 rooms. The partial dependence plot includes these unrealistic houses in the feature effect estimation and pretends that everything is fine.

Strongly correlated features x1 and x2. To calculate the feature effect of x1 at 0.75, the PDP replaces x1 of all instances with 0.75, falsely assuming that the distribution of x2 at x1 = 0.75 is the same as the marginal distribution of x2 (vertical line). This results in unlikely combinations of x1 and x2 (e.g. x2=0.2 at x1=0.75), which the PDP uses for the calculation of the average effect.

To find the feature effects of correlated features, we can average over the conditional distribution of the feature, meaning at a grid value of x1, we average the predictions of instances with a similar x1 value. The solution for calculating feature effects using the conditional distribution is called Marginal Plots or M-Plots. But here also we have a problem. If we average the predictions of all houses of about 40 m2, we estimate the combined effect of the sqft_living and the number of rooms, due to the correlation. Even if the sqft_living has no effect on the price of a house, the M-plot will still show that an increase in the sqft_living increases the price of the house. The following plot shows for two correlated features how M-plots work.

Strongly correlated features x1 and x2. M-Plots average over the conditional distribution. Here the conditional distribution of x2 at x1 = 0.75. Averaging the local predictions leads to mixing the effects of both features.

M-Plots avoid averaging predictions of unlikely data instances, but they mix the effect of a feature with the effects of all correlated features. ALE plots solve this problem by calculating the differences in predictions instead of averages.  For the sqft_living variable at a value of 40 m2, the ALE technique uses all houses with about 40 m2, gets the model predictions pretending those houses were 41m2 minus the prediction pretending they were 39 m2. This gives us the pure feature effect of the sqft_living variable, without taking into account the effect of the correlated features.  The following graphic provides intuition on how ALE plots are calculated:

Calculation of ALE for feature x1, which is correlated with x2. First, we divide the feature into intervals (vertical lines). For the data instances (points) in an interval, we calculate the difference in the prediction when we replace the feature with the upper and lower limit of the interval (horizontal lines). These differences are later accumulated and centered, resulting in the ALE curve.

 

Implementation

Let us see how to implement ALE for a regression problem of predicting the house prices of King’s County. The dataset includes homes sold between May 2014 and May 2015. The Dataset has 21 features and 21613 observations. The dataset has been split into train, validation, and test, with the Test data having 2217 observations, as against train and validation data having 9761 and 9635 observations respectively. We train the model on the Train data. Evaluate several models on the Validation data. The final model is then used for predicting the target variable (Price) for the Test data.

We need to perform data cleaning and an exploratory data analysis to get to the model building stage. You can find the code here:  Link to code

After cleaning the data and performing the EDA, we ended with the following variables:

  • Predictors – bedrooms, bathrooms, log-transformed sqft_living, log-transformed sqft_lot, grade, log-transformed sqft_above, and yr_built.
  • Target – Log transformed the prices of the houses.

We will perform a Multiple Linear Regression and a Random Forest model to understand the technique. We have used the ‘alibi‘ library.

Accumulated Local Effects

Next, we used the ALE technique for the Regression and the Random Forest model.

Accumulated Local Effects

 

Interpretation

Let us consider the ALE plot of the sqft_living variable to interpret the results.

Accumulated Local Effects

The ALE on the y_axis of the plot above is in the units of the prediction variable, i.e. the log-transformed price of the house in $. The ALE value for the point sqft-living = 8.5 is ~0.4, which has the interpretation that for neighborhoods for which the average log-transformed sqft_living is ~8.5 the model predicts an up-lift of log-transformed 0.4 units of price in $ due to the feature sqft_living with respect to the average prediction.

On the other hand, for the neighborhoods with an average log-transformed sqft_living lower than ~7.5, the feature effect on the prediction becomes negative, i.e. the log-transformed price in $ falls.

The ALE plots for the linear regression model are linear themselves—the feature effects are after all linear by definition. In fact, the slopes of the ALE lines are exactly the coefficients of the linear regression.

Thus the slopes of the ALE plots for linear regression have exactly the same interpretation as the coefficients of the learned model—global feature effects.

We can compare the ALE results for the two models.

In the above plot, we can see Linear Regression feature effects of sqft_living are positively correlated, whereas Random Forest feature effects of sqft_living are not monotonic.

To compare multiple models and multiple features we can plot the ALE’s on a common axis that is big enough to accommodate all features of interest:

Accumulated Local Effects

 

Advantages of Accumulated Local Effects(ALE) Plots

  • ALE plots are unbiased, meaning they work with correlated features.
  • ALE plots are computationally fast to compute.
  • The interpretation of the ALE plot is clear.

 

Disadvantages of Accumulated Local Effects(ALE) Plots

  • The implementation of ALE plots is complicated and difficult to understand.
  • Interpretation still remains difficult if features are strongly correlated.

 

Conclusion

For visualizing the effects of the predictor variables in black box supervised learning models, PD plots are the most widely used method. The Accumulated Local Effects (ALE) plots are an alternative to the PD plots that work well on moderately correlated variables. This paper has been dedicated to ‘Sir Christoph Molnar‘. The motivation was his holistic work ‘A Guide for Making Black Box Models Explainable‘.

Reference

‘Visualizing the effects of predictor variables in black
box supervised learning models’ by Daniel W. Apley and Jingyu Zhu.

Aman
Aman

Free Courses

Generative AI 4.7

Generative AI - A Way of Life

Explore Generative AI for beginners: create text and images, use top AI tools, learn practical skills, and ethics.
Large Language Models 4.5

Getting Started with Large Language Models

Master Large Language Models (LLMs) with this course, offering clear guidance in NLP and model training made simple.
Prompt Engineering 4.6

Building LLM Applications using Prompt Engineering

This free course guides you on building LLM apps, mastering prompt engineering, and developing chatbots with enterprise data.
LlamaIndex 4.8

Improving Real World RAG Systems: Key Challenges & Practical Solutions

Explore practical solutions, advanced retrieval strategies, and agentic RAG systems to improve context, relevance, and accuracy in AI-driven applications.
RAG systems using LlamaIndex 4.7

Microsoft Excel: Formulas & Functions

Master MS Excel for data analysis with key formulas, functions, and LookUp tools in this comprehensive course.

Recommended Articles

Responses From Readers

Clear

Write for us

Write, captivate, and earn accolades and rewards for your work
  • Reach a Global Audience
  • Get Expert Feedback
  • Build Your Brand & Audience
  • Cash In on Your Knowledge
  • Join a Thriving Community
  • Level Up Your Data Science Game
imag

We use cookies essential for this site to function well. Please click to help us improve its usefulness with additional cookies. Learn about our use of cookies in our Privacy Policy & Cookies Policy.

Show details