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shapley values logistic regression

This is a living document, and serves It is mind-blowing to explain a prediction as a game played by the feature values. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. If your model is a deep learning model, use the deep learning explainer DeepExplainer(). In this example, I use the Radial Basis Function (RBF) with the parameter gamma. Methods like LIME assume linear behavior of the machine learning model locally, but there is no theory as to why this should work. The Shapley value allows contrastive explanations. A variant of Relative Importance Analysis has been developed for binary dependent variables. A Support Vector Machine (AVM) finds the optimal hyperplane to separate observations into classes. But we would use those to compute the features Shapley value. Content Discovery initiative April 13 update: Related questions using a Review our technical responses for the 2023 Developer Survey. This formulation can take two The value of the j-th feature contributed \(\phi_j\) to the prediction of this particular instance compared to the average prediction for the dataset. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. BreakDown also shows the contributions of each feature to the prediction, but computes them step by step. Finally, the R package DALEX (Descriptive mAchine Learning EXplanations) also contains various explainers that help to understand the link between input variables and model output. center of the partial dependence plot with respect to the data distribution. Does shapley support logistic regression models? First, lets load the same data that was used in Explain Your Model with the SHAP Values. Mathematically, the plot contains the following points: {(x ( i) j, ( i) j)}ni = 1. For each iteration, a random instance z is selected from the data and a random order of the features is generated. This contrastiveness is also something that local models like LIME do not have. To simulate that a feature value is missing from a coalition, we marginalize the feature. The result is the arithmetic average of the mean (or expected) marginal contributions of xi to z. Be Fluent in R and Python, Dimension Reduction Techniques with Python, Explain Any Models with the SHAP Values Use the KernelExplainer, If I were to earn 300 more a year, my credit score would increase by 5 points.. Why does the narrative change back and forth between "Isabella" and "Mrs. John Knightley" to refer to Emma's sister? The Shapley value is a solution for computing feature contributions for single predictions for any machine learning model. We start with an empty team, add the feature value that would contribute the most to the prediction and iterate until all feature values are added. Lets understand what's fair distribution using Shapley value. I will repeat the following four plots for all of the algorithms: The entire code is available at the end of the article, or via this Github. Given the current set of feature values, the contribution of a feature value to the difference between the actual prediction and the mean prediction is the estimated Shapley value. P.S. We are interested in how each feature affects the prediction of a data point. While conditional sampling fixes the issue of unrealistic data points, a new issue is introduced: But when I run the code in cell 36 in the image above I get an. You can produce a very elegant plot for each observation called the force plot. Shapley values tell us how to distribute the prediction among the features fairly. Besides SHAP, you may want to check LIME in Explain Your Model with LIME for the LIME approach, and Microsofts InterpretML in Explain Your Model with Microsofts InterpretML. Thus, Yi will have only k-1 variables. Can I use the spell Immovable Object to create a castle which floats above the clouds? The SHAP module includes another variable that alcohol interacts most with. Parabolic, suborbital and ballistic trajectories all follow elliptic paths. \(val_x(S)\) is the prediction for feature values in set S that are marginalized over features that are not included in set S: \[val_{x}(S)=\int\hat{f}(x_{1},\ldots,x_{p})d\mathbb{P}_{x\notin{}S}-E_X(\hat{f}(X))\]. Has anyone been diagnosed with PTSD and been able to get a first class medical? There are 160 data points in our X_test, so the X-axis has 160 observations. The players are the feature values of the instance that collaborate to receive the gain (= predict a certain value). # 100 instances for use as the background distribution, # compute the SHAP values for the linear model, # make a standard partial dependence plot, # the waterfall_plot shows how we get from shap_values.base_values to model.predict(X)[sample_ind], # make a standard partial dependence plot with a single SHAP value overlaid, # the waterfall_plot shows how we get from explainer.expected_value to model.predict(X)[sample_ind], # a classic adult census dataset price dataset, # set a display version of the data to use for plotting (has string values), "distilbert-base-uncased-finetuned-sst-2-english", # build an explainer using a token masker, # explain the model's predictions on IMDB reviews, An introduction to explainable AI with Shapley values, A more complete picture using partial dependence plots, Reading SHAP values from partial dependence plots, Be careful when interpreting predictive models in search of causalinsights, Explaining quantitative measures of fairness. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. This is fine as long as the features are independent. I suggest looking at KernelExplainer which as described by the creators here is. Using the kernalSHAP, first you need to find the shaply value and then find the single instance, as following below; as the original text is "good article interested natural alternatives treat ADHD" and Label is "1". \[\sum\nolimits_{j=1}^p\phi_j=\hat{f}(x)-E_X(\hat{f}(X))\], Symmetry To learn more, see our tips on writing great answers. Once all Shapley value shares are known, one may retrieve the coefficients (with original scale and origin) by solving an optimization problem suggested by Lipovetsky (2006) using any appropriate optimization method. Be careful to interpret the Shapley value correctly: This is the predicted value for the data point x minus the average predicted value. The concept of Shapley value was introduced in (cooperative collusive) game theory where agents form collusion and cooperate with each other to raise the value of a game in their favour and later divide it among themselves. There are two options: one-vs-rest (ovr) or one-vs-one (ovo) (see the scikit-learn api). We replace the feature values of features that are not in a coalition with random feature values from the apartment dataset to get a prediction from the machine learning model. What should I follow, if two altimeters show different altitudes? This section goes deeper into the definition and computation of the Shapley value for the curious reader. where x is the instance for which we want to compute the contributions. The park-nearby contributed 30,000; area-50 contributed 10,000; floor-2nd contributed 0; cat-banned contributed -50,000. The most common way to define what it means for a feature to join a model is to say that feature has joined a model when we know the value of that feature, and it has not joined a model when we dont know the value of that feature. Like the random forest section above, I use the function KernelExplainer() to generate the SHAP values. Adding EV Charger (100A) in secondary panel (100A) fed off main (200A), User without create permission can create a custom object from Managed package using Custom Rest API. The answer could be: The book discusses linear regression, logistic regression, other linear regression extensions, decision trees, decision rules and the RuleFit algorithm in more detail. The SHAP values look like this: SHAP values, first 5 passengers The higher the SHAP value the higher the probability of survival and vice versa. for a feature to join or not join a model. It connects optimal credit allocation with local explanations using the classic Shapley values from game theory and their related extensions (see papers for details and citations). Copyright 2018, Scott Lundberg. rev2023.5.1.43405. where \(E(\beta_jX_{j})\) is the mean effect estimate for feature j. You are supposed to use a different explainder for different models, Shap is model agnostic by definition. My issue is that I want to be able to analyze a single prediction and get something more along these lines: In other words, I want to know which specific words contribute the most to the prediction. The Shapley value requires a lot of computing time. The first one is the Shapley value. If we are willing to deal with a bit more complexity we can use a beeswarm plot to summarize the entire distribution of SHAP values for each feature. If your model is a tree-based machine learning model, you should use the tree explainer TreeExplainer() which has been optimized to render fast results. (2016). All possible coalitions (sets) of feature values have to be evaluated with and without the j-th feature to calculate the exact Shapley value. With a prediction of 0.57, this womans cancer probability is 0.54 above the average prediction of 0.03. Continue exploring All interpretable models explained in this book are interpretable on a modular level, with the exception of the k-nearest neighbors method. The following figure shows all coalitions of feature values that are needed to determine the Shapley value for cat-banned. In order to connect game theory with machine learning models it is nessecary to both match a models input features with players in a game, and also match the model function with the rules of the game. While there are many ways to train these types of models (like setting an XGBoost model to depth-1), we will Model Interpretability Does Not Mean Causality. . Players cooperate in a coalition and receive a certain profit from this cooperation. Feature contributions can be negative. The prediction of SVM for this observation is 6.00, different from 5.11 by the random forest. What is the connection to machine learning predictions and interpretability? Studied Mathematics, graduated in Cryptanalysis, working as a Senior Data Scientist. This step can take a while. This plot has loaded information. Another solution comes from cooperative game theory: Transfer learning for image classification. What does 'They're at four. The output of the SVM shows a mild linear and positive trend between alcohol and the target variable. This powerful methodology can be used to analyze data from various fields, including medical and health Instead, we model the payoff using some random variable and we have samples from this random variable. 2. By default a SHAP bar plot will take the mean absolute value of each feature over all the instances (rows) of the dataset. It signifies the effect of including that feature on the model prediction. Entropy criterion is used for constructing a binary response regression model with a logistic link. The forces that drive the prediction lower are similar to those of the random forest; in contrast, total sulfur dioxide is a strong force to drive the prediction up. For a certain apartment it predicts 300,000 and you need to explain this prediction. 566), Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI. To evaluate an existing model \(f\) when only a subset \(S\) of features are part of the model we integrate out the other features using a conditional expected value formulation. In the following figure we evaluate the contribution of the cat-banned feature value when it is added to a coalition of park-nearby and area-50. After calculating data Shapley values, we removed data points from the training set, starting from the most valuable datum to the least valuable, and trained a new logistic regression model each . For anyone lookibg for the citation: Papers are helpful, but it would be even more helpful if you could give a precis of these (maybe a paragraph or so) & say what SR is. Approximate Shapley estimation for single feature value: First, select an instance of interest x, a feature j and the number of iterations M. The Shapley value is the average contribution of a feature value to the prediction in different coalitions. The feature value is the numerical or categorical value of a feature and instance; The Shapley value of a feature value is the average change in the prediction that the coalition already in the room receives when the feature value joins them. This research was designed to compare the ability of different machine learning (ML) models and nomogram to predict distant metastasis in male breast cancer (MBC) patients and to interpret the optimal ML model by SHapley Additive exPlanations (SHAP) framework. The random forest model showed the best predictive performance (AUROC 0.87) and there was a statistically significant difference between the traditional logistic regression model and the test dataset. Could a subterranean river or aquifer generate enough continuous momentum to power a waterwheel for the purpose of producing electricity? The contribution \(\phi_j\) of the j-th feature on the prediction \(\hat{f}(x)\) is: \[\phi_j(\hat{f})=\beta_{j}x_j-E(\beta_{j}X_{j})=\beta_{j}x_j-\beta_{j}E(X_{j})\]. Let us reuse the game analogy: Thanks for contributing an answer to Stack Overflow! The prediction of GBM for this observation is 5.00, different from 5.11 by the random forest. Not the answer you're looking for? The questions are not about the calculation of the SHAP values, but the audience thought about what SHAP values can do. The following code displays a very similar output where its easy to see how the model made its prediction and how much certain words contributed. The number of diagnosed STDs increased the probability the most. SHAP values can be very complicated to compute (they are NP-hard in general), but linear models are so simple that we can read the SHAP values right off a partial dependence plot. If you want to get deeper into the Machine Learning algorithms, you can check my post My Lecture Notes on Random Forest, Gradient Boosting, Regularization, and The Shapley value applies primarily in situations when the contributions . Using the kernalSHAP, first you need to find the shaply value and then find the single instance, as following below; #convert your training and testing data using the TF-IDF vectorizer tfidf_vectorizer = TfidfVectorizer (use_idf=True) tfidf_train = tfidf_vectorizer.fit_transform (IV_train) tfidf_test = tfidf_vectorizer.transform (IV_test) model . get_feature_names (), plot_type = 'dot') Explain the sentiment for one review I tried to follow the example notebook Github - SHAP: Sentiment Analysis with Logistic Regression but it seems it does not work as it is due to json . Think about this: If you ask me to swallow a black pill without telling me whats in it, I certainly dont want to swallow it. All clear now? Logistic Regression is a linear model, so you should use the linear explainer. Works within all common types of modelling framework: Logistic and ordinal, as well as linear models. It is often crucial that the machine learning models are interpretable. Averaging implicitly weighs samples by the probability distribution of X. ', referring to the nuclear power plant in Ignalina, mean? Connect and share knowledge within a single location that is structured and easy to search. We predict the apartment price for the coalition of park-nearby and area-50 (320,000). The difference between the prediction and the average prediction is fairly distributed among the feature values of the instance the Efficiency property of Shapley values. This has to go back to the Vapnik-Chervonenkis (VC) theory. Note that the blue partial dependence plot line (which the is average value of the model output when we fix the median income feature to a given value) always passes through the interesection of the two gray expected value lines. How can I solve this? . Suppose we want to get the dependence plot of alcohol. The intrinsic models obtain knowledge by restricting the rules of machine learning models, e.g., linear regression, logistic analysis, and Grad-CAM . The Shapley value works for both classification (if we are dealing with probabilities) and regression. The sum of Shapley values yields the difference of actual and average prediction (-2108). The Shapley value fairly distributes the difference of the instance's prediction and the datasets average prediction among the features. Explanations created with the Shapley value method always use all the features. Is there any known 80-bit collision attack? You actually perform multiple integrations for each feature that is not contained S. The value floor-2nd was replaced by the randomly drawn floor-1st. The Shapley value is a solution concept in cooperative game theory.It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. A higher-than-the-average sulfur dioxide (= 18 > 14.98) pushes the prediction to the right. The exponential growth in the time needed to run Shapley regression places a constraint on the number of predictor variables that can be included in a model. Note that Pr is null for r=0, and thus Qr contains a single variable, namely xi. This is an introduction to explaining machine learning models with Shapley values. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, Use SHAP values to explain LogisticRegression Classification, When AI meets IP: Can artists sue AI imitators? The feature importance for linear models in the presence of multicollinearity is known as the Shapley regression value or Shapley value13. Here I use the test dataset X_test which has 160 observations. The contribution of cat-banned was 310,000 - 320,000 = -10,000. It provides both global and local model-agnostic interpretation methods. The prediction for this observation is 5.00 which is similar to that of GBM. The Shapley value is the average marginal contribution of a feature value across all possible coalitions. It says mapping into a higher dimensional space often provides greater classification power. Is there a generic term for these trajectories? There are two good papers to tell you a lot about the Shapley Value Regression: Lipovetsky, S. (2006). The dependence plot of GBM also shows that there is an approximately linear and positive trend between alcohol and the target variable. Before using Shapley values to explain complicated models, it is helpful to understand how they work for simple models. Lundberg et al. I can see how this works for regression. Whats tricky is that H2O has its data frame structure. In the example it was cat-allowed, but it could have been cat-banned again. We simulate that only park-nearby, cat-banned and area-50 are in a coalition by randomly drawing another apartment from the data and using its value for the floor feature. The exponential number of the coalitions is dealt with by sampling coalitions and limiting the number of iterations M. We . The Dataman articles are my reflections on data science and teaching notes at Columbia University, rf = RandomForestRegressor(max_depth=6, random_state=0, n_estimators=10), shap.summary_plot(rf_shap_values, X_test), shap.dependence_plot("alcohol", rf_shap_values, X_test), # plot the SHAP values for the 10th observation, shap.force_plot(rf_explainer.expected_value, rf_shap_values, X_test), shap.summary_plot(gbm_shap_values, X_test), shap.dependence_plot("alcohol", gbm_shap_values, X_test), shap.force_plot(gbm_explainer.expected_value, gbm_shap_values, X_test), shap.summary_plot(knn_shap_values, X_test), shap.dependence_plot("alcohol", knn_shap_values, X_test), shap.force_plot(knn_explainer.expected_value, knn_shap_values, X_test), shap.summary_plot(svm_shap_values, X_test), shap.dependence_plot("alcohol", svm_shap_values, X_test), shap.force_plot(svm_explainer.expected_value, svm_shap_values, X_test), X_train, X_test = train_test_split(df, test_size = 0.1), X_test = X_test_hex.drop('quality').as_data_frame(), h2o_wrapper = H2OProbWrapper(h2o_rf,X_names), h2o_rf_explainer = shap.KernelExplainer(h2o_wrapper.predict_binary_prob, X_test), shap.summary_plot(h2o_rf_shap_values, X_test), shap.dependence_plot("alcohol", h2o_rf_shap_values, X_test), shap.force_plot(h2o_rf_explainer.expected_value, h2o_rf_shap_values, X_test), Explain Your Model with Microsofts InterpretML, My Lecture Notes on Random Forest, Gradient Boosting, Regularization, and, Explaining Deep Learning in a Regression-Friendly Way, A Technical Guide on RNN/LSTM/GRU for Stock Price Prediction, A unified approach to interpreting model predictions, Identify Causality by Regression Discontinuity, Identify Causality by Difference in Differences, Identify Causality by Fixed-Effects Models, Design of Experiments for Your Change Management. Regress (least squares) z on Pr to obtain R2p. Let me walk you through: You want to save the summary plots. The SHAP builds on ML algorithms. An intuitive way to understand the Shapley value is the following illustration: What is Shapley value regression and how does one implement it? In Explain Your Model with the SHAP Values I use the function TreeExplainer() for a random forest model. The Additivity property guarantees that for a feature value, you can calculate the Shapley value for each tree individually, average them, and get the Shapley value for the feature value for the random forest. I am indebted to seanPLeary who has contributed to the H2O community on how to produce the SHAP values with AutoML. One solution might be to permute correlated features together and get one mutual Shapley value for them. When compared with the output of the random forest, GBM shows the same variable ranking for the first four variables but differs for the rest variables. Each \(x_j\) is a feature value, with j = 1,,p. Shapley Value Regression and the Resolution of Multicollinearity. It also lists other interpretable models. Then for each predictor, the average improvement will be calculated that is created when adding that variable to a model. The output shows that there is a linear and positive trend between alcohol and the target variable. So if you have feedback or contributions please open an issue or pull request to make this tutorial better! Another package is iml (Interpretable Machine Learning). I was going to flag this as plagiarized, then realized you're actually the original author. A Medium publication sharing concepts, ideas and codes. LIME does not guarantee that the prediction is fairly distributed among the features. Why refined oil is cheaper than cold press oil? Should I re-do this cinched PEX connection? Because the goal here is to demonstrate the SHAP values, I just set the KNN 15 neighbors and care less about optimizing the KNN model. Then I will provide four plots. What does ** (double star/asterisk) and * (star/asterisk) do for parameters? Be Fluent in R and Python in which I compare the most common data wrangling tasks in R dply and Python Pandas. Explaining prediction models and individual predictions with feature contributions. Knowledge and information systems 41.3 (2014): 647-665., Lundberg, Scott M., and Su-In Lee. In the current work, the SV approach to the logistic regression modeling is considered. I provide more detail in the article How Is the Partial Dependent Plot Calculated?. Revision 45b85c18. Background The progression of Alzheimer's dementia (AD) can be classified into three stages: cognitive unimpairment (CU), mild cognitive impairment (MCI), and AD. The sum of contributions yields the difference between actual and average prediction (0.54). Here is what a linear model prediction looks like for one data instance: \[\hat{f}(x)=\beta_0+\beta_{1}x_{1}+\ldots+\beta_{p}x_{p}\]. Binary outcome variables use logistic regression. You can pip install SHAP from this Github. The forces driving the prediction to the right are alcohol, density, residual sugar, and total sulfur dioxide; to the left are fixed acidity and sulphates. Instead of fitting a straight line or hyperplane, the logistic regression model uses the logistic function to squeeze the output of a linear equation between 0 and 1. How to Increase accuracy and precision for my logistic regression model? These consist of models like Linear regression, Logistic regression ,Decision tree, Nave Bayes and k-nearest neighbors etc. The instance \(x_{-j}\) is the same as \(x_{+j}\), but in addition has feature j replaced by the value for feature j from the sample z. We will take a practical hands-on approach, using the shap Python package to explain progressively more complex models. How to handle multicollinearity in a linear regression with all dummy variables? Readers are recommended to purchase books by Chris Kuo: Your home for data science. PMLR (2020)., Staniak, Mateusz, and Przemyslaw Biecek. The gain is the actual prediction for this instance minus the average prediction for all instances. The Shapley value, coined by Shapley (1953)63, is a method for assigning payouts to players depending on their contribution to the total payout. features: HouseAge - median house age in block group, AveRooms - average number of rooms per household, AveBedrms - average number of bedrooms per household, AveOccup - average number of household members. It is available here. A boy can regenerate, so demons eat him for years. The features values of an instance cooperate to achieve the prediction. SHAP, an alternative estimation method for Shapley values, is presented in the next chapter. This departure is expected because KNN is prone to outliers and here we only train a KNN model. Mishra, S.K. : Shapley value regression / driver analysis with binary dependent variable. For more complex models, we need a different solution. Thats exactly what the KernelExplainer, a model-agnostic method, is designed to do. One main comment is Can you identify the drivers for us to set strategies?, The above comment is plausible, showing the data scientists already delivered effective content.

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