permutation feature importance vs shap

The target for the regression model is the prediction for a coalition. Red SHAP values increase the prediction, blue values decrease it. There are two reasons why SHAP got its own chapter and is not a subchapter of Shapley values. There is a big difference between both importance measures: Permutation feature importance is based on the decrease in model performance. For each feature, I generated a weight, which was sampled from a gamma distribution with specified gamma and scale parameters (gamma=1, scale=1). The Shapley interaction index from game theory is defined as: \[\phi_{i,j}=\sum_{S\subseteq\setminus\{i,j\}}\frac{|S|!(M-|S|-2)!}{2(M-1)! SHAP also satisfies these, since it computes Shapley values. Copyright 2018, Scott Lundberg. Effects might be due to confounding (e.g. number of training samples in that node). For more years on contraceptives, the occurence of a STD reduces the predicted risk. Shapley values can be misinterpreted and access to data is needed to compute them for new data (except for TreeSHAP). Let \(\hat{f}_x(z')=\hat{f}(h_x(z'))\) and \(z_{\setminus{}j}'\) indicate that \(z_j'=0\). We can use the fast TreeSHAP estimation method instead of the slower KernelSHAP method, since a random forest is an ensemble of trees. This notebooks demonstrates how to use the Permutation explainer on some simple datasets. \(h_x\) for tabular data treats \(X_C\) and \(X_S\) as independent and integrates over the marginal distribution: Sampling from the marginal distribution means ignoring the dependence structure between present and absent features. A player can be an individual feature value, e.g. (I am not so sure whether the resulting coefficients would still be valid Shapley values though.). Then I calculate the Spearman rank correlation between calculated importance and actual importances of features. SHAP feature dependence might be the simplest global interpretation plot: (2019) 71. Next, we sort the features by decreasing importance and plot them. When we have enough budget left (current budget is K - 2M), we can include coalitions with 2 features and with M-2 features and so on. Also, relearning approaches took approximately n_features times more time to run. We get better Shapley value estimates by using some of the sampling budget K to include these high-weight coalitions instead of sampling blindly. The following example uses hierarchical agglomerative clustering to order the instances. # train an XGBoost model (but any other model type would also work), # build a Permutation explainer and explain the model predictions on the given dataset, # get just the explanations for the positive class, # build a clustering of the features based on shared information about y, # above we implicitly used shap.maskers.Independent by passing a raw dataframe as the masker, # now we explicitly use a Partition masker that uses the clustering we just computed, Tabular data with independent (Shapley value) masking, Tabular data with partition (Owen value) masking. Assigning the average color of surrounding pixels or similar would also be an option. All dataset features correlated one with each other with a max_correlation correlation. The baseline for Shapley values is the average of all predictions. While TreeSHAP solves the problem of extrapolating to unlikely data points, it does so by changing the value function and therefore slightly changes the game. many 1s) get the largest weights. The idea behind SHAP feature importance is simple: The number of years with hormonal contraceptives was the most important feature, changing the predicted absolute cancer probability on average by 2.4 percentage points (0.024 on x-axis). Code snippet to illustrate the calculations: Permutation importance is easy to explain, implement, and use. Then the logit of a target was calculated as a linear combination of feature and corresponding feature weight (a sign of feature weight was selected at random). Conditional Variable Importance permute features conditional, based on the values of remaining features to avoid unseen regions; Dropped Variable Importance equivalent to the leave-one-covariate-out methods explored in, Permute-and-Relearn Importance the approach is taken in, The most important and second most important features ranks are mismatched. License. From the remaining coalition sizes, we sample with readjusted weights. Its not clear, why that happened, but I may hypothesis, that more correlated features lead to more accurate models (which could be seen from Figure 11 Models score= f(mean of feature correlations)), because of denser features spaces and fewer unknown regions. The problem is that we have to apply this procedure for each possible subset S of the feature values. It shows the drop in the score if the feature would be replaced with randomly permuted values. propose the SHAP kernel: \[\pi_{x}(z')=\frac{(M-1)}{\binom{M}{|z'|}|z'|(M-|z'|)}\]. Unreachable means that the decision path that leads to this node contradicts values in \(x_S\). We can interpret the entire model by analyzing the Shapley values in this matrix. It is calculated with several straightforward steps. SHAP specifies the explanation as: where g is the explanation model, \(z'\in\{0,1\}^M\) is the coalition vector, M is the maximum coalition size and \(\phi_j\in\mathbb{R}\) is the feature attribution for a feature j, the Shapley values. Although calculation requires to make predictions on training data n_featurs times, it's not a substantial operation, compared to model retraining or precise SHAP values calculation. In this subsection, I compare permutation importances with relearning approaches. The noise magnitude for each feature was selected randomly from an uniform distribution between [-0.5*noise_magnitude_max, 0.5*noise_magnitude_max], noise_magnitude_max = var. Also, permutation importance allows you to select features: if the score on the permuted dataset is higher then on normal it's a clear sign to . If a coalition consists of a single feature, we can learn about this features isolated main effect on the prediction. If S contains some, but not all, features, we ignore predictions of unreachable nodes. With the change in the value function, features that have no influence on the prediction can get a TreeSHAP value different from zero. That was done to reduce the influence of random weights generation on the final results. history 4 of 4. 2) For each data instance, plot a point with the feature value on the x-axis and the corresponding Shapley value on the y-axis. The Missingness property enforces that missing features get a Shapley value of 0. Lundberg, Scott M., and Su-In Lee. Again, this is not a causal model. Head over to, \(z_k'\in\{0,1\}^M,\quad{}k\in\{1,\ldots,K\}\). Indeed, the models top important features may give us inspiration for further feature engineering and provide insights on what is going on. I recommend reading the chapters on Shapley values and local models (LIME) first. KernelSHAP therefore suffers from the same problem as all permutation-based interpretation methods. By replacing feature values with values from random instances, it is usually easier to randomly sample from the marginal distribution. The non-zero estimate can happen when the feature is correlated with another feature that actually has an influence on the prediction. The experiment illustration notebook could be found here: experiment illustration. How much faster is TreeSHAP? The dependence plot can be improved by highlighting these feature interactions. Parameters of the experiment are: Part of the correlation matrix of the generated dataset: We may see that the features are highly correlated with one with others (mean absolute correlation is about 0.96). It is possible to create intentionally misleading interpretations with SHAP, which can hide biases 72. I will give you some intuition on how we can compute the expected prediction for a single tree, an instance x and feature subset S. To compute Shapley values, we simulate that only some feature values are playing (present) and some are not (absent). SHAP connects LIME and Shapley values. For example, a feature that might not have been used by the model at all can have a non-zero Shapley value when the conditional sampling is used. While others are universal, they could be applied to almost any model: methods such as SHAP values, permutation importances, drop-and-relearn approach, and many others. Data scientists need features importances calculations for a variety of tasks. There is no difference between importance calculated using SHAP of built-in gain. The Permutation explainer is model-agnostic, so it can compute Shapley values and Owen values for any model. With SHAP, global interpretations are consistent with the local explanations, since the Shapley values are the atomic unit of the global interpretations. The model has not been trained on these binary coalition data and cannot make predictions for them.) Also note that both random features have very low importances (close to 0) as expected. Superpixels are groups of pixels. This is what we do below: Note that only the Relationship and Marital status features share more that 50% of their explanation power (as measured by R2) with each other, so all the other parts of the clustering tree are removed by the the default clustering_cutoff=0.5 setting: Note that there is a strong similarity between the explanation from the Independent masker above and the Partition masker here. If a coalition consists of all but one feature, we can learn about this features total effect (main effect plus feature interactions). Missingness says that a missing feature gets an attribution of zero. You can use any clustering method. KernelSHAP consists of five steps: We can create a random coalition by repeated coin flips until we have a chain of 0s and 1s. A total of 1200 runs was made for Permutations vs SHAP vs Gain and 120 runs for Permutations vs Relearning experiments. 180-186 (2020)., Interested in an in-depth, hands-on course on SHAP and Shapley values? Normally, clustering is based on features. Actual importances are equal to rank(-weights). All SHAP values have the same unit the unit of the prediction space. The disadvantages of Shapley values also apply to SHAP: While PDP and ALE plot show average effects, SHAP dependence also shows the variance on the y-axis. By doing this, changing one feature at a time we can minimize the number of model evaluations that are required, and always ensure we satisfy efficiency no matter how many executions of the original model we The SHAP explanation method computes Shapley values from coalitional game theory. This matrix has one row per data instance and one column per feature. The mean of the remaining terminal nodes, weighted by the number of instances per node, is the expected prediction for x given S. for tabular data. a game with rules about valid input feature coalitions), and when that structure is a nest set of feature grouping we get the Owen values as a recursive application of Shapley values to the group. First, the SHAP authors proposed KernelSHAP, an alternative, kernel-based estimation approach for Shapley values inspired by local surrogate models. Your regular reminder: All effects describe the behavior of the model and are not necessarily causal in the real world. If you define \(\phi_0=E_X(\hat{f}(x))\) and set all \(x_j'\) to 1, this is the Shapley efficiency property. For x, the instance of interest, the coalition vector x is a vector of all 1s, i.e. This is the good old boring sum of squared errors that we usually optimize for linear models. TreeSHAP was introduced as a fast, model-specific alternative to KernelSHAP, but it turned out that it can produce unintuitive feature attributions. Each feature value is a force that either increases or decreases the prediction. The more 0s in the coalition vector, the smaller the weight in LIME. (2019) 70 and Janzing et al. Enforcing such a structure produces a structure game (i.e. The function \(h_x\) maps 1s to the corresponding value from the instance x that we want to explain. }\delta_{ij}(S)\], \[\delta_{ij}(S)=\hat{f}_x(S\cup\{i,j\})-\hat{f}_x(S\cup\{i\})-\hat{f}_x(S\cup\{j\})+\hat{f}_x(S)\]. Fooling lime and shap: Adversarial attacks on post hoc explanation methods. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, pp. KernelSHAP ignores feature dependence. Indeed, if one could run pip install lib, lib.explain(model), why bother on the theory behind? KernelSHAP is slow. I hope this post will help data scientists to interpret their models correctly. Each feature weight was then divided by the sum of weights, making the sum of weights equal to one. Since SHAP computes Shapley values, all the advantages of Shapley values apply: This implementation works for tree-based models in the scikit-learn machine learning library for Python. Each position on the x-axis is an instance of the data. SHAP Feature Importance with Feature Engineering. These were explanations for individual predictions. If a coalition consists of half the features, we learn little about an individual features contribution, as there are many possible coalitions with half of the features. correlated, this leads to putting too much weight on unlikely data points. For example, height might be measured in meters, color intensity from 0 to 100 and some sensor output between -1 and 1. For example to explain an image, pixels can be grouped to superpixels and the prediction distributed among them. The formula simplifies to: You can find this formula in similar notation in the Shapley value chapter. The following figure shows SHAP explanation force plots for two women from the cervical cancer dataset: FIGURE 9.24: SHAP values to explain the predicted cancer probabilities of two individuals. The following figure shows the SHAP feature dependence for years on hormonal contraceptives: FIGURE 9.27: SHAP dependence plot for years on hormonal contraceptives. Note that \(x_j'\) refers to the coalitions where a value of 0 represents the absence of a feature value. Compared to 0 years, a few years lower the predicted probability and a high number of years increases the predicted cancer probability. That view connects LIME and Shapley values. Gamma distribution was selected because it looks very similar to a typical feature importance distribution. SHAP feature importance is an alternative to permutation feature importance. I showed how and why highly correlated features might affect permutation importance, which will give misleading results. Dont use permute-and-relearn or drop-and-relearn approaches for finding important features. After a dataset is generated, I added a uniformly-distributed noise to each feature. A sigmoid function was applied to a standard-scaled logit of a target. Also, importance is frequently using for understanding the underlying process and making business decisions. Logs. The algorithm has to keep track of the overall weight of the subsets in each node. The global interpretation methods include feature importance, feature dependence, interactions, clustering and summary plots. (Hold on!, you say. FIGURE 9.25: SHAP feature importance measured as the mean absolute Shapley values. Pull requests that add to this documentation notebook are encouraged! Some of them are based on the models type, e.g., coefficients of linear regression, gain importance in tree-based models, or batch norm parameters in neural nets (BN params are often used for NN pruning, i.e., neural network compression; for example, this paper addresses CNN nets, but the same logic could be applicable to fully-connected nets). TreeSHAP computes in polynomial time instead of exponential. In the summary plot, we see first indications of the relationship between the value of a feature and the impact on the prediction. features importances are in the same order as actual importances (weights of features). This depends on the subsets in the parent node and the split feature. SHAP has a fast implementation for tree-based models. Giles Hooker and Lucas Mentch combined them in their paper Please Stop Permuting Features An Explanation and Alternatives: The possible explanation for this is the models extrapolation. Permutation importance is a frequently used type of feature importance. Since we are in a linear regression setting, we can also make use of the standard tools for regression. permutation based importance. Lundberg et al. And they proposed TreeSHAP, an efficient estimation approach for tree-based models. We will use SHAP to explain individual predictions. This shows that the low cardinality categorical feature, sex and pclass are the most important feature. The following figure shows the SHAP feature importance for the random forest trained before for predicting cervical cancer. The topic of the post and conducted experiment were inspired by Please Stop Permuting Features An Explanation and Alternatives, work done by Giles Hooker and Lucas Mentch. tree to represent the structure of the data. Although the models black box unboxing is an integral part of the model development pipeline, a study conducted by Harmanpreet et al. SHAP clustering works by clustering the Shapley values of each instance. Shapley values are the only solution that satisfies properties of Efficiency, Symmetry, Dummy and Additivity. These forces balance each other out at the actual prediction of the data instance. The consistency property says that if a model changes so that the marginal contribution of a feature value increases or stays the same (regardless of other features), the Shapley value also increases or stays the same. The fast computation makes it possible to compute the many Shapley values needed for the global model interpretations. Dont use permutation importance for tree-based models interpretation (or any model which interpolates in unseen regions badly). If we add an L1 penalty to the loss L, we can create sparse explanations. The color represents the value of the feature from low to high. But with the Python shap package comes a different visualization: The interaction effect is the additional combined feature effect after accounting for the individual feature effects. This was done to decrease features correlation. We have the data, the target and the weights; You can visualize feature attributions such as Shapley values as forces. For absent features (0), \(h_x\) maps to the values of a randomly sampled data instance. Also, permutation importance allows you to select features: if the score on the permuted dataset is higher then on normal its a clear sign to remove the feature and retrain a model. This means that we equate feature value is absent with feature value is replaced by random feature value from data. In the coalition vector, an entry of 1 means that the corresponding feature value is present and 0 that it is absent. Features with large absolute Shapley values are important. To calculate the importance of feature x1, we shuffle the feature and make predictions for a shuffled points (red points on the center plot). Statistics of correlation: Distribution of generated features weights: Calculated Spearman rank correlation between calculated importance and actual importances of features: And the illustration of expected and calculated features importances ranks: We may see several problems here (marked with green circles): Heres an illustration of expected and calculated features importances ranks for the same experiment parameters, except NOISE_MAGNITUDE_MAX, which is now equal to 10 (abs_correlation_mean dropped from 0.96 to 0.36): Still not perfect, but even visually much better, if we are talking about the top ten most important features. LIME weights the instances according to how close they are to the original instance. For a more informative plot, we will next look at the summary plot. The mean of all features was equal to 0, the standard deviation was equal to 1. permutation feature importance vs shap. The features are ordered according to their importance. But instead of relying on the conditional distribution, this example uses the marginal distribution. This notebooks demonstrates how to use the Permutation explainer on some simple datasets. However, if features are dependent, e.g. In SHAP, we take the partitioning to the limit and build a binary herarchial clustering SHAP is integrated into the tree boosting frameworks xgboost and LightGBM. Thanks to the Additivity property of Shapley values, the Shapley values of a tree ensemble is the (weighted) average of the Shapley values of the individual trees. Revision 45b85c18. Features for the task are ready! SHAP (SHapley Additive exPlanations) by Lundberg and Lee (2017)69 is a method to explain individual predictions. From the following plots, we may see that correlation between actual features importances and calculated using permutations, SHAP values, and gain is, as expected, negatively correlated with the mean and max of features correlation.
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