permutation feature importance vs shap

We get better Shapley value estimates by using some of the sampling budget K to include these high-weight coalitions instead of sampling blindly. From Consistency the Shapley properties Linearity, Dummy and Symmetry follow, as described in the Appendix of Lundberg and Lee. A Medium publication sharing concepts, ideas and codes. If you are the data scientist creating the explanations, this is not an actual problem (it would even be an advantage if you are the evil data scientist who wants to create misleading explanations). 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. How can we use the interaction index? Age of 51 and 34 years of smoking increase her predicted cancer risk. As a result, the Shapley values have a different interpretation: To compute Shapley values, we simulate that only some feature values are playing (present) and some are not (absent). We will use SHAP to explain individual predictions. Also, we may see that that correlation between actual features importances and calculated depends on the models score: higher the score lower the correlation (Figure 10 Spearman features rank correlation = f(models score)). The algorithm has to keep track of the overall weight of the subsets in each node. The feature values of a data instance act as players in a coalition. This was done to decrease features correlation. Because the Permutation explainer has important performance optimizations, and does not require regularization parameter tuning like Kernel explainer, the Permutation explainer is the default model agnostic explainer used for tabular datasets that have more features than would be appropriate for the Exact explainer. For absent features (0), \(h_x\) greys out the corresponding area. That was done to reduce the influence of random weights generation on the final results. 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 Notebook has been released under the Apache 2.0 open source license. Again, this is not a causal model. The plot consists of many force plots, each of which explains the prediction of an instance. 151.9s . Each feature weight was then divided by the sum of weights, making the sum of weights equal to one. In the plot, each Shapley value is an arrow that pushes to increase (positive value) or decrease (negative value) the prediction. SHAP describes the following three desirable properties: \[\hat{f}(x)=g(x')=\phi_0+\sum_{j=1}^M\phi_jx_j'\]. The experiment is run fifty times with different seeds and with varying combinations of max_correlation and noise_magnitude_max. number of training samples in that node). Although the models black box unboxing is an integral part of the model development pipeline, a study conducted by Harmanpreet et al. \[\hat{f}(x)=\phi_0+\sum_{j=1}^M\phi_jx_j'=E_X(\hat{f}(X))+\sum_{j=1}^M\phi_j\]. Data. 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)! Dont use permute-and-relearn or drop-and-relearn approaches for finding important features. In this subsection, I compare feature importances ranks calculated using permutation importances, SHAP values, and built-in gain. Features are often on different scales. This should sound familiar to you if you know about Shapley values. TreeSHAP defines the value function using the conditional expectation \(E_{X_S|X_C}(\hat{f}(x)|x_S)\) instead of the marginal expectation. It shows the drop in the score if the feature would be replaced with randomly permuted values. KernelSHAP ignores feature dependence. There is a big difference between both importance measures: Permutation feature importance is based on the decrease in model performance. FIGURE 9.29: Stacked SHAP explanations clustered by explanation similarity. To get the label, I rounded the result. Effects might be due to confounding (e.g. The baseline for Shapley values is the average of all predictions. We have the data, the target and the weights; 180-186 (2020)., Interested in an in-depth, hands-on course on SHAP and Shapley values? SHAP clustering works by clustering the Shapley values of each instance. Features for the task are ready! Below we domonstrate how to use the Permutation explainer on a simple adult income classification dataset and model. After a dataset is generated, I added a uniformly-distributed noise to each feature. A player can be an individual feature value, e.g. Superpixels are groups of pixels. For a more informative plot, we will next look at the summary plot. I also run the same experiment with drop and relearn and permute and relearn approaches but only five times due to required heavy computations. We rotate the force plots vertically and place them side by side according to their clustering similarity. Missingness says that a missing feature gets an attribution of zero. Lundberg, Scott M., and Su-In Lee. Repeating the permutation and averaging the importance measures over repetitions stabilizes the measure, but increases the time of computation. Shapley values tell us how to fairly distribute the payout (= the prediction) among the features. For a generated dataset and target, I trained a single LightGBM model with the following parameters: All other parameters were default. In cases close to 0 years, the occurence of a STD increases the predicted cancer risk. Features with large absolute Shapley values are important. Fooling lime and shap: Adversarial attacks on post hoc explanation methods. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, pp. Overlapping points are jittered in y-axis direction, so we get a sense of the distribution of the Shapley values per feature. The summary plot combines feature importance with feature effects. For tabular data, the following figure visualizes the mapping from coalitions to feature values: FIGURE 9.22: Function \(h_x\) maps a coalition to a valid instance. For example to explain an image, pixels can be grouped to superpixels and the prediction distributed among them. If we add an L1 penalty to the loss L, we can create sparse explanations. TreeSHAP solves this problem by explicitly modeling the conditional expected prediction. In this subsection, I compare permutation importances with relearning approaches. The baseline the average predicted probability is 0.066. for tabular data. Actual importances are equal to rank(-weights). pedialyte electrolyte powder . In SHAP, we take the partitioning to the limit and build a binary herarchial clustering SHAP also satisfies these, since it computes Shapley values. Normally, clustering is based on features. For more years on contraceptives, the occurence of a STD reduces the predicted risk. For present features (1), \(h_x\) returns the corresponding part of the original image. This chapter explains both the new estimation approaches and the global interpretation methods. By replacing feature values with values from random instances, it is usually easier to randomly sample from the marginal distribution. Permutation importance is easy to explain, implement, and use. This matrix has one row per data instance and one column per feature. (Hold on!, you say. where Z is the training data. The Permutation explainer is model-agnostic, so it can compute Shapley values and Owen values for any model. With the change in the value function, features that have no influence on the prediction can get a TreeSHAP value different from zero. TreeSHAP uses the conditional expectation \(E_{X_S|X_C}(\hat{f}(x)|x_S)\) to estimate effects. Two Sigma: Using News to Predict Stock Movements. TreeSHAP computes in polynomial time instead of exponential. Next, we sort the features by decreasing importance and plot them. But with the Python shap package comes a different visualization: SHAP is based on the game theoretically optimal Shapley values. The shap package was also used for the examples in this chapter. KernelSHAP estimates for an instance x the contributions of each feature value to the prediction. FIGURE 9.25: SHAP feature importance measured as the mean absolute Shapley values. These were explanations for individual predictions. SHAP connects LIME and Shapley values. Lundberg et al. The more 0s in the coalition vector, the smaller the weight in LIME. But instead of relying on the conditional distribution, this example uses the marginal distribution. SHAP has a fast implementation for tree-based models. But to see the exact form of the relationship, we have to look at SHAP dependence plots. So why do we need it for SHAP? KernelSHAP consists of five steps: We can create a random coalition by repeated coin flips until we have a chain of 0s and 1s. The best possible correlation is 1.0, i.e. 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). TreeSHAP can produce unintuitive feature attributions. This implementation works for tree-based models in the scikit-learn machine learning library for Python. The difficulty is to compute distances between instances with such different, non-comparable features. The target is ready! image data, the images are not represented on the pixel level, but aggregated to superpixels. From the remaining coalition sizes, we sample with readjusted weights. This means that you cluster instances by explanation similarity. tree to represent the structure of the data. We get contrastive explanations that compare the prediction with the average prediction. I will show that in some cases, permutation importance gives wrong, misleading results. Feature relevance quantification in explainable AI: A causal problem. International Conference on Artificial Intelligence and Statistics. Lundberg calls it a minor book-keeping property. 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. I also showed that, despite relearning approaches expected to be promising, they perform worse then permutation importances, and require much more time to run. Each point on the summary plot is a Shapley value for a feature and an instance. Since we are in a linear regression setting, we can also make use of the standard tools for regression. LIME weights the instances according to how close they are to the original instance. All models extrapolate badly, thus making unexpected predictions. Revision 45b85c18. The authors implemented SHAP in the shap Python package. Only with a different name and using the coalition vector. Indeed, permuting the values of these features will lead to most decrease in accuracy score of the model on the test set. This means that we equate feature value is absent with feature value is replaced by random feature value from data. Let \(\hat{f}_x(z')=\hat{f}(h_x(z'))\) and \(z_{\setminus{}j}'\) indicate that \(z_j'=0\). Data of each experiment (dataset correlation statistics, Spearman rank correlation between the models importance and actual importance of features for built-in gain importance, SHAP importance, and permutation importance) was saved for further analysis. Unfortunately, subsets of different sizes have different weights. However, if features are dependent, e.g. SHAP Feature Importance with Feature Engineering. propose the SHAP kernel: \[\pi_{x}(z')=\frac{(M-1)}{\binom{M}{|z'|}|z'|(M-|z'|)}\]. SHAP (SHapley Additive exPlanations) by Lundberg and Lee (2017)69 is a method to explain individual predictions. PMLR (2020)., Slack, Dylan, Sophie Hilgard, Emily Jia, Sameer Singh, and Himabindu Lakkaraju. While Shapley values result from treating each feature independently of the other features, it is often useful to enforce a structure on the model inputs. The presence of a 0 would mean that the feature value is missing for the instance of interest. features importances are in the same order as actual importances (weights of features). 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 For example, to automatically color the SHAP feature dependence plot with the strongest interaction: FIGURE 9.28: SHAP feature dependence plot with interaction visualization. To get from coalitions of feature values to valid data instances, we need a function \(h_x(z')=z\) where \(h_x:\{0,1\}^M\rightarrow\mathbb{R}^p\). There is a big difference between both importance measures: Importances could help us to understand if we have biases in our data or bugs in models. The interaction effect is the additional combined feature effect after accounting for the individual feature effects. Surprisingly, relearning approaches performed significantly worse than permutation across all correlations, which could be seen from plots below. (I am not so sure whether the resulting coefficients would still be valid Shapley values though.). In general the distinctions between these methods for tabular data are not large, though the Partition masker allows for much faster runtime and potentially more realistic manipulations of the model inputs (since groups of clustered features are masked/unmasked together). The color represents the value of the feature from low to high. 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. \(h_x\) 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. First, the SHAP authors proposed KernelSHAP, an alternative, kernel-based estimation approach for Shapley values inspired by local surrogate models. Permutation importance is a frequently used type of feature importance. This is described in the package, but not in the original paper. I trained a random forest classifier with 100 trees to predict the risk for cervical cancer. For the marginal game, this feature value would always get a Shapley value of 0, because otherwise it would violate the Dummy axiom. 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. 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. The SHAP explanation method computes Shapley values from coalitional game theory. In the coalition vector, an entry of 1 means that the corresponding feature value is present and 0 that it is absent. The features are ordered according to their importance. How much faster is TreeSHAP? Suppose, the model was trained using two highly positively-correlated features x1 and x2 (left plot on the illustration below). In this post, Id like to address a bias of over-using permutation importance for finding the influencing features. The representation as a linear model of coalitions is a trick for the computation of the \(\phi\)s. For a more informative plot, we will next look at the summary plot. A player can also be a group of feature values. Also, relearning approaches took approximately n_features times more time to run. We can interpret the entire model by analyzing the Shapley values in this matrix. history 4 of 4. This formula subtracts the main effect of the features so that we get the pure interaction effect after accounting for the individual effects. choose to use for appoximation the feature attribution values. More about the actual estimation comes later. This notebooks demonstrates how to use the Permutation explainer on some simple datasets. permutation feature importance vs shap. The target for the regression model is the prediction for a coalition. The computation can be expanded to more trees: One innovation that SHAP brings to the table is that the Shapley value explanation is represented as an additive feature attribution method, a linear model. The goal of SHAP is to explain the prediction of an instance x by computing the contribution of each feature to the prediction. The 3 ways to compute the feature importance for the scikit-learn Random Forest were presented: built-in feature importance. 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. The formula simplifies to: You can find this formula in similar notation in the Shapley value chapter. Years on hormonal contraceptives interacts with STDs. Red SHAP values increase the prediction, blue values decrease it. The intuition behind it is: You can cluster your data with the help of Shapley values. The following figure shows the SHAP feature dependence for years on hormonal contraceptives: FIGURE 9.27: SHAP dependence plot for years on hormonal contraceptives. If S contains some, but not all, features, we ignore predictions of unreachable nodes. The estimated coefficients of the model, the \(\phi_j\)s, are the Shapley values. It works by iterating over complete permutations of the features forward and the reversed. Assigning the average color of surrounding pixels or similar would also be an option. The non-zero estimate can happen when the feature is correlated with another feature that actually has an influence on the prediction. Pull requests that add to this documentation notebook are encouraged! FIGURE 9.26: SHAP summary plot. And they proposed TreeSHAP, an efficient estimation approach for tree-based models. SHAP Feature Importance with Feature Engineering . Compared to 0 years, a few years lower the predicted probability and a high number of years increases the predicted cancer probability. Head over to, \(z_k'\in\{0,1\}^M,\quad{}k\in\{1,\ldots,K\}\). I showed how and why highly correlated features might affect permutation importance, which will give misleading results. In my opinion, it is always good to check all methods, and compare the results. Lundberg and Lee show that linear regression with this kernel weight yields Shapley values. For example, we can add regularization terms to make the model sparse. It also helps to unify the field of interpretable machine learning. Small coalitions (few 1s) and large coalitions (i.e. This makes KernelSHAP impractical to use when you want to compute Shapley values for many instances. The mean of the remaining terminal nodes, weighted by the number of instances per node, is the expected prediction for x given S. This structure could be chosen in many ways, but for tabular data it is often helpful to build the structure from the redundancy of information between the input features about the output label. 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. The mean of all features was equal to 0, the standard deviation was equal to 1. So the SHAP values computed, while approximate, do exactly sum up to the difference between the base value of the model and the output of the model for each explained instance. The following example uses hierarchical agglomerative clustering to order the instances. The feature importance plot is useful, but contains no information beyond the importances. Use SHAP values or built-in gain importance instead. For present features (1), \(h_x\) maps to the feature values of x. All SHAP values have the same unit the unit of the prediction space. We start with all possible coalitions with 1 and M-1 features, which makes 2 times M coalitions in total. many 1s) get the largest weights. importance computed with SHAP values. Enforcing such a structure produces a structure game (i.e. The permutation feature importance depends on shuffling the feature, which adds randomness to the measurement. In coalition notation, all feature values \(x_j'\) of the instance to be explained should be 1. Each position on the x-axis is an instance of the data. If a coalition consists of all but one feature, we can learn about this features total effect (main effect plus feature interactions). For images, the following figure describes a possible mapping function: FIGURE 9.23: Function \(h_x\) maps coalitions of superpixels (sp) to images. 1) Pick a feature. TreeSHAP changes the value function by relying on the conditional expected prediction. Especially in case of interactions, the SHAP dependence plot will be much more dispersed in the y-axis. (2019) 71. It works by iterating over complete permutations of the features forward and the reversed. SHAP dependence plots are an alternative to partial dependence plots and accumulated local effects. correlated, this leads to putting too much weight on unlikely data points. If you would use the SHAP kernel with LIME on the coalition data, LIME would also estimate Shapley values! Logs. (2019) 70 and Janzing et al. This property is not among the properties of the normal Shapley values. With SHAP, global interpretations are consistent with the local explanations, since the Shapley values are the atomic unit of the global interpretations. There are a lot of ways how we could calculate feature importance nowadays. For x, the instance of interest, the coalition vector x is a vector of all 1s, i.e. There is no difference between importance calculated using SHAP of built-in gain. At first, I generated a normally-distributed dataset with a specified number of features and samples (n_features=50, n_samples=10,000). I conducted the described experiments and plot results, which are presented in this section. If we would not condition the prediction on any feature if S was empty we would use the weighted average of predictions of all terminal nodes. SHAP is based on magnitude of feature attributions. For each decision node we have to keep track of the number of subsets. But the model hasnt seen any training examples of x1 in the left upper corner and right bottom corner. The Permutation explainer is model-agnostic, so it can compute Shapley values and Owen values for any model. I think this name was chosen, because for e.g. Because we use the marginal distribution here, the interpretation is the same as in the Shapley value chapter. The big difference to LIME is the weighting of the instances in the regression model. 3) Done. Indeed, the models top important features may give us inspiration for further feature engineering and provide insights on what is going on. 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). The basic idea is to push all possible subsets S down the tree at the same time. In practice, this is only relevant for features that are constant. Compared to exact KernelSHAP, it reduces the computational complexity from \(O(TL2^M)\) to \(O(TLD^2)\), where T is the number of trees, L is the maximum number of leaves in any tree and D the maximal depth of any tree. I hope this post will help data scientists to interpret their models correctly. 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. Everything we need to build our weighted linear regression model: We train the linear model g by optimizing the following loss function L: \[L(\hat{f},g,\pi_{x})=\sum_{z'\in{}Z}[\hat{f}(h_x(z'))-g(z')]^2\pi_{x}(z')\]. One cluster stands out: On the right is a group with a high predicted cancer risk. I believe it is helpful to think about the zs as describing coalitions: The many Shapley values for model explanation. arXiv preprint arXiv:1908.08474 (2019)., Janzing, Dominik, Lenon Minorics, and Patrick Blbaum. This notebooks demonstrates how to use the Permutation explainer on some simple datasets. 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. The Missingness property enforces that missing features get a Shapley value of 0. Gamma distribution was selected because it looks very similar to a typical feature importance distribution. For example, the vector of (1,0,1,0) means that we have a coalition of the first and third features. SHAP is also included in the R xgboost package. It is calculated with several straightforward steps. SHAP is based on magnitude of feature attributions. A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems (2017)., Sundararajan, Mukund, and Amir Najmi. If you liked this, you might be interested in reading my other post on problems with LIME importance: Your home for data science. Also, importance is frequently using for understanding the underlying process and making business decisions. 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. To calculate the importance of feature x1, we shuffle the feature and make predictions for a shuffled points (red points on the center plot). When the permutation is repeated, the results might vary greatly. The availability and simplicity of the methods are making them golden hammer. For each feature, I generated a weight, which was sampled from a gamma distribution with specified gamma and scale parameters (gamma=1, scale=1). You can visualize feature attributions such as Shapley values as forces. Code snippet to illustrate the calculations: Permutation importance is easy to explain, implement, and use. SHAP is integrated into the tree boosting frameworks xgboost and LightGBM. Shapley values can be combined into global explanations. It is possible to create intentionally misleading interpretations with SHAP, which can hide biases 72. Your regular reminder: All effects describe the behavior of the model and are not necessarily causal in the real world. We can use the fast TreeSHAP estimation method instead of the slower KernelSHAP method, since a random forest is an ensemble of trees. I recommend reading the chapters on Shapley values and local models (LIME) first. Data scientists need features importances calculations for a variety of tasks. For absent features (0), \(h_x\) maps to the values of a randomly sampled data instance. Shapley values can be misinterpreted and access to data is needed to compute them for new data (except for TreeSHAP). I conducted an experiment, which showed that permutation importance suffers the most from highly correlated features (among importances calculated using SHAP values and gain). The experiment illustration notebook could be found here: experiment illustration. The second woman has a high predicted risk of 0.71. While being a very attractive choice for model interpretation, permutation importance has several problems, especially when working with correlated features. While PDP and ALE plot show average effects, SHAP dependence also shows the variance on the y-axis. The problem with the conditional expectation is that features that have no influence on the prediction function f can get a TreeSHAP estimate different from zero as shown by Sundararajan et al. These points from new regions strongly affect the final score and hence, permutation importance. Next, we will look at SHAP explanations in action. The prediction starts from the baseline. All dataset features correlated one with each other with a max_correlation correlation. For any two models f and f that satisfy: \[\hat{f}_x'(z')-\hat{f}_x'(z_{\setminus{}j}')\geq{}\hat{f}_x(z')-\hat{f}_x(z_{\setminus{}j}')\], \[\phi_j(\hat{f}',x)\geq\phi_j(\hat{f},x)\]. To achieve Shapley compliant weighting, Lundberg et al. Thus, to make predictions, it must extrapolate to previously unseen regions (right plot). For tabular data, it maps 0s to the values of another instance that we sample from the data. For the receivers of a SHAP explanation, it is a disadvantage: they cannot be sure about the truthfulness of the explanation. We learn most about individual features if we can study their effects in isolation. 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 . The smallest and largest coalitions take up most of the weight. SHAP weights the sampled instances according to the weight the coalition would get in the Shapley value estimation. Unreachable means that the decision path that leads to this node contradicts values in \(x_S\). The fast computation makes it possible to compute the many Shapley values needed for the global model interpretations.

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