SHAP Feature Importance with Feature Engineering . permutation based importance. Years on hormonal contraceptives interacts with STDs. The disadvantages of Shapley values also apply to SHAP: The function \(h_x\) maps 1s to the corresponding value from the instance x that we want to explain. Only with a different name and using the coalition vector. 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)! 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. All SHAP values have the same unit the unit of the prediction space. For the receivers of a SHAP explanation, it is a disadvantage: they cannot be sure about the truthfulness of the explanation. Also note that both random features have very low importances (close to 0) as expected. SHAP feature dependence might be the simplest global interpretation plot: The formula simplifies to: You can find this formula in similar notation in the Shapley value chapter. The following figure shows the SHAP feature dependence for years on hormonal contraceptives: FIGURE 9.27: SHAP dependence plot for years on hormonal contraceptives. Copyright 2018, Scott Lundberg. 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. SHAP (SHapley Additive exPlanations) by Lundberg and Lee (2017)69 is a method to explain individual predictions. For a more informative plot, we will next look at the summary plot. Shapley values can be combined into global explanations. The baseline for Shapley values is the average of all predictions. Let \(\hat{f}_x(z')=\hat{f}(h_x(z'))\) and \(z_{\setminus{}j}'\) indicate that \(z_j'=0\). To get the label, I rounded the result. Head over to, \(z_k'\in\{0,1\}^M,\quad{}k\in\{1,\ldots,K\}\). Permutation importance is easy to explain, implement, and use. More about the actual estimation comes later. 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. 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). I also showed that, despite relearning approaches expected to be promising, they perform worse then permutation importances, and require much more time to run. This matrix has one row per data instance and one column per feature. This depends on the subsets in the parent node and the split feature. 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). TreeSHAP changes the value function by relying on the conditional expected prediction. We can use the fast TreeSHAP estimation method instead of the slower KernelSHAP method, since a random forest is an ensemble of trees. Code snippet to illustrate the calculations: Permutation importance is easy to explain, implement, and use. Data Scientist at Unity, Helsinki. SHAP dependence plots are an alternative to partial dependence plots and accumulated local effects. Use SHAP values or built-in gain importance instead. For absent features (0), \(h_x\) greys out the corresponding area. Pull requests that add to this documentation notebook are encouraged! 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. 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). SHAP is based on magnitude of feature attributions. Feature relevance quantification in explainable AI: A causal problem. International Conference on Artificial Intelligence and Statistics. }\delta_{ij}(S)\], \[\delta_{ij}(S)=\hat{f}_x(S\cup\{i,j\})-\hat{f}_x(S\cup\{i\})-\hat{f}_x(S\cup\{j\})+\hat{f}_x(S)\]. 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. Each feature weight was then divided by the sum of weights, making the sum of weights equal to one. 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. Thus, to make predictions, it must extrapolate to previously unseen regions (right plot). A player can be an individual feature value, e.g. But instead of relying on the conditional distribution, this example uses the marginal distribution. In the summary plot, we see first indications of the relationship between the value of a feature and the impact on the prediction. propose the SHAP kernel: \[\pi_{x}(z')=\frac{(M-1)}{\binom{M}{|z'|}|z'|(M-|z'|)}\]. Suppose, the model was trained using two highly positively-correlated features x1 and x2 (left plot on the illustration below). Indeed, permuting the values of these features will lead to most decrease in accuracy score of the model on the test set. Unreachable means that the decision path that leads to this node contradicts values in \(x_S\). This shows that the low cardinality categorical feature, sex and pclass are the most important feature. Gamma distribution was selected because it looks very similar to a typical feature importance distribution. 3rd most important feature according to permutation importance should be 9th; Actual 8th important features dropped to 39th position if we trust permutation importance. First, the SHAP authors proposed KernelSHAP, an alternative, kernel-based estimation approach for Shapley values inspired by local surrogate models. \(h_x\) 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. Actual importances are equal to rank(-weights). TreeSHAP computes in polynomial time instead of exponential. Also, relearning approaches took approximately n_features times more time to run. 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. Indeed, the models top important features may give us inspiration for further feature engineering and provide insights on what is going on. SHAP is integrated into the tree boosting frameworks xgboost and LightGBM. Age of 51 and 34 years of smoking increase her predicted cancer risk. In coalition notation, all feature values \(x_j'\) of the instance to be explained should be 1. SHAP is also included in the R xgboost package. A sigmoid function was applied to a standard-scaled logit of a target. However, if features are dependent, e.g. 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 plot consists of many force plots, each of which explains the prediction of an instance. The best possible correlation is 1.0, i.e. The intuition behind it is: Mathematically, the plot contains the following points: \(\{(x_j^{(i)},\phi_j^{(i)})\}_{i=1}^n\). When the permutation is repeated, the results might vary greatly. This means that we equate feature value is absent with feature value is replaced by random feature value from data. Features are often on different scales. But with the Python shap package comes a different visualization: correlated, this leads to putting too much weight on unlikely data points. Have an idea for more helpful examples? For the marginal game, this feature value would always get a Shapley value of 0, because otherwise it would violate the Dummy axiom. How can we use the interaction index? There is a big difference between both importance measures: Permutation feature importance is based on the decrease in model performance. Overlapping points are jittered in y-axis direction, so we get a sense of the distribution of the Shapley values per feature. permutation feature importance vs shap. The following example uses hierarchical agglomerative clustering to order the instances. Shapley values tell us how to fairly distribute the payout (= the prediction) among the features. As a result, the Shapley values have a different interpretation: 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. The model has not been trained on these binary coalition data and cannot make predictions for them.) The feature importance plot is useful, but contains no information beyond the importances. (2019) 70 and Janzing et al. 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. TreeSHAP solves this problem by explicitly modeling the conditional expected prediction. KernelSHAP is slow. 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). The fast computation makes it possible to compute the many Shapley values needed for the global model interpretations. This is very useful to better understand both methods. SHAP connects LIME and Shapley values. 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. The representation as a linear model of coalitions is a trick for the computation of the \(\phi\)s. This chapter explains both the new estimation approaches and the global interpretation methods. This implementation works for tree-based models in the scikit-learn machine learning library for Python. pedialyte electrolyte powder . The baseline the average predicted probability is 0.066. This makes KernelSHAP impractical to use when you want to compute Shapley values for many instances. 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. We average the values over all possible feature coalitions S, as in the Shapley value computation. 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)). Also all global SHAP methods such as SHAP feature importance require computing Shapley values for a lot of instances. We learn most about individual features if we can study their effects in isolation. The basic idea is to push all possible subsets S down the tree at the same time. What I call coalition vector is called simplified features in the SHAP paper. 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 . A unified approach to interpreting model predictions. Advances in Neural Information Processing Systems (2017)., Sundararajan, Mukund, and Amir Najmi. So why do we need it for SHAP? The SHAP explanation method computes Shapley values from coalitional game theory. If we conditioned on all features if S was the set of all features then the prediction from the node in which the instance x falls would be the expected prediction. For example, we can add regularization terms to make the model sparse. For x, the instance of interest, the coalition vector x is a vector of all 1s, i.e. From the remaining coalition sizes, we sample with readjusted weights. Red SHAP values increase the prediction, blue values decrease it. We get contrastive explanations that compare the prediction with the average prediction. By replacing feature values with values from random instances, it is usually easier to randomly sample from the marginal distribution. all feature values are present. 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. After a dataset is generated, I added a uniformly-distributed noise to each feature. From Consistency the Shapley properties Linearity, Dummy and Symmetry follow, as described in the Appendix of Lundberg and Lee. 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. If a coalition consists of all but one feature, we can learn about this features total effect (main effect plus feature interactions). But to see the exact form of the relationship, we have to look at SHAP dependence plots. I refer to the original paper for details of TreeSHAP. In my opinion, it is always good to check all methods, and compare the results. We start with all possible coalitions with 1 and M-1 features, which makes 2 times M coalitions in total. Since SHAP computes Shapley values, all the advantages of Shapley values apply: The mean of the remaining terminal nodes, weighted by the number of instances per node, is the expected prediction for x given S. 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. Although calculation requires to make predictions on training data n_featurs times, its not a substantial operation, compared to model retraining or precise SHAP values calculation. importance computed with SHAP values. The global interpretation methods include feature importance, feature dependence, interactions, clustering and summary plots. Surprisingly, relearning approaches performed significantly worse than permutation across all correlations, which could be seen from plots below. 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. The non-zero estimate can happen when the feature is correlated with another feature that actually has an influence on the prediction. 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. A total of 1200 runs was made for Permutations vs SHAP vs Gain and 120 runs for Permutations vs Relearning experiments. SHAP has a fast implementation for tree-based models. For images, the following figure describes a possible mapping function: FIGURE 9.23: Function \(h_x\) maps coalitions of superpixels (sp) to images. The code and analysis of the experiment could be found in the repository of the project: To make you familiar with what is going on, Ill illustrate a single experiment. One cluster stands out: On the right is a group with a high predicted cancer risk. Next, we sort the features by decreasing importance and plot them. Repeating the permutation and averaging the importance measures over repetitions stabilizes the measure, but increases the time of computation. 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. This complicates the algorithm. For example, when the first split in a tree is on feature x3, then all the subsets that contain feature x3 will go to one node (the one where x goes). There is no difference between importance calculated using SHAP of built-in gain. It also helps to unify the field of interpretable machine learning. history 4 of 4. You can visualize feature attributions such as Shapley values as forces. Low number of years on hormonal contraceptives reduce the predicted cancer risk, a large number of years increases the risk. Below we domonstrate how to use the Permutation explainer on a simple adult income classification dataset and model. The computation can be expanded to more trees: 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. Your regular reminder: All effects describe the behavior of the model and are not necessarily causal in the real world. That was done to reduce the influence of random weights generation on the final results. Revision 45b85c18. FIGURE 9.25: SHAP feature importance measured as the mean absolute Shapley values. 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. where Z is the training data. A player can also be a group of feature values. With SHAP, global interpretations are consistent with the local explanations, since the Shapley values are the atomic unit of the global interpretations. Subsets that do not contain feature x3 go to both nodes with reduced weight. Notebook. For those reasons, permutation importance is wildly applied in many machine learning pipelines. The many Shapley values for model explanation. arXiv preprint arXiv:1908.08474 (2019)., Janzing, Dominik, Lenon Minorics, and Patrick Blbaum. You can use any clustering method. Importances could help us to understand if we have biases in our data or bugs in models. SHAP is based on the game theoretically optimal Shapley values. How much faster is TreeSHAP? Here, M is the maximum coalition size and \(|z'|\) the number of present features in instance z. If we add an L1 penalty to the loss L, we can create sparse explanations. It works by iterating over complete permutations of the features forward and the reversed. KernelSHAP estimates for an instance x the contributions of each feature value to the prediction. I believe it is helpful to think about the zs as describing coalitions: Lundberg et al. If you would use the SHAP kernel with LIME on the coalition data, LIME would also estimate Shapley values! SHAP Feature Importance with Feature Engineering. The 3 ways to compute the feature importance for the scikit-learn Random Forest were presented: built-in feature importance. The features are ordered according to their importance. The permutation feature importance depends on shuffling the feature, which adds randomness to the measurement.
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