permutation feature importance vs shap

The permutation feature importance depends on shuffling the feature, which adds randomness to the measurement. # 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. The presence of a 0 would mean that the feature value is missing for the instance of interest. 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 experiment illustration notebook could be found here: experiment illustration. I also showed that, despite relearning approaches expected to be promising, they perform worse then permutation importances, and require much more time to run. At first, I generated a normally-distributed dataset with a specified number of features and samples (n_features=50, n_samples=10,000). Have an idea for more helpful examples? This Notebook has been released under the Apache 2.0 open source license. To get the label, I rounded the result. (2019) 71. The position on the y-axis is determined by the feature and on the x-axis by the Shapley value. FIGURE 9.25: SHAP feature importance measured as the mean absolute Shapley values. The prediction starts from the baseline. 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). I conducted an experiment, which showed that permutation importance suffers the most from highly correlated features (among importances calculated using SHAP values and gain). 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. Shapley values can be misinterpreted and access to data is needed to compute them for new data (except for TreeSHAP). Comments (4) Competition Notebook. This notebooks demonstrates how to use the Permutation explainer on some simple datasets. This makes KernelSHAP impractical to use when you want to compute Shapley values for many instances. 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). Pull requests that add to this documentation notebook are encouraged! The authors implemented SHAP in the shap Python package. If we run SHAP for every instance, we get a matrix of Shapley values. With the change in the value function, features that have no influence on the prediction can get a TreeSHAP value different from zero. Everything we need to build our weighted linear regression model: We train the linear model g by optimizing the following loss function L: \[L(\hat{f},g,\pi_{x})=\sum_{z'\in{}Z}[\hat{f}(h_x(z'))-g(z')]^2\pi_{x}(z')\]. In this post I described the permutation importance approach and problems associated with it. Assigning the average color of surrounding pixels or similar would also be an option. Each feature value is a force that either increases or decreases the prediction. SHAP is based on magnitude of feature attributions. If S contains some, but not all, features, we ignore predictions of unreachable nodes. Indeed, if one could run pip install lib, lib.explain(model), why bother on the theory behind? But instead of relying on the conditional distribution, this example uses the marginal distribution. The target is ready! The mean of the remaining terminal nodes, weighted by the number of instances per node, is the expected prediction for x given S. history 4 of 4. This depends on the subsets in the parent node and the split feature. 180-186 (2020)., Interested in an in-depth, hands-on course on SHAP and Shapley values? For a more informative plot, we will next look at the summary plot. I recommend reading the chapters on Shapley values and local models (LIME) first. Each position on the x-axis is an instance of the data. 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). From the remaining coalition sizes, we sample with readjusted weights. Giles Hooker and Lucas Mentch proposed several alternatives to use instead of permutation importance: To understand, how heavily features correlation influences permutation importance and other features importances methods, I conducted the following experiment. Features for the task are ready! 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 function \(h_x\) maps 1s to the corresponding value from the instance x that we want to explain. How can we use the interaction index? Dont use permute-and-relearn or drop-and-relearn approaches for finding important features. Risk increasing effects such as STDs are offset by decreasing effects such as age. Suppose, the model was trained using two highly positively-correlated features x1 and x2 (left plot on the illustration below). All dataset features correlated one with each other with a max_correlation correlation. We have the data, the target and the weights; The estimation puts too much weight on unlikely instances. 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. We learn most about individual features if we can study their effects in isolation. TreeSHAP solves this problem by explicitly modeling the conditional expected prediction. permutation feature importance vs shap. Superpixels are groups of pixels. The estimated coefficients of the model, the \(\phi_j\)s, are the Shapley values. 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. The Python TreeSHAP function is slower with the marginal distribution, but still faster than KernelSHAP, since it scales linearly with the rows in the data. The summary plot combines feature importance with feature effects. STDs and lower cancer risk could be correlated with more doctor visits). The more 0s in the coalition vector, the smaller the weight in LIME. The basic idea is to push all possible subsets S down the tree at the same time. Logs. Each point on the summary plot is a Shapley value for a feature and an instance. The representation as a linear model of coalitions is a trick for the computation of the \(\phi\)s. \[\hat{f}(x)=\phi_0+\sum_{j=1}^M\phi_jx_j'=E_X(\hat{f}(X))+\sum_{j=1}^M\phi_j\]. 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. 3rd most important feature according to permutation importance should be 9th; Actual 8th important features dropped to 39th position if we trust permutation importance. The following figure shows the SHAP feature importance for the random forest trained before for predicting cervical cancer. Thus, to make predictions, it must extrapolate to previously unseen regions (right plot). TreeSHAP can produce unintuitive feature attributions. Note that \(x_j'\) refers to the coalitions where a value of 0 represents the absence of a feature value. The idea behind SHAP feature importance is simple: For example, height might be measured in meters, color intensity from 0 to 100 and some sensor output between -1 and 1. These points from new regions strongly affect the final score and hence, permutation importance. 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. The 3 ways to compute the feature importance for the scikit-learn Random Forest were presented: built-in feature importance. Age of 51 and 34 years of smoking increase her predicted cancer risk. 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. The following figure shows the SHAP feature dependence for years on hormonal contraceptives: FIGURE 9.27: SHAP dependence plot for years on hormonal contraceptives. for tabular data. SHAP feature dependence might be the simplest global interpretation plot: We can interpret the entire model by analyzing the Shapley values in this matrix. Since SHAP computes Shapley values, all the advantages of Shapley values apply: Lundberg, Scott M., and Su-In Lee. SHAP is integrated into the tree boosting frameworks xgboost and LightGBM. More about the actual estimation comes later. 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. This matrix has one row per data instance and one column per feature. It also helps to unify the field of interpretable machine learning. 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 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. If you use LIME for local explanations and partial dependence plots plus permutation feature importance for global explanations, you lack a common foundation. For tabular data, it maps 0s to the values of another instance that we sample from the data. We get contrastive explanations that compare the prediction with the average prediction. SHAP weights the sampled instances according to the weight the coalition would get in the Shapley value estimation. The following example uses hierarchical agglomerative clustering to order the instances. I trained a random forest classifier with 100 trees to predict the risk for cervical cancer. Actual importances are equal to rank(-weights). TreeSHAP was introduced as a fast, model-specific alternative to KernelSHAP, but it turned out that it can produce unintuitive feature attributions. This notebooks demonstrates how to use the Permutation explainer on some simple datasets. permutation based importance. The second woman has a high predicted risk of 0.71. For each feature, I generated a weight, which was sampled from a gamma distribution with specified gamma and scale parameters (gamma=1, scale=1). 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. The computation can be expanded to more trees: 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 color represents the value of the feature from low to high. There is no difference between importance calculated using SHAP of built-in gain. Cell link copied. Shapley values can be combined into global explanations. Lundberg et al. The shap package was also used for the examples in this chapter. Dont use permutation importance for tree-based models interpretation (or any model which interpolates in unseen regions badly). This means that you cluster instances by explanation similarity. To get from coalitions of feature values to valid data instances, we need a function \(h_x(z')=z\) where \(h_x:\{0,1\}^M\rightarrow\mathbb{R}^p\). 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. 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)! KernelSHAP is slow. SHAP feature importance is an alternative to permutation feature importance. Since we are in a linear regression setting, we can also make use of the standard tools for regression. In practice, this is only relevant for features that are constant. SHAP clustering works by clustering the Shapley values of each instance. To compute Shapley values, we simulate that only some feature values are playing (present) and some are not (absent). 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. Compared to 0 years, a few years lower the predicted probability and a high number of years increases the predicted cancer probability. Because we use the marginal distribution here, the interpretation is the same as in the Shapley value chapter. The difficulty is to compute distances between instances with such different, non-comparable features. For the receivers of a SHAP explanation, it is a disadvantage: they cannot be sure about the truthfulness of the explanation. There is a big difference between both importance measures: Permutation feature importance is based on the decrease in model performance. 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. 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 those reasons, permutation importance is wildly applied in many machine learning pipelines. Fooling lime and shap: Adversarial attacks on post hoc explanation methods. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, pp. You can visualize feature attributions such as Shapley values as forces. This should sound familiar to you if you know about Shapley values. Small coalitions (few 1s) and large coalitions (i.e. KernelSHAP ignores feature dependence. TreeSHAP defines the value function using the conditional expectation \(E_{X_S|X_C}(\hat{f}(x)|x_S)\) instead of the marginal expectation. Now we need to create a target. These were explanations for individual predictions. 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. The smallest and largest coalitions take up most of the weight. With SHAP, global interpretations are consistent with the local explanations, since the Shapley values are the atomic unit of the global interpretations. The Permutation explainer is model-agnostic, so it can compute Shapley values and Owen values for any model. This means that we equate feature value is absent with feature value is replaced by random feature value from data. And they proposed TreeSHAP, an efficient estimation approach for tree-based models. Most other permutation based interpretation methods have this problem. The feature importance plot is useful, but contains no information beyond the importances. This is very useful to better understand both methods. The best possible correlation is 1.0, i.e.

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