Interpretable feature subset selection: A Shapley value based approach
IIT Bombay（印度理工学院孟买分校）
Sandhya Tripathi, N. Hemachandra, Prashant Trivedi
备注：
A shorter version of this work appeared in a special session titled Explainable AI at IEEE BigData'20 conference. More experiments and a new notion of interpretable FSS introduced in this version. Earlier plots for sample bias robustness are corrected and updated
For feature selection and related problems, we introduce the notion of classification game, a cooperative game, with features as players and hinge loss based characteristic function and relate a feature's contribution to Shapley value based error apportioning (SVEA) of total training error. Our major contribution is ($\star$) to show that for any dataset the threshold 0 on SVEA value identifies feature subset whose joint interactions for label prediction is significant or those features that span a subspace where the data is predominantly lying. In addition, our scheme ($\star$) identifies the features on which Bayes classifier doesn't depend but any surrogate loss function based finite sample classifier does; this contributes to the excess $0$-$1$ risk of such a classifier, ($\star$) estimates unknown true hinge risk of a feature, and ($\star$) relate the stability property of an allocation and negative valued SVEA by designing the analogue of core of classification game. Due to Shapley value's computationally expensive nature, we build on a known Monte Carlo based approximation algorithm that computes characteristic function (Linear Programs) only when needed. We address the potential sample bias problem in feature selection by providing interval estimates for SVEA values obtained from multiple sub-samples. We illustrate all the above aspects on various synthetic and real datasets and show that our scheme achieves better results than existing recursive feature elimination technique and ReliefF in most cases. Our theoretically grounded classification game in terms of well defined characteristic function offers interpretability (which we formalize in terms of final task) and explainability of our framework, including identification of important features.
GRASP: group-Shapley feature selection for patients
1 Chinese Academy of Medical Sciences \& Peking Union Medical College, Beijing, China 2 Queen's University, Belfast, United Kingdom. 3 Heidelberg University, Heidelberg, Germany. Email
Nvidia Corporation（英伟达公司）；University of South Carolina（南卡罗来纳大学）；University of Waikato（怀卡托大学）
Game-theoretic attribution techniques based on Shapley values are used to interpret black-box machine learning models, but their exact calculation is generally NP-hard, requiring approximation methods for non-trivial models. As the computation of Shapley values can be expressed as a summation over a set of permutations, a common approach is to sample a subset of these permutations for approximation. Unfortunately, standard Monte Carlo sampling methods can exhibit slow convergence, and more sophisticated quasi-Monte Carlo methods have not yet been applied to the space of permutations. To addres…
In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are based on the functional variance decomposition and their interpretation become difficult in the presence of statistical dependence between the inputs. However, as there is dependence in many application studies, that enhances the development of interpretable sensitivity indices. Recently, the Shapley values developed in the field of cooperative games theory …
In the institutional research mode, in order to explore which characteristics are the best indicators for predicting academic risk from the student behavior data sets that have high-dimensional, unbalanced classified small sample, it transforms the academic risk prediction of college students into a binary classification task. It predicts academic risk based on the LightGBM model and the interpretable machine learning method of Shapley value. The simulation results show that from the global perspective of the prediction model, characteristics such as the quality of academic partners, the seati…
Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this pa…
Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values is a game theoretic concept that can be used for this purpose. The Shapley value framework has a series of desirable theoretical properties, and can in principle handle any predictive model. Kernel SHAP is a computationally efficient approximation to Shapley values in higher dimensions. Like several other existing methods, this approach assumes that the fea…
Functional Decomposition and Shapley Interactions for Interpreting Survival Models
Leibniz Institute for Prevention Research（预防研究与流行病学研究所）；Faculty of Mathematics（数学系）；Computer Science, University of Bremen（计算机科学，不莱梅大学）；University of Warsaw（华沙大学）；Centre for Credible AI, Warsaw University of Technology（可信人工智能中心，华沙技术大学）；Bielefeld University（比勒菲尔德大学）
ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation
Department of Statistics, LMU Munich（LMU慕尼黑统计系）；Institute for Informatics, LMU Munich（LMU慕尼黑信息学院）；Department of Computer Science, TU Dortmund University（图腾大学计算机科学系）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Lamarr Institute for Machine Learning（拉马尔机器学习研究所）
Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative approach to interpret tree ensemble classifiers by surfacing representative points for each class -- prototypes. We introduce a new distance for Gradient Boosted Tree models, and propose new, adaptive prototype selection methods with theoretical guarantees, with the flexibility to choose a different number of prototypes in each class. We demonstrate our meth…
Imputation Uncertainty in Interpretable Machine Learning Methods
Leibniz Institute for Prevention Research & Epidemiology – BIPS（预防研究与流行病学研究所）；Faculty of Mathematics and Computer Science, University of Bremen（数学与计算机科学学院）
Which Hyperparameters Matter? A Game-Theoretic Framework for Interpretable Hyperparameter Sensitivity Analysis
Department of Mechanical and Industrial Engineering（机械与工业工程系）；Louisiana State University（路易斯安那州立大学）；Department of Electrical and Computer Engineering（电气与计算机工程系）
The importance of explainability in machine learning continues to grow, as both neural-network architectures and the data they model become increasingly complex. Unique challenges arise when a model's input features become high dimensional: on one hand, principled model-agnostic approaches to explainability become too computationally expensive; on the other, more efficient explainability algorithms lack natural interpretations for general users. In this work, we introduce a framework for human-interpretable explainability on high-dimensional data, consisting of two modules. First, we apply a s…
University of the Witwatersrand（威特沃特斯兰德大学）；ETH Zurich（苏黎世联邦理工学院）
Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep learning models is that their solutions are difficult to interpret and explain, and variable selection is not easily possible because deep learning models solve feature engineering and variable selection internally in a nontransparent way. Inspired by the appealing structure of generalized linear models, we propose a new network architecture that shares simi…
Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision rules. In this paper, we consider a submodular optimization based approach for learning rule sets. The learning problem is framed as a subset selection task in which a subset of all possible rules needs to be selected to form an accurate and interpretable rule set. We employ an objective function that exhibits submodularity and thus is amenable to submodular op…
A new ensemble framework for interpretable model called Linear Iterative Feature Embedding (LIFE) has been developed to achieve high prediction accuracy, easy interpretation and efficient computation simultaneously. The LIFE algorithm is able to fit a wide single-hidden-layer neural network (NN) accurately with three steps: defining the subsets of a dataset by the linear projections of neural nodes, creating the features from multiple narrow single-hidden-layer NNs trained on the different subsets of the data, combining the features with a linear model. The theoretical rationale behind LIFE is…
Rice University（莱斯大学）；Department of Statistics（统计系）
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with post-selection inference. We address these challenges from a Bayesian perspective. Given any Bayesian predictive model $\mathcal{M}$, we extract a family of near-optimal subsets of variables for linear prediction or classification. This strategy deemphasizes the role of a single "best" subset and instead advances the broader perspective that often many subsets …
