Generative models have the ability to synthesize data points drawn from the data distribution, however, not all generated samples are high quality. In this paper, we propose using a combination of coresets selection methods and ``entropic regularization'' to select the highest fidelity samples. We leverage an Energy-Based Model which resembles a variational auto-encoder with an inference and generator model for which the latent prior is complexified by an energy-based model. In a semi-supervised learning scenario, we show that augmenting the labeled data-set, by adding our selected subset of samples, leads to better accuracy improvement rather than using all the synthetic samples.

Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. In this paper, we introduce probabilistic sufficient explanations, which formulate explaining an instance of classification as choosing the "simplest" subset of features such that only observing those features is "sufficient" to explain the classification. That is, sufficient to give us strong probabilistic guarantees that the model will behave similarly when all features are observed under the data distribution. In addition, we leverage tractable probabilistic reasoning tools such as probabilistic circuits and expected predictions to design a scalable algorithm for finding the desired explanations while keeping the guarantees intact. Our experiments demonstrate the effectiveness of our algorithm in finding sufficient explanations, and showcase its advantages compared to Anchors and logical explanations.

However, most of these are heuristics in nature (Twala et al., 2008), tailored towards some specific tree induction algorithm Decision trees are a popular family of models (Chen & Guestrin, 2016; Prokhorenkova et al., 2018), due to their attractive properties such as interpretability or make strong distributional assumptions about the data, and ability to handle heterogeneous such as the feature distribution factorizing completely (e.g., data. Concurrently, missing data is a prevalent mean, median imputation (Rubin, 1976)) or according to the occurrence that hinders performance of machine tree structure (Quinlan, 1993). As many works have compared learning models. As such, handling missing data the most prominent ones in empirical studies (Batista in decision trees is a well studied problem. In & Monard, 2003; Saar-Tsechansky & Provost, 2007), there this paper, we tackle this problem by taking a is no clear winner and ultimately, the adoption of a particular probabilistic approach. At deployment time, we strategy in practice boils down to its availability in the use tractable density estimators to compute the ML libraries employed. "expected prediction" of our models. At learning time, we fine-tune parameters of already learned In this work, we tackle handling missing data in trees at trees by minimizing their "expected prediction both learning and deployment time from a principled probabilistic loss" w.r.t.

Computing expected predictions has many interesting applications in areas such as fairness, handling missing values, and data analysis. Unfortunately, computing expectations of a discriminative model with respect to a probability distribution defined by an arbitrary generative model has been proven to be hard in general. In fact, the task is intractable even for simple models such as logistic regression and a naive Bayes distribution. In this paper, we identify a pair of generative and discriminative models that enables tractable computation of expectations of the latter with respect to the former, as well as moments of any order, in case of regression. Specifically, we consider expressive probabilistic circuits with certain structural constraints that support tractable probabilistic inference. Moreover, we exploit the tractable computation of high-order moments to derive an algorithm to approximate the expectations, for classification scenarios in which exact computations are intractable. We evaluate the effectiveness of our exact and approximate algorithms in handling missing data during prediction time where they prove to be competitive to standard imputation techniques on a variety of datasets. Finally, we illustrate how expected prediction framework can be used to reason about the behaviour of discriminative models.

While discriminative classifiers often yield strong predictive performance, missing feature values at prediction time can still be a challenge. Classifiers may not behave as expected under certain ways of substituting the missing values, since they inherently make assumptions about the data distribution they were trained on. In this paper, we propose a novel framework that classifies examples with missing features by computing the expected prediction on a given feature distribution. We then use geometric programming to learn a naive Bayes distribution that embeds a given logistic regression classifier and can efficiently take its expected predictions. Empirical evaluations show that our model achieves the same performance as the logistic regression with all features observed, and outperforms standard imputation techniques when features go missing during prediction time. Furthermore, we demonstrate that our method can be used to generate 'sufficient explanations' of logistic regression classifications, by removing features that do not affect the classification.