Rethinking Stability for Attribution-based Explanations

As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an input. However, previous works have shown that state-of-the-art explanation methods generate unstable explanations. Here, we introduce metrics to quantify the stability of an explanation and show that several popular explanation methods are unstable. In particular, we propose new Relative Stability metrics that measure the change in output explanation with respect to change in input, model representation, or output of the underlying predictor. Finally, our experimental evaluation with three real-world datasets demonstrates interesting insights for seven explanation methods and different stability metrics.

Algorithmic Recourse in the Face of Noisy Human Responses

As machine learning (ML) models are increasingly being deployed in high-stakes applications, there has been growing interest in providing recourse to individuals adversely impacted by model predictions (e.g., an applicant whose loan has been denied). To this end, several post hoc techniques have been proposed in recent literature. These techniques generate recourses under the assumption that the affected individuals will implement the prescribed recourses exactly. However, recent studies suggest that individuals often implement recourses in a noisy and inconsistent manner - e.g., raising their salary by \$505 if the prescribed recourse suggested an increase of \$500. Motivated by this, we introduce and study the problem of recourse invalidation in the face of noisy human responses. More specifically, we theoretically and empirically analyze the behavior of state-of-the-art algorithms, and demonstrate that the recourses generated by these algorithms are very likely to be invalidated if small changes are made to them. We further propose a novel framework, EXPECTing noisy responses (EXPECT), which addresses the aforementioned problem by explicitly minimizing the probability of recourse invalidation in the face of noisy responses. Experimental evaluation with multiple real world datasets demonstrates the efficacy of the proposed framework, and supports our theoretical findings

Deep Neural Networks and Tabular Data: A Survey

Heterogeneous tabular data are the most commonly used form of data and are essential for numerous critical and computationally demanding applications. On homogeneous data sets, deep neural networks have repeatedly shown excellent performance and have therefore been widely adopted. However, their application to modeling tabular data (inference or generation) remains highly challenging. This work provides an overview of state-of-the-art deep learning methods for tabular data. We start by categorizing them into three groups: data transformations, specialized architectures, and regularization models. We then provide a comprehensive overview of the main approaches in each group. A discussion of deep learning approaches for generating tabular data is complemented by strategies for explaining deep models on tabular data. Our primary contribution is to address the main research streams and existing methodologies in this area, while highlighting relevant challenges and open research questions. To the best of our knowledge, this is the first in-depth look at deep learning approaches for tabular data. This work can serve as a valuable starting point and guide for researchers and practitioners interested in deep learning with tabular data.

CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms

Counterfactual explanations provide means for prescriptive model explanations by suggesting actionable feature changes (e.g., increase income) that allow individuals to achieve favorable outcomes in the future (e.g., insurance approval). Choosing an appropriate method is a crucial aspect for meaningful counterfactual explanations. As documented in recent reviews, there exists a quickly growing literature with available methods. Yet, in the absence of widely available opensource implementations, the decision in favor of certain models is primarily based on what is readily available. Going forward - to guarantee meaningful comparisons across explanation methods - we present CARLA (Counterfactual And Recourse LibrAry), a python library for benchmarking counterfactual explanation methods across both different data sets and different machine learning models. In summary, our work provides the following contributions: (i) an extensive benchmark of 11 popular counterfactual explanation methods, (ii) a benchmarking framework for research on future counterfactual explanation methods, and (iii) a standardized set of integrated evaluation measures and data sets for transparent and extensive comparisons of these methods. We have open-sourced CARLA and our experimental results on Github, making them available as competitive baselines. We welcome contributions from other research groups and practitioners.

On the Connections between Counterfactual Explanations and Adversarial Examples

Counterfactual explanations and adversarial examples have emerged as critical research areas for addressing the explainability and robustness goals of machine learning (ML). While counterfactual explanations were developed with the goal of providing recourse to individuals adversely impacted by algorithmic decisions, adversarial examples were designed to expose the vulnerabilities of ML models. While prior research has hinted at the commonalities between these frameworks, there has been little to no work on systematically exploring the connections between the literature on counterfactual explanations and adversarial examples. In this work, we make one of the first attempts at formalizing the connections between counterfactual explanations and adversarial examples. More specifically, we theoretically analyze salient counterfactual explanation and adversarial example generation methods, and highlight the conditions under which they behave similarly. Our analysis demonstrates that several popular counterfactual explanation and adversarial example generation methods such as the ones proposed by Wachter et. al. and Carlini and Wagner (with mean squared error loss), and C-CHVAE and natural adversarial examples by Zhao et. al. are equivalent. We also bound the distance between counterfactual explanations and adversarial examples generated by Wachter et. al. and DeepFool methods for linear models. Finally, we empirically validate our theoretical findings using extensive experimentation with synthetic and real world datasets.

Gaussian Experts Selection using Graphical Models

Local approximations are popular methods to scale Gaussian processes (GPs) to big data. Local approximations reduce time complexity by dividing the original dataset into subsets and training a local expert on each subset. Aggregating the experts' prediction is done assuming either conditional dependence or independence between the experts. Imposing the \emph{conditional independence assumption} (CI) between the experts renders the aggregation of different expert predictions time efficient at the cost of poor uncertainty quantification. On the other hand, modeling dependent experts can provide precise predictions and uncertainty quantification at the expense of impractically high computational costs. By eliminating weak experts via a theory-guided expert selection step, we substantially reduce the computational cost of aggregating dependent experts while ensuring calibrated uncertainty quantification. We leverage techniques from the literature on undirected graphical models, using sparse precision matrices that encode conditional dependencies between experts to select the most important experts. Moreov

On Counterfactual Explanations under Predictive Multiplicity

Counterfactual explanations are usually obtained by identifying the smallest change made to an input to change a prediction made by a fixed model (hereafter called sparse methods). Recent work, however, has revitalized an old insight: there often does not exist one superior solution to a prediction problem with respect to commonly used measures of interest (e.g. error rate). In fact, often multiple different classifiers give almost equal solutions. This phenomenon is known as predictive multiplicity (Breiman, 2001; Marx et al., 2019). In this work, we derive a general upper bound for the costs of counterfactual explanations under predictive multiplicity. Most notably, it depends on a discrepancy notion between two classifiers, which describes how differently they treat negatively predicted individuals. We then compare sparse and data support approaches empirically on real-world data. The results show that data support methods are more robust to multiplicity of different models. At the same time, we show that those methods have provably higher cost of generating counterfactual explanations under one fixed model. In summary, our theoretical and empiricaln results challenge the commonly held view that counterfactual recommendations should be sparse in general.

Leveraging Model Inherent Variable Importance for Stable Online Feature Selection

Feature selection can be a crucial factor in obtaining robust and accurate predictions. Online feature selection models, however, operate under considerable restrictions; they need to efficiently extract salient input features based on a bounded set of observations, while enabling robust and accurate predictions. In this work, we introduce FIRES, a novel framework for online feature selection. The proposed feature weighting mechanism leverages the importance information inherent in the parameters of a predictive model. By treating model parameters as random variables, we can penalize features with high uncertainty and thus generate more stable feature sets. Our framework is generic in that it leaves the choice of the underlying model to the user. Strikingly, experiments suggest that the model complexity has only a minor effect on the discriminative power and stability of the selected feature sets. In fact, using a simple linear model, FIRES obtains feature sets that compete with state-of-the-art methods, while dramatically reducing computation time. In addition, experiments show that the proposed framework is clearly superior in terms of feature selection stability.

Towards User Empowerment

Counterfactual explanations can be obtained by identifying the smallest change made to a feature vector to qualitatively influence a prediction; for example, from 'loan rejected' to 'awarded' or from 'high risk of cardiovascular disease' to 'low risk'. Previous approaches often emphasized that counterfactuals should be easily interpretable to humans, motivating sparse solutions with few changes to the feature vectors. However, these approaches would not ensure that the produced counterfactuals be proximate (i.e., not local outliers) and connected to regions with substantial data density (i.e., close to correctly classified observations), two requirements known as counterfactual faithfulness. These requirements are fundamental when making suggestions to individuals that are indeed attainable. Our contribution is twofold. On one hand, we suggest to complement the catalogue of counterfactual quality measures [1] using a criterion to quantify the degree of difficulty for a certain counterfactual suggestion. On the other hand, drawing ideas from the manifold learning literature, we develop a framework that generates attainable counterfactuals. We suggest the counterfactual conditional heterogeneous variational autoencoder (C-CHVAE) to identify attainable counterfactuals that lie within regions of high data density.