We propose answer-set programs that specify and compute counterfactual interventions as a basis for causality-based explanations to the outcomes from classification models. They can be applied with black-box models, and also with models that can be specified as logic programs, such as rule-based classifiers. The main focus is on the specification and computation of maximum-responsibility counterfactual explanations, with responsibility becoming an explanation score for features of entities under classification. We also extend the programs to bring into the picture semantic or domain knowledge. We show how the approach could be extended by means of probabilistic methods, and how the underlying probability distributions could be modified through the use of constraints.

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep learning algorithms are lacking of theoretical support. On the other hand, another line of works have proposed theoretical frameworks that are computationally infeasible. In this paper, we train sparse deep neural networks with a fully Bayesian treatment under spike-and-slab priors, and develop a set of computationally efficient variational inferences via continuous relaxation of Bernoulli distribution. The variational posterior contraction rate is provided, which justifies the consistency of the proposed variational Bayes method. Notably, our empirical results demonstrate that this variational procedure provides uncertainty quantification in terms of Bayesian predictive distribution and is also capable to accomplish consistent variable selection by training a sparse multi-layer neural network.

This paper presents a focused analysis of human studies in explainable artificial intelligence (XAI) entailing qualitative investigation. We draw on the social science corpora of qualitative research to illustrate opportunities for making the human studies where XAI researchers used observations, interviews, focus groups, and/or questionnaires to capture qualitative data more rigorous. We contextualize the presentation of the XAI contributions included in our analysis according to the components of rigor described in the qualitative research literature: 1) underlying theories or frameworks, 2) methodological approaches, 3) data collection methods, and 4) data analysis processes. The results of our analysis support calls from others in the XAI community advocating for collaboration with experts from social disciplines to bolster rigor and effectiveness in human studies.

Let $(X, S, Y) \in \mathbb{R}^p \times \{1, 2\} \times \mathbb{R}$ be a triplet following some joint distribution $\mathbb{P}$ with feature vector $X$, sensitive attribute $S$ , and target variable $Y$. The Bayes optimal prediction $f^*$ which does not produce Disparate Treatment is defined as $f^*(x) = \mathbb{E}[Y | X = x]$. We provide a non-trivial example of a prediction $x \to f(x)$ which satisfies two common group-fairness notions: Demographic Parity \begin{align} (f(X) | S = 1) &\stackrel{d}{=} (f(X) | S = 2) \end{align} and Equal Group-Wise Risks \begin{align} \mathbb{E}[(f^*(X) - f(X))^2 | S = 1] = \mathbb{E}[(f^*(X) - f(X))^2 | S = 2]. \end{align} To the best of our knowledge this is the first explicit construction of a non-constant predictor satisfying the above. We discuss several implications of this result on better understanding of mathematical notions of algorithmic fairness.

We consider the problem of expected risk minimization when the population loss is strongly convex and the target domain of the decision variable is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. We restrict focus to the case that the decision variable belongs to a nonparametric Reproducing Kernel Hilbert Space (RKHS). To solve it, we consider stochastic mirror descent that employs (i) pseudo-gradients and (ii) projections. Compressive projections are executed via kernel orthogonal matching pursuit (KOMP), and overcome the fact that the vanilla RKHS parameterization grows unbounded with time. Moreover, pseudo-gradients are needed, e.g., when stochastic gradients themselves define integrals over unknown quantities that must be evaluated numerically, as in estimating the intensity parameter of an inhomogeneous Poisson Process, and multi-class kernel logistic regression with latent multi-kernels. We establish tradeoffs between accuracy of convergence in mean and the projection budget parameter under constant step-size and compression budget, as well as non-asymptotic bounds on the model complexity. Experiments demonstrate that we achieve state-of-the-art accuracy and complexity tradeoffs for inhomogeneous Poisson Process intensity estimation and multi-class kernel logistic regression.

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. Here we consider sequential algorithms that greedily minimise MMD over a discrete candidate set. We propose a novel non-myopic algorithm and, in order to both improve statistical efficiency and reduce computational cost, we investigate a variant that applies this technique to a mini-batch of the candidate set at each iteration. When the candidate points are sampled from the target, the consistency of these new algorithm - and their mini-batch variants - is established. We demonstrate the algorithms on a range of important computational problems, including optimisation of nodes in Bayesian cubature and the thinning of Markov chain output.

Naive Bayes Classifiers are probabilistic models that are used for the classification task. It is based on the Bayes theorem with an assumption of independence among predictors. In the real-world, the independence assumption may or may not be true, but still, Naive Bayes performs well. Naive It is called naive because it assumes that all features in the dataset are mutually independent. Bayes, It is based on Bayes Theorem.

Many scientifically well-motivated statistical models in natural, engineering, and environmental sciences are specified through a generative process. However, in some cases, it may not be possible to write down the likelihood for these models analytically. Approximate Bayesian computation (ABC) methods allow Bayesian inference in such situations. The procedures are nonetheless typically computationally intensive. Recently, computationally attractive empirical likelihood-based ABC methods have been suggested in the literature. All of these methods rely on the availability of several suitable analytically tractable estimating equations, and this is sometimes problematic. We propose an easy-to-use empirical likelihood ABC method in this article. First, by using a variational approximation argument as a motivation, we show that the target log-posterior can be approximated as a sum of an expected joint log-likelihood and the differential entropy of the data generating density. The expected log-likelihood is then estimated by an empirical likelihood where the only inputs required are a choice of summary statistic, it's observed value, and the ability to simulate the chosen summary statistics for any parameter value under the model. The differential entropy is estimated from the simulated summaries using traditional methods. Posterior consistency is established for the method, and we discuss the bounds for the required number of simulated summaries in detail. The performance of the proposed method is explored in various examples.

Domain adaptation solves the learning problem in a target domain by leveraging the knowledge in a relevant source domain. While remarkable advances have been made, almost all existing domain adaptation methods heavily require large amounts of unlabeled target domain data for learning domain invariant representations to achieve good generalizability on the target domain. In fact, in many real-world applications, target domain data may not always be available. In this paper, we study the cases where at the training phase the target domain data is unavailable and only well-labeled source domain data is available, called robust domain adaptation. To tackle this problem, under the assumption that causal relationships between features and the class variable are robust across domains, we propose a novel Causal AutoEncoder (CAE), which integrates deep autoencoder and causal structure learning into a unified model to learn causal representations only using data from a single source domain. Specifically, a deep autoencoder model is adopted to learn low-dimensional representations, and a causal structure learning model is designed to separate the low-dimensional representations into two groups: causal representations and task-irrelevant representations. Using three real-world datasets the extensive experiments have validated the effectiveness of CAE compared to eleven state-of-the-art methods.

Anomaly detection is an important research problem because anomalies often contain critical insights for understanding the unusual behavior in data. One type of anomaly detection approach is dependency-based, which identifies anomalies by examining the violations of the normal dependency among variables. These methods can discover subtle and meaningful anomalies with better interpretation. Existing dependency-based methods adopt different implementations and show different strengths and weaknesses. However, the theoretical fundamentals and the general process behind them have not been well studied. This paper proposes a general framework, DepAD, to provide a unified process for dependency-based anomaly detection. DepAD decomposes unsupervised anomaly detection tasks into feature selection and prediction problems. Utilizing off-the-shelf techniques, the DepAD framework can have various instantiations to suit different application domains. Comprehensive experiments have been conducted over one hundred instantiated DepAD methods with 32 real-world datasets to evaluate the performance of representative techniques in DepAD. To show the effectiveness of DepAD, we compare two DepAD methods with nine state-of-the-art anomaly detection methods, and the results show that DepAD methods outperform comparison methods in most cases. Through the DepAD framework, this paper gives guidance and inspiration for future research of dependency-based anomaly detection and provides a benchmark for its evaluation.