The statistical decision theoretic foundations of modern machine learning have largely focused on the minimization of the expectation of some loss function for a given task. However, seminal results in behavioral economics have shown that human decision-making is based on different risk measures than the expectation of any given loss function. In this paper, we pose the following simple question: in contrast to minimizing expected loss, could we minimize a better human-aligned risk measure? While this might not seem natural at first glance, we analyze the properties of such a revised risk measure, and surprisingly show that it might also better align with additional desiderata like fairness that have attracted considerable recent attention. We focus in particular on a class of human-aligned risk measures inspired by cumulative prospect theory.

We consider objective evaluation measures of saliency explanations for complex black-box machine learning models. We propose simple robust variants of two notions that have been considered in recent literature: (in)fidelity, and sensitivity. We analyze optimal explanations with respect to both these measures, and while the optimal explanation for sensitivity is a vacuous constant explanation, the optimal explanation for infidelity is a novel combination of two popular explanation methods. By varying the perturbation distribution that defines infidelity, we obtain novel explanations by optimizing infidelity, which we show to out-perform existing explanations in both quantitative and qualitative measurements. Another salient question given these measures is how to modify any given explanation to have better values with respect to these measures.

The ability to inferring latent psychological traits from human behavior is key to developing personalized human-interacting machine learning systems. Approaches to infer such traits range from surveys to manually-constructed experiments and games. However, these traditional games are limited because they are typically designed based on heuristics. In this paper, we formulate the task of designing behavior diagnostic games that elicit distinguishable behavior as a mutual information maximization problem, which can be solved by optimizing a variational lower bound. Our framework is instantiated by using prospect theory to model varying player traits, and Markov Decision Processes to parameterize the games. We validate our approach empirically, showing that our designed games can successfully distinguish among players with different traits, outperforming manually-designed ones by a large margin.

We consider the multiple linear regression problem, in a setting where some of the set of relevant features could be shared across the tasks. A lot of recent research has studied the use of $\ell_1/\ell_q$ norm block-regularizations with $q 1$ for such (possibly) block-structured problems, establishing strong guarantees on recovery even under high-dimensional scaling where the number of features scale with the number of observations. However, these papers also caution that the performance of such block-regularized methods are very dependent on the {\em extent} to which the features are shared across tasks. Indeed they show \citep{NWJoint} that if the extent of overlap is less than a threshold, or even if parameter {\em values} in the shared features are highly uneven, then block $\ell_1/\ell_q$ regularization could actually perform {\em worse} than simple separate elementwise $\ell_1$ regularization. We are far away from a realistic multi-task setting: not only do the set of relevant features have to be exactly the same across tasks, but their values have to as well.

Despite the large amount of literature on upper bounds on complexity of convex analysis, surprisingly little is known about the fundamental hardness of these problems. The extensive use of convex optimization in machine learning and statistics makes such an understanding critical to understand fundamental computational limits of learning and estimation. In this paper, we study the complexity of stochastic convex optimization in an oracle model of computation. We improve upon known results and obtain tight minimax complexity estimates for some function classes. We also discuss implications of these results to the understanding the inherent complexity of large-scale learning and estimation problems.

The L_1 regularized Gaussian maximum likelihood estimator has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to other state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton's method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and also present experimental results using synthetic and real application data that demonstrate the considerable improvements in performance of our method when compared to other state-of-the-art methods. Papers published at the Neural Information Processing Systems Conference.

In this paper, we consider the $\ell_1$ regularized sparse inverse covariance matrix estimation problem with a very large number of variables. Even in the face of this high dimensionality, and with limited number of samples, recent work has shown this estimator to have strong statistical guarantees in recovering the true structure of the sparse inverse covariance matrix, or alternatively the underlying graph structure of the corresponding Gaussian Markov Random Field. Our proposed algorithm divides the problem into smaller sub-problems, and uses the solutions of the sub-problems to build a good approximation for the original problem. We derive a bound on the distance of the approximate solution to the true solution. Based on this bound, we propose a clustering algorithm that attempts to minimize this bound, and in practice, is able to find effective partitions of the variables.

Increasingly, optimization problems in machine learning, especially those arising from high-dimensional statistical estimation, have a large number of variables. Modern statistical estimators developed over the past decade have statistical or sample complexity that depends only weakly on the number of parameters when there is some structure to the problem, such as sparsity. A central question is whether similar advances can be made in their computational complexity as well. In this paper, we propose strategies that indicate that such advances can indeed be made. In particular, we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse.

In this paper, we address the problem of learning the structure of a pairwise graphical model from samples in a high-dimensional setting. Our first main result studies the sparsistency, or consistency in sparsity pattern recovery, properties of a forward-backward greedy algorithm as applied to general statistical models. As a special case, we then apply this algorithm to learn the structure of a discrete graphical model via neighborhood estimation. As a corollary of our general result, we derive sufficient conditions on the number of samples n, the maximum node-degree d and the problem size p, as well as other conditions on the model parameters, so that the algorithm recovers all the edges with high probability. Our result guarantees graph selection for samples scaling as n Omega(d log(p)), in contrast to existing convex-optimization based algorithms that require a sample complexity of Omega(d 2 log(p)).

Undirected graphical models, or Markov networks, such as Gaussian graphical models and Ising models enjoy popularity in a variety of applications. In many settings, however, data may not follow a Gaussian or binomial distribution assumed by these models. We introduce a new class of graphical models based on generalized linear models (GLM) by assuming that node-wise conditional distributions arise from exponential families. Our models allow one to estimate networks for a wide class of exponential distributions, such as the Poisson, negative binomial, and exponential, by fitting penalized GLMs to select the neighborhood for each node. A major contribution of this paper is the rigorous statistical analysis showing that with high probability, the neighborhood of our graphical models can be recovered exactly.