As local explanations of black box models are increasingly being employed to establish model credibility in high stakes settings, it is important to ensure that these explanations are accurate and reliable. However, local explanations generated by existing techniques are often prone to high variance. Further, these techniques are computationally inefficient, require significant hyper-parameter tuning, and provide little insight into the quality of the resulting explanations. We identify lack of uncertainty modeling as a main cause of these challenges and develop a novel set of tools for analyzing explanation uncertainty in a Bayesian framework. In particular, we estimate credible intervals (CIs) that capture the uncertainty associated with each feature importance in local explanations. These credible intervals are tight when we have high confidence in the feature importances of a local explanation. The CIs are also informative both for estimating how many perturbations we need to sample -- sampling can proceed until the CIs are sufficiently narrow -- and where to sample -- sampling in regions with high predictive uncertainty leads to faster convergence. We instantiate this framework to generate Bayesian versions of LIME and KernelSHAP. Experimental evaluation with multiple real world datasets and user studies demonstrate the efficacy of our framework and the resulting explanations.

Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference. While there are extensive references on QML estimation in batch settings, the QML estimation in streaming settings has attracted little attention until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE). This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol's stability and the ability to adapt to time-varying estimates for real-life data.

Automated scheduling is potentially a very useful tool for facilitating efficient, intuitive interactions between a robot and a human teammate. However, a current gapin automated scheduling is that it is not well understood how to best represent the timing uncertainty that human teammates introduce. This paper attempts to address this gap by designing an online human-robot collaborative packaging game that we use to build a model of human timing uncertainty from a population of crowd-workers. We conclude that heavy-tailed distributions are the best models of human temporal uncertainty, with a Log-Normal distribution achieving the best fit to our experimental data. We discuss how these results along with our collaborative online game will inform and facilitate future explorations into scheduling for improved human-robot fluency.

In this paper, we investigate the problem of computing Bayesian estimators using Langevin Monte-Carlo type approximation. The novelty of this paper is to consider together the statistical and numerical counterparts (in a general log-concave setting). More precisely, we address the following question: given $n$ observations in $\mathbb{R}^q$ distributed under an unknown probability $\mathbb{P}_{\theta^\star}$ with $\theta^\star \in \mathbb{R}^d$ , what is the optimal numerical strategy and its cost for the approximation of $\theta^\star$ with the Bayesian posterior mean? To answer this question, we establish some quantitative statistical bounds related to the underlying Poincar\'e constant of the model and establish new results about the numerical approximation of Gibbs measures by Cesaro averages of Euler schemes of (over-damped) Langevin diffusions. These last results include in particular some quantitative controls in the weakly convex case based on new bounds on the solution of the related Poisson equation of the diffusion.

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined cases, where an incorrectly chosen loss function leads to implausible predictions. Example tasks include conditional point-cloud reconstruction and predicting future states of molecules. In this paper, we propose an alternative to training via set losses by viewing learning as conditional density estimation. Our learning framework fits deep energy-based models and approximates the intractable likelihood with gradient-guided sampling. Furthermore, we propose a stochastically augmented prediction algorithm that enables multiple predictions, reflecting the possible variations in the target set. We empirically demonstrate on a variety of datasets the capability to learn multi-modal densities and produce multiple plausible predictions. Our approach is competitive with previous set prediction models on standard benchmarks. More importantly, it extends the family of addressable tasks beyond those that have unambiguous predictions.

Modifying the reward-biased maximum likelihood method originally proposed in the adaptive control literature, we propose novel learning algorithms to handle the explore-exploit trade-off in linear bandits problems as well as generalized linear bandits problems. We develop novel index policies that we prove achieve order-optimality, and show that they achieve empirical performance competitive with the state-of-the-art benchmark methods in extensive experiments. The new policies achieve this with low computation time per pull for linear bandits, and thereby resulting in both favorable regret as well as computational efficiency.

We study the problem of obtaining accurate policy gradient estimates using a finite number of samples. Monte-Carlo methods have been the default choice for policy gradient estimation, despite suffering from high variance in the gradient estimates. On the other hand, more sample efficient alternatives like Bayesian quadrature methods are less scalable due to their high computational complexity. In this work, we propose deep Bayesian quadrature policy gradient (DBQPG), a computationally efficient high-dimensional generalization of Bayesian quadrature, for policy gradient estimation. We show that DBQPG can substitute Monte-Carlo estimation in policy gradient methods, and demonstrate its effectiveness on a set of continuous control benchmarks. In comparison to Monte-Carlo estimation, DBQPG provides (i) more accurate gradient estimates with a significantly lower variance, (ii) a consistent improvement in the sample complexity and average return for several deep policy gradient algorithms, and, (iii) the uncertainty in gradient estimation that can be incorporated to further improve the performance.

The SIGTYP 2020 shared task (Bjerva et al., 2020) We reach the accuracy of 70.7% on the test data and rank first in the shared task. The task specification envisions a constrained The World Atlas of Language Structures (WALS) and an unconstrained track, where the constrained (Dryer and Haspelmath, 2013) is a database of systems can use only the provided WALS data, over 2,000 languages, which lists structural properties while an unconstrained system can use additional ('features') of each language, gathered from external resources, such as texts or pre-trained word reference grammars.

This paper deals with chain graphs (CGs) under the Andersson–Madigan–Perlman (AMP) interpretation. We address the problem of finding a minimal separator in an AMP CG, namely, finding a set Z of nodes that separates a given non-adjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial time algorithms for each. These include finding a minimal separator from a restricted set of nodes, finding a minimal separator for two given disjoint sets, and testing whether a given separator is minimal. To address the problem of learning the structure of AMP CGs from data, we show that the PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. We propose several modifications of the PC-like algorithm that remove part or all of this order-dependence. We also extend the decomposition-based approach for learning Bayesian networks (BNs) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption. We prove the correctness of our extension using the minimal separator results. Using standard benchmarks and synthetically generated models and data in our experiments demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified versions of) PC-like algorithm. The LCD-AMP algorithm usually outperforms the PC-like algorithm, and our modifications of the PC-like algorithm learn structures that are more similar to the underlying ground truth graphs than the original PC-like algorithm, especially in high-dimensional settings. In particular, we empirically show that the results of both algorithms are more accurate and stabler when the sample size is reasonably large and the underlying graph is sparse

Investigating real-world systems and phenomena typically requires complex models that involve a large number of parameters. Even with sizeable amount of observation data, the high complexity of the model may render accurate parameter estimation impossible. While finding a reliable point estimate of the parameter vector may not be possible in such a case, it may be possible to identify the parameter ranges based on the available data and/or prior system knowledge, or in a more general setting, we may assume a joint distribution of the model parameters. Since different parameter values are possible, this gives rise to an uncertainty class of all possible models [1, 2]. Furthermore, this naturally places the model in a Bayesian framework, where the likelihood of every possible model in the uncertainty class is described by a prior that could be constructed from prior system knowledge and existing data [3, 4]. Given an uncertain model and its uncertainty class, how can one mathematically quantify the amount of uncertainty present in the model? Common approaches include estimating the variance or entropy of the uncertain parameters, as they both provide a simple and intuitive measure of the model uncertainty. However, they both have a critical downside from a practical perspective. In practical applications that involve mathematical modeling of a complex system, one cares about the model as it can serve as a vehicle for designing an effective operator (i.e., controller, classifier, filter) that can act on the system of interest or the data produced therefrom.