Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is crucial in high-stakes applications that involve critical decision-making. Bayesian neural networks (BNNs) aim at solving this problem by placing a prior distribution over the network's parameters, thereby inducing a posterior distribution that encapsulates predictive uncertainty. While existing variants of BNNs based on Monte Carlo dropout produce reliable (albeit approximate) uncertainty estimates over in-distribution data, they tend to exhibit over-confidence in predictions made on target data whose feature distribution differs from the training data, i.e., the covariate shift setup. In this paper, we develop an approximate Bayesian inference scheme based on posterior regularisation, wherein unlabelled target data are used as "pseudo-labels" of model confidence that are used to regularise the model's loss on labelled source data. We show that this approach significantly improves the accuracy of uncertainty quantification on covariate-shifted data sets, with minimal modification to the underlying model architecture. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.

Set classification aims to classify a set of observations as a whole, as opposed to classifying individual observations separately. To formally understand the unfamiliar concept of binary set classification, we first investigate the optimal decision rule under the normal distribution, which utilizes the empirical covariance of the set to be classified. We show that the number of observations in the set plays a critical role in bounding the Bayes risk. Under this framework, we further propose new methods of set classification. For the case where only a few parameters of the model drive the difference between two classes, we propose a computationally-efficient approach to parameter estimation using linear programming, leading to the Covariance-engaged LInear Programming Set (CLIPS) classifier. Its theoretical properties are investigated for both independent case and various (short-range and long-range dependent) time series structures among observations within each set. The convergence rates of estimation errors and risk of the CLIPS classifier are established to show that having multiple observations in a set leads to faster convergence rates, compared to the standard classification situation in which there is only one observation in the set. The applicable domains in which the CLIPS performs better than competitors are highlighted in a comprehensive simulation study. Finally, we illustrate the usefulness of the proposed methods in classification of real image data in histopathology.

Automated machine learning (AutoML) can produce complex model ensembles by stacking, bagging, and boosting many individual models like trees, deep networks, and nearest neighbor estimators. While highly accurate, the resulting predictors are large, slow, and opaque as compared to their constituents. To improve the deployment of AutoML on tabular data, we propose FAST-DAD to distill arbitrarily complex ensemble predictors into individual models like boosted trees, random forests, and deep networks. At the heart of our approach is a data augmentation strategy based on Gibbs sampling from a self-attention pseudolikelihood estimator. Across 30 datasets spanning regression and binary/multiclass classification tasks, FAST-DAD distillation produces significantly better individual models than one obtains through standard training on the original data. Our individual distilled models are over 10x faster and more accurate than ensemble predictors produced by AutoML tools like H2O/AutoSklearn.

Active search refers to the problem of efficiently locating targets in an unknown environment by actively making data-collection decisions, and has many applications including detecting gas leaks, radiation sources or human survivors of disasters using aerial and/or ground robots (agents). Existing active search methods are in general only amenable to a single agent, or if they extend to multi agent they require a central control system to coordinate the actions of all agents. However, such control systems are often impractical in robotics applications. In this paper, we propose two distinct active search algorithms called SPATS (Sparse Parallel Asynchronous Thompson Sampling) and LATSI (LAplace Thompson Sampling with Information gain) that allow for multiple agents to independently make data-collection decisions without a central coordinator. Throughout we consider that targets are sparsely located around the environment in keeping with compressive sensing assumptions and its applicability in real world scenarios. Additionally, while most common search algorithms assume that agents can sense the entire environment (e.g. compressive sensing) or sense point-wise (e.g. Bayesian Optimization) at all times, we make a realistic assumption that each agent can only sense a contiguous region of space at a time. We provide simulation results as well as theoretical analysis to demonstrate the efficacy of our proposed algorithms.

A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for instance in density estimation or to achieve excess risk bounds derived from single-scale entropy regularizers (Xu-Raginsky '17). This paper investigates a generalization of these results to a multiscale setting. We present different ways of generalizing the maximum entropy result by incorporating the notion of scale. For different entropies and arbitrary scale transformations, it is shown that the distribution maximizing a multiscale entropy is characterized by a procedure which has an analogy to the renormalization group procedure in statistical physics. For the case of decimation transformation, it is further shown that this distribution is Gaussian whenever the optimal single-scale distribution is Gaussian. This is then applied to neural networks, and it is shown that in a teacher-student scenario, the multiscale Gibbs posterior can achieve a smaller excess risk than the single-scale Gibbs posterior.

In this paper, we present a new idea for Transfer Learning (TL) based on Gibbs Sampling. Gibbs sampling is an algorithm in which instances are likely to transfer to a new state with a higher possibility with respect to a probability distribution. We find that such an algorithm can be employed to transfer instances between domains. Restricted Boltzmann Machine (RBM) is an energy based model that is very feasible for being trained to represent a data distribution and also for performing Gibbs sampling. We used RBM to capture data distribution of the source domain and use it in order to cast target instances into new data with a distribution similar to the distribution of source data. Using datasets that are commonly used for evaluation of TL methods, we show that our method can successfully enhance target classification by a considerable ratio. Additionally, the proposed method has the advantage over common DA methods that it needs no target data during the process of training of models.

We propose a simple, practical, and intuitive approach for domain adaptation in reinforcement learning. Our approach stems from the idea that the agent's experience in the source domain should look similar to its experience in the target domain. Building off of a probabilistic view of RL, we formally show that we can achieve this goal by compensating for the difference in dynamics by modifying the reward function. This modified reward function is simple to estimate by learning auxiliary classifiers that distinguish source-domain transitions from target-domain transitions. Intuitively, the modified reward function penalizes the agent for visiting states and taking actions in the source domain which are not possible in the target domain. Said another way, the agent is penalized for transitions that would indicate that the agent is interacting with the source domain, rather than the target domain. Our approach is applicable to domains with continuous states and actions and does not require learning an explicit model of the dynamics. On discrete and continuous control tasks, we illustrate the mechanics of our approach and demonstrate its scalability to high-dimensional tasks.

Consider learning a policy purely on the basis of demonstrated behavior---that is, with no access to reinforcement signals, no knowledge of transition dynamics, and no further interaction with the environment. This *strictly batch imitation learning* problem arises wherever live experimentation is costly, such as in healthcare. One solution is simply to retrofit existing algorithms for apprenticeship learning to work in the offline setting. But such an approach bargains heavily on model estimation or off-policy evaluation, and can be indirect and inefficient. We argue that a good solution should be able to explicitly parameterize a policy (i.e. respecting action conditionals), implicitly account for rollout dynamics (i.e. respecting state marginals), and---crucially---operate in an entirely offline fashion. To meet this challenge, we propose a novel technique by *energy-based distribution matching* (EDM): By identifying parameterizations of the (discriminative) model of a policy with the (generative) energy function for state distributions, EDM provides a simple and effective solution that equivalently minimizes a divergence between the occupancy measures of the demonstrator and the imitator. Through experiments with application to control tasks and healthcare settings, we illustrate consistent performance gains over existing algorithms for strictly batch imitation learning.

Evidence-based decision-making entails collecting (costly) observations about an underlying phenomenon of interest, and subsequently committing to an (informed) decision on the basis of accumulated evidence. In this setting, active sensing is the goal-oriented problem of efficiently selecting which acquisitions to make, and when and what decision to settle on. As its complement, inverse active sensing seeks to uncover an agent's preferences and strategy given their observable decision-making behavior. In this paper, we develop an expressive, unified framework for the general setting of evidence-based decision-making under endogenous, context-dependent time pressure---which requires negotiating (subjective) tradeoffs between accuracy, speediness, and cost of information. Using this language, we demonstrate how it enables modeling intuitive notions of surprise, suspense, and optimality in decision strategies (the forward problem). Finally, we illustrate how this formulation enables understanding decision-making behavior by quantifying preferences implicit in observed decision strategies (the inverse problem).

Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations of individual principal component scores that yield low-dimensional embedding of samples. That hinders the analysis of various spectral methods. In this paper, we first develop an $\ell_p$ perturbation theory for a hollowed version of PCA in Hilbert spaces which provably improves upon the vanilla PCA in the presence of heteroscedastic noises. Through a novel $\ell_p$ analysis of eigenvectors, we investigate entrywise behaviors of principal component score vectors and show that they can be approximated by linear functionals of the Gram matrix in $\ell_p$ norm, which includes $\ell_2$ and $\ell_\infty$ as special examples. For sub-Gaussian mixture models, the choice of $p$ giving optimal bounds depends on the signal-to-noise ratio, which further yields optimality guarantees for spectral clustering. For contextual community detection, the $\ell_p$ theory leads to a simple spectral algorithm that achieves the information threshold for exact recovery. These also provide optimal recovery results for Gaussian mixture and stochastic block models as special cases.