To use machine learning in high stakes applications (e.g. medicine), we need tools for building confidence in the system and evaluating whether it is reliable. Methods to improve model reliability are often applied at train time (e.g. using Bayesian inference to obtain uncertainty estimates). An alternative is to audit a fixed model subsequent to training. In this paper, we describe resampling uncertainty estimation (RUE), an algorithm to audit the pointwise reliability of predictions. Intuitively, RUE estimates the amount that a single prediction would change if the model had been fit on different training data drawn from the same distribution by using the gradient and Hessian of the model's loss on training data. Experimentally, we show that RUE more effectively detects inaccurate predictions than existing tools for auditing reliability subsequent to training. We also show that RUE can create predictive distributions that are competitive with state-of-the-art methods like Monte Carlo dropout, probabilistic backpropagation, and deep ensembles, but does not depend on specific algorithms at train-time like these methods do.

Strong worst-case performance bounds for episodic reinforcement learning exist but fortunately in practice RL algorithms perform much better than such bounds would predict. Algorithms and theory that provide strong problem-dependent bounds could help illuminate the key features of what makes a RL problem hard and reduce the barrier to using RL algorithms in practice. As a step towards this we derive an algorithm for finite horizon discrete MDPs and associated analysis that both yields state-of-the art worst-case regret bounds in the dominant terms and yields substantially tighter bounds if the RL environment has small environmental norm, which is a function of the variance of the next-state value functions. An important benefit of our algorithmic is that it does not require apriori knowledge of a bound on the environmental norm. As a result of our analysis, we also help address an open learning theory question~\cite{jiang2018open} about episodic MDPs with a constant upper-bound on the sum of rewards, providing a regret bound with no $H$-dependence in the leading term that scales a polynomial function of the number of episodes.

We show tight convergence rate bounds for gradient descent and MM algorithms for maximum likelihood estimation and maximum aposteriori probability estimation of a popular Bayesian inference method for generalized Bradley-Terry models. This class of models includes the Bradley-Terry model of paired comparisons, the Rao-Kupper model of paired comparisons with ties, the Luce choice model, and the Plackett-Luce ranking model. Our results show that MM algorithms have same convergence rates as gradient descent algorithms up to constant factors. For the maximum likelihood estimation, the convergence is linear with the rate crucially determined by the algebraic connectivity of the matrix of item pair co-occurrences in observed comparison data. For the Bayesian inference, the convergence rate is also linear, with the rate determined by a parameter of the prior distribution in a way that can make convergence arbitrarily slow for small values of this parameter. We propose a simple, first-order acceleration method that resolves the slow convergence issue.

In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin methods---have their own distinct strengths but also possess significant drawbacks. Conditional random fields (CRFs) are Fisher consistent, but they do not permit integration of customized loss metrics into their learning process. Large-margin models, such as structured support vector machines (SSVMs), have the flexibility to incorporate customized loss metrics, but lack Fisher consistency guarantees. We present adversarial graphical models (AGM), a distributionally robust approach for constructing a predictor that performs robustly for a class of data distributions defined using a graphical structure. Our approach enjoys both the flexibility of incorporating customized loss metrics into its design as well as the statistical guarantee of Fisher consistency. We present exact learning and prediction algorithms for AGM with time complexity similar to existing graphical models and show the practical benefits of our approach with experiments.

We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with $\beta$-divergences. The resulting inference procedure is doubly robust for both the predictive and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a construction for exponential models and demonstrate it on the Bayesian Linear Regression model. In so doing, we make two additional contributions: Firstly, we make GBI scalable using Structural Variational approximations that are exact as $\beta \to 0$. Secondly, we give a principled way of choosing the divergence parameter $\beta$ by minimizing expected predictive loss on-line. Reducing False Discovery Rates of \CPs from up to 99\% to 0\% on real world data, this offers the state of the art.

Based on non-local prior distributions, we propose a Bayesian model selection (BMS) procedure for boundary detection in a sequence of data with multiple systematic mean changes. The BMS method can effectively suppress the non-boundary spike points with large instantaneous changes. We speed up the algorithm by reducing the multiple change points to a series of single change point detection problems. We establish the consistency of the estimated number and locations of the change points under various prior distributions. Extensive simulation studies are conducted to compare the BMS with existing methods, and our approach is illustrated with application to the magnetic resonance imaging guided radiation therapy data.

Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision rule, but this ideal is difficult to achieve since these functions are frequently non-trivial to optimize. This statement is especially true when evaluating queries in parallel, where acquisition functions are routinely non-convex, high-dimensional, and intractable. We first show that acquisition functions estimated via Monte Carlo integration are consistently amenable to gradient-based optimization. Subsequently, we identify a common family of acquisition functions, including EI and UCB, whose characteristics not only facilitate but justify use of greedy approaches for their maximization.

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and the Wasserstein distance as special cases. The gradients of the Wasserstein variational loss are obtained by backpropagating through the Sinkhorn iterations. This technique results in a very stable likelihood-free training method that can be used with implicit distributions and probabilistic programs. Using the Wasserstein variational inference framework, we introduce several new forms of autoencoders and test their robustness and performance against existing variational autoencoding techniques.

In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labelling. Our method employs Bayesian optimization framework and Bradley-Terry model to construct the utility function, then to obtain the Expected Information Gain (EIG) of each pair. For computational efficiency, Gaussian-Hermite quadrature is used for estimation of EIG. In this work, a hybrid active sampling strategy is proposed, either using Global Maximum (GM) EIG sampling or Minimum Spanning Tree (MST) sampling in each trial, which is determined by the test budget. The proposed method has been validated on both simulated and real-world datasets, where it shows higher preference aggregation ability than the state-of-the-art methods.

We propose Lomax delegate racing (LDR) to explicitly model the mechanism of survival under competing risks and to interpret how the covariates accelerate or decelerate the time to event. LDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-risks, and consequently relaxes the ubiquitous proportional-hazards assumption which may be too restrictive. Moreover, LDR is naturally able to model not only censoring, but also missing event times or event types. For inference, we develop a Gibbs sampler under data augmentation for moderately sized data, along with a stochastic gradient descent maximum a posteriori inference algorithm for big data applications. Illustrative experiments are provided on both synthetic and real datasets, and comparison with various benchmark algorithms for survival analysis with competing risks demonstrates distinguished performance of LDR.