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We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds…

There is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the…

Modular Bayesian methods perform inference in models that are specified through a collection of coupled sub-models, known as modules. These modules often arise from modelling different data sources or from combining domain knowledge from…

Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…

Various optimality properties of universal sequence predictors based on Bayes-mixtures in general, and Solomonoff's prediction scheme in particular, will be studied. The probability of observing $x_t$ at time $t$, given past observations…

We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average $L_p$ distance between the learned classifier and the…

We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…

The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…

When humans infer underlying probabilities from stochastic observations, they exhibit biases and variability that cannot be explained on the basis of sound, Bayesian manipulations of probability. This is especially salient when beliefs are…

We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's information exponential inequality (IEI) gives a general recipe…

Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…

The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the…

We study the optimal portfolio allocation problem from a Bayesian perspective using value at risk (VaR) and conditional value at risk (CVaR) as risk measures. By applying the posterior predictive distribution for the future portfolio…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Given the cost and duration of phase III and phase IV clinical trials, the development of statistical methods for go/no-go decisions is vital. In this paper, we introduce a Bayesian methodology to compute the probability of success based on…

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…

We present a framework and analysis of consistent binary classification for complex and non-decomposable performance metrics such as the F-measure and the Jaccard measure. The proposed framework is general, as it applies to both batch and…

Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…