Related papers: Optimal Belief Approximation

We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a…

This paper presents some ideas to reduce the computational cost of evidence-based robust design optimization. Evidence Theory crystallizes both the aleatory and epistemic uncertainties in the design parameters, providing two quantitative…

We consider the fundamental problem of estimating a discrete distribution on a domain of size $K$ with high probability in Kullback-Leibler divergence. We provide upper and lower bounds on the minimax estimation rate, which show that the…

This paper compares three approaches to the problem of selecting among probability models to fit data (1) use of statistical criteria such as Akaike's information criterion and Schwarz's "Bayesian information criterion," (2) maximization of…

A myriad of explainability methods have been proposed in recent years, but there is little consensus on how to evaluate them. While automatic metrics allow for quick benchmarking, it isn't clear how such metrics reflect human interaction…

This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…

A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be…

Bayesian coresets speed up posterior inference in the large-scale data regime by approximating the full-data log-likelihood function with a surrogate log-likelihood based on a small, weighted subset of the data. But while Bayesian coresets…

Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370--418; 54 296--325] introduced the observed likelihood function to statistical inference and provided a weight function to calibrate the parameter; he also introduced a confidence…

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…

Accurately forecasting the probability distribution of phenomena of interest is a classic and ever more widespread goal in statistics and decision theory. In comparison to point forecasts, probabilistic forecasts aim to provide a more…

Elicitable functionals and (strictly) consistent scoring functions are of interest due to their utility of determining (uniquely) optimal forecasts, and thus the ability to effectively backtest predictions. However, in practice, assuming…

We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…

We study an extension of the standard two-party communication model in which Alice and Bob hold probability distributions $p$ and $q$ over domains $X$ and $Y$, respectively. Their goal is to estimate \[ \mathbb{E}_{x \sim p,\, y \sim…

In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model…

We consider estimating the predictive density under Kullback-Leibler loss in an $\ell_0$ sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

We discuss optimal prediction for families of probability distributions with a locally compact topological group structure. Right-invariant priors were previously shown to yield a posterior predictive distribution minimizing the worst-case…