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To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…
We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
We propose an efficient transfer Bayesian optimization method, which finds the maximum of an expensive-to-evaluate black-box function by using data on related optimization tasks. Our method uses auxiliary information that represents the…
We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…
The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…
We discuss the problem of input design for uncertainty reduction in a parameter estimation procedure. Assuming a linear continuous-time control system with noisy measurements, we formulate an objective of variance reduction in a Bayesian…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…