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We consider Empirical Bayes (EB) estimation in the normal means problem, when the standard deviations of the observations are not known precisely, but estimated with error -- which is almost always the case in practical applications. In…
Dropout has recently emerged as a powerful and simple method for training neural networks preventing co-adaptation by stochastically omitting neurons. Dropout is currently not grounded in explicit modelling assumptions which so far has…
Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides…
An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of…
Unknown constraints arise in many types of expensive black-box optimization problems. Several methods have been proposed recently for performing Bayesian optimization with constraints, based on the expected improvement (EI) heuristic.…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…
Bayesian optimisation (BO) is widely used to optimise stochastic black box functions. While most BO approaches focus on optimising conditional expectations, many applications require risk-averse strategies and alternative criteria…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of…
Though learning has become a core component of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced systems. The need to impose requirements on learning is therefore paramount,…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
This paper studies the problem of mapping optimization in decentralized control problems. A global optimization algorithm is proposed based on the ideas of ``deterministic annealing" - a powerful non-convex optimization framework derived…
Randomized algorithms are used in many state-of-the-art solvers for constraint satisfaction problems (CSP) and Boolean satisfiability (SAT) problems. For many of these problems, there is no single solver which will dominate others. Having…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
We explore the notion of uncertainty in the context of modern abstractive summarization models, using the tools of Bayesian Deep Learning. Our approach approximates Bayesian inference by first extending state-of-the-art summarization models…