相关论文: Approximation of the fixed-probability level for a…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

We consider the classic Kelly gambling problem with general distribution of outcomes, and an additional risk constraint that limits the probability of a drawdown of wealth to a given undesirable level. We develop a bound on the drawdown…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

Standard uniform convergence results bound the generalization gap of the expected loss over a hypothesis class. The emergence of risk-sensitive learning requires generalization guarantees for functionals of the loss distribution beyond the…

In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…

Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…

During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance…

Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the…

It is common practice to collect observations of feature and response pairs from different environments. A natural question is how to identify features that have consistent prediction power across environments. The invariant causal…

Process capability indices such as $C_{pk}$ are widely used for manufacturing decisions, yet are typically applied via deterministic thresholding of finite-sample estimates, ignoring uncertainty and leading to unstable outcomes near the…

We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…

We review the question of the extreme values attained by a random process. We relate it to level crossings either to one boundary (first-passage problems) and two boundaries (escape problems). The extremes studied are the maximum, the…

In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…

The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained…

The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…

An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…