Related papers: What is the correct cost functional for variationa…
We study the inverse problem of estimating a field $u$ from data comprising a finite set of nonlinear functionals of $u$, subject to additive noise; we denote this observed data by $y$. Our interest is in the reconstruction of piecewise…
We model a set of point-to-point transports on a network as a system of polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. The ends of each SAW may be located both at random, uniformly distributed, positions…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the…
We treat the problem of risk-aware control for stochastic shortest path (SSP) on Markov decision processes (MDP). Typically, expectation is considered for SSP, which however is oblivious to the incurred risk. We present an alternative view,…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…
Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a…
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of…
Recent research in robot exploration and mapping has focused on sampling environmental hotspot fields. This exploration task is formalized by Low, Dolan, and Khosla (2008) in a sequential decision-theoretic planning under uncertainty…
In this survey paper we present a class of shape optimization problems where the cost function involves the solution of a PDE of elliptic type in the unknown domain. In particular, we consider cost functions which depend on the spectrum of…
This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such an analysis can be used for pruning redundant measurements, and for designing future sensor…
This paper introduces two objective functions for computing the expected cost in the Stochastic Collection and Replenishment (SCAR) scenario. In the SCAR scenario, multiple user agents have a limited supply of a resource that they either…
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…
The next generation of Department of Energy supercomputers will be capable of exascale computation. For these machines, far more computation will be possible than that which can be saved to disk. As a result, users will be unable to rely on…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when…
The paper addresses two variants of the stochastic shortest path problem ('optimize the accumulated weight until reaching a goal state') in Markov decision processes (MDPs) with integer weights. The first variant optimizes partial expected…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…