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This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
A typical problem in the detection of the gravitational waves in the data of gravitational antennas is the non-stationarity of the Gaussian noise (and so the varying sensitivity) and the presence of big impulsive disturbances. In such…
We compute the Fr\'echet mean $\mathscr{E}_t$ of the solution $X_{t}$ to a continuous-time stochastic differential equation in a Lie group. It provides an estimator with minimal variance of $X_{t}$. We use it in the context of Kalman…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
An important objective of the classical processing of stationary random sequences under nonparametric uncertainty is the problem of filtering in case when the distribution of the underlying signal is unknown. In this paper it is assumed…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…
In this paper, we derive new model formulations for computing generalized singular values of a Grassman matrix pair. These new formulations make use of truncated filter matrices to locate the $i$-th generalized singular value of a Grassman…
This paper investigates a channel estimator based on Gaussian mixture models (GMMs) in the context of linear inverse problems with additive Gaussian noise. We fit a GMM to given channel samples to obtain an analytic probability density…
This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential…
We investigate a Kyle model under Gaussian assumptions where a risk-averse informed trader has imperfect information on the fundamental price of an asset. We show that an equilibrium can be constructed by considering an optimal transport…
So-called improper complex signals have been shown to be beneficial in the single-antenna two-user Gaussian interference channel under the assumptions that all input signals are Gaussian and that we treat interference as noise (TIN). This…
The matrix differential equation $x'(t) = Q(t)x(t), x(0) = x_0$ is considered in the case where $Q(t)$ is an unspecified matrix function of time, with the only constraint that $Q(t)\in \mset$ for every $t$, where $\mset$ is a prescribed…
We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a…
Wyner's Common Information and a natural relaxation are studied in the special case of Gaussian random variables. The relaxation replaces conditional independence by a bound on the conditional mutual information. The main contribution is…
The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…
To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are…