Related papers: A parameter identification problem in stochastic h…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
This paper addresses a detection problem where several spatially distributed sensors independently observe a time-inhomogeneous stochastic process. The task is to decide between two hypotheses regarding the statistics of the observed…
In this paper, we study optimization problems where the cost function contains time-varying parameters that are unmeasurable and evolve according to linear, yet unknown, dynamics. We propose a solution that leverages control theoretic tools…
The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…
We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…
We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…
We provide an efficient method to approximate the covariance between decision variables and uncertain parameters in solutions to a general class of stochastic nonlinear complementarity problems. We also develop a sensitivity metric to…
In most (weakly interacting) extensions of the Standard Model the relation mapping the parameter values onto experimentally measurable quantities can be computed (with some uncertainties), but the inverse relation is usually not known. In…
We present a new approach and an algorithm for optimizing the material configuration and behaviour of a fluid saturated porous medium in a two-scale setting. The state problem is governed by the Biot model describing the fluid-structure…
Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Given an unknown dynamic system such as a coupled harmonic oscillator with $n$ springs and point masses. We are often interested in gaining insights into its physical parameters, i.e. stiffnesses and masses, by observing trajectories of…
For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…
We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…