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Missing data is frequently encountered in many areas of statistics. Propensity score weighting is a popular method for handling missing data. The propensity score method employs a response propensity model, but correct specification of the…
In this paper we investigate the connection between supervised learning and linear inverse problems. We first show that a linear inverse problem can be view as a function approximation problem in a reproducing kernel Hilbert space (RKHS)…
Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population,…
This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…
The linear functional strategy for the regularization of inverse problems is considered. For selecting the regularization parameter therein, we propose the heuristic quasi-optimality principle and some modifications including the smoothness…
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…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source's original…
This paper provides clear and practical guidance on the specification of imputation models when multiple imputation is used in conjunction with doubly robust estimation methods for causal inference. Through theoretical arguments and…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
Robot data collected in complex real-world scenarios are often biased due to safety concerns, human preferences, and mission or platform constraints. Consequently, robot learning from such observational data poses great challenges for…
This paper is concerned with identification of a spatial source function from final time observation in a bi-parabolic equation, where the full source function is assumed to be a product of time dependent and a space dependent function. Due…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Non-injective functions are not globally invertible. However, they can often be restricted to locally injective subdomains where the inversion is well-defined. In many settings a preferred solution can be selected even when multiple valid…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
The inverse problem of identifying the unknown spacewise dependent source F(x) in 1D wave equation is considered. Measured data are taken in the form g(t) := u(0; t). The relationship between that problem and Ground Penetrating Radar (GRR)…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
We discuss methods for {\em a priori} selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an…