Related papers: Solving Non-parametric Inverse Problem in Continuo…
In this paper we propose a new statistical stopping rule for constrained maximum likelihood iterative algorithms applied to ill-posed inverse problems. To this aim we extend the definition of Tikhonov regularization in a statistical…
In numerous practical applications, especially in medical image reconstruction, it is often infeasible to obtain a large ensemble of ground-truth/measurement pairs for supervised learning. Therefore, it is imperative to develop unsupervised…
The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…
Finite state space hidden Markov models are flexible tools to model phenomena with complex time dependencies: any process distribution can be approximated by a hidden Markov model with enough hidden states.We consider the problem of…
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
Mixtures of shifted asymmetric Laplace distributions were introduced as a tool for model-based clustering that allowed for the direct parameterization of skewness in addition to location and scale. Following common practices, an…
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
The montecarlo method, which is quite commonly used to solve maximum entropy problems in statistical physics, can actually be used to solve inverse problems in a much wider context. The probability distribution which maximizes entropy can…
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…
Approximating marginals of a graphical model is one of the fundamental problems in the theory of networks. In a recent paper a method was shown to construct a variational free energy such that the linear response estimates, and maximum…
While most approaches to the problem of Inverse Reinforcement Learning (IRL) focus on estimating a reward function that best explains an expert agent's policy or demonstrated behavior on a control task, it is often the case that such…
Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In…
We propose a self-supervised learning approach for solving the following constrained optimization task in log-linear models or Markov networks. Let $f$ and $g$ be two log-linear models defined over the sets $\mathbf{X}$ and $\mathbf{Y}$ of…
In this paper we present a synthesis of the work performed on two inference algorithms: the Pearl's belief propagation (BP) algorithm applied to Bayesian networks without loops (i.e. polytree) and the Loopy belief propagation (LBP)…
We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…