Related papers: Statistical Physics Analysis of Maximum a Posterio…
We present a randomized maximum a posteriori (rMAP) method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems. We derive the rMAP approach by: 1) casting…
The article studies different methods for estimating the Viterbi path in the Bayesian framework. The Viterbi path is an estimate of the underlying state path in hidden Markov models (HMMs), which has a maximum posterior probability (MAP).…
In this paper, we aim to design robust estimation techniques based on the compound-Gaussian (CG) process and adapted for calibration of radio interferometers. The motivation beyond this is due to the presence of outliers leading to an…
To glean the benefits offered by massive multi-input multi-output (MIMO) systems, channel state information must be accurately acquired. Despite the high accuracy, the computational complexity of classical linear minimum mean squared error…
We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from…
The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…
Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…
Efficiently finding the maximum a posteriori (MAP) configuration of a graphical model is an important problem which is often implemented using message passing algorithms. The optimality of such algorithms is only well established for…
We develop a predictive-first optimisation framework for streaming hidden Markov models. Unlike classical approaches that prioritise full posterior recovery under a fully specified generative model, we assume access to regime-specific…
We introduce novel blind and semi-blind channel estimation methods for cellular time-division duplexing systems with a large number of antennas at each base station. The methods are based on the maximum a-posteriori principle given a prior…
Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…
The article studies segmentation problem (also known as classification problem) with pairwise Markov models (PMMs). A PMM is a process where the observation process and underlying state sequence form a two-dimensional Markov chain, it is a…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
Any data modeling exercise has two main components: parameter estimation and model selection. The latter will be the topic of this lecture note. More concretely we will introduce several Monte-Carlo sampling-based rules for model selection…
In this paper, we study the remote estimation problem of a Markov process over a channel with a cost. We formulate this problem as an infinite horizon optimization problem with two players, i.e., a sensor and a monitor, that have distinct…