Related papers: Parameter Estimation in Gaussian Mixture Models wi…

In this paper, we expand the theory of depth-unbiased source localization to unbiased parameter estimation and signal reconstruction of an arbitrary number of non-zero parameters to be recovered. The topic touches on the concept of exact…

This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

We consider the problem of estimating the factors of a low-rank $n \times d$ matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known)…

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…

We analyse the precision limits for simultaneous estimation of a pair of conjugate parameters in a displacement channel using Gaussian probes. Having a set of squeezed states as an initial resource, we compute the Holevo Cram\'er-Rao bound…

This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by…

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…

We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…

Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…

Gaussian mixture distributions are commonly employed to represent general probability distributions. Despite the importance of using Gaussian mixtures for uncertainty estimation, the entropy of a Gaussian mixture cannot be calculated…

This article presents an algorithm for reducing measurement uncertainty of one physical quantity when given oversampled measurements of two physical quantities with correlated noise. The algorithm assumes that the aleatoric measurement…

We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

Phase retrieval has been mainly considered in the presence of Gaussian noise. However, the performance of the algorithms proposed under the Gaussian noise model severely degrades when grossly corrupted data, i.e., outliers, exist. This…

This paper studies the multi-task high-dimensional linear regression models where the noise among different tasks is correlated, in the moderately high dimensional regime where sample size $n$ and dimension $p$ are of the same order. Our…

This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown…

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…