Related papers: Mixed Noise and Posterior Estimation with Conditio…

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

Although the expectation maximisation (EM) algorithm was introduced in 1970, it remains somewhat inaccessible to machine learning practitioners due to its obscure notation, terse proofs and lack of concrete links to modern machine learning…

Image denoising has achieved unprecedented progress as great efforts have been made to exploit effective deep denoisers. To improve the denoising performance in realworld, two typical solutions are used in recent trends: devising better…

We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our…

Classical Mixtures of Experts (MoE) are Machine Learning models that involve partitioning the input space, with a separate "expert" model trained on each partition. Recently, MoE-based model architectures have become popular as a means to…

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…

The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…

We consider the problem of estimating means of two Gaussians in a 2-Gaussian mixture, which is not balanced and is corrupted by noise of an arbitrary distribution. We present a robust algorithm to estimate the parameters, together with…

Efficient learning and model compression algorithm for deep neural network (DNN) is a key workhorse behind the rise of deep learning (DL). In this work, we propose a message passing based Bayesian deep learning algorithm called EM-TDAMP to…

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…

One of the tasks of the Bayesian inverse problem is to find a good estimate based on the posterior probability density. The most common point estimators are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

We propose a Bayesian approach to the problem of multi-reference alignment -- the recovery of signals from noisy, randomly shifted observations. While existing frequentist methods accurately recover the signal at arbitrarily low…

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…

Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…

Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for…

We extend the linear mixed-effects state model to accommodate the correlated individuals and investigate its parameter and state estimation based on disturbance smoothing in this paper. For parameter estimation, EM and score based…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…