Related papers: A hierarchical Bayesian perspective on majorizatio…

The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…

The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to…

Meta-Learning is a family of methods that use a set of interrelated tasks to learn a model that can quickly learn a new query task from a possibly small contextual dataset. In this study, we use a probabilistic framework to formalize what…

When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…

This paper devises a fully Bayesian sample size determination method for hierarchical model-based small area estimation with a decision risk approach. A new loss function specified around a desired maximum posterior variance target…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

Huber's criterion can be used for robust joint estimation of regression and scale parameters in the linear model. Huber's (Huber, 1981) motivation for introducing the criterion stemmed from non-convexity of the joint maximum likelihood…

The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…

Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific…

This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…

Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single…

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…

We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is $L_1$ regularization, which is often used in compressed sensing, a technique for reconstructing…

We introduce a means of automating machine learning (ML) for big data tasks, by performing scalable stochastic Bayesian optimisation of ML algorithm parameters and hyper-parameters. More often than not, the critical tuning of ML algorithm…

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high…

Structural damage due to excessive loading or environmental degradation typically occurs in localized areas in the absence of collapse. This prior information about the spatial sparseness of structural damage is exploited here by a…

In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is…