Related papers: Maximum a Posteriori Inference for Factor Graphs v…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

Bayesian modeling and analysis of the MEG and EEG modalities provide a flexible framework for introducing prior information complementary to the measured data. This prior information is often qualitative in nature, making the translation of…

In Bayesian inference, the maximum a posteriori (MAP) problem combines the most probable explanation (MPE) and marginalization (MAR) problems. The counterpart in propositional logic is the exist-random stochastic satisfiability (ER-SSAT)…

Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture…

We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…

Arising from many applications at the intersection of decision making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) Problems unify the two main classes of inference, namely maximization (optimization) and marginal…

In this report a derivation of the MAP state estimator objective function for general (possibly non-square) discrete time causal/non-causal descriptor systems is presented. The derivation made use of the Kronecker Canonical Transformation…

Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…

In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…

While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…

In certain applications it is useful to fit multinomial distributions to observed data with a penalty term that encourages sparsity. For example, in probabilistic latent audio source decomposition one may wish to encode the assumption that…

Diffusion Posterior Sampling (DPS) provides a principled Bayesian approach to inverse problems by sampling from $p(x_0 \mid y)$. While posterior sampling is valuable for capturing uncertainty and multi-modality, many classical and practical…

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…

It is well known that the Lasso can be interpreted as a Bayesian posterior mode estimate with a Laplacian prior. Obtaining samples from the full posterior distribution, the Bayesian Lasso, confers major advantages in performance as compared…

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes,…

Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for…

Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While…

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…