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Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function,…
Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
We consider the task of obtaining the maximum a posteriori estimate of discrete pairwise random fields with arbitrary unary potentials and semimetric pairwise potentials. For this problem, we propose an accurate hierarchical move making…
We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…
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…
Standard regularized training procedures correspond to maximizing a posterior distribution over parameters, known as maximum a posteriori (MAP) estimation. However, model parameters are of interest only insomuch as they combine with the…
Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and…
Quantitative MR imaging is increasingly favoured for its richer information content and standardised measures. However, computing quantitative parameter maps, such as those encoding longitudinal relaxation rate (R1), apparent transverse…
We address the problem of computing reliable policies in reinforcement learning problems with limited data. In particular, we compute policies that achieve good returns with high confidence when deployed. This objective, known as the…
Channel and frequency offset estimation is a classic topic with a large body of prior work using mainly maximum likelihood (ML) approach together with Cram\'er-Rao Lower bounds (CRLB) analysis. We provide the maximum a posteriori (MAP)…
MAP is the problem of finding a most probable instantiation of a set of nvariables in a Bayesian network, given some evidence. MAP appears to be a significantly harder problem than the related problems of computing the probability of…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
Perturb-and-MAP offers an elegant approach to approximately sample from a energy-based model (EBM) by computing the maximum-a-posteriori (MAP) configuration of a perturbed version of the model. Sampling in turn enables learning. However,…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
Motivated by better modeling of intra-individual variability in longitudinal data, we propose a class of location-scale mixed effects models, in which the data of each individual is modeled by a parameter-varying generalized hyperbolic…
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…