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This paper examines the issue of fairness in the estimation of graphical models (GMs), particularly Gaussian, Covariance, and Ising models. These models play a vital role in understanding complex relationships in high-dimensional data.…
Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…
We introduce a new deal of kernel density estimation using an exponentiated form of kernel density estimators. The density estimator has two hyperparameters flexibly controlling the smoothness of the resulting density. We tune them in a…
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…
We analyze the behavior of the Barvinok estimator of the hafnian of even dimension, symmetric matrices with nonnegative entries. We introduce a condition under which the Barvinok estimator achieves subexponential errors, and show that this…
In \cite{KumarS15J2}, it was shown that a generalized maximum likelihood estimation problem on a (canonical) $\alpha$-power-law model ($\mathbb{M}^{(\alpha)}$-family) can be solved by solving a system of linear equations. This was due to an…
With observational data alone, causal structure learning is a challenging problem. The task becomes easier when having access to data collected from perturbations of the underlying system, even when the nature of these is unknown. Existing…
We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to…
Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We…
Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations,…
The linear classifier is widely used in various image classification tasks. It works by optimizing the distance between a sample and its corresponding class center. However, in real-world data, one class can contain several local clusters,…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
We discuss weighted scoring rules for forecast evaluation and their connection to hypothesis testing. First, a general construction principle for strictly locally proper weighted scoring rules based on conditional densities and scoring…
We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data…
We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…
Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…
Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…