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Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet…
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin,…
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…
In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for…
The Causal Roadmap outlines a systematic approach to asking and answering questions of cause-and-effect: define the quantity of interest, evaluate needed assumptions, conduct statistical estimation, and carefully interpret results. To…
We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
We present a boosting-based method to learn additive Structural Equation Models (SEMs) from observational data, with a focus on the theoretical aspects of determining the causal order among variables. We introduce a family of score…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This…
Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The…
In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…
The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive $p-$values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework of the…
Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization…
Gaussian graphical models (GGMs) are widely used to recover the conditional independence structure among random variables. Recent work has sought to incorporate auxiliary covariates to improve estimation, particularly in applications such…
Conditional Gaussian graphical models (cGGM) are a recent reparametrization of the multivariate linear regression model which explicitly exhibits $i)$ the partial covariances between the predictors and the responses, and $ii)$ the partial…
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The…
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…