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Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…
The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
Most successful machine intelligence systems rely on gradient-based learning, which is made possible by backpropagation. Some systems are designed to aid us in interpreting data when explicit goals cannot be provided. These unsupervised…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and…
The use of machine learning methods helps to improve decision making in different fields. In particular, the idea of bridging predictions (machine learning models) and prescriptions (optimization problems) is gaining attention within the…
Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in…
This paper introduces a framework for Chance-Constrained Optimization with Complex Variables, addressing complex linear programming for both individual and joint probabilistic constraints in the complex domain. We first analyze the 3CP…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear…
Selecting powerful predictors for an outcome is a cornerstone task for machine learning. However, some types of questions can only be answered by identifying the predictors that causally affect the outcome. A recent approach to this causal…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…
We outline new approaches to incorporate ideas from deep learning into wave-based least-squares imaging. The aim, and main contribution of this work, is the combination of handcrafted constraints with deep convolutional neural networks, as…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor…
Boosting techniques from the field of statistical learning have grown to be a popular tool for estimating and selecting predictor effects in various regression models and can roughly be separated in two general approaches, namely gradient…
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within…
We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…