Related papers: Sparse/Robust Estimation and Kalman Smoothing with…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…

Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…

We formulate approximate Bayesian inference in non-conjugate temporal and spatio-temporal Gaussian process models as a simple parameter update rule applied during Kalman smoothing. This viewpoint encompasses most inference schemes,…

The structure uncertainty optimization problem is usually treated as double-loop optimization process, which is computation-intensive. In this paper, an efficient interval uncertainty optimization approach based on Quasi-sparse response…

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main…

Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…

Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…

Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…

This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic…

In this work we study the non-parametric reconstruction of spatio-temporal dynamical Gaussian processes (GPs) via GP regression from sparse and noisy data. GPs have been mainly applied to spatial regression where they represent one of the…

The goal of this paper is to investigate the complexity of gradient algorithms when learning sparse functions (juntas). We introduce a type of Statistical Queries ($\mathsf{SQ}$), which we call Differentiable Learning Queries…

Quantile regression (QR) is now widely used to analyze the effect of covariates on the conditional distribution of a response variable. It provides a more comprehensive picture of the relationship between a response and covariates compared…

Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex…

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…

Least squares support vector machines are a commonly used supervised learning method for nonlinear regression and classification. They can be implemented in either their primal or dual form. The latter requires solving a linear system,…

In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…

The standard linear quadratic Gaussian (LQG) framework assumes a Brownian noise process and relies on classical stochastic calculus tools, such as those based on It\^o calculus. In this paper, we solve a generalized linear quadratic optimal…