相关论文: Sparse/Robust Estimation and Kalman Smoothing with…
Smoothing classifiers and probability density functions with Gaussian kernels appear unrelated, but in this work, they are unified for the problem of robust classification. The key building block is approximating the $\textit{energy…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…
Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…
Recently, in a series of papers [32,38,39,41], the ratio of $\ell_1$ and $\ell_2$ norms was proposed as a sparsity inducing function for noiseless compressed sensing. In this paper, we further study properties of such model in the noiseless…
We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…
Spline quantile regression (SQR) is a method introduced recently by Li and Megiddo (2026) for linear quantile regression where the regression coefficients are treated as smooth functions of the quantile level. With the coefficients…
Underdetermined or ill-posed inverse problems require additional information for \ldd{d} sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal…
In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…
In this paper, we present the optimization formulation of the Kalman filtering and smoothing problems, and use this perspective to develop a variety of extensions and applications. We first formulate classic Kalman smoothing as a least…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
In this paper, we establish a connection between the recently developed data-driven time-frequency analysis \cite{HS11,HS13-1} and the classical second order differential equations. The main idea of the data-driven time-frequency analysis…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
Recent methods for imitation learning directly learn a $Q$-function using an implicit reward formulation rather than an explicit reward function. However, these methods generally require implicit reward regularization to improve stability…
Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…