Related papers: Max-Affine Regression: Provable, Tractable, and Ne…

A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model…

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…

In this article we develop a max-strategy improvement algorithm for computing least fixpoints of operators on on the reals that are point-wise maxima of finitely many monotone and order-concave operators. Computing the uniquely determined…

We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…

We consider the problem of breakpoint detection in a regression modeling framework. To that end, we introduce a novel method, the max-EM algorithm which combines a constrained Hidden Markov Model with the Classification-EM (CEM) algorithm.…

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

In this work, we develop a novel fairness learning approach for multi-task regression models based on a biased training dataset, using a popular rank-based non-parametric independence test, i.e., Mann Whitney U statistic, for measuring the…

We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

We consider the problem of minimizing a strongly convex function that depends on an uncertain parameter $\theta$. The uncertainty in the objective function means that the optimum, $x^*(\theta)$, is also a function of $\theta$. We propose an…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special convex-concave structure. While some recent…

We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average $K$-NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on…

In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…

A recently proposed convex formulation of the phase retrieval problem estimates the unknown signal by solving a simple linear program. This new scheme, known as PhaseMax, is computationally efficient compared to standard convex relaxation…

Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…