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In this paper, we address the problem of feature selection in the context of multi-label learning, by using a new estimator based on implicit regularization and label embedding. Unlike the sparse feature selection methods that use a…
The problem of corrupted data, missing features, or missing modalities continues to plague the modern machine learning landscape. To address this issue, a class of regularization methods that enforce consistency between imputed and fully…
Penalty functions are widely used to enforce constraints in optimization problems and reinforcement leaning algorithms. Softplus and algebraic penalty functions are proposed to overcome the sensitivity of the Courant-Beltrami method to…
The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the corresponding reduced problems are solved using a bundle method of…
This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…
In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…
This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
We introduce a general framework for analyzing learning algorithms based on the notion of self-regularization, which captures implicit complexity control without requiring explicit regularization. This is motivated by previous observations…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by…
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A…
We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the…
In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the…
In previous literature, backward error analysis was used to find ordinary differential equations (ODEs) approximating the gradient descent trajectory. It was found that finite step sizes implicitly regularize solutions because terms…
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point…