Related papers: A Dual Approach for Hierarchical Information-Theor…

In this paper, we introduce the application of Information Bottleneck as a method to investigate properties of questionnaires developed for the study of motivational profiles based on self-determination theory. Founded on information…

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…

Dual decomposition, and more generally Lagrangian relaxation, is a classical method for combinatorial optimization; it has recently been applied to several inference problems in natural language processing (NLP). This tutorial gives an…

An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are…

We prove weak duality between two recent convex relaxation methods for bounding the optimal value of a constrained variational problem in which the objective is an integral functional. The first approach, proposed by Valmorbida et al. (IEEE…

Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse…

The muti-layer information bottleneck (IB) problem, where information is propagated (or successively refined) from layer to layer, is considered. Based on information forwarded by the preceding layer, each stage of the network is required…

Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…

Split learning is a privacy-preserving distributed learning paradigm in which an ML model (e.g., a neural network) is split into two parts (i.e., an encoder and a decoder). The encoder shares so-called latent representation, rather than raw…

Information Bottleneck (IB) based multi-view learning provides an information theoretic principle for seeking shared information contained in heterogeneous data descriptions. However, its great success is generally attributed to estimate…

We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…

Bundle methods are often used to solve dual problems that arise from Lagrangian relaxations of large scale optimization problems. An example of such problems is the train timetabling problem. This paper focuses on solving a dual problem…

In this paper, we design a theoretical framework allowing to apply model predictive control on hybrid systems. For this, we develop a theory of approximate dynamic programming by leveraging the concept of alternating simulation. We show how…

It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…

Clustering is a well-known and studied problem, one of its variants, called contiguity-constrained clustering, accepts as a second input a graph used to encode prior information about cluster structure by means of contiguity constraints…

Application of the turbo principle to multiuser decoding results in an exchange of probability distributions between two sets of constraints. Firstly, constraints imposed by the multiple-access channel, and secondly, individual constraints…

Computer programs, so-called solvers, for solving the well-known Boolean satisfiability problem (Sat) have been improving for decades. Among the reasons, why these solvers are so fast, is the implicit usage of the formula's structural…

We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of…