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This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local…

Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and…

As one of the central tasks in machine learning, regression finds lots of applications in different fields. An existing common practice for solving regression problems is the mean square error (MSE) minimization approach or its regularized…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). In particular, most of the numerical approximation schemes studied in the scientific…

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…

We study logit-based multi-purchase choice models and develop an exact solution methodology for the resulting assortment optimization problems, which we show are NP-hard to approximate. We introduce a hypergraph representation that captures…

With the rapid development of Large Language Models (LLMs), a large number of benchmarks have been proposed. However, most benchmarks lack unified evaluation standard and require the manual implementation of custom scripts, making results…

We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optimal cubature schemes and rational optimization. Using the…

Retrieval-Augmented Generation (RAG) has been proposed to mitigate hallucinations in large language models (LLMs), where generated outputs may be factually incorrect. However, existing RAG approaches predominantly rely on vector similarity…

On the basis of the classical theory of envelopes, we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.

Probabilistic language models are widely used in Information Retrieval (IR) to rank documents by the probability that they generate the query. However, the implementation of the probabilistic representations with programming languages that…

In document-level relation extraction, entities may appear multiple times in a document, and their relationships can shift from one context to another. Accurate prediction of the relationship between two entities across an entire document…

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…

The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…

Many problems in statistics and machine learning can be formulated as model selection problems, where the goal is to choose an optimal parsimonious model among a set of candidate models. It is typical to conduct model selection by…

Extending the popular Answer Set Programming (ASP) paradigm by introspective reasoning capacities has received increasing interest within the last years. Particular attention is given to the formalism of epistemic logic programs (ELPs)…

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover, a type of integer programming (IP) problem. A lattice-gas model on the Erd\"os-R\'enyi random graphs of $\alpha$-uniform…

Maximum a posteriori (MAP) inference is an important task for graphical models. Due to complex dependencies among variables in realistic model, finding an exact solution for MAP inference is often intractable. Thus, many approximation…

In recent deep image compression neural networks, the entropy model plays a critical role in estimating the prior distribution of deep image encodings. Existing methods combine hyperprior with local context in the entropy estimation…

We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…