Related papers: Machine Learning for Hilbert Series

The Computational Algebraic Geometry applied in Algebraic Statistics; are beginning to exploring new branches and applications; in artificial intelligence and others areas. Currently, the development of the mathematics is very extensive and…

We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…

Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…

Machine learning (ML) is becoming an increasingly important component of cutting-edge physics research, but its computational requirements present significant challenges. In this white paper, we discuss the needs of the physics community…

These lecture notes were written for a mini-course that was designed to introduce students and researchers to {\it $q$-series,} which are also called {\it basic hypergeometric series} because of the parameter $q$ that is used as a base in…

In recent years, machine learning has emerged as a powerful computational tool and novel problem-solving perspective for physics, offering new avenues for studying strongly interacting QCD matter properties under extreme conditions. This…

Neutrino experiments study the least understood of the Standard Model particles by observing their direct interactions with matter or searching for ultra-rare signals. The study of neutrinos typically requires overcoming large backgrounds,…

Neural networks are gaining widespread relevance for their versatility, holding the promise to yield a significant methodological shift in different domain of applied research. Here, we provide a simple pedagogical account of the basic…

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…

Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…

Machine learning is now used in many applications thanks to its ability to predict, generate, or discover patterns from large quantities of data. However, the process of collecting and transforming data for practical use is intricate. Even…

This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…

Though being seemingly disparate and with relatively new intersection, high energy nuclear physics and machine learning have already begun to merge and yield interesting results during the last few years. It's worthy to raise the profile of…

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…

These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…

Posets are discrete mathematical structures which are ubiquitous in a broad range of data analysis and machine learning applications. Research connecting posets to the data science domain has been ongoing for many years. In this paper, a…

This tutorial overviews the state of the art in learning models over relational databases and makes the case for a first-principles approach that exploits recent developments in database research. The input to learning classification and…

Statistical machine learning plays an important role in modern statistics and computer science. One main goal of statistical machine learning is to provide universally consistent algorithms, i.e., the estimator converges in probability or…

Here we will give a perspective on new possible interplays between Machine Learning and Quantum Physics, including also practical cases and applications. We will explore the ways in which machine learning could benefit from new quantum…

Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…