Related papers: A machine learning approach to commutative algebra…

In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to…

Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…

Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…

Spreadsheet tables are often labeled, and these labels effectively constitute types for the data in the table. In such cases tables can be considered to be built from typed data where the placement of values within the table is controlled…

Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point…

Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual…

Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic…

The success of self-supervised learning in computer vision and natural language processing has motivated pretraining methods on tabular data. However, most existing tabular self-supervised learning models fail to leverage information across…

Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature…

Table foundation models bring high hopes to data science: pre-trained on tabular data to embark knowledge or priors, they should facilitate downstream tasks on tables. One specific challenge is that of data semantics: numerical entries take…

Many data we collect today are in tabular form, with rows as records and columns as attributes associated with each record. Understanding the structural relationship in tabular data can greatly facilitate the data science process.…

The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…

Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…

The algebras considered in this paper are commutative rings of which the additive group is a finite-dimensional vector space over the field of rational numbers. We present deterministic polynomial-time algorithms that, given such an…

Machine learning and pattern recognition techniques have been successfully applied to algorithmic problems in free groups. In this paper, we seek to extend these techniques to finitely presented non-free groups, with a particular emphasis…

Tabular data is a fundamental form of data structure. The evolution of table analysis tools reflects humanity's continuous progress in data acquisition, management, and processing. The dynamic changes in table columns arise from…

We propose to utilize gradients for detecting adversarial and out-of-distribution samples. We introduce confounding labels -- labels that differ from normal labels seen during training -- in gradient generation to probe the effective…

Indexing large-scale databases in main memory is still challenging today. Learned index structures -- in which the core components of classical indexes are replaced with machine learning models -- have recently been suggested to…

Since a vast number of tables can be easily collected from web pages, spreadsheets, PDFs, and various other document types, a flurry of table pre-training frameworks have been proposed following the success of text and images, and they have…

Machine learning is permeating every conceivable domain to promote data-driven decision support. The focus is often on advanced black-box models due to their assumed performance advantages, whereas interpretable models are often associated…