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We present {\em smart drill-down}, an operator for interactively exploring a relational table to discover and summarize "interesting" groups of tuples. Each group of tuples is described by a {\em rule}. For instance, the rule $(a, b, \star,…

Databases · Computer Science 2016-12-20 Manas Joglekar , Hector Garcia-Molina , Aditya Parameswaran

A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…

Computation · Statistics 2013-01-18 Matthew T. Harrison , Jeffrey W. Miller

In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and…

Artificial Intelligence · Computer Science 2021-01-29 Necla Kircali Gursoy , Ibrahim Senturk , Tahsin Oner , Arif Gursoy

Originating in game theory, Shapley values are widely used for explaining a machine learning model's prediction by quantifying the contribution of each feature's value to the prediction. This requires a scalar prediction as in binary…

Machine Learning · Computer Science 2025-02-13 Paul-Gauthier Noé , Miquel Perelló-Nieto , Jean-François Bonastre , Peter Flach

In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…

Symbolic Computation · Computer Science 2016-10-06 Moulay A. Barkatou , Maximilian Jaroschek , Suzy S. Maddah

For a subfamily of multiplicative measures on integer partitions we give conditions for properly rescaled associated Young diagrams to converge in probability to a certain deterministic curve named the limit shape of partitions. We provide…

Combinatorics · Mathematics 2009-04-20 Yuri Yakubovich

Multi-label classification is an important learning problem with many applications. In this work, we propose a principled similarity-based approach for multi-label learning called SML. We also introduce a similarity-based approach for…

Machine Learning · Statistics 2017-10-31 Ryan A. Rossi , Nesreen K. Ahmed , Hoda Eldardiry , Rong Zhou

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

Probability · Mathematics 2026-05-01 Joel A. Tropp

We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but…

Number Theory · Mathematics 2021-05-10 Doron Zeilberger , Wadim Zudilin

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

We introduce generalization of famous Macdonald polynomials for the case of super-Young diagrams that contain half-boxes on the equal footing with full boxes. These super-Macdonald polynomials are polynomials of extended set of variables:…

High Energy Physics - Theory · Physics 2024-08-09 Dmitry Galakhov , Alexei Morozov , Nikita Tselousov

We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…

Algebraic Geometry · Mathematics 2015-05-25 Juan Gerardo Alcázar , Gema M. Diaz-Toca , Carlos Hermosa

Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…

Numerical Analysis · Mathematics 2026-01-22 Inna K. Shingareva , Andrei D. Polyanin

We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain…

Data Structures and Algorithms · Computer Science 2014-06-04 Dimitris Papailiopoulos , Anastasios Kyrillidis , Christos Boutsidis

We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…

Artificial Intelligence · Computer Science 2013-02-28 Judea Pearl

We investigate hierarchical structure in various complex systems according to Minimum Spanning Tree methods. Firstly, we investigate stock markets where the graphis obtained from the matrix of correlations coefficient computed between all…

General Finance · Quantitative Finance 2014-06-13 Andrzej Jarynowski , Andrzej Buda

We present new links between some remarkable martingales found in the study of the Binary Search Tree, or of the Bisection Problem, looking at them on the probability space of a continuous time binary branching process.

Probability · Mathematics 2007-05-23 B. Chauvin , A. Rouault

The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…

Combinatorics · Mathematics 2007-05-23 Piotr Sniady

We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…

Group Theory · Mathematics 2013-04-19 Alexey Kanel-Belov , Boris Kunyavskii , Eugene Plotkin

We prove that in every cover of a Young diagram with $\binom{2k}{k}$ steps with generalized rectangles there is a row or a column in the diagram that is used by at least $k+1$ rectangles. We show that this is best-possible by partitioning…

Combinatorics · Mathematics 2019-02-25 Stefan Felsner , Torsten Ueckerdt
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