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The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…

We study some features of learning models based on "delayed" and undifferentiated reinforcement and realized by simple algorithms which may be considered of a very elementary nature. We show that a modification of the Hebb-rule works well…

This paper presents a distinctive prime detection approach. This method use GM-(n+1) sequences to effectively eliminate complex numbers. The sequences, which consist of odd a number of (n+1), exclude all components except for the initial…

One of the core applications of machine learning to knowledge discovery consists on building a function (a hypothesis) from a given amount of data (for instance a decision tree or a neural network) such that we can use it afterwards to…

We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…

The problem of interpretability of machine learning architecture in particle physics has no agreed-upon definition, much less any proposed solution. We present a first modest step toward these goals by proposing a definition and…

In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…

Fingerprinting is a well known technique, which is often used in designing Monte Carlo algorithms for verifying identities involving ma- trices, integers and polynomials. The book by Motwani and Raghavan [1] shows how this technique can be…

Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…

Machine learning algorithms have been used to determine probabilistic classifications of unassociated sources. Often classification into two large classes, such as Galactic and extra-galactic, is considered. However, there are many more…

Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…

A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects. We provide an automated, model-based approach to inferring…

Benford's Law is an empirical law which predicts the frequency of significant digits in databases corresponding to various phenomena, natural or artificial. Although counter intuitive at the first sight, it predicts a higher occurrence of…

We present an approach for using machine learning to automatically discover the governing equations and hidden properties of real physical systems from observations. We train a "graph neural network" to simulate the dynamics of our solar…

Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…

In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `matrix properties'. In this paper we extend this algorithm to…

We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…

Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly…

Recently supervised machine learning has been ascending in providing new predictive approaches for chemical, biological and materials sciences applications. In this Perspective we focus on the interplay of machine learning algorithm with…

Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…