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Matching one set of objects to another is a ubiquitous task in machine learning and computer vision that often reduces to some form of the quadratic assignment problem (QAP). The QAP is known to be notoriously hard, both in theory and in…

Judging whether an integer can be divided by prime numbers such as 2 or 3 may appear trivial to human beings, but can be less straightforward for computers. Here, we tested multiple deep learning architectures and feature engineering…

Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…

Machine learning is a field which studies how machines can alter and adapt their behavior, improving their actions according to the information they are given. This field is subdivided into multiple areas, among which the best known are…

In representation learning, there has been recent interest in developing algorithms to disentangle the ground-truth generative factors behind a dataset, and metrics to quantify how fully this occurs. However, these algorithms and metrics…

In machine learning, classification is usually seen as a function approximation problem, where the goal is to learn a function that maps input features to class labels. In this paper, we propose a novel clustering and classification…

The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement…

There is a mismatch between the standard theoretical analyses of statistical machine learning and how learning is used in practice. The foundational assumption supporting the theory is that we can represent features and models using…

Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this…

As robots and other intelligent agents move from simple environments and problems to more complex, unstructured settings, manually programming their behavior has become increasingly challenging and expensive. Often, it is easier for a…

We theoretically analyze and compare the following five popular multiclass classification methods: One vs. All, All Pairs, Tree-based classifiers, Error Correcting Output Codes (ECOC) with randomly generated code matrices, and Multiclass…

We consider the problem of learning to choose from a given set of objects, where each object is represented by a feature vector. Traditional approaches in choice modelling are mainly based on learning a latent, real-valued utility function,…

In this paper, we present a complete classification of all imaginary $n$-quadratic fields of class number 1.

Recognition of objects with subtle differences has been used in many practical applications, such as car model recognition and maritime vessel identification. For discrimination of the objects in fine-grained detail, we focus on deep…

In [1, 2], we have explored the theoretical aspects of feature extraction optimization processes for solving largescale problems and overcoming machine learning limitations. Majority of optimization algorithms that have been introduced in…

Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).

Multivariate goodness-of-fit and two-sample tests are important components of many nuclear and particle physics analyses. While a variety of powerful methods are available if the dimensionality of the feature space is small, such tests…

Contemporary machine learning applications often involve classification tasks with many classes. Despite their extensive use, a precise understanding of the statistical properties and behavior of classification algorithms is still missing,…

Machine learning models deployed in real-world applications are often evaluated with precision-based metrics such as F1-score or AUC-PR (Area Under the Curve of Precision Recall). Heavily dependent on the class prior, such metrics make it…

This paper targets the question of predicting machine learning classification model performance, when taking into account the number of training examples per class and not just the overall number of training examples. This leads to the a…