Related papers: Machine Learning and Data Analysis Using Posets: A…

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…

Human pose is typically represented by a coordinate vector of body joints or their heatmap embeddings. While easy for data processing, unrealistic pose estimates are admitted due to the lack of dependency modeling between the body joints.…

We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…

Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…

We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are…

Human pose analysis has garnered significant attention within both the research community and practical applications, owing to its expanding array of uses, including gaming, video surveillance, sports performance analysis, and…

Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…

Pose Machines provide a sequential prediction framework for learning rich implicit spatial models. In this work we show a systematic design for how convolutional networks can be incorporated into the pose machine framework for learning…

Like many computer vision problems, human pose estimation is a challenging problem in that recognizing a body part requires not only information from local area but also from areas with large spatial distance. In order to spatially pass…

Given a measurable space (X, M) there is a (Galois) connection between sub-sigma-algebras of M and equivalence relations on X. On the other hand equivalence relations on X are closely related to congruences on stochastic relations. In…

This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…

The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and…

Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…

Machine learning techniques have had a long list of applications in recent years. However, the use of machine learning in information and network security is not new. Machine learning and cryptography have many things in common. The most…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Clustering is a fundamental machine learning task which has been widely studied in the literature. Classic clustering methods follow the assumption that data are represented as features in a vectorized form through various representation…

We survey some recent applications of machine learning to problems in geometry and theoretical physics. Pure mathematical data has been compiled over the last few decades by the community and experiments in supervised, semi-supervised and…

Human modelling and pose estimation stands at the crossroads of Computer Vision, Computer Graphics, and Machine Learning. This paper presents a thorough investigation of this interdisciplinary field, examining various algorithms,…