Related papers: Mathematical Data Science
A growing number of students are completing undergraduate degrees in statistics and entering the workforce as data analysts. In these positions, they are expected to understand how to utilize databases and other data warehouses, scrape data…
The utility of machine learning in understanding the motor system is promising a revolution in how to collect, measure, and analyze data. The field of movement science already elegantly incorporates theory and engineering principles to…
We take a data-scientific approach to study whether Kronecker coefficients are zero or not. Motivated by principal component analysis and kernel methods, we define loadings of partitions and use them to describe a sufficient condition for…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
Machine learning (ML) is revolutionizing the world, affecting almost every field of science and industry. Recent algorithms (in particular, deep networks) are increasingly data-hungry, requiring large datasets for training. Thus, the…
We explore the possibility of using machine learning to identify interesting mathematical structures by using certain quantities that serve as fingerprints. In particular, we extract features from integer sequences using two empirical laws:…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
Data science, and machine learning in particular, is rapidly transforming the scientific and industrial landscapes. The aerospace industry is poised to capitalize on big data and machine learning, which excels at solving the types of…
Weighting strategy prevails in machine learning. For example, a common approach in robust machine learning is to exert lower weights on samples which are likely to be noisy or quite hard. This study reveals another undiscovered strategy,…
Social science concerns issues on individuals, relationships, and the whole society. The complexity of research topics in social science makes it the amalgamation of multiple disciplines, such as economics, political science, and sociology,…
Causal inference from observational data is the goal of many data analyses in the health and social sciences. However, academic statistics has often frowned upon data analyses with a causal objective. The introduction of the term "data…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
As large-scale social data explode and machine-learning methods evolve, scholars of entrepreneurship and innovation face new research opportunities but also unique challenges. This chapter discusses the difficulties of leveraging…
Mechanical learning is a computing system that is based on a set of simple and fixed rules, and can learn from incoming data. A learning machine is a system that realizes mechanical learning. Importantly, we emphasis that it is based on a…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
Data Science is a complex and evolving field, but most agree that it can be defined as a combination of expertise drawn from three broad areascomputer science and technology, math and statistics, and domain knowledge -- with the purpose of…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…