Related papers: Mathematical Data Science
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Although data science builds on knowledge from computer science, mathematics, statistics, and other disciplines, data science is a unique field with many mysteries to unlock: challenging scientific questions and pressing questions of…
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate…
We critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the…
Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to…
Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…
Data science has emerged from the proliferation of digital data, coupled with advances in algorithms, software and hardware (e.g., GPU computing). Innovations in structural biology have been driven by similar factors, spurring us to ask:…
A number of scientific competitions have been organised in the last few years with the objective of discovering innovative techniques to perform typical High Energy Physics tasks, like event reconstruction, classification and new physics…
The idea that data lies on a non-linear space has brought up the concept of manifold learning as a part of machine learning.
Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
The area of declarative data analytics explores the application of the declarative paradigm on data science and machine learning. It proposes declarative languages for expressing data analysis tasks and develops systems which optimize…
We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…
Data collection and labeling are critical bottlenecks in the deployment of machine learning applications. With the increasing complexity and diversity of applications, the need for efficient and scalable data collection and labeling…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…
This work presents the current collection of mathematical models related to neural networks and proposes a new family of such with extended structure and dynamics in order to attain a selection of cognitive capabilities. It starts by…
Compositional data analysis is concerned with multivariate data that have a constant sum, usually 1 or 100\%. These are data often found in biochemistry and geochemistry, but also in the social sciences, when relative values are of interest…
Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…