Related papers: Compositional data analysis -- linear algebra, vis…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering,…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
We live in a world where data generation is omnipresent. Innovations in computer hardware in the last few decades coupled with increasingly reliable connectivity among them have fueled this phenomenon. We are constantly creating and…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Massive data collection holds the promise of a better understanding of complex phenomena and, ultimately, better decisions. Representation learning has become a key driver of deep learning applications, as it allows learning latent spaces…
Classical Biplot Methods allow for the simultaneous representation of individuals (rows) and variables (columns) of a data matrix. For Binary data, Logistic biplots have been recently developed.When data are nominal, linear or even binary…
With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…
Multivariate categorical data are routinely collected in many application areas. As the number of cells in the table grows exponentially with the number of variables, many or even most cells will contain zero observations. This severe…
Many engineered systems must balance competing objectives, such as performance and safety, cost and reliability, or efficiency and sustainability, and are naturally modeled as compositions of interacting subsystems. We study online…
Data Visualization has become an important aspect of big data analytics and has grown in sophistication and variety. We specifically identify the need for an analytical framework for data visualization with textual information. Data…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
The basic objective of data visualization is to provide an efficient graphical display for summarizing and reasoning about quantitative information. During the last decades, political science has accumulated a large corpus of various kinds…
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
Two important aspects of semantic parsing for question answering are the breadth of the knowledge source and the depth of logical compositionality. While existing work trades off one aspect for another, this paper simultaneously makes…
Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…