Related papers: Multivariate information measures: a unification u…
Missing data remains a very common problem in large datasets, including survey and census data containing many ordinal responses, such as political polls and opinion surveys. Multiple imputation (MI) is usually the go-to approach for…
Let $B$ be a finite Boolean algebra. Let $\mathcal A$ be the partial order of all implication sublattices of $B$. We will compute the M\"obius function on $\mathcal A$ in two different ways.
Mutual information has many applications in image alignment and matching, mainly due to its ability to measure the statistical dependence between two images, even if the two images are from different modalities (e.g., CT and MRI). It…
As the availability of omics data has increased in the last few years, more multi-omics data have been generated, that is, high-dimensional molecular data consisting of several types such as genomic, transcriptomic, or proteomic data, all…
We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using…
Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
Mutual information is a widely-used information theoretic measure to quantify the amount of association between variables. It is used extensively in many applications such as image registration, diagnosis of failures in electrical machines,…
Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU…
Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…
Measures of association play a role in selecting 2x2 tables exhibiting strong dependence in high-dimensional binary data. Several measures are in use differing on specific tables and in their dependence on the margins. We study a…
Mass-spectrometry technologies are widely used in the fields of ionomics and metabolomics to simultaneously profile at the genome scale intracellular concentrations of e.g. amino acids or elements. Short profiles of molecular or…
Information has intrinsic geometric and topological structure, arising from relative relationships beyond absolute values or types. For instance, the fact that two people share a meal describes a relationship independent of the meal's…
Several mathematical ideas have been investigated for Quantitative Information Flow. Information theory, probability, guessability are the main ideas in most proposals. They aim to quantify how much information is leaked, how likely is to…
Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses…
We provide an approach to exploratory data analysis in matched observational studies with a single intervention and multiple endpoints. In such settings, the researcher would like to explore evidence for actual treatment effects among these…
In this paper, we propose a unified information theoretic framework for learning-motivated methods aimed at odometry estimation, a crucial component of many robotics and vision tasks such as navigation and virtual reality where relative…
Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been…