Related papers: On the choice of weights in aggregate compositiona…
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…
Traditional methods for the analysis of compositional data consider the log-ratios between all different pairs of variables with equal weight, typically in the form of aggregated contributions. This is not meaningful in contexts where it is…
In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a "whole". The sum of these components must be equal to one. Compositional…
Many scientific datasets are compositional in nature. Important biological examples include species abundances in ecology, cell-type compositions derived from single-cell sequencing data, and amplicon abundance data in microbiome research.…
Compositional data sets are ubiquitous in science, including geology, ecology, and microbiology. In microbiome research, compositional data primarily arise from high-throughput sequence-based profiling experiments. These data comprise…
This article present a method of mutual transformation between count model and composition model. Offer the mathematical view of classical radio and log-radio in compositional data analysis and expand the idea of mixture model of counts…
Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular,…
Many data sources are naturally modeled by multiple weight assignments over a set of keys: snapshots of an evolving database at multiple points in time, measurements collected over multiple time periods, requests for resources served at…
Composites are often created to facilitate the work of decision-makers. Therefore, practical or theoretical considerations may lead to a priori weights of the indicators forming a composite. Composites that are created a weighted aggregates…
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature,…
Information aggregation is a vital tool for human and machine decision making in the presence of uncertainty. Traditionally, approaches to aggregation broadly diverge into two categories, those which attribute a worth or weight to…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
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…
Identifying the relations that exist between words (or entities) is important for various natural language processing tasks such as, relational search, noun-modifier classification and analogy detection. A popular approach to represent the…
A vector composition of a vector $\mathbf{\ell}$ is a matrix $\mathbf{A}$ whose rows sum to $\mathbf{\ell}$. We define a weighted vector composition as a vector composition in which the column values of $\mathbf{A}$ may appear in different…
The study of immune cellular composition has been of great scientific interest in immunology because of the generation of multiple large-scale data. From the statistical point of view, such immune cellular data should be treated as…
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…