Related papers: Partial Correlations in Compositional Data Analysi…
Many applications, e.g., Web service composition, complex system design, team formation, etc., rely on methods for identifying collections of objects or entities satisfying some functional requirement. Among the collections that satisfy the…
Treatment effect estimation from observational data is a fundamental problem in causal inference. There are two very different schools of thought that have tackled this problem. On one hand, Pearlian framework commonly assumes structural…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
In linear regression modelling the distortion of effects after marginalizing over variables of the conditioning set has been widely studied in several contexts. For Gaussian variables, the relationship between marginal and partial…
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…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
In a causal graphical model, an instrument for a variable X and its effect Y is a random variable that is a cause of X and independent of all the causes of Y except X. (Pearl (1995), Spirtes et al (2000)). Instrumental variables can be used…
Compositional observations arise when measurements are recorded as parts of a whole, so that only relative information is meaningful and the natural sample space is the simplex equipped with Aitchison geometry. Despite extensive development…
Compositional understanding is crucial for human intelligence, yet it remains unclear whether contemporary vision models exhibit it. The dominant machine learning paradigm is built on the premise that scaling data and model sizes will…
We explore the effects of data and design considerations through the example case of part-to-whole data relationships. Standard part-to-whole representations like pie charts and stacked bar charts make the relationships of parts to the…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
We introduce uncertainty regions to perform inference on partial correlations when data are missing not at random. These uncertainty regions are shown to have a desired asymptotic coverage. Their finite sample performance is illustrated via…
For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…
This chapter reviews the microeconometrics literature on partial identification, focusing on the developments of the last thirty years. The topics presented illustrate that the available data combined with credible maintained assumptions…
Learning causal relationships among a set of variables, as encoded by a directed acyclic graph, from observational data is complicated by the presence of unobserved confounders. Instrumental variables (IVs) are a popular remedy for this…
A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
We show how the Bell correlations can be modelled locally by relaxing the joint probability relation for independent variables $P(a,b)=P(a)P(b)$ outside classical settings, with complex/quaternion generators for the measurement outcomes…
Nonlinear relations, such as the curvilinear relationship between childhood trauma and resilience in patients with schizophrenia and the moderation relationship between mentalizing, and internalizing and externalizing symptoms and quality…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…