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Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…

Bidirectional causal relationships arising from mutual interactions between variables are commonly observed within biomedical, econometrical, and social science contexts. When such relationships are further complicated by unobserved…

Observational studies of treatment effects require adjustment for confounding variables. However, causal inference methods typically cannot deliver perfect adjustment on all measured baseline variables, and there is often ambiguity about…

We consider the problem of learning a linear subspace from data corrupted by outliers. Classical approaches are typically designed for the case in which the subspace dimension is small relative to the ambient dimension. Our approach works…

Inducing causal relationships from observations is a classic problem in machine learning. Most work in causality starts from the premise that the causal variables themselves are observed. However, for AI agents such as robots trying to make…

Vine pair-copula constructions exist for a mix of continuous and ordinal variables. In some steps, this can involve estimating a bivariate copula for a pair of mixed continuous-ordinal variables. To assess the adequacy of copula fits for…

Variable importance, interaction measures, and partial dependence plots are important summaries in the interpretation of statistical and machine learning models. In this paper we describe new visualization techniques for exploring these…

We propose a novel approach to electron correlation for multireference systems. It is based on particle-hole (ph) and particle-particle (pp) theories in the second-order, developed in the random phase approximation (RPA) framework for…

In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined,…

We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small…

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further…

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…

This work approaches the multidimensional scaling problem from a novel angle. We introduce a scalable method based on the h-plot, which inherently accommodates asymmetric proximity data. Instead of embedding the objects themselves, the…

The article investigates the possibility of measuring the strength of a linear correlation relationship between nominal data and numerical data. Correlation coefficients for variables coded with real numbers as well as for variables coded…

Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…

The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…

Symbol letters are crucial for analytically calculating Feynman integrals in terms of iterated integrals. We present a novel method to construct the symbol letters for a given integral family without prior knowledge of the canonical…

Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late…