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The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
Causality is essential for understanding complex systems, such as the economy, the brain, and the climate. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former…
Confirmatory factor analysis (CFA) is a statistical method for identifying and confirming the presence of latent factors among observed variables through the analysis of their covariance structure. Compared to alternative factor models, CFA…
We develop a mathematical and interpretative foundation for the enterprise of decision-theoretic statistical causality (DT), which is a straightforward way of representing and addressing causal questions. DT reframes causal inference as…
A dynamic factor model with a mixture distribution of the loadings is introduced and studied for multivariate, possibly high-dimensional time series. The correlation matrix of the model exhibits a block structure, reminiscent of correlation…
Human-factor analysis typically employs correlation analysis and significance testing to identify relationships between variables. However, these descriptive ('what-is') methods, while effective for identifying associations, are often…
Social and behavioral scientists are increasingly employing technologies such as fMRI, smartphones, and gene sequencing, which yield 'high-dimensional' datasets with more columns than rows. There is increasing interest, but little…
Factor analysis has been extensively used to reveal the dependence structures among multivariate variables, offering valuable insight in various fields. However, it cannot incorporate the spatial heterogeneity that is typically present in…
The Exploration-Exploitation tradeoff arises in Reinforcement Learning when one cannot tell if a policy is optimal. Then, there is a constant need to explore new actions instead of exploiting past experience. In practice, it is common to…
Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…
Deep learning (DL) has achieved remarkable progress over the past decade and been widely applied to many safety-critical applications. However, the robustness of DL systems recently receives great concerns, such as adversarial examples…
Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis…
This thesis scrutinizes common assumptions underlying traditional machine learning approaches to fairness in consequential decision making. After challenging the validity of these assumptions in real-world applications, we propose ways to…
A mixture of common skew-t factor analyzers model is introduced for model-based clustering of high-dimensional data. By assuming common component factor loadings, this model allows clustering to be performed in the presence of a large…
Conjoint analysis is a popular experimental design used to measure multidimensional preferences. Researchers examine how varying a factor of interest, while controlling for other relevant factors, influences decision-making. Currently,…
Combinatorial Testing (CT) is a potentially powerful testing technique, whereas its failure revealing ability might be dramatically reduced if it fails to handle constraints in an adequate and efficient manner. To ensure the wider…
In many longitudinal settings, economic theory does not guide practitioners on the type of restrictions that must be imposed to solve the rotational indeterminacy of factor-augmented linear models. We study this problem and offer several…
Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focussing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery…
We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of…
Causal discovery aims to uncover cause-and-effect relationships encoded in causal graphs by leveraging observational, interventional data, or their combination. The majority of existing causal discovery methods are developed assuming…