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In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is…

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…

This paper considers endogenous selection models, in particular nonparametric ones. Estimating the unconditional law of the outcomes is possible when one uses instrumental variables. Using a selection equation which is additively separable…

Nonlinear independent component analysis (ICA) aims to uncover the true latent sources from their observable nonlinear mixtures. Despite its significance, the identifiability of nonlinear ICA is known to be impossible without additional…

Using modifications of Lindeberg's interpolation technique, I propose a new identification-robust test for the structural parameter in a heteroskedastic instrumental variables model. While my analysis allows the number of instruments to be…

Causal disentanglement aims to learn about latent causal factors behind data, holding the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability…

Unobserved discrete data are ubiquitous in many scientific disciplines, and how to learn the causal structure of these latent variables is crucial for uncovering data patterns. Most studies focus on the linear latent variable model or…

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

We introduce several methods for assessing sensitivity to unmeasured confounding in marginal structural models; importantly we allow treatments to be discrete or continuous, static or time-varying. We consider three sensitivity models: a…

Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…

We investigate the representation of hierarchical models in terms of marginals of other hierarchical models with smaller interactions. We focus on binary variables and marginals of pairwise interaction models whose hidden variables are…

One of the most common mistakes made when performing data analysis is attributing causal meaning to regression coefficients. Formally, a causal effect can only be computed if it is identifiable from a combination of observational data and…

Physically interpretable models are essential for next-generation industrial systems, as these representations enable effective control, support design validation, and provide a foundation for monitoring strategies. The aim of this paper is…

The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…

One of the most important empirical findings in microeconometrics is the pervasiveness of heterogeneity in economic behaviour (cf. Heckman 2001). This paper shows that cumulative distribution functions and quantiles of the nonparametric…

We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to nonignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for…

Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based…

Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution {induced} by a structural causal model, and additional data from (in the best case) \textit{only…

Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…