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We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on…
Results in epidemiology and social science often require the removal of confounding effects from measurements of the pairwise correlation of variables in survey data. This is typically accomplished by some variant of linear regression…
In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^\star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^\star$. This problem has a long history…
Missing covariate data pose a significant challenge to statistical inference and machine learning, particularly for classification tasks like logistic regression. Classical iterative approaches (EM, multiple imputation) are often…
We analyze principal component regression (PCR) in a high-dimensional error-in-variables setting with fixed design. Under suitable conditions, we show that PCR consistently identifies the unique model with minimum $\ell_2$-norm. These…
In classical causal inference, inferring cause-effect relations from data relies on the assumption that units are independent and identically distributed. This assumption is violated in settings where units are related through a network of…
Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as…
Missing data problems arise in many applied research studies. They may jeopardize statistical inference of the model of interest, if the missing mechanism is nonignorable, that is, the missing mechanism depends on the missing values…
Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
It is often said that the fundamental problem of causal inference is a missing data problem -- the comparison of responses to two hypothetical treatment assignments is made difficult because for every experimental unit only one potential…
We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with non-ignorable missingness. The missingness mechanism is driven by two sets…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…
A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of…
Inferring causal effects of a treatment, intervention or policy from observational data is central to many applications. However, state-of-the-art methods for causal inference seldom consider the possibility that covariates have missing…
Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…
Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail…
In this paper, we study difference-in-differences identification and estimation strategies when the parallel trends assumption holds after conditioning on covariates. We consider empirically relevant settings where the covariates can be…
Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate…
This paper addresses theoretical issues associated with probabilistic partial least squares (PLS) regression. As in the case of factor analysis, the probabilistic PLS regression with unique variance suffers from the issues of improper…