arXiv subjects

Leihao Chen

Publications and source records attributed to Leihao Chen.

6 recordsLinked to original sources

arXiv2026

Complete Causal Identification from Ancestral Graphs under Selection Bias

Many causal discovery algorithms, including the celebrated FCI algorithm, output a Partial Ancestral Graph (PAG). PAGs serve as an abstract graphical representation of the underlying causal structure, modeled by directed acyclic graphs with latent and selection variables. This paper develops a characterization of the set of extended-type conditional independence relations that are invariant across all causal models represented by a PAG. This theory allows us to formulate a general measure-theoretic version of Pearl's causal calculus and a sound and complete identification algorithm for PAGs under selection bias. Our results also apply when PAGs are learned by certain algorithms that integrate observational data with experimental data and incorporate background knowledge.

stat.ME↗

arXiv2026

Notes on Forr\'e's Notion of Conditional Independence and Causal Calculus for Continuous Variables

Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes a strong global Markov property connecting transitional conditional independencies with suitable graphical separation criteria for directed mixed graphs with input nodes (iDMGs), together with a version of causal calculus for iDMGs in a general measure-theoretic setting. These notes aim to further illustrate the motivations behind this framework and its connections to the literature, highlight certain subtlies in the general measure-theoretic causal calculus, and extend the "one-line" formulation of the ID algorithm of Richardson et al. (Ann. Statist. 51(1):334--361, 2023) to the general measure-theoretic setting.

math.ST↗

arXiv2025

Foundations of Structural Causal Models with Latent Selection

Three distinct phenomena complicate statistical causal analysis: latent common causes, causal cycles, and latent selection. Foundational works on Structural Causal Models (SCMs), e.g., Bongers et al. (2021, Ann. Stat., 49(5): 2885-2915), treat cycles and latent variables, while an analogous account of latent selection is missing. The goal of this article is to develop a theoretical foundation for modeling latent selection with SCMs. To achieve that, we introduce a conditioning operation for SCMs: it maps an SCM with explicit selection mechanisms to one without them while preserving the causal semantics of the selected subpopulation. Graphically, in Directed Mixed Graphs we extend bidirected edge--beyond latent common cause--to also encode latent selection. We prove that the conditioning operation preserves simplicity, acyclicity, and linearity of SCMs, and interacts well with marginalization, conditioning, and interventions. These properties make those three operations valuable tools for causal modeling, reasoning, and learning after abstracting away latent details (latent common causes and selection). Examples show how this abstraction streamlines analysis and clarifies when standard tools (e.g., adjustment, causal calculus, instrumental variables) remain valid under selection bias. We hope that these results deepen the SCM-based understanding of selection bias and become part of the standard causal modeling toolbox to build more reliable causal analysis.

stat.ME↗

arXiv2025

The Aldous$\unicode{x2013}$Hoover Theorem in Categorical Probability

The Aldous-Hoover Theorem concerns an infinite matrix of random variables whose distribution is invariant under finite permutations of rows and columns. It states that, up to equality in distribution, each random variable in the matrix can be expressed as a function only depending on four key variables: one common to the entire matrix, one that encodes information about its row, one that encodes information about its column, and a fourth one specific to the matrix entry. We state and prove the theorem within a category-theoretic approach to probability, namely the theory of Markov categories. This makes the proof more transparent and intuitive when compared to measure-theoretic ones. A key role is played by a newly identified categorical property, the Cauchy--Schwarz axiom, which also facilitates a new synthetic de Finetti Theorem. We further provide a variant of our proof using the ordered Markov property and the d-separation criterion, both generalized from Bayesian networks to Markov categories. We expect that this approach will facilitate a systematic development of more complex results in the future, such as categorical approaches to hierarchical exchangeability.

math.ST↗

arXiv2025

Bias correction for Chatterjee's graph-based correlation coefficient

Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of dependence that equals 0 if and only if the variables are independent, and 1 if and only if they are functionally dependent. However, this NN estimator includes a bias term that may vanish at a rate slower than root-$n$, preventing root-$n$ consistency in general. In this article, we (i) analyze this bias term closely and show that it could become asymptotically negligible when the dimension is smaller than four; and (ii) propose a bias-correction procedure for more general settings. In both regimes, we obtain estimators (either the original or the bias-corrected version) that are root-$n$ consistent and asymptotically normal.

stat.ME↗

arXiv2021

Safer Illinois and RokWall: Privacy Preserving University Health Apps for COVID-19

COVID-19 has fundamentally disrupted the way we live. Government bodies, universities, and companies worldwide are rapidly developing technologies to combat the COVID-19 pandemic and safely reopen society. Essential analytics tools such as contact tracing, super-spreader event detection, and exposure mapping require collecting and analyzing sensitive user information. The increasing use of such powerful data-driven applications necessitates a secure, privacy-preserving infrastructure for computation on personal data. In this paper, we analyze two such computing infrastructures under development at the University of Illinois at Urbana-Champaign to track and mitigate the spread of COVID-19. First, we present Safer Illinois, a system for decentralized health analytics supporting two applications currently deployed with widespread adoption: digital contact tracing and COVID-19 status cards. Second, we introduce the RokWall architecture for privacy-preserving centralized data analytics on sensitive user data. We discuss the architecture of these systems, design choices, threat models considered, and the challenges we experienced in developing production-ready systems for sensitive data analysis.

cs.CR↗