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Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and…

Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…

We examine a probabilistic model for the diagnosis of multiple diseases. In the model, diseases and findings are represented as binary variables. Also, diseases are marginally independent, features are conditionally independent given…

This paper offers a systematic method for creating medical knowledge-grounded patient records for use in activities involving differential diagnosis. Additionally, an assessment of machine learning models that can differentiate between…

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods which rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC,…

We consider linear structural equation models with explicitly modelled latent variables. In such models, observed and latent variables solve linear equations including stochastic noise terms. The goal of our work is to identify the direct…

Understanding the causal effects of organ-specific features from medical imaging on clinical outcomes is essential for biomedical research and patient care. We propose a novel Functional Linear Structural Equation Model (FLSEM) to capture…

Time series forecasting remains a critical challenge across numerous domains, yet the effectiveness of complex models often varies unpredictably across datasets. Recent studies highlight the surprising competitiveness of simple linear…

Rare diseases are very difficult to identify among large number of other possible diagnoses. Better availability of patient data and improvement in machine learning algorithms empower us to tackle this problem computationally. In this…

Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by…

Weak identification arises in many statistical problems when key variables exhibit weak correlations-for example, when instrumental variables correlate weakly with treatment, or when proxy variables correlate weakly with unmeasured…

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…

Modeling disease progression through multiple stages is critical for clinical decision-making for chronic diseases, e.g., cancer, diabetes, chronic kidney diseases, and so on. Existing approaches often model the disease progression as a…

The prediction of disease risk factors can screen vulnerable groups for effective prevention and treatment, so as to reduce their morbidity and mortality. Machine learning has a great demand for high-quality labeling information, and…

Real-time monitoring in modern medical research introduces functional longitudinal data, characterized by continuous-time measurements of outcomes, treatments, and confounders. This complexity leads to uncountably infinite…

Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…

Discovering causal relations among observed variables in a given data set is a major objective in studies of statistics and artificial intelligence. Recently, some techniques to discover a unique causal model have been explored based on…

Causal discovery, the task of inferring causal structure from data, has the potential to uncover mechanistic insights from biological experiments, especially those involving perturbations. However, causal discovery algorithms over larger…

The development of data-driven heart sound classification models has been an active area of research in recent years. To develop such data-driven models in the first place, heart sound signals need to be captured using a signal acquisition…

Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…