Causal interaction inference is prone to spurious causal interactions, due to the substantial confounders in a biological system. While many existing methods attempt to address misidentification challenges, there remains a notable lack of effective methods to infer causal interaction under latent/unobserved confounders. In this work, we propose a method to overcome such challenges to infer dynamical causality under invisible confounders (CIC) and further reconstruct the latent confounders from time-series data by developing an orthogonal decomposition theorem in a delay embedding space. This theoretical foundation ensures the causal detection for any high-dimensional system even with only two observed variables under many latent confounders, which is a long-standing problem in the field. In addition to the latent confounder problem, such a decomposition makes the coupled variables separable in the embedding space, thus also solving the non-separability problem of causal inference. Extensive validation of the CIC method is carried out using various real datasets, which all demonstrates its effectiveness to reconstruct real biological networks and unobserved confounders.

Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class classification, there lacks a principled approach to guide the label combination for all data points by any optimality criterion. To address this problem, we propose the information-theoretic classification accuracy (ITCA), a criterion that balances the trade-off between prediction accuracy (how well do predicted labels agree with actual labels) and classification resolution (how many labels are predictable), to guide practitioners on how to combine ambiguous outcome labels. To find the optimal label combination indicated by ITCA, we propose two search strategies: greedy search and breadth-first search. ITCA and the two search strategies are adaptive to all machine-learning classification algorithms. Coupled with a classification algorithm and a search strategy, ITCA has two uses: improving prediction accuracy and identifying ambiguous labels. We first verify that ITCA achieves high accuracy with both search strategies in finding the correct label combinations on synthetic and real data. Then we demonstrate the effectiveness of ITCA in diverse applications, including medical prognosis, cancer survival prediction, user demographics prediction, and cell type classification. We also provide theoretical insights into ITCA by studying the oracle and the linear discriminant analysis classification algorithms. Python package itca (available at https://github.com/JSB-UCLA/ITCA) implements ITCA and the search strategies.

Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine. Moreover, big data are often distributedly collected and stored on different machines. Thus, such data generally bear strong heterogeneous noise. It is essential and useful to develop distributed matrix decomposition for big data analytics. Such a method should scale up well, model the heterogeneous noise, and address the communication issue in a distributed system. To this end, we propose a distributed Bayesian matrix decomposition model (DBMD) for big data mining and clustering. Specifically, we adopt three strategies to implement the distributed computing including 1) the accelerated gradient descent, 2) the alternating direction method of multipliers (ADMM), and 3) the statistical inference. We investigate the theoretical convergence behaviors of these algorithms. To address the heterogeneity of the noise, we propose an optimal plug-in weighted average that reduces the variance of the estimation. Synthetic experiments validate our theoretical results, and real-world experiments show that our algorithms scale up well to big data and achieves superior or competing performance compared to two typical distributed methods including Scalable-NMF and scalable k-means++.

Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of the matrix decomposition methods have been extended for such multi-view data integration and pattern discovery while only a few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, in this article, we propose a joint matrix decomposition framework (BJMD), which models the heterogeneity of noise by the Gaussian distribution in a Bayesian framework. We develop two algorithms to solve this model: one is a variational Bayesian inference algorithm, which makes full use of the posterior distribution; and another is a maximum a posterior algorithm, which is more scalable and can be easily paralleled. Extensive experiments on synthetic and real-world datasets demonstrate that BJMD is superior or competitive to the state-of-the-art methods.