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Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…

This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…

Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…

Designing equivariance as an inductive bias into deep-nets has been a prominent approach to build effective models, e.g., a convolutional neural network incorporates translation equivariance. However, incorporating these inductive biases…

Utilizing covariate information has been a powerful approach to improve the efficiency and accuracy for causal inference, which support massive amount of randomized experiments run on data-driven enterprises. However, state-of-art…

The paper studies quantum complexity, tractability, and strong tractability for high dimensional multivariate approximation. We study a space of functions important in many applications. A function space is weighted if certain variables are…

We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a…

Representing graphs by their homomorphism counts has led to the beautiful theory of homomorphism indistinguishability in recent years. Moreover, homomorphism counts have promising applications in database theory and machine learning, where…

Covariance-based data processing is widespread across signal processing and machine learning applications due to its ability to model data interconnectivities and dependencies. However, harmful biases in the data may become encoded in the…

We propose a dynamic multiplicative factor model for process data, which arise from complex problem-solving items, an emerging testing mode in large-scale educational assessment. The proposed model can be viewed as an extension of the…

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…

Knockoffs are a popular statistical framework that addresses the challenging problem of conditional variable selection in high-dimensional settings with statistical control. Such statistical control is essential for the reliability of…

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is…

Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…

Reliable state estimation hinges on accurate specification of sensor noise covariances, which weigh heterogeneous measurements. In practice, these covariances are difficult to identify due to environmental variability, front-end…

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major…

Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…

Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…

Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…