The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based R\'enyi's entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank R\'enyi's entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from $\mathcal{O}(n^3)$ to $\mathcal{O}(n^2 s)$ or even $\mathcal{O}(ns^2)$, where $n$ is the number of data samples and $s \ll n$. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based R\'enyi's entropy in terms of both performance and computational efficiency.

Robust and Fast Measure of Information via Low-rank Representation

Despite their great success in many artificial intelligence tasks, deep neural networks (DNNs) still suffer from a few limitations, such as poor generalization behavior for out-of-distribution (OOD) data and the "black-box" nature. Information theory offers fresh insights to solve these challenges.

In this talk, we first present a novel matrix-based Renyi's entropy functional estimator, which measures information-theoretic quantities (e.g., mutual information) in terms of the eigenspectrum of the Hermitian matrix of the projected data in the reproducing kernel Hilbert space (RKHS), without explicit evaluation of the underlying data distributions. Second, we give two recent applications of this estimator. In particular, we show how to analyze and understand the inner mechanism (e.g., the flow of information, the Information Bottleneck hypothesis) of DNNs and how to improve the generalization performance of a DNN from an information-theoretic perspective. We finally present the applications of information-theoretic learning principles (e.g., the Information Bottleneck and the Principle of Relevant Information) to develop interpretable and generalizable graph neural networks for brain network-based psychiatric diagnosis.

The Analysis of Deep Neural Networks by Information Theory: From Explainability to Generalization

We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn a Granger causal graph from a multivariate time series x and incorporates the underlying causal mechanism into its data generation process. Distinct to the classical recurrent VAEs, our CR-VAE uses a multi-head decoder, in which the p-th head is responsible for generating the p-th dimension of x (i.e., x^p). By imposing a sparsity-inducing penalty on the weights (of the decoder) and encouraging specific sets of weights to be zero, our CR-VAE learns a sparse adjacency matrix that encodes causal relations between all pairs of variables. Thanks to this causal matrix, our decoder strictly obeys the underlying principles of Granger causality, thereby making the data generating process transparent. We develop a two-stage approach to train the overall objective. Empirically, we evaluate the behavior of our model in synthetic data and two real-world human brain datasets involving, respectively, the electroencephalography (EEG) signals and the functional magnetic resonance imaging (fMRI) data. Our model consistently outperforms state-of-the-art time series generative models both qualitatively and quantitatively. Moreover, it also discovers a faithful causal graph with similar or improved accuracy over existing Granger causality-based causal inference methods. 

Causal Recurrent Variational Autoencoder for Medical Time Series Generation

The similarity of feature representations plays a pivotal role in the success of problems related to domain adaptation. Feature similarity includes both the invariance of marginal distributions and the closeness of conditional distributions given the desired response y (e.g., class labels). Unfortunately, traditional methods always learn such features without fully taking into consideration the information in y, which in turn may lead to a mismatch of the conditional distributions or the mixup of discriminative structures underlying data distributions. In this work, we introduce the recently proposed von Neumann conditional divergence to improve the transferability across multiple domains. We show that this new divergence is differentiable and eligible to easily quantify the functional dependence between features and y. Given multiple source tasks, we integrate this divergence to capture discriminative information in y and design novel learning objectives assuming those source tasks are observed either simultaneously or sequentially. In both scenarios, we obtain favorable performance against state-of-the-art methods in terms of smaller generalization error on new tasks and less catastrophic forgetting on source tasks (in the sequential setup).

Learning to Transfer with von Neumann Conditional Divergence

Posters & Demos III

poster

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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AAAI 2023

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

New Faculty Highlights 3/3

technical paper

ML: Deep Generative Models & Autoencoders 2

Main_Track

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Shujian Yu

4

SHORT BIO

Presentations

Robust and Fast Measure of Information via Low-rank Representation

The Analysis of Deep Neural Networks by Information Theory: From Explainability to Generalization

Causal Recurrent Variational Autoencoder for Medical Time Series Generation

Learning to Transfer with von Neumann Conditional Divergence

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