On Learning and Generalization to Solve Inverse Problem of Electrophysiological Imaging

In this dissertation, we are interested in solving a linear inverse problem: inverse electrophysiological (EP) imaging, where our objective is to computationally reconstruct personalized cardiac electrical signals based on body surface electrocardiogram (ECG) signals. EP imaging has shown promise in the diagnosis and treatment planning of cardiac dysfunctions such as atrial flutter, atrial fibrillation, ischemia, infarction and ventricular arrhythmia. Towards this goal, we frame it as a problem of learning a function from the domain of measurements to signals. Depending upon the assumptions, we present two classes of solutions: 1) Bayesian inference in a probabilistic graphical model, 2) Learning from samples using deep networks. In both of these approaches, we emphasize on learning the inverse function with good generalization ability, which becomes a main theme of the dissertation. In a Bayesian framework, we argue that this translates to appropriately integrating different sources of knowledge into a common probabilistic graphical model framework and using it for patient specific signal estimation through Bayesian inference. In learning from samples setting, this translates to designing a deep network with good generalization ability, where good generalization refers to the ability to reconstruct inverse EP signals in a distribution of interest (which could very well be outside the sample distribution used during training). By drawing ideas from different areas like functional analysis (e.g. Fenchel duality), variational inference (e.g. Variational Bayes) and deep generative modeling (e.g. variational autoencoder), we show how we can incorporate different prior knowledge in a principled manner in a probabilistic graphical model framework to obtain a good inverse solution with generalization ability. Similarly, to improve generalization of deep networks learning from samples, we use ideas from information theory (e.g. information bottleneck), learning theory (e.g. analytical learning theory), adversarial training, complexity theory and functional analysis (e.g. RKHS). We test our algorithms on synthetic data and real data of the patients who had undergone through catheter ablation in clinics and show that our approach yields significant improvement over existing methods. Towards the end of the dissertation, we investigate general questions on generalization and stabilization of adversarial training of deep networks and try to understand the role of smoothness and function space complexity in answering those questions. We conclude by identifying limitations of the proposed methods, areas of further improvement and open questions that are specific to inverse electrophysiological imaging as well as broader, encompassing theory of learning and generalization

Proposal-Based Multiple Instance Learning for Weakly-Supervised Temporal Action Localization

Weakly-supervised temporal action localization aims to localize and recognize actions in untrimmed videos with only video-level category labels during training. Without instance-level annotations, most existing methods follow the Segment-based Multiple Instance Learning (S-MIL) framework, where the predictions of segments are supervised by the labels of videos. However, the objective for acquiring segment-level scores during training is not consistent with the target for acquiring proposal-level scores during testing, leading to suboptimal results. To deal with this problem, we propose a novel Proposal-based Multiple Instance Learning (P-MIL) framework that directly classifies the candidate proposals in both the training and testing stages, which includes three key designs: 1) a surrounding contrastive feature extraction module to suppress the discriminative short proposals by considering the surrounding contrastive information, 2) a proposal completeness evaluation module to inhibit the low-quality proposals with the guidance of the completeness pseudo labels, and 3) an instance-level rank consistency loss to achieve robust detection by leveraging the complementarity of RGB and FLOW modalities. Extensive experimental results on two challenging benchmarks including THUMOS14 and ActivityNet demonstrate the superior performance of our method.Comment: Accepted by CVPR 2023. Code is available at https://github.com/RenHuan1999/CVPR2023_P-MI