We study in this work the problem of multi-class logistic regression with one major class and multiple rare classes, which is motivated by a real application in TikTok live stream data. The model is inspired by the two-class logistic regression model of Wang (2020) but with surprising theoretical findings, which in turn motivate new estimation methods with excellent statistical and computational efficiency. Specifically, since rigorous theoretical analysis suggests that the resulting maximum likelihood estimators of different rare classes should be asymptotically independent, we consider to solve multiple pairwise two-class logistic regression problems instead of optimizing the joint log-likelihood function with computational challenge in multi-class problem, which are computationally much easier and can be conducted in a fully parallel way. To further reduce the computation cost, a subsample-based pairwise likelihood estimator is developed by down-sampling the major class. We show rigorously that the resulting estimators could be as asymptotically efficient as the global maximum likelihood estimator under appropriate regularity conditions. Extensive simulation studies are presented to support our theoretical findings and a TikTok live stream dataset is analyzed for illustration purpose.

In recent years, significant breakthroughs have been made in audio-guided 3D facial animation. However, existing methods mainly focus on lip shape and audio consistency and still face key challenges to achieve alignment between facial emotions and speech emotions. To overcome this limitation, we introduce EmoRLTalk, a novel framework that integrates offline reinforcement learning to implicitly capture the intricate relationship between 3D facial landmarks and blendshape parameters, thereby enhancing the granularity of emotional expression. Furthermore, we harness the strength of conditional diffusion models to synthesize facial motions that are emotionally coherent with the input speech. Additionally, based on the multi-task learning paradigm, we construct a collaborative training framework of a regression main task and a classification sub-task. Specifically, we use emotion classification of blendshape as a sub-task to further improve the model’s ability to express facial emotions. To further enhance system controllability, we integrate the ControlNet module, allowing users to achieve precise facial expression control. Extensive experiments demonstrate that EmoRLTalk achieves superior emotional expressiveness and lip-sync performance compared to previous approaches.

We study here a Gaussian mixture model (GMM) with rare events data. In this case, the commonly used Expectation-Maximization (EM) algorithm exhibits extremely slow numerical convergence rate. To theoretically understand this phenomenon, we formulate the numerical convergence problem of the EM algorithm with rare events data as a problem about a contraction operator. Theoretical analysis reveals that the spectral radius of the contraction operator in this case could be arbitrarily close to 1 asymptotically. This theoretical finding explains the empirical slow numerical convergence of the EM algorithm with rare events data. To overcome this challenge, a Mixed EM (MEM) algorithm is developed, which utilizes the information provided by partially labeled data. As compared with the standard EM algorithm, the key feature of the MEM algorithm is that it requires additionally labeled data. We find that MEM algorithm significantly improves the numerical convergence rate as compared with the standard EM algorithm. The finite sample performance of the proposed method is illustrated by both simulation studies and a real-world dataset of Swedish traffic signs.

Colorectal cancer(CRC), which is derived from polyps, is a common malignant tumor with a high incidence and mortality. Currently the colonoscopy is the most effective approach for early detection of the colorectal cancer. With the development of object detection, some polyp detection algorithms have achieved satisfied results. However, most of them need the support of hardware accelerators such as GPU, which is unsuitable for actual clinical environment due to its high power consumption and loud noise. To solve the problem, this paper proposes a solution to implement real-time polyp detection for colonoscopy video on general-purpose computing platforms, i.e. CPU. Our solution incorporates several methods to improve efficiency of polyp detection. Firstly, by analyzing the similarity and difference between successive frames in colonoscopy videos, we use the abrupt shot detection method to reduce the unnecessary detection for frames that contain non-polyps; secondly, for the frames that need to be detected, we iterated a procedure of sparse training, pruning and knowledge distillation to search for compressed models. Our approach is evaluated with both public datasets and actual colonoscopy videos, and results show that our approach can process 35.28 frames per second on colonoscopy videos with satisfied precision on CPU.