Large-scale Heteroscedastic Regression via Gaussian Process

Heteroscedastic regression considering the varying noises among observations has many applications in the fields like machine learning and statistics. Here we focus on the heteroscedastic Gaussian process (HGP) regression which integrates the latent function and the noise function together in a unified non-parametric Bayesian framework. Though showing remarkable performance, HGP suffers from the cubic time complexity, which strictly limits its application to big data. To improve the scalability, we first develop a variational sparse inference algorithm, named VSHGP, to handle large-scale datasets. Furthermore, two variants are developed to improve the scalability and capability of VSHGP. The first is stochastic VSHGP (SVSHGP) which derives a factorized evidence lower bound, thus enhancing efficient stochastic variational inference. The second is distributed VSHGP (DVSHGP) which (i) follows the Bayesian committee machine formalism to distribute computations over multiple local VSHGP experts with many inducing points; and (ii) adopts hybrid parameters for experts to guard against over-fitting and capture local variety. The superiority of DVSHGP and SVSHGP as compared to existing scalable heteroscedastic/homoscedastic GPs is then extensively verified on various datasets.Comment: 14 pages, 15 figure

Understanding and Comparing Scalable Gaussian Process Regression for Big Data

As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP however leads to poor scalability, which poses challenges in the era of big data. Hence, various scalable GPs have been developed in the literature in order to improve the scalability while retaining desirable prediction accuracy. This paper devotes to investigating the methodological characteristics and performance of representative global and local scalable GPs including sparse approximations and local aggregations from four main perspectives: scalability, capability, controllability and robustness. The numerical experiments on two toy examples and five real-world datasets with up to 250K points offer the following findings. In terms of scalability, most of the scalable GPs own a time complexity that is linear to the training size. In terms of capability, the sparse approximations capture the long-term spatial correlations, the local aggregations capture the local patterns but suffer from over-fitting in some scenarios. In terms of controllability, we could improve the performance of sparse approximations by simply increasing the inducing size. But this is not the case for local aggregations. In terms of robustness, local aggregations are robust to various initializations of hyperparameters due to the local attention mechanism. Finally, we highlight that the proper hybrid of global and local scalable GPs may be a promising way to improve both the model capability and scalability for big data.Comment: 25 pages, 15 figures, preprint submitted to KB

Facial Action Unit Detection Using Attention and Relation Learning

Attention mechanism has recently attracted increasing attentions in the field of facial action unit (AU) detection. By finding the region of interest of each AU with the attention mechanism, AU-related local features can be captured. Most of the existing attention based AU detection works use prior knowledge to predefine fixed attentions or refine the predefined attentions within a small range, which limits their capacity to model various AUs. In this paper, we propose an end-to-end deep learning based attention and relation learning framework for AU detection with only AU labels, which has not been explored before. In particular, multi-scale features shared by each AU are learned firstly, and then both channel-wise and spatial attentions are adaptively learned to select and extract AU-related local features. Moreover, pixel-level relations for AUs are further captured to refine spatial attentions so as to extract more relevant local features. Without changing the network architecture, our framework can be easily extended for AU intensity estimation. Extensive experiments show that our framework (i) soundly outperforms the state-of-the-art methods for both AU detection and AU intensity estimation on the challenging BP4D, DISFA, FERA 2015 and BP4D+ benchmarks, (ii) can adaptively capture the correlated regions of each AU, and (iii) also works well under severe occlusions and large poses.Comment: This paper is accepted by IEEE Transactions on Affective Computin

Sharpness-aware Quantization for Deep Neural Networks

Network quantization is an effective compression method to reduce the model size and computational cost. Despite the high compression ratio, training a low-precision model is difficult due to the discrete and non-differentiable nature of quantization, resulting in considerable performance degradation. Recently, Sharpness-Aware Minimization (SAM) has been proposed to improve the generalization performance of the models by simultaneously minimizing the loss value and the loss curvature. However, SAM can not be directly applied to quantized models due to the discretization process in network quantization. In this paper, we devise a Sharpness-Aware Quantization (SAQ) method to train quantized models, leading to better generalization performance. Moreover, since each layer contributes differently to the loss value and the loss sharpness of a network, we further devise an effective method that learns a configuration generator to automatically determine the bitwidth configurations of each layer, encouraging lower bits for flat regions and vice versa for sharp landscapes, while simultaneously promoting the flatness of minima to enable more aggressive quantization. Extensive experiments on CIFAR-100 and ImageNet show the superior performance of the proposed methods. For example, our quantized ResNet-18 with 53.7x Bit-Operation (BOP) reduction even outperforms the full-precision one by 0.7% in terms of the Top-1 accuracy. Code is available at https://github.com/zip-group/SAQ.Comment: Tech repor

Dynamic Mechanical and Failure Properties of Solder Joints

Ph.DDOCTOR OF PHILOSOPH