Tao Yang

Tao Yang, Prashant G. Mehta, Sean P. Meyn

A new formulation of the particle filter for nonlinear filtering is presented, based on concepts from optimal control, and from the mean-field game theory. The optimal control is chosen so that the posterior distribution of a particle matches as closely as possible the posterior distribution of the true state given the observations. This is achieved by introducing a cost function, defined by the Kullback-Leibler (K-L) divergence between the actual posterior, and the posterior of any particle. The optimal control input is characterized by a certain Euler-Lagrange (E-L) equation, and is shown to admit an innovation error-based feedback structure. For diffusions with continuous observations, the value of the optimal control solution is ideal. The two posteriors match exactly, provided they are initialized with identical priors. The feedback particle filter is defined by a family of stochastic systems, each evolving under this optimal control law. A numerical algorithm is introduced and implemented in two general examples, and a neuroscience application involving coupled oscillators. Some preliminary numerical comparisons between the feed- back particle filter and the bootstrap particle filter are described.

Shuang Li, Longhui Yuan, Binhui Xie et al.

Test-time adaptation (TTA) adapts the pre-trained models to test distributions during the inference phase exclusively employing unlabeled test data streams, which holds great value for the deployment of models in real-world applications. Numerous studies have achieved promising performance on simplistic test streams, characterized by independently and uniformly sampled test data originating from a fixed target data distribution. However, these methods frequently prove ineffective in practical scenarios, where both continual covariate shift and continual label shift occur simultaneously, i.e., data and label distributions change concurrently and continually over time. In this study, a more challenging Practical Test-Time Adaptation (PTTA) setup is introduced, which takes into account the concurrent presence of continual covariate shift and continual label shift, and we propose a Generalized Robust Test-Time Adaptation (GRoTTA) method to effectively address the difficult problem. We start by steadily adapting the model through Robust Parameter Adaptation to make balanced predictions for test samples. To be specific, firstly, the effects of continual label shift are eliminated by enforcing the model to learn from a uniform label distribution and introducing recalibration of batch normalization to ensure stability. Secondly, the continual covariate shift is alleviated by employing a source knowledge regularization with the teacher-student model to update parameters. Considering the potential information in the test stream, we further refine the balanced predictions by Bias-Guided Output Adaptation, which exploits latent structure in the feature space and is adaptive to the imbalanced label distribution. Extensive experiments demonstrate GRoTTA outperforms the existing competitors by a large margin under PTTA setting, rendering it highly conducive for adoption in real-world applications.

Xuanchi Ren, Tao Yang, Yuwang Wang et al.

Content and style (C-S) disentanglement intends to decompose the underlying explanatory factors of objects into two independent subspaces. From the unsupervised disentanglement perspective, we rethink content and style and propose a formulation for unsupervised C-S disentanglement based on our assumption that different factors are of different importance and popularity for image reconstruction, which serves as a data bias. The corresponding model inductive bias is introduced by our proposed C-S disentanglement Module (C-S DisMo), which assigns different and independent roles to content and style when approximating the real data distributions. Specifically, each content embedding from the dataset, which encodes the most dominant factors for image reconstruction, is assumed to be sampled from a shared distribution across the dataset. The style embedding for a particular image, encoding the remaining factors, is used to customize the shared distribution through an affine transformation. The experiments on several popular datasets demonstrate that our method achieves the state-of-the-art unsupervised C-S disentanglement, which is comparable or even better than supervised methods. We verify the effectiveness of our method by downstream tasks: domain translation and single-view 3D reconstruction. Project page at https://github.com/xrenaa/CS-DisMo.

Tao Yang, Georgios Arvanitidis, Dongmei Fu et al.

Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances tend to not reflect semantic similarities well. This renders unsupervised tasks, such as clustering, difficult when working with the latent representations. We demonstrate that taking the geometry of the generative model into account is sufficient to make simple clustering algorithms work well over latent representations. Leaning on the recent finding that deep generative models constitute stochastically immersed Riemannian manifolds, we propose an efficient algorithm for computing geodesics (shortest paths) and computing distances in the latent space, while taking its distortion into account. We further propose a new architecture for modeling uncertainty in variational autoencoders, which is essential for understanding the geometry of deep generative models. Experiments show that the geodesic distance is very likely to reflect the internal structure of the data.