Break The Spell Of Total Correlation In betaTCVAE

In the absence of artificial labels, the independent and dependent features in the data are cluttered. How to construct the inductive biases of the model to flexibly divide and effectively contain features with different complexity is the main focal point of unsupervised disentangled representation learning. This paper proposes a new iterative decomposition path of total correlation and explains the disentangled representation ability of VAE from the perspective of model capacity allocation. The newly developed objective function combines latent variable dimensions into joint distribution while relieving the independence constraints of marginal distributions in combination, leading to latent variables with a more manipulable prior distribution. The novel model enables VAE to adjust the parameter capacity to divide dependent and independent data features flexibly. Experimental results on various datasets show an interesting relevance between model capacity and the latent variable grouping size, called the "V"-shaped best ELBO trajectory. Additionally, we empirically demonstrate that the proposed method obtains better disentangling performance with reasonable parameter capacity allocation

Motion-DVAE: Unsupervised learning for fast human motion denoising

Pose and motion priors are crucial for recovering realistic and accurate human motion from noisy observations. Substantial progress has been made on pose and shape estimation from images, and recent works showed impressive results using priors to refine frame-wise predictions. However, a lot of motion priors only model transitions between consecutive poses and are used in time-consuming optimization procedures, which is problematic for many applications requiring real-time motion capture. We introduce Motion-DVAE, a motion prior to capture the short-term dependencies of human motion. As part of the dynamical variational autoencoder (DVAE) models family, Motion-DVAE combines the generative capability of VAE models and the temporal modeling of recurrent architectures. Together with Motion-DVAE, we introduce an unsupervised learned denoising method unifying regression- and optimization-based approaches in a single framework for real-time 3D human pose estimation. Experiments show that the proposed approach reaches competitive performance with state-of-the-art methods while being much faster

Multi-Rate VAE: Train Once, Get the Full Rate-Distortion Curve

Variational autoencoders (VAEs) are powerful tools for learning latent representations of data used in a wide range of applications. In practice, VAEs usually require multiple training rounds to choose the amount of information the latent variable should retain. This trade-off between the reconstruction error (distortion) and the KL divergence (rate) is typically parameterized by a hyperparameter $\beta$. In this paper, we introduce Multi-Rate VAE (MR-VAE), a computationally efficient framework for learning optimal parameters corresponding to various $\beta$ in a single training run. The key idea is to explicitly formulate a response function that maps $\beta$ to the optimal parameters using hypernetworks. MR-VAEs construct a compact response hypernetwork where the pre-activations are conditionally gated based on $\beta$. We justify the proposed architecture by analyzing linear VAEs and showing that it can represent response functions exactly for linear VAEs. With the learned hypernetwork, MR-VAEs can construct the rate-distortion curve without additional training and can be deployed with significantly less hyperparameter tuning. Empirically, our approach is competitive and often exceeds the performance of multiple $\beta$-VAEs training with minimal computation and memory overheads.Comment: 22 pages, 9 figure

Learning Directed Graphical Models with Optimal Transport

Estimating the parameters of a probabilistic directed graphical model from incomplete data remains a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without further assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to black-box variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the flexibility and versatility of our approach. Across experiments, we show that not only can our method recover the ground-truth parameters but it also performs comparably or better on downstream applications, notably the non-trivial task of discrete representation learning