Learning Generative Models across Incomparable Spaces

Generative Adversarial Networks have shown remarkable success in learning a distribution that faithfully recovers a reference distribution in its entirety. However, in some cases, we may want to only learn some aspects (e.g., cluster or manifold structure), while modifying others (e.g., style, orientation or dimension). In this work, we propose an approach to learn generative models across such incomparable spaces, and demonstrate how to steer the learned distribution towards target properties. A key component of our model is the Gromov-Wasserstein distance, a notion of discrepancy that compares distributions relationally rather than absolutely. While this framework subsumes current generative models in identically reproducing distributions, its inherent flexibility allows application to tasks in manifold learning, relational learning and cross-domain learning.Comment: International Conference on Machine Learning (ICML

Aligning Time Series on Incomparable Spaces

Dynamic time warping (DTW) is a useful method for aligning, comparing and combining time series, but it requires them to live in comparable spaces. In this work, we consider a setting in which time series live on different spaces without a sensible ground metric, causing DTW to become ill-defined. To alleviate this, we propose Gromov dynamic time warping (GDTW), a distance between time series on potentially incomparable spaces that avoids the comparability requirement by instead considering intra-relational geometry. We demonstrate its effectiveness at aligning, combining and comparing time series living on incomparable spaces. We further propose a smoothed version of GDTW as a differentiable loss and assess its properties in a variety of settings, including barycentric averaging, generative modeling and imitation learning

Stochastic Prediction of Multi-Agent Interactions from Partial Observations

We present a method that learns to integrate temporal information, from a learned dynamics model, with ambiguous visual information, from a learned vision model, in the context of interacting agents. Our method is based on a graph-structured variational recurrent neural network (Graph-VRNN), which is trained end-to-end to infer the current state of the (partially observed) world, as well as to forecast future states. We show that our method outperforms various baselines on two sports datasets, one based on real basketball trajectories, and one generated by a soccer game engine.Comment: ICLR 2019 camera read

Heterogeneous Wasserstein Discrepancy for Incomparable Distributions

Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be supported on the $\textit{same}$ metric space. Because of its high computational complexity, several approximate Wasserstein distances have been proposed based on entropy regularization or on slicing, and one-dimensional Wassserstein computation. In this paper, we propose a novel extension of Wasserstein distance to compare two incomparable distributions, that hinges on the idea of $\textit{distributional slicing}$, embeddings, and on computing the closed-form Wassertein distance between the sliced distributions. We provide a theoretical analysis of this new divergence, called $\textit{heterogeneous Wasserstein discrepancy (HWD)}$, and we show that it preserves several interesting properties including rotation-invariance. We show that the embeddings involved in HWD can be efficiently learned. Finally, we provide a large set of experiments illustrating the behavior of HWD as a divergence in the context of generative modeling and in query framework

Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.Comment: 49 pages including appendi

Auto-regressive Image Synthesis with Integrated Quantization

Deep generative models have achieved conspicuous progress in realistic image synthesis with multifarious conditional inputs, while generating diverse yet high-fidelity images remains a grand challenge in conditional image generation. This paper presents a versatile framework for conditional image generation which incorporates the inductive bias of CNNs and powerful sequence modeling of auto-regression that naturally leads to diverse image generation. Instead of independently quantizing the features of multiple domains as in prior research, we design an integrated quantization scheme with a variational regularizer that mingles the feature discretization in multiple domains, and markedly boosts the auto-regressive modeling performance. Notably, the variational regularizer enables to regularize feature distributions in incomparable latent spaces by penalizing the intra-domain variations of distributions. In addition, we design a Gumbel sampling strategy that allows to incorporate distribution uncertainty into the auto-regressive training procedure. The Gumbel sampling substantially mitigates the exposure bias that often incurs misalignment between the training and inference stages and severely impairs the inference performance. Extensive experiments over multiple conditional image generation tasks show that our method achieves superior diverse image generation performance qualitatively and quantitatively as compared with the state-of-the-art.Comment: Accepted to ECCV 2022 as Oral Presentatio