In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Ex Input:
Generative modeling of high dimensional data like images is a notoriously difficult and ill-defined problem. In particular, how to evaluate a learned generative model is unclear.
 In this paper, we argue that *adversarial learning*, pioneered with generative adversarial networks (GANs), provides an interesting framework to implicitly define more meaningful task losses for unsupervised tasks, such as for generating "visually realistic" images. By relating GANs and structured prediction under the framework of statistical decision theory, we put into light links between recent advances in structured prediction theory and the choice of the divergence in GANs. We argue that the insights about the notions of "hard" and "easy" to learn losses can be analogously extended to adversarial divergences. We also discuss the attractive properties of parametric adversarial divergences for generative modeling, and perform experiments to show the importance of choosing a divergence that reflects the final task.

Ex Output:
Parametric adversarial divergences implicitly define more meaningful task losses for generative modeling, we make parallels with structured prediction to study the properties of these divergences and their ability to encode the task of interest.


Ex Input:
We consider the problem of unsupervised learning of a low dimensional, interpretable, latent state of a video containing a moving object. The problem of distilling dynamics from pixels has been extensively considered through the lens of graphical/state space models that exploit Markov structure for cheap computation and structured graphical model priors for enforcing interpretability on latent representations. We take a step towards extending these approaches by discarding the Markov structure; instead, repurposing the recently proposed Gaussian Process Prior Variational Autoencoder for learning sophisticated latent trajectories. We describe the model and perform experiments on a synthetic dataset and see that the model reliably reconstructs smooth dynamics exhibiting U-turns and loops. We also observe that this model may be trained without any beta-annealing or freeze-thaw of training parameters. Training is performed purely end-to-end on the unmodified evidence lower bound objective. This is in contrast to previous works, albeit for slightly different use cases, where application specific training tricks are often required.

Ex Output:
We learn sohpisticated trajectories of an object purely from pixels with a toy video dataset by using a VAE structure with a Gaussian process prior.


Ex Input:
In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties. In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, defined via an embedding of probability distributions into a reproducing kernel Hilbert space. We show that this MMD-Bayes posterior is consistent and robust to model misspecification. As the posterior obtained in this way might be intractable, we also prove that reasonable variational approximations of this posterior enjoy the same properties. We provide details on a stochastic gradient algorithm to compute these variational approximations. Numerical simulations indeed suggest that our estimator is more robust to misspecification than the ones based on the likelihood.


Ex Output:

Robust Bayesian Estimation via Maximum Mean Discrepancy