Li K. Wenliang

Li K. Wenliang, Heishiro Kanagawa

Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of normalising constants. Although these methods enjoy theoretical guarantees, a little-known fact is that they exhibit practical failure modes when the unnormalised distribution of interest has isolated components -- they cannot discover isolated components or identify the correct mixing proportions between components. We demonstrate these findings using simple distributions and present heuristic attempts to address these issues. We hope to bring the attention of theoreticians and practitioners to these issues when developing new algorithms and applications.

Tianlin Xu, Li K. Wenliang, Michael Munn et al.

We introduce COT-GAN, an adversarial algorithm to train implicit generative models optimized for producing sequential data. The loss function of this algorithm is formulated using ideas from Causal Optimal Transport (COT), which combines classic optimal transport methods with an additional temporal causality constraint. Remarkably, we find that this causality condition provides a natural framework to parameterize the cost function that is learned by the discriminator as a robust (worst-case) distance, and an ideal mechanism for learning time dependent data distributions. Following Genevay et al.\ (2018), we also include an entropic penalization term which allows for the use of the Sinkhorn algorithm when computing the optimal transport cost. Our experiments show effectiveness and stability of COT-GAN when generating both low- and high-dimensional time series data. The success of the algorithm also relies on a new, improved version of the Sinkhorn divergence which demonstrates less bias in learning.

Li K. Wenliang, Theodore Moskovitz, Heishiro Kanagawa et al.

Models that employ latent variables to capture structure in observed data lie at the heart of many current unsupervised learning algorithms, but exact maximum-likelihood learning for powerful and flexible latent-variable models is almost always intractable. Thus, state-of-the-art approaches either abandon the maximum-likelihood framework entirely, or else rely on a variety of variational approximations to the posterior distribution over the latents. Here, we propose an alternative approach that we call amortised learning. Rather than computing an approximation to the posterior over latents, we use a wake-sleep Monte-Carlo strategy to learn a function that directly estimates the maximum-likelihood parameter updates. Amortised learning is possible whenever samples of latents and observations can be simulated from the generative model, treating the model as a "black box". We demonstrate its effectiveness on a wide range of complex models, including those with latents that are discrete or supported on non-Euclidean spaces.