A differentiable estimation of the distance between two distributions based on samples is important for many deep learning tasks. One such estimation is maximum mean discrepancy (MMD). However, MMD suffers from its sensitive kernel bandwidth hyper-parameter, weak gradients, and large mini-batch size when used as a training objective. In this paper, we propose population matching discrepancy (PMD) for estimating the distribution distance based on samples, as well as an algorithm to learn the parameters of the distributions using PMD as an objective. PMD is defined as the minimum weight matching of sample populations from each distribution, and we prove that PMD is a strongly consistent estimator of the first Wasserstein metric. We apply PMD to two deep learning tasks, domain adaptation and generative modeling. Empirical results demonstrate that PMD overcomes the aforementioned drawbacks of MMD, and outperforms MMD on both tasks in terms of the performance as well as the convergence speed.

However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value functions.

Policy Mirror Descent (PMD) is a general family of algorithms that covers a wide range of novel and fundamental methods in reinforcement learning.

A differentiable estimation of the distance between two distributions based on samples is important for many deep learning tasks. One such estimation is maximum mean discrepancy (MMD). However, MMD suffers from its sensitive kernel bandwidth hyper-parameter, weak gradients, and large mini-batch size when used as a training objective. In this paper, we propose population matching discrepancy (PMD) for estimating the distribution distance based on samples, as well as an algorithm to learn the parameters of the distributions using PMD as an objective. PMD is defined as the minimum weight matching of sample populations from each distribution, and we prove that PMD is a strongly consistent estimator of the first Wasserstein metric. We apply PMD to two deep learning tasks, domain adaptation and generative modeling. Empirical results demonstrate that PMD overcomes the aforementioned drawbacks of MMD, and outperforms MMD on both tasks in terms of the performance as well as the convergence speed.

One such estimation is maximum mean discrepancy (MMD).

NER learns to regress continuous representations of neural dynamics (i.e., embeddings) on continuous movements.

We would like to thank all the reviewers for their thoughtful comments and their enthusiasm for our work. These results are consistent with those of Zoltowski et al. [2020], where they found Laplace EM compared Section 3. Segmenting the continuous latent states for each population (which is equivalent to imposing hard constraints On top of that, the "sticky" parameterization of discrete state transitions reveals which neural populations C. elegans offers an illustrative demonstration of the mp-srSLDS For example, we explore interactions between ganglia in Appendix C. Thanks again for spending the time to provide valuable feedback on our work.

However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value functions.