Related papers: Kernelized Wasserstein Natural Gradient
Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by…
The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications. However, finding these directions usually requires an iterative optimization procedure over the space of…
Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of…
We develop an online gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the…
In min-min optimization or max-min optimization, one has to compute the gradient of a function defined as a minimum. In most cases, the minimum has no closed-form, and an approximation is obtained via an iterative algorithm. There are two…
We present and study a novel algorithm for the computation of 2-Wasserstein population barycenters of absolutely continuous probability measures on Euclidean space. The proposed method can be seen as a stochastic gradient descent procedure…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics.…
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…
We propose a general purpose variational inference algorithm that forms a natural counterpart of gradient descent for optimization. Our method iteratively transports a set of particles to match the target distribution, by applying a form of…
The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired…
Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve…
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…
Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…
We propose a stable method to train Wasserstein generative adversarial networks. In order to enhance stability, we consider two objective functions using the $c$-transform based on Kantorovich duality which arises in the theory of optimal…
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this paper investigates the composite geodesically convex…