Related papers: Wasserstein Neural Processes
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language…
A novel optimization approach is proposed for application to policy gradient methods and evolution strategies for reinforcement learning (RL). The procedure uses a computationally efficient Wasserstein natural gradient (WNG) descent that…
We show that several machine learning estimators, including square-root LASSO (Least Absolute Shrinkage and Selection) and regularized logistic regression can be represented as solutions to distributionally robust optimization (DRO)…
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…
It is well known that the output of a Neural Network trained to disentangle between two classes has a probabilistic interpretation in terms of the a-posteriori Bayesian probability, provided that a unary representation is taken for the…
Optimal transport (OT) offers a versatile framework to compare complex data distributions in a geometrically meaningful way. Traditional methods for computing the Wasserstein distance and geodesic between probability measures require…
Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the…
We introduce Markov Neural Processes (MNPs), a new class of Stochastic Processes (SPs) which are constructed by stacking sequences of neural parameterised Markov transition operators in function space. We prove that these Markov transition…
Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…
Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
Neural Processes (NPs) families encode distributions over functions to a latent representation, given context data, and decode posterior mean and variance at unknown locations. Since mean and variance are derived from the same latent space,…
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…
The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…
Bayesian models of cognition hypothesize that human brains make sense of data by representing probability distributions and applying Bayes' rule to find the best explanation for available data. Understanding the neural mechanisms underlying…
A key challenge in complex visuomotor control is learning abstract representations that are effective for specifying goals, planning, and generalization. To this end, we introduce universal planning networks (UPN). UPNs embed differentiable…
We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…