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Related papers: Kernelized Wasserstein Natural Gradient

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Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend…

Machine Learning · Statistics 2020-11-09 Wu Lin , Mohammad Emtiyaz Khan , Mark Schmidt

Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model…

Machine Learning · Computer Science 2022-10-18 Kartik Chandra , Audrey Xie , Jonathan Ragan-Kelley , Erik Meijer

A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction…

Quantum Physics · Physics 2020-05-27 James Stokes , Josh Izaac , Nathan Killoran , Giuseppe Carleo

Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving…

Machine Learning · Computer Science 2018-08-10 Ruiyi Zhang , Changyou Chen , Chunyuan Li , Lawrence Carin

In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…

Machine Learning · Statistics 2022-02-22 Wu Lin , Frank Nielsen , Mohammad Emtiyaz Khan , Mark Schmidt

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in…

Numerical Analysis · Mathematics 2022-08-10 Yihang Gao , Michael K. Ng

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Machine Learning · Computer Science 2021-02-02 Fengzhen Tang , Haifeng Feng , Peter Tino , Bailu Si , Daxiong Ji

Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for…

Quantum Physics · Physics 2024-06-04 Yidong Liao , Min-Hsiu Hsieh , Chris Ferrie

We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…

Statistics Theory · Mathematics 2022-05-10 Jie Wang , Rui Gao , Yao Xie

Communication is one of the bottlenecks of distributed optimisation and learning. To overcome this bottleneck, we propose a novel quantization method that transforms a vector into a sample of components' indices drawn from a categorical…

Optimization and Control · Mathematics 2025-01-31 Dmitrii Pasechniuk , Pavel Dvurechensky , César A. Uribe , Alexander Gasnikov

The Kullback-Leibler (KL) divergence plays a central role in probabilistic machine learning, where it commonly serves as the canonical loss function. Optimization in such settings is often performed over the probability simplex, where the…

Machine Learning · Computer Science 2025-07-31 Adwait Datar , Nihat Ay

Wasserstein-GANs have been introduced to address the deficiencies of generative adversarial networks (GANs) regarding the problems of vanishing gradients and mode collapse during the training, leading to improved convergence behaviour and…

Machine Learning · Computer Science 2019-12-17 Jan Müller , Reinhard Klein , Michael Weinmann

We cast Amari's natural gradient in statistical learning as a specific case of Kalman filtering. Namely, applying an extended Kalman filter to estimate a fixed unknown parameter of a probabilistic model from a series of observations, is…

Machine Learning · Statistics 2018-08-29 Yann Ollivier

We develop in this paper a new regularized flow dynamic approach to construct efficient numerical schemes for Wasserstein gradient flows in Lagrangian coordinates. Instead of approximating the Wasserstein distance which needs to solve…

Numerical Analysis · Mathematics 2024-06-24 Qing Cheng , Qianqian Liu , Wenbin Chen , Jie Shen

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…

Machine Learning · Statistics 2019-08-23 Leon Bottou , Martin Arjovsky , David Lopez-Paz , Maxime Oquab

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum…

Quantum Physics · Physics 2019-02-04 Jarrod R. McClean , Sergio Boixo , Vadim N. Smelyanskiy , Ryan Babbush , Hartmut Neven

Fisher information and natural gradient provided deep insights and powerful tools to artificial neural networks. However related analysis becomes more and more difficult as the learner's structure turns large and complex. This paper makes a…

Machine Learning · Computer Science 2016-06-21 Ke Sun , Frank Nielsen

We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…

Machine Learning · Computer Science 2024-04-02 Zhuoran Yang , Yufeng Zhang , Yongxin Chen , Zhaoran Wang

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…

Machine Learning · Computer Science 2024-04-16 Wei Zhang , Zihao Wang , Jie Fan , Hao Wu , Yong Zhang

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

Systems and Control · Electrical Eng. & Systems 2023-04-07 Nicolas Lanzetti , Efe C. Balta , Dominic Liao-McPherson , Florian Dörfler