相关论文: Sobolev Regularized MMD Gradient Flow

The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…

We propose a simple neural network model to deal with the domain adaptation problem in object recognition. Our model incorporates the Maximum Mean Discrepancy (MMD) measure as a regularization in the supervised learning to reduce the…

For the problem of nonparametric regression of smooth functions, we reconsider and analyze a constrained variational approach, which we call the MultIscale Nemirovski-Dantzig (MIND) estimator. This can be viewed as a multiscale extension of…

We study the global convergence of policy gradient for infinite-horizon, continuous state and action space, and entropy-regularized Markov decision processes (MDPs). We consider a softmax policy with (one-hidden layer) neural network…

We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific…

Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient…

The modified Method of Successive Approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin Optimality Principle which, starting with an initial open loop…

In recent years, even though Stochastic Gradient Descent (SGD) and its variants are well-known for training neural networks, it suffers from limitations such as the lack of theoretical guarantees, vanishing gradients, and excessive…

Comparing conditional distributions is a fundamental challenge in statistics and machine learning, with applications across a wide range of domains. While proposed methods for measuring discrepancies using kernel embeddings of distributions…

Learning new tasks by drawing on prior experience gathered from other (related) tasks is a core property of any intelligent system. Gradient-based meta-learning, especially MAML and its variants, has emerged as a viable solution to…

The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale…

Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the…

It is well-known that the reparameterisation gradient estimator, which exhibits low variance in practice, is biased for non-differentiable models. This may compromise correctness of gradient-based optimisation methods such as stochastic…

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…

Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent…

The multiplicative structure of parameters and input data in the first layer of neural networks is explored to build connection between the landscape of the loss function with respect to parameters and the landscape of the model function…

Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the…