Related papers: Convergence rate of implicit iteration process and…

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…

We study the rate of convergence of the Mallows distance between the empirical distribution of a sample and the underlying population. The surprising feature of our results is that the convergence rate is slower in the discrete case than in…

Iterative-based methods have become mainstream in stereo matching due to their high performance. However, these methods heavily rely on labeled data and face challenges with unlabeled real-world data. To this end, we propose a…

We analyse and explain the increased generalisation performance of iterate averaging using a Gaussian process perturbation model between the true and batch risk surface on the high dimensional quadratic. We derive three phenomena…

Self-training, a semi-supervised learning algorithm, leverages a large amount of unlabeled data to improve learning when the labeled data are limited. Despite empirical successes, its theoretical characterization remains elusive. To the…

We consider the discrete-time Schr\"odinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution, the…

This paper proposes an implicit family of sub-step integration algorithms grounded in the explicit singly diagonally implicit Runge-Kutta (ESDIRK) method. The proposed methods achieve third-order consistency per sub-step and thus the…

Inference metaprogramming enables effective probabilistic programming by supporting the decomposition of executions of probabilistic programs into subproblems and the deployment of hybrid probabilistic inference algorithms that apply…

First-order optimization methods tend to inherently favor certain solutions over others when minimizing an underdetermined training objective that has multiple global optima. This phenomenon, known as implicit bias, plays a critical role in…

The accessibility of vast volumes of unlabeled data has sparked growing interest in semi-supervised learning (SSL) and covariate shift transfer learning (CSTL). In this paper, we present an inference framework for estimating regression…

The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…

Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS…

The goal of imitation learning is to mimic expert behavior from demonstrations, without access to an explicit reward signal. A popular class of approach infers the (unknown) reward function via inverse reinforcement learning (IRL) followed…

Semi-supervised learning is an important and active topic of research in pattern recognition. For classification using linear discriminant analysis specifically, several semi-supervised variants have been proposed. Using any one of these…

In reinforcement learning, the TD($\lambda$) algorithm is a fundamental policy evaluation method with an efficient online implementation that is suitable for large-scale problems. One practical drawback of TD($\lambda$) is its sensitivity…

We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…

The superiority of stochastic symplectic methods over non-symplectic counterparts has been verified by plenty of numerical experiments, especially in capturing the asymptotic behaviour of the underlying solution process. How can one…

Enforcing orthonormal or isometric property for the weight matrices has been shown to enhance the training of deep neural networks by mitigating gradient exploding/vanishing and increasing the robustness of the learned networks. However,…

In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…