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Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…

Convolutional neural networks (CNNs) often perform well, but their stability is poorly understood. To address this problem, we consider the simple prototypical problem of signal denoising, where classical approaches such as nonlinear…

Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively…

The multitask diffusion LMS is an efficient strategy to simultaneously infer, in a collaborative manner, multiple parameter vectors. Existing works on multitask problems assume that all agents respond to data synchronously. In several…

Diffusion models (DMs) have enabled breakthroughs in image synthesis tasks but lack an intuitive interface for consistent image-to-image (I2I) translation. Various methods have been explored to address this issue, including mask-based…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

Recently, diffusion models have excelled in image generation tasks and have also been applied to neural language processing (NLP) for controllable text generation. However, the application of diffusion models in a cross-lingual setting is…

This paper studies the theoretical underpinnings of machine learning of ergodic It\^o diffusions. The objective is to understand the convergence properties of the invariant statistics when the underlying system of stochastic differential…

This work studies social learning under non-stationary conditions. Although designed for online inference, classic social learning algorithms perform poorly under drifting conditions. To mitigate this drawback, we propose the Adaptive…

Consistency is the theoretical property of a meta learning algorithm that ensures that, under certain assumptions, it can adapt to any task at test time. An open question is whether and how theoretical consistency translates into practice,…

In this paper, we simulated a diffusion adaptive network in the underwater environment. The communication method between the nodes of this network is assumed to be the visible light communication technology (VLC) which in the underwater…

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they…

Diffusion models surpass previous generative models in sample quality and training stability. Recent works have shown the advantages of diffusion models in improving reinforcement learning (RL) solutions. This survey aims to provide an…

In this work, we analyze the generalization ability of distributed online learning algorithms under stationary and non-stationary environments. We derive bounds for the excess-risk attained by each node in a connected network of learners…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

When learning from streaming data, a change in the data distribution, also known as concept drift, can render a previously-learned model inaccurate and require training a new model. We present an adaptive learning algorithm that extends…

Diffusion Models (DMs), as a leading class of generative models, offer key advantages for reinforcement learning (RL), including multi-modal expressiveness, stable training, and trajectory-level planning. This survey delivers a…