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We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
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…
Despite the success of Deep Learning (DL), the deployment of modern DL models requiring large computational power poses a significant problem for resource-constrained systems. This necessitates building compact networks that reduce…
Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples…
Diffusion models now set the benchmark in high-fidelity generative sampling, yet they can, in principle, be prone to memorization. In this case, their learned score overfits the finite dataset so that the reverse-time SDE samples are mostly…
Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $\pi\propto e^{-V}$ on $\mathbb{R}^d$. In the population limit, SVGD performs gradient…
Pansharpening seeks to fuse high-resolution panchromatic (PAN) and low-resolution multispectral (LRMS) images into a single image with both fine spatial and rich spectral detail. Despite progress in deep learning-based approaches, existing…
Over the past few years, several approaches utilizing score-based diffusion have been proposed to sample from probability distributions, that is without having access to exact samples and relying solely on evaluations of unnormalized…
The diffusion based distributed learning approaches have been found to be a viable solution for learning over linearly separable datasets over a network. However, approaches till date are suitable for linearly separable datasets and need to…
Diffusion and flow-based models are ubiquitously used for generative modelling and density estimation. They admit a deterministic probability flow ordinary differential equation (PF-ODE), analogous to continuous normalizing flows (CNFs),…
Dynamic texture (DT) exhibits statistical stationarity in the spatial domain and stochastic repetitiveness in the temporal dimension, indicating that different frames of DT possess a high similarity correlation that is critical prior…
Recent work of Klivans, Stavropoulos, and Vasilyan initiated the study of testable learning with distribution shift (TDS learning), where a learner is given labeled samples from training distribution $\mathcal{D}$, unlabeled samples from…
The task of steel surface defect recognition is an industrial problem with great industry values. The data insufficiency is the major challenge in training a robust defect recognition network. Existing methods have investigated to enlarge…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
Stochastic Gradient Descent (SGD) and its variants are mainstream methods for training deep networks in practice. SGD is known to find a flat minimum that often generalizes well. However, it is mathematically unclear how deep learning can…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…