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Influence maximization is key topic in data mining, with broad applications in social network analysis and viral marketing. In recent years, researchers have increasingly turned to machine learning techniques to address this problem. They…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Missing values in high-dimensional, mixed-type datasets pose significant challenges for data imputation, particularly under Missing Not At Random (MNAR) mechanisms. Existing methods struggle to integrate local and global data…

Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces…

Missing data frequently arises across diverse domains, including time-series and image domains. In the real world, missing occurrences often depend on the unobservable values themselves, which are referred to as Missing Not at Random…

Graph generation is a fundamental problem in graph learning with broad applications across Web-scale systems, knowledge graphs, and scientific domains such as drug and material discovery. Recent approaches leverage diffusion models for…

Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with analytic transition kernels and score functions. The…

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…

Understanding the risks posed by extreme rainfall events requires analysis of precipitation fields with high resolution (to assess localized hazards) and extensive historical coverage (to capture sufficient examples of rare occurrences).…

Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…

Denoising Diffusion Probabilistic Model (DDPM) is able to make flexible conditional image generation from prior noise to real data, by introducing an independent noise-aware classifier to provide conditional gradient guidance at each time…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an EDI formulation of our PDE and prove that under some…

Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such…

The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…

We study ``nonlocal diffusion equations'' of the form \[ \partial_{t}\frac{d\rho_{t}}{d\pi}(x)+\int_{X}\left(\frac{d\rho_{t}}{d\pi}(x)-\frac{d\rho_{t}}{d\pi}(y)\right)\eta(x,y)d\pi(y)=0\qquad(\dagger) \] where $X$ is either $\mathbb{R}^{d}$…

Imbalanced datasets pose a difficulty in fraud detection, as classifiers are often biased toward the majority class and perform poorly on rare fraudulent transactions. Synthetic data generation is therefore commonly used to mitigate this…

Diffusion model deployment has been suffering from high energy consumption and inference latency despite its superior performance in visual generation tasks. Dynamic voltage and frequency scaling (DVFS) offers a promising solution to…

Transfer learning has gained significant attention in recent deep learning research due to its ability to accelerate convergence and enhance performance on new tasks. However, its success is often contingent on the similarity between source…