Related papers: An Online Sample Based Method for Mode Estimation …
Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…
Deep metric learning aims to learn a deep embedding that can capture the semantic similarity of data points. Given the availability of massive training samples, deep metric learning is known to suffer from slow convergence due to a large…
Density-based Out-of-distribution (OOD) detection has recently been shown unreliable for the task of detecting OOD images. Various density ratio based approaches achieve good empirical performance, however methods typically lack a…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
Estimating the mode of a unimodal distribution is a classical problem in statistics. Although there are several approaches for point-estimation of mode in the literature, very little has been explored about the interval-estimation of mode.…
Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…
We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…
Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…
Although diffusion models can generate remarkably high-quality samples, they are intrinsically bottlenecked by their expensive iterative sampling procedure. Consistency models (CMs) have recently emerged as a promising diffusion model…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have…
We consider parameter estimation of ordinary differential equation (ODE) models from noisy observations. For this problem, one conventional approach is to fit numerical solutions (e.g., Euler, Runge--Kutta) of ODEs to data. However, such a…
Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network…
We study the problem of high-dimensional robust mean estimation in an online setting. Specifically, we consider a scenario where $n$ sensors are measuring some common, ongoing phenomenon. At each time step $t=1,2,\ldots,T$, the $i^{th}$…
Given points $p_1, \dots, p_n$ in $\mathbb{R}^d$, how do we find a point $x$ which maximizes $\frac{1}{n} \sum_{i=1}^n e^{-\|p_i - x\|^2}$? In other words, how do we find the maximizing point, or mode of a Gaussian kernel density estimation…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…