Related papers: An Online Sample Based Method for Mode Estimation …
Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
The number of modes in a probability density function is representative of the complexity of a model and can also be viewed as the number of subpopulations. Despite its relevance, there has been limited research in this area. A novel…
Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…
Recent transportation network studies on uncertainty and reliability call for modeling the probabilistic O-D demand and probabilistic network flow. Making the best use of day-to-day traffic data collected over many years, this paper…
We consider the problem of estimating a function from $n$ noisy samples whose discrete Total Variation (TV) is bounded by $C_n$. We reveal a deep connection to the seemingly disparate problem of Strongly Adaptive online learning (Daniely et…
Parametric density estimation, for example as Gaussian distribution, is the base of the field of statistics. Machine learning requires inexpensive estimation of much more complex densities, and the basic approach is relatively costly…
Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…
We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
Many neural network-based out-of-distribution (OoD) detection methods have been proposed. However, they require many training data for each target task. We propose a simple yet effective meta-learning method to detect OoD with small…
We study the decentralized online regularized linear regression algorithm over random time-varying graphs. At each time step, every node runs an online estimation algorithm consisting of an innovation term processing its own new…
Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…
Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a…
Foundation models enable prompt-based classifiers for zero-shot and few-shot learning. Nonetheless, the conventional method of employing fixed prompts suffers from distributional shifts that negatively impact generalizability to unseen…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
Given a sequence of $n$ independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing…
Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…
The ODE method has been a workhorse for algorithm design and analysis since the introduction of the stochastic approximation. It is now understood that convergence theory amounts to establishing robustness of Euler approximations for ODEs,…