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We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our…
As inverter-based resources (IBRs) penetrate power systems, the dynamics become more complex, exhibiting multiple timescales, including electromagnetic transient (EMT) dynamics of power electronic controllers and electromechanical dynamics…
Recently, the statistical properties of empirical Entropic Optimal Transport (EOT) have attracted great interest, as this quantity has been shown to be useful for complex data analysis, among other reasons due to its computational…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
We develop a Bayesian "sum-of-trees" model where each tree is constrained by a regularization prior to be a weak learner, and fitting and inference are accomplished via an iterative Bayesian backfitting MCMC algorithm that generates samples…
BART (Bayesian Additive Regression Trees) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear…
Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory,…
We propose an Euler particle transport (EPT) approach for generative learning. The proposed approach is motivated by the problem of finding an optimal transport map from a reference distribution to a target distribution characterized by the…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von F\"orster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary…
We investigate the optimal structure of dynamic regression models used in multivariate time series prediction and propose a scheme to form the lagged variable structure called Backward-in-Time Selection (BTS) that takes into account…
Electromagnetic transient (EMT) simulation is a crucial tool for power system dynamic analysis because of its detailed component modeling and high simulation accuracy. However, it suffers from computational burdens for large power grids…
Kato's theory on the construction of strongly continuous evolution systems associated with hyperbolic equations is applied to the linear equation describing an age-structured population that is subject to time-dependent diffusion. The…
Bayesian additive regression trees (BART) is a flexible prediction model/machine learning approach that has gained widespread popularity in recent years. As BART becomes more mainstream, there is an increased need for a paper that walks…
We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we present a full kinetic framework for age-structured interacting populations undergoing birth, death and…
Decision trees and models that use them as primitives are workhorses of machine learning in Euclidean spaces. Recent work has further extended these models to the Lorentz model of hyperbolic space by replacing axis-parallel hyperplanes with…
The enhanced binary tree (EBT) is a nontransitive graph which has two percolation thresholds $p_{c1}$ and $p_{c2}$ with $p_{c1}<p_{c2}$. Our Monte Carlo study implies that the second threshold $p_{c2}$ is significantly lower than a recent…
In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of…
We introduce the new concept of an EBV to assess the sensitivity of model outputs to changes in initial conditions for weather forecasting. The new algorithm, which we call the "Ensemble Bred Vector" or EBV, is based on collective dynamics…
States of quantum many-body systems are defined in a high-dimensional Hilbert space, where rich and complex interactions among subsystems can be modelled. In machine learning, complex multiple multilinear correlations may also exist within…