Related papers: Path-Kernel Method for Differentiating Unstable Di…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
Change-point analysis plays a significant role in various fields to reveal discrepancies in distribution in a sequence of observations. While a number of algorithms have been proposed for high-dimensional data, kernel-based methods have not…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in many applications where diversity is desired. While DPPs have many appealing properties, such as efficient sampling, learning the…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…
This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…
This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…
This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively…
Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
We present the path-integral solutions to the distributions in classical (Gibbs) and quantum (Wigner) statistical mechanics. The kernel of the distributions are derived in two ways - one by time slicing and defining the appropriate…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…
The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and…
Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…