Related papers: Converting High-Dimensional Regression to High-Dim…
Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR)…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…
In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to…
Density estimation plays a key role in many tasks in machine learning, statistical inference, and visualization. The main bottleneck in high-dimensional density estimation is the prohibitive computational cost and the slow convergence rate.…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…
Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…
We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…
The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of coordinates the data have been collected in. This dependence…
Raptor code ensembles with linear random outer codes in a fixed-rate setting are considered. An expression for the average distance spectrum is derived and this expression is used to obtain the asymptotic exponent of the weight…
Recent advances in generative artificial intelligence have had a significant impact on diverse domains spanning computer vision, natural language processing, and drug discovery. This work extends the reach of generative models into physical…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields…
We presented an efficient algorithm, fast adaptive flat-histogram ensemble (FAFE), to estimate the density of states (DOS) and to enhance sampling in large systems. FAFE calculates the means of an arbitrary extensive variable $U$ in…
Considering a continuous random variable Y together with a continuous random vector X, I propose a nonparametric estimator f^(.|x) for the conditional density of Y given X=x. This estimator takes the form of an exponential series whose…
Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…
Climate models play a crucial role in understanding the effect of environmental and man-made changes on climate to help mitigate climate risks and inform governmental decisions. Large global climate models such as the Community Earth System…
Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…