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This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
Joint probability density function (PDF)-based models in turbulent combustion provide direct closure for turbulence-chemistry interactions. The joint PDFs capture the turbulent flame dynamics at different spatial locations and hence it is…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
A robust uncertainty estimate in global analyses of Parton Distribution Functions (PDFs) is essential at the Large Hadron Collider (LHC), especially in view of the high-precision data anticipated by experimentalists in the High-Luminosity…
Probabilistic optimal power flow (POPF) is an important analytical tool to ensure the secure and economic operation of power systems. POPF needs to solve enormous nonlinear and nonconvex optimization problems. The huge computational burden…
Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…
Existing point cloud semantic segmentation networks cannot identify unknown classes and update their knowledge, due to a closed-set and static perspective of the real world, which would induce the intelligent agent to make bad decisions. To…
We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical…
Neural networks have been widely used as predictive models to fit data distribution, and they could be implemented through learning a collection of samples. In many applications, however, the given dataset may contain noisy samples or…
We propose the periodic scaled Korobov kernel (PSKK) method for nonparametric density estimation on $\mathbb{R}^d$. By first wrapping the target density into a periodic version through modulo operation and subsequently applying kernel ridge…
Survival analysis holds a crucial role across diverse disciplines, such as economics, engineering and healthcare. It empowers researchers to analyze both time-invariant and time-varying data, encompassing phenomena like customer churn,…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
Particle flow (PFL) is an effective method for overcoming particle degeneracy, the main limitation of particle filtering. In PFL, particles are migrated towards regions of high likelihood based on the solution of a partial differential…
3D microscopy is key in the investigation of diverse biological systems, and the ever increasing availability of large datasets demands automatic cell identification methods that not only are accurate, but also can imply the uncertainty in…
Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…
In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…