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Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and…

Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the…

Parameter updating is an important stage in parallelism-based distributed deep learning. Synchronous methods are widely used in distributed training the Deep Neural Networks (DNNs). To reduce the communication and synchronization overhead…

The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting…

We propose a novel algorithm for combined unit and layer pruning of deep neural networks that functions during training and without requiring a pre-trained network to apply. Our algorithm optimally trades-off learning accuracy and pruning…

Density Estimation Trees (DETs) are decision trees trained on a multivariate dataset to estimate its probability density function. While not competitive with kernel techniques in terms of accuracy, they are incredibly fast, embarrassingly…

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…

Beyond their impressive sampling capabilities, score-based diffusion models offer a powerful analysis tool in the form of unbiased density estimation of a query sample under the training data distribution. In this work, we investigate the…

We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…

Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of training parameters. We enrich POU-Nets with a Gaussian noise model…

A plethora of recent research has focused on improving the memory footprint and inference speed of deep networks by reducing the complexity of (i) numerical representations (for example, by deterministic or stochastic quantization) and (ii)…

Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…

We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…

The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the $k^{th}$ order differentiable multivariate functions with equal hyper-volumes (region bounded by…