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When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…

We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze Stochastic Differential Equations (SDEs) that model SGD either…

This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

Crime prediction is crucial for public safety and resource optimization, yet is very challenging due to two aspects: i) the dynamics of criminal patterns across time and space, crime events are distributed unevenly on both spatial and…

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…

Multivariate time series modeling and prediction problems are abundant in many machine learning application domains. Accurate interpretation of such prediction outcomes from a machine learning model that explicitly captures temporal…

Modern learning systems increasingly interact with data that evolve over time and depend on hidden internal state. We ask a basic question: when is such a dynamical system learnable from observations alone? This paper proposes a research…

Physical computing has the potential to enable widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction. While individual devices provide basic data…

Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…

In this paper we construct a framework for doing statistical inference for discretely observed stochastic differential equations (SDEs) where the driving noise has 'memory'. Classical SDE models for inference assume the driving noise to be…

Large-scale multimodal contrastive learning has recently achieved impressive success in learning rich and transferable representations, yet it remains fundamentally limited by the uniform treatment of feature dimensions and the neglect of…

Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…

Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…

Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…