The remarkable success of deep neural networks (DNN) is often attributed to their high expressive power and their ability to approximate functions of arbitrary complexity.
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids.
Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity.
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle.
This paper introduces Bayesian uncertainty modeling using Stochastic Weight Averaging-Gaussian (SWAG) in Natural Language Understanding (NLU) tasks.
Generating new molecules is fundamental to advancing critical applications such as drug discovery and material synthesis.
Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice.
We present a simple approach to incorporate prior knowledge in BNNs based on external summary information about the predicted classification probabilities for a given dataset.
While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature.
In this paper, we interpret these latent noise variables as implicit representations of simple and domain-agnostic data perturbations during training, producing BNNs that perform well under covariate shift due to input corruptions.
Parallel to LD, Stein variational gradient descent (SVGD) similarly minimizes the KL, albeit endowed with a novel Stein-Wasserstein distance, by deterministically transporting a set of particle samples, thus de-randomizes the stochastic diffusion process.
Data-driven neural network models have recently shown great success in modelling and learning complex PDE systems.
Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data.
In this paper, we present affine transport -- a variant of optimal transport, which models the mapping between state transition distributions between the source and target domains with an affine transformation.
Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time.
In model-based reinforcement learning efficiency is improved by learning to simulate the world dynamics.
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning.
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures.
In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations.
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models.
We present Ordinary Differential Equation Variational Auto-Encoder (ODE2VAE), a latent second order ODE model for high-dimensional sequential data.
We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data.
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We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions.
We propose a novel deep learning paradigm of differential flows that learn a stochastic differential equation transformations of inputs prior to a standard classification or regression function.
We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE).
Flux analysis methods commonly place unrealistic assumptions on fluxes due to the convenience of formulating the problem as a linear programming model, and most methods ignore the notable uncertainty in flux estimates.
We propose a novel model family of zero-inflated Gaussian processes (ZiGP) for such zero-inflated datasets, produced by sparse kernels through learning a latent probit Gaussian process that can zero out kernel rows and columns whenever the signal is absent.
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated.
We introduce a Bayesian data fusion model that re-calibrates the experimental and in silico data sources and then learns a predictive GP model from the combined data.
We introduce a novel kernel that models input-dependent couplings across multiple latent processes.
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces.
We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent.
Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics.