Related papers: Amortized Reparametrization: Efficient and Scalabl…
Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
Although with progress in introducing auxiliary amortized inference models, learning discrete latent variable models is still challenging. In this paper, we show that the annoying difficulty of obtaining reliable stochastic gradients for…
We propose to learn deep undirected graphical models (i.e., MRFs) with a non-ELBO objective for which we can calculate exact gradients. In particular, we optimize a saddle-point objective deriving from the Bethe free energy approximation to…
Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…
Despite the popularity of Shapley Values in explaining neural text classification models, computing them is prohibitive for large pretrained models due to a large number of model evaluations. In practice, Shapley Values are often estimated…
We propose a sparse grid stochastic collocation method for long-time simulations of stochastic differential equations (SDEs) driven by white noise. The method uses pre-determined sparse quadrature rules for the forcing term and constructs…
Variational autoencoders (VAEs) rely on amortized variational inference to enable efficient posterior approximation, but this efficiency comes at the cost of a shared parametrization, giving rise to the amortization gap. We propose the…
We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to…
Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…
The paper presents a general strategy to solve ordinary differential equations (ODE), where some coefficient depend on the spatial variable and on additional random variables. The approach is based on the application of a recently developed…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
Stochastic differential equations (SDEs) have been widely used to model real world random phenomena. Existing works mainly focus on the case where the time series is modeled by a single SDE, which might be restrictive for modeling time…
This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…
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…
Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization…
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…
(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…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…