arXiv research

sFML learns stochastic dynamical systems from data.

Riemannian stochastic gradient descent approximates a diffusion process called Riemannian stochastic modified flow.

Itô maps provide a method for any-step SDE integration.

This work broadens optimal transport map estimation theory to stochastic settings.

We show that stochastic interpolation flow maps are Lipschitz with a sharp constant.

New analysis of stochastic approximation with non-expansive mappings.

Unified view of SOMs and SNE from a common framework.

We first prove stochastic representation formulae for space-time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions. Space-time harmonic mappings which are defined globally in time correspond to an…

Wave maps with noise can lead to self-similar blowup from arbitrary initial data.

In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks represent mappings from a set of inputs to a set of probability distributions o…

The MAP estimate's log-likelihood sub-optimality is hard to bound in general.

Study efficient derivative computation for nondifferentiable maps in machine learning.

Develops Bayesian approach for end-to-end learning in stochastic optimization.

Study on stochastic hypergradient computation for machine learning problems.

Stochastic optimization improves semi-discrete OT map estimation with a minimax rate.

Optimal transport for functional data using Hilbert-Schmidt operators.

For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the surface of the environment using a continuous mesh of triangular surface element…

We consider stochastic versions of Euler--Arnold equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden. For the Euler equation on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution (in the stochastic sense) in spaces…

We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained v…

The paper introduces Causal Neural Operators to approximate operators in stochastic analysis.

This work establishes uniform convergence of subdifferentials in stochastic optimization.

Improved spatial distribution learning with Bayesian transport maps and parametric shrinkage.

Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate variables with boundaries such as non-negative ones or those in a finite interval.…

We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic composite gradient method that employs an incremental variance-reduced estimator…

This work introduces a new method for coupling base and target densities in generative models.

We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of invariance with respect to these maps. Second, we consider the Fish…

Studying SGD on deep neural networks using diffusion maps.

GenFormer uses deep learning to generate complex stochastic data.

Sparked by Alòs, León, and Vives (2007); Fukasawa (2011, 2017); Gatheral, Jaisson, and Rosenbaum (2018), so-called rough stochastic volatility models such as the rough Bergomi model by Bayer, Friz, and Gatheral (2016) constitute the latest evolution in option price modeling. Unlike standard bivariate diffusion models s…

We have completely rewritten the paper, and corrected the proofs. We construct an exponential map at any point in the (n-1)-skeleton minus the (n-2)-skeleton of an n-dimensional Riemannian polyhedron. We have added allover the extra-assumption that the exponential map is totally geodesic at points in the (n-1)-skeleton…

The paper solves a complex control problem with stochastic elements and switching conditions.

MFMs enable efficient reward alignment for generative models.

Stochastic flows of Stratonovich stochastic differential equations on exotic spheres have been studied. The consequences of the choice of exotic differential structure on stochastic processes taking place on the topological space $S^{m+n+1}$ as state space of the processes have been investigated. More precisely, we hav…

Linking SV and PDV models for better volatility forecasts.

New method for risk quantification using quantile processes and measure distortions.

Covariance shrinkage via stochastic interpolation

Study shows Stochastic Mirror Descent optimizes convex problems with infinite noise variance.

New method estimates SDE parameters efficiently using WCE and SGD.

The paper analyzes convergence of Riemannian SA schemes for stochastic optimization.

Study how noisy labels affect semi-supervised learning.

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a pr…

Stochastic binary hidden units in a multi-layer perceptron (MLP) network give at least three potential benefits when compared to deterministic MLP networks. (1) They allow to learn one-to-many type of mappings. (2) They can be used in structured prediction problems, where modeling the internal structure of the output i…

Optimal algorithms for Riemannian optimization with reduced complexity.

This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but n…

We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an $ε$ stationary point where the expected norm of the subgradient of corresponding augmented Lag…

A new method synthesizes expressions from characteristics using GAN for healthcare.

New algorithm improves on existing methods for solving transport problems.

Solves imaging inverse problems using autoencoding priors.