arXiv research

Paper introduces non-linearity signature to measure deep neural network performance.

Enhances RJMCMC efficiency with non-linear transport-based proposals.

Study non-Gaussian measures' concentration properties in metric spaces.

A new geometric framework resolves singularities in anomalous transport.

Survey of Sinkhorn algorithm for optimal transport, emphasizing its geometric origins.

We show that a properly convex projective structure $\mathfrak{p}$ on a closed oriented surface of negative Euler characteristic arises from a Weyl connection if and only if $\mathfrak{p}$ is hyperbolic. We phrase the problem as a non-linear PDE for a Beltrami differential by using that $\mathfrak{p}$ admits a compatib…

The study establishes stability in WMOT, crucial for finance with imprecise data.

In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the equivalence of the non-linear Schrödinger equation and non-linear heat system to the…

Optimal transport reformulates multiple quantile hedging problem.

Differentiable PF via entropy-regularized OT for better inference.

With this work we try to analyse the agglomeration process in the Portuguese regions, using the New Economic Geography models. In these models the base idea is that where has increasing returns to scale in the manufactured industry and low transport costs, there is agglomeration. Of referring, as summary conclusion, th…

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these method…

Sliced Optimal Transport simplifies OT for fast computation.

We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for providing a relevant geometry to the copulas, and clustering for summarizing the ma…

In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimise our cost function given the prices of a finite number…

This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such at…

Deep learning improves trip prediction accuracy in transportation planning.

Integrates side information for robust portfolio optimization.

Extracts invariant features to predict Y without confounding by Z, using conditional independence and optimal transport.

Method calibrates stock price models with stochastic interest rates using optimal transport.

This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function $f$ in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. Our work makes the following assumption: there exists a non-linea…

Study numerical methods for singular FBSDEs with degenerate forward component.

GeONet learns the Wasserstein geodesic without mesh discretization.

Dynamic linear models improve travel time prediction for congested freeways.

Neural networks predict traffic flow in smart cities.

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding the $L^2$-Wasserstein distance of optimal mass transport, and the Fisher--Rao me…

We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convol…

In this paper we develop a data-driven smoothing technique for high-dimensional and non-linear panel data models. We allow for individual specific (non-linear) functions and estimation with econometric or machine learning methods by using weighted observations from other individuals. The weights are determined by a dat…

This work extends VQR to non-linear cases and provides scalable solvers.

Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on road networks, (2) non-linear temporal dynamics with changing road conditions and (…

New methods estimate transport-growth pairs in unbalanced optimal transport.

Introduces statistical optimal transport for probabilistic lectures.

Study shows how optimal transport behaves in higher dimensions.

A concise discussion of the axiomatic approach to the concept of parallel transport is presented. Attention is drawn to a bijective map between the sets of connections and (axiomatically defined) parallel transports. The transports along paths are pointed as a generalization of the (axiomatically defined) parallel tran…

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts "conn…

New framework uses cohomology to analyze probabilistic distortions and arbitrage.

Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $π_1, π_2, \ldots$ converges weakly to a transport plan $π$, then $π$ is also optimal (between its marginals). Alfonsi, Corbetta and Jourdain asked whether the same property is true for th…

NOT learns optimal transport plans, kernel costs improve performance.

New algorithm solves unbalanced optimal transport on trees in quasi-linear time.

A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the former.

Using McCann's transportation map, we establish a transport inequality on compact manifolds with positive Ricci curvature. This inequality contains the sharp spectral comparison estimates.

New metric for probability measures connects physics and geometry.

A new algorithm for parallel transport on shape spaces is presented and compared to existing methods.

Extends optimal transport to dynamic and martingale settings.

Review of modern computational optimal transport methods for biomedical applications.

Paper relaxes optimal transport using convex functions for data science.

Study optimal transport on simplex boundary, proving transport map and potential regularity.

Bayesian approach to optimal transport with stochastic costs.