arXiv research

Estimates discontinuous optimal transport maps between a discrete and continuous distribution.

Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.

Study optimal stopping for variable annuity contracts with discontinuous rewards.

New algorithm tackles optimization problems with discontinuous gradients in finance and insurance.

This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.

Algorithm uncovers treatment effect heterogeneity in educational RD designs.

In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…

Causal inference from observational data is hard due to discontinuous causal effects.

RLGP model improves robustness and accuracy for discontinuous response surfaces.

Proves nonemptyness of domains for specific group actions.

The paper analyzes optimal retirement strategies in a market with habit persistence and jump diffusion, finding discontinuous investment strategies.

The results on the mean-variance hedging problem in Gouriéroux, Laurent and Pham (1998), Rheinländer and Schweizer (1997) and Arai (2005) are extended to discontinuous semimartingale models. When the numéraire method is used, we only assume the Radon-Nikodym derivative of the variance-optimal signed martingale measure …

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…

Post-processing predictors reduces calibration errors for decision-making.

Cut-DeepONet handles discontinuities and sharp transitions in neural operators.

Study proves existence of equilibrium in incomplete economies with discontinuous volatility.

New domains of discontinuity found for Anosov representations.

A new geometry for comparing signals, overcoming traditional limitations.

As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…

Study bandit problems with BMO functions, achieving poly-log $δ$-regret.

Mini-batch sub-sampling in neural network training is unavoidable, due to growing data demands, memory-limited computational resources such as graphical processing units (GPUs), and the dynamics of on-line learning. In this study we specifically distinguish between static mini-batch sub-sampled loss functions, where mi…

Study the discontinuity of functions not embeddable in Euclidean space.

New method finds optimal learning rates for neural nets.

Bayesian nonparametric discontinuity design improves causal inference without randomization.

Study new symmetries in non-symmetric spaces and discontinuous groups.

In recent years, an increasing number of neural network models have included derivatives with respect to inputs in their loss functions, resulting in so-called double backpropagation for first-order optimization. However, so far no general description of the involved derivatives exists. Here, we cover a wide array of s…

Selecting input variables or design points for statistical models has been of great interest in adaptive design and active learning. Motivated by two scientific examples, this paper presents a strategy of selecting the design points for a regression model when the underlying regression function is discontinuous. The fi…

New continuous-time optimization algorithms converge in finite time to local minima.

Paper finds surface groups can deform in reductive symmetric spaces.

A new method for unsupervised disentanglement using axis-aligned cliffs.

This work builds the connection between the regularity theory of optimal transportation map, Monge-Ampère equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse. According to the regularity theory of Monge-Ampère equation, if the support of the …

The paper analyzes Variable Annuities with surrender charges, providing a pricing formula and optimal exercise boundary.

New method estimates active subspaces for jump-discontinuous functions.

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

Bayesian approach for estimating heterogeneous treatment effects in RDD designs.

Paper analyzes error in stochastic approximation for discontinuous functions.

Bayesian emulator tackles models with discontinuities efficiently.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.

This work improves SGMs' convergence guarantees for semiconvex distributions with discontinuous gradients.

Volunteer labor can temporarily yield lower benefits to charities than its costs. In such instances, organizations may wish to defer volunteer donations to a later date. Exploiting a discontinuity in blood donations' eligibility criteria, we show that deferring donors reduces their future volunteerism. In our setting, …

We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamic…

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of …

Study proves rigid spectral properties of planets with metric discontinuities.

In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.