arXiv research

The paper tackles continuous ranking problems with real-valued labels.

Reconstructs piecewise constant functions from geodesic integrals.

Injectivity of geodesic ray transform for piecewise constants on compact manifolds.

LinXGBoost extends XGBoost for better regression of piecewise linear functions.

Study identifies change points in piecewise constant reward functions with fixed exploration budget.

New TVD estimator adapts to piecewise constant functions, improving performance.

We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqu…

We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and Roughgarden (2016). Majority of the machine learning literature has focused on Lipsc…

GraN-GAN normalizes gradients for better GAN performance.

The paper extends a variance gamma model to quadratic functions, reducing arbitrage and computational costs.

Neural network models improve survival analysis with reduced computation time.

Efficiently calibrates Heston model with time-varying parameters for financial derivatives.

Transformers struggle to approximate smooth functions, relying on piecewise constant approximations.

This paper aims at formulating the issue of ranking multivariate unlabeled observations depending on their degree of abnormality as an unsupervised statistical learning task. In the 1-d situation, this problem is usually tackled by means of tail estimation techniques: univariate observations are viewed as all the more …

New method uses DC functions for piecewise linear regression.

A method identifies abrupt changes in functions with fixed confidence under noisy feedback.

Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $Ω$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition o…

Investigates chaotic financial time series with monthly contributions and devaluation.

The double tetrahedron is the triangulation of the three-sphere gotten by gluing together two congruent tetrahedra along their boundaries. As a piecewise flat manifold, its geometry is determined by its six edge lengths, giving a notion of a metric on the double tetrahedron. We study notions of Einstein metrics, consta…

A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as the geometry varies in a particular way, which we call a conformal variation. This…

We develop a method to learn neural network activations with controlled Lipschitz constant.

Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whos…

The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.

Given a piecewise linear (PL) function $p$ defined on an open subset of $\R^n$, one may construct by elementary means a unique polyhedron with multiplicities $\D(p)$ in the cotangent bundle $\R^n\times \R^{n*}$ representing the graph of the differential of $p$. Restricting to dimension 2, we show that any smooth functi…

A new method solves complex financial equations efficiently.

A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an isometric embedding into the background geometry with the chosen edge lengths. Ad…

Estimates piecewise polynomials and bounded variation functions using optimal decision trees.

Paper introduces differentiable sorting and ranking with $O(n \log n)$ time complexity.

New methods for multivariate nonparametric regression reduce dimensionality issues.

A new distortion measure optimizes function approximations in vector quantization.

The paper introduces a scalable unsupervised learning framework to improve deep neural networks.

Algorithm learns mixtures of Gaussians efficiently using diffusion models.

Smoothing graphons improve link prediction in Bayesian SBM without increasing computational complexity.

Deep ReLU networks can approximate piecewise smooth functions efficiently.

The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the approach proposed in LiptonSepp2011 is developed by i) replacing a piecewise constant…

In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial Yamabe flow on the space of all piecewise flat metrics associated to a triangul…

Total variation denoising improves image quality adaptively.

Extends Local Variance Gamma model with geometric Brownian motion and piecewise linear local variance.

Score matching efficiency tied to distribution isoperimetric properties.

We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also consider continuous modification of Gauss density in $\R^2$. Finally, we give a list…

We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of segments in the prototypes, $P$, is chosen by the user and optimally distributed am…

Neural networks can represent complex piecewise functions efficiently.

Analyzes limits of flat metrics on complex curves.

Proposes methods to estimate posterior probability and propensity score functions without assuming constant propensity score.

We show that if $g$ is a Riemannian metric on a closed piecewise locally symmetric manifold $M$, then the lift of $g$ to the universal cover $\widetilde{M}$ has a discrete isometry group. We also show that the index $[\Isom(\widetilde{M}): π_1(M)]$ is bounded by a constant independent of $g$.

Defines hierarchical clustering axioms for various densities.

The paper proves a theorem for discretizing Gaussian curvature on surfaces.

New GMM models fit high-dimensional data with fewer parameters.