arXiv research

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

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…

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

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

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…

Investigates chaotic financial time series with monthly contributions and devaluation.

We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on how to further improve the calibration procedure.

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

Algorithm learns optimal parameters from infinite space for computational resource optimization.

Reconstructs piecewise constant functions from geodesic integrals.

We develop closed-form approximations for European put options under stochastic volatility models.

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

LinXGBoost extends XGBoost for better regression of piecewise linear functions.

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

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

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…

GraN-GAN normalizes gradients for better GAN performance.

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

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumpt…

Study of Dirac-like operators on spin manifolds with large mass parameters.

Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of pena…

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.

The study provides a theory for deriving generalization guarantees for data-driven algorithm design.

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

Constructs CMC hypersurfaces in S^4 from piecewise-smooth unions of spheres.

Neural network models improve survival analysis with reduced computation time.

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 $g$.

NODEs with explicit time dependence can interpolate and generalize like piecewise-constant estimators.

Defines hierarchical clustering axioms for various densities.

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

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…

We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.

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

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

Piecewise-linear regression trees improve tree-based regression with theoretical and practical benefits.

Paper proposes variational inference for piecewise-linear systems.

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…

Two algorithms improve performance in piecewise-stationary cascading bandits.

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…

PFE embeds images into sparse regions for better segmentation.

A new method solves complex financial equations efficiently.

New method uses DC functions for piecewise linear regression.

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

We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an…

We study algebraic varieties of ReLU networks to understand their representable functions.

We consider the generic regularized optimization problem $\hat{\mathsfβ}(λ)=\arg \min_βL({\sf{y}},X{\sfβ})+λJ({\sfβ})$. Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for the LASSO--that is, if $L$ is squared error loss and $J(β)=\|β\|_1$ is the $\ell_1$ norm of $β$--the opti…

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…