arXiv research

A new method for signal processing using piecewise convex fitting.

Efficiently finds sparse solutions to max-plus equations for convex regression.

New method uses DC functions for piecewise linear regression.

Tropical geometry and weighted lattices improve curve and surface fitting.

Proposes adaptive ridge regression for functional linear models with piecewise shapes.

Neural networks can represent complex piecewise functions efficiently.

CNR uses convex optimization to estimate conditional distributions.

Paper proposes algorithms to accurately identify breakpoints in piecewise regression.

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

Exact LAD line fitting via PALB with linear scaling and speed.

Polytopes in high dimensions have at least 2n+4 normals.

We consider the problem of predicting an outcome variable using $p$ covariates that are measured on $n$ independent observations, in the setting in which flexible and interpretable fits are desirable. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant…

GeoCert finds robustness of neural networks by fitting a ball in polytopes.

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

Analyzes vector fields in polytope decompositions, proving curve finiteness.

Study groups of piecewise isometries in tessellations of Euclidean space.

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models such as Lasso. This work proposes learning the feature nonlinearities by binning fe…

For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(Ω, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of stationary harmonic map and prove the partial regularity. We also discuss the global Li…

Paper introduces $\ell$-DER for regression tasks using morphological operators and convex-concave procedure.

This study improves graph signal denoising for vector-valued data with non-convex penalties.

ParamBoost uses gradient boosting to create interpretable non-linear models with constraints.

Reconstructs piecewise constant functions from geodesic integrals.

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 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.

Investigates neural network approximation power with bounds.

A fundamental object in a hyperbolic 3-manifold M is its convex core C(M), defined as the smallest closed non-empty convex subset of M. We investigate the way the geometry of the boundary S of C(M) varies as we vary the hyperbolic metric of M. Thurston observed that the intrinsic metric of S is hyperbolic, and that its…

BlitzWS is a working set algorithm for convex problems with theoretical guarantees.

PAR provides a flexible framework for quantization in optimization problems.

Discrete conformal maps on surfaces with vertex decorations are studied.

New methods for multivariate nonparametric regression reduce dimensionality issues.

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…

Study shows non-spectrality of certain curves and line segments.

Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to empirical data, particularly for the accurate quantification of self- and mutual-exc…

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, resp…

Deep neural nets on 1-D data are convex Lasso models with reflection features.

Spectrahedral regression fits convex functions via a non-convex optimization problem.

A framework for eliciting utility functions from investor preferences.

New SGD covering technique yields dimension-independent generalization bounds.

Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate constraints or objective functions for optimization. Ensemble methods, like bagging, sm…

Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.

FAST optimizes additive segmentation for faster, more interpretable models.

New method for sorting with interacting criteria using value functions and convex programming.

PPGD solves nonconvex nonsmooth optimization problems without KL property.

The paper develops a method to approximate arbitrary Bregman divergences from supervision.

New proof for global rigidity of vertex scaling on polyhedral surfaces.

Near-convex archetypal analysis improves interpretability and fitting error in NMF.

We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $\mathbf{x} \mapsto \max(0, \mathbf{w} \cdot \mathbf{x})$ with $\mathbf{w} \in \mathbb{S}^{n-1}$. Our algorithm works in the challenging Reliable Agnostic learning model of Kalai, Kanade, and Ma…

Convex dual network improves neural network reconstruction for medical imaging.