A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper connects probability density cuts to graph theory eigenfunctions.
Deep Reinforcement Learning (DRL) algorithms for continuous action spaces are known to be brittle toward hyperparameters as well as \cut{being}sample inefficient. Soft Actor Critic (SAC) proposes an off-policy deep actor critic algorithm within the maximum entropy RL framework which offers greater stability and empiric…
New methods show sparse portfolios offer no advantage over mean-variance in diversification.
A new framework for sparse regression models with slow variations.
Fast classification for sparse models, even with correlated features.
Paper improves DOA estimation in sparse arrays using Siamese neural networks.
MOSS optimizes decision rules for accuracy and stability.
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies, we propose efficient dictionary learning schemes to solve several practical for…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity constraints on model structures. In this paper, we describe two new approaches to Bay…
Let φ(G) be the minimum conductance of an undirected graph G, and let 0=λ_1 <= λ_2 <=... <= λ_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, φ(G) = O(k) λ_2 / \sqrt{λ_k}, and this performance guarantee is achieved by the spectral partitioning algorithm. …
SSVI efficiently trains sparse Bayesian neural networks with minimal compression and performance loss.
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes n and number of regressors p in the 100,000s, that…
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…
NeuralCut learns to select cutting planes by looking ahead, outperforming traditional methods.
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
We present a novel method for exact hierarchical sparse polynomial regression. Our regressor is that degree polynomial which depends on at most inputs, counting at most monomial terms, which minimizes the sum of the squares of its prediction errors. The previous hierarchical sparse specification aligns w…
Study Riemannian metrics on lens spaces, find cut loci and diameters.
Study Riemannian metrics on lens spaces, find cut loci and diameters.
We consider a left invariant Riemannian metric on SO(3) with two equal eigenvalues. We find the cut locus and the equation for the cut time. We find the diameter of such metric and describe the set of all most distant points from the identity. Also we prove that the cut locus and the cut time converge to the cut locus …
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption. By relating the method's rate of convergence to an initial outer approximation's diameter, we argue that the method performs well when initialized with a second-…
Stability of cut locus under metric perturbations in compact Riemannian manifolds.
New equivalence relation for links using cut-diagrams.
Study shows convergence rates for Cheeger cuts on data clouds.
Unified framework for differentiable graph partitioning with probabilistic cuts.
We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements. We propose and study an iterative algorithm to minimize a penalized least-squares objective, with a penalty given by the "l_0-norm" of the signal's discrete graph gradient. The method proce…
We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollobás et al. [2007], we show that i) the class of models is sparse and ii) depending on the choice of the parameters, the model is either scale…
Stochastic cutting planes improve data-driven optimization speed.
Study of Randers metrics on spheres with simple cut loci.
We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process involves a choice of a spin-c prequantization for the complex plane. We prove that …
A symplectic cut of a manifold M with a Hamiltonian circle action is a symplectic quotient of M x C. If M is Kaehler then, since C is Kaehler, the cut space is Kaehler as well. The symplectic structure on the cut is well understood. In this paper we describe the complex structure (and hence the metric) on the cut. We t…
In this note, we study the cut locus of the free, step two Carnot groups with generators, equipped with their left-invariant Carnot-Carathéodory metric. In particular, we disprove the conjectures on the shape of the cut loci proposed in [Myasnichenko - 2002] and [Montanari, Morbidelli - 2016], by exh…
Max flow/min cut theorem extended to currents and topology.
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced -cut of the graph, are either based on greedy techniques or heuristics which have weak connection to th…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data since they tend to emphasize cut sizes over cut values. We propose a graph partit…
This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our f…
New upper bound for geodesic complexity derived from cut locus decompositions.
New 2-spheres of revolution with simple cut locus structures.
We consider the Lie group PSL(2) (the group of orientation preserving isometries of the hyperbolic plane) and a left-invariant Riemannian metric on this group with two equal eigenvalues that correspond to space-like eigenvectors (with respect to the Killing form). For such metrics we find a parametrization of geodesics…
In this article we extend cutting and blowing up to the nonrational symplectic toric setting. This entails the possibility of cutting and blowing up for symplectic toric manifolds and orbifolds in nonrational directions.
Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes sin…
Functor connects symplectic and contact structures via cutting and blowups.
In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate poi…
Proves a generalized Whitehead cut vertex lemma for tree groups.
Extends Milnor invariants to surface-links using cut-diagrams.
We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X.
Surgeons normally need surgical scissors and tissue grippers to cut through a deformable surgical tissue. The cutting accuracy depends on the skills to manipulate these two tools. Such skills are part of basic surgical skills training as in the Fundamentals of Laparoscopic Surgery. The gripper is used to pinch a point …
Sparse representations using overcomplete dictionaries have proved to be a powerful tool in many signal processing applications such as denoising, super-resolution, inpainting, compression or classification. The sparsity of the representation very much depends on how well the dictionary is adapted to the data at hand. …