arXiv research

Currents on cusped hyperbolic surfaces have a denseness property similar to compact surfaces.

Algorithm selects variables and bandwidths for geographically weighted regression.

IWeS selects examples by entropy-based importance sampling for subset selection.

We discuss optimal lower bounds for eigenvalues of Laplacians on weighted graphs. These bounds are formulated in terms of the geometry and, more specifically, the inradius of subsets of the graph. In particular, we study the first non-zero eigenvalue in the finite volume case and the first eigenvalue of the Dirichlet L…

A new portfolio model DEWSP improves Sharpe ratio by 0.24% to 5.15%.

Abstract result on correlations of pairs in exponentially growing discrete subsets.

This paper improves volatility forecasting using dynamic subset selection in genetic programming.

The study explores weightings on submanifolds and their geometric properties.

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets…

New sampler reduces MCMC complexity for Bayesian variable selection.

We prove that if $N\ge 2$ and $α: F_N\to π_1(Γ)$ is a marking on $F_N$, then for any integer $r\ge 2$ and any $F_N$-invariant collection of non-negative integral "weights" associated to all subtrees $K$ of $\widetilde Γ$ of radius $\le r$ satisfying some natural "switch" conditions, there exists a finite cyclically red…

The paper classifies hypersurfaces with constant weighted mean curvature.

A new method subsamples data without weights to improve model performance.

Constructs a function to count closed geodesics on Riemannian manifolds.

The paper is motivated by the study of graded representations of Takiff algebras, cominuscule parabolics, and their generalizations. We study certain special subsets of the set of weights (and of their convex hull) of the generalized Verma modules (or GVM's) of a semisimple Lie algebra $\lie g$. In particular, we exten…

We study some basic analytic questions related to differential operators on Lie manifolds, which are manifolds whose large scale geometry can be described by a a Lie algebra of vector fields on a compactification. We extend to Lie manifolds several classical results on Sobolev spaces, elliptic regularity, and mapping p…

The paper predicts edge weights in weighted directed networks using metric geometry.

We study stable smooth solutions to the isoperimetric type problem for a Gaussian weight on Euclidean Space. That is, we study hypersurfaces $Σ^n \subset \mathbb R^{n+1}$ that are second order stable critical points of compact variations that minimize Gaussian weighted area and preserve Gaussian weighted volume. We sho…

The paper proves cohomology vanishing for a specific type of minimal submanifolds in a weighted Euclidean ball.

Paper tackles dense subgraph discovery with noisy feedback.

Bayesian deep learning method using subnetwork inference.

Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and matrix factorizations. We suggest an algorithm that gets a finite set of $n$ $d…

SCS identifies a range of plausible equally weighted portfolios, quantifying selection uncertainty.

Stable capillary surfaces in weighted balls are disks.

The aim of this thesis is to construct new examples of compact orbifolds $\mathcal{O}^4(Θ)$ which admit a self dual Einstein (SDE) metric of positive scalar curvature $s>0$, with a one-dimensional group of isometries. In particular we want to prove that these examples are different from those described by Boyer, Galick…

Optimizes sample weights for representative data averages.

Improved neural networks by averaging late-stage weights.

Let $G=(V,E,w)$ be a finite, connected graph with weighted edges. We are interested in the problem of finding a subset $W \subset V$ of vertices and weights $a_w$ such that $\frac{1}{|V|}\sum_{v \in V}^{}{f(v)} \sim \sum_{w \in W}{a_w f(w)}$ for functions $f:V \rightarrow \mathbb{R}$ that are `smooth' with respect t…

We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the minimality of the resulting representation, the other insensitivity to nuisance va…

New loss function helps learn unstable dynamical systems.

Optimizes sparse fine-tuning for privacy in neural networks.

Simplifies RF predictions by focusing on a subset of nearest neighbors.

In the paper arXiv:1411.4887 [math.AP] it is shown that the set of Riemannian metrics which do not admit global limiting Carleman weights is open and dense, by studying the conformally invariant Weyl and Cotton tensors. In the paper arXiv:1011.2507 [math.DG] it is shown that the set of Riemannian metrics which do not a…

The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science to disentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use to country specific food production data to study binary and weighted topologi…

Improved loss functions adapt to weight-space anisotropy, outperforming isotropic counterparts.

New measure defined for Brakke flow, linking classical and new definitions.

We introduce higher-order Poincar'e constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue of the $p$-Laplacian. In the case of the closed eigenvalue problem and the Neuma…

The paper shows neural networks can approximate functions over non-compact domains with non-polynomial activation.

ModHiFi identifies critical components for model modification without gradients or loss function.

Paper proposes efficient weight updates for edge nodes with minimal communication.

A new method reduces the computational cost of KernelSHAP for explaining predictions.

A novel method selects genes for high-dimensional gene expression data with class imbalance.

Gradient-based method prunes large models to create transferable architectures.

Selective forgetting method cleans deep network weights of forgotten data.

The paper proves geometric inequalities for hypersurfaces in weighted manifolds.

Neural networks with learned biases can approximate any function.

Incremental gradient (IG) methods, such as stochastic gradient descent and its variants are commonly used for large scale optimization in machine learning. Despite the sustained effort to make IG methods more data-efficient, it remains an open question how to select a training data subset that can theoretically and pra…

We propose using five data-driven community detection approaches from social networks to partition the label space for the task of multi-label classification as an alternative to random partitioning into equal subsets as performed by RAkELd: modularity-maximizing fastgreedy and leading eigenvector, infomap, walktrap an…