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.
A boosting method improves nonparametric density estimation without smoothing assumptions.
There is a large body of work on convergence rates either in passive or active learning. Here we first outline some of the main results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness of the regression function (or the boundary between classes) and the margin…
There is a large body of work on convergence rates either in passive or active learning. Here we outline some of the results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness and the margin noise. We also discuss the relative merits of these underlying assumpti…
This paper analyzes the convergence of Federated Average under relaxed assumptions.
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].
Extends Kollár's result to fibered Calabi-Yau varieties with cohomological assumption.
Improved model for non-smooth signals with complex spectra.
We study contextual bandit learning with an abstract policy class and continuous action space. We obtain two qualitatively different regret bounds: one competes with a smoothed version of the policy class under no continuity assumptions, while the other requires standard Lipschitz assumptions. Both bounds exhibit data-…
New algorithms SVCA and SSPA improve robustness to noise in nonnegative matrix factorization.
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
Generalizes Thurston's jiggling lemma for piecewise smooth solutions.
New method improves RL in continuous spaces with kernel smoothing.
Smooth submetries between curved spaces are smooth.
New active learning algorithm adapts to data without strict assumptions.
Confirming operator characterization on smooth manifolds.
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong a…
We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.
Under the assumption that the X-ray transform over symmetric solenoidal 2-tensors is injective, we prove that smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set are locally marked boundary rigid.
Lower bounds for higher-order methods in non-convex optimization.
New method removes scalar curvature assumption in Ricci flow smoothing.
We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm…
New shuffling methods improve convergence without Lipschitz smoothness.
Study of elliptic boundary value problems on non-compact manifolds.
New moving plane method for varifolds promotes smoothness from boundary to interior.
First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also introduce a kernel-fr…
We consider open globally hyperbolic spacetimes of dimension , , which are spatially asymptotic to a Robertson-Walker spacetime or an open Friedmann universe with spatial curvature and prove, under reasonable assumptions, that there exists a unique foliation by hypersurfaces of constant…
Kernel smoothing on unknown manifolds with bounds and asymptotic normality.
In this paper we continue the study of spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold, initiated in a previous paper. Under assumption that the singular foliation generated by the distribution is smooth, we prove that the Laplacian associated with the distributi…
For binary classification we establish learning rates up to the order of for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometr…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density. However concrete statements in the literature are often invoked in very specific …
In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS) algorithm for solving a family of non-smooth problems that is composed of a non-smooth term with an explicit max-structure and a smooth term or a simple non-smooth term whose proximal mapping is easy to compute. The best known iteration compl…
New algorithm learns halfspaces over hypercube with random bit flips.
New Langevin algorithm works well even for rough distributions.
In this paper, we study the partial convexity of smooth solutions to the heat equation on a compact or complete non-compact Riemannian manifold M or Kahler-Ricci flow. We show that under a natural assumption, a new partial convexity property for smooth solutions to the heat equation is preserved.
Develops PRPCA for smooth image recovery combining low-rank and smoothness.
It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard . Similarly, a smooth 4-manifold homeomorphic to the produc…
Paper studies Adam's convergence under relaxed assumptions, proving a rate of O(poly(log T)/sqrt(T)).
We consider Fano manifolds M that admit a collection of finite automorphism groups G_1, ..., G_k, such that the quotients M/G_i are smooth Fano manifolds possessing a Kaehler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kaehler-Einstein metric t…
New SPS variant improves non-smooth optimization without small gradients.
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth object…
Let be a smooth area decreasing map between two Riemannian manifolds $(M,\gm)$ and $(N,\gn)$. Under weak and natural assumptions on the curvatures of $(M,\gm)$ and $(N,\gn)$, we prove that the mean curvature flow provides a smooth homotopy of to a constant map.
Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the regression function is smooth over high-density clusters or manifolds supporting the dat…
New polynomial convergence guarantees for SGM on general data distributions.
Adam converges to stationary points under relaxed conditions.
Paper optimizes multi-fidelity function with fast learning rates.
In this note, we prove that smooth self-shrinkers in $\Real^{n+1}$, that are entire graphs, are hyperplanes. Previously Ecker and Huisken showed that smooth self-shrinkers, that are entire graphs and have at most polynomial growth, are hyperplanes. The point of this note is that no growth assumption at infinity is need…
Full-batch GD achieves generalization close to any stationary point with fewer assumptions.