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.
Thompson Sampling with bilateral uncertainty improves performance in Bayesian Optimization.
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…
Ancient solutions to Ricci flow on torus bundles have additional symmetries.
Study finds rigidity of biconservative hypersurfaces in space forms without curvature assumptions.
New proof removes decay assumptions for spacetime positive mass theorem.
This paper analyzes the convergence of Federated Average under relaxed assumptions.
v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition is used in the proof of Lemma 4.62.
The paper clarifies the distinction between CATE and ITE under ignorability assumptions.
Frölicher spaces form a cartesian closed category which contains the category of smooth manifolds as a full subcategory. Therefore, mapping groups such as C^\infty(M,G) or \Diff(M), but also projective limits of Lie groups are in a natural way objects of that category, and group operations are morphisms in the category…
Improved Bayesian optimization for conditional parameter spaces.
Theoretical analysis of deep neural networks for time series data.
We propose a flexible method for estimating value functions in reinforcement learning without parametric assumptions.
Novel covariance function improves Bayesian optimization efficiency.
We prove that a smooth complex projective threefold with a Kähler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef dimension of the canonical line bundle is maximal. With certain additional assumptions, …
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. In this work we show how shape constraints such as convexity/concavity and their extensions, can be integrated into additive models. The proposed sparse difference of convex additive models (SDCAM) can est…
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel …
We develop the celebrated semigroup approach à la Bakry et al on Finsler manifolds, where natural Laplacian and heat semigroup are nonlinear, based on the Bochner-Weitzenböck formula established by Sturm and the author. We show the -gradient estimate on Finsler manifolds (under some additional assumptions in the n…
You are a financial analyst. At the beginning of every week, you are able to rank every pair of stochastic processes starting from that week up to the horizon. Suppose that two processes are equal at the beginning of the week. Your ranking procedure is time consistent if the ranking does not change between this week an…
New algorithm identifies best intervention without graph knowledge.
New assumptions and algorithm solve offline two-player zero-sum Markov games.
Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predict…
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces…
The paper generalizes rigidity results for contact Anosov flows with bunching assumption.
New analysis improves sample complexity for vanilla policy gradient methods.
We prove that Riemannian foliations on complete contractible manifolds have a closed leaf, and that all leaves are closed if one closed leaf has a finitely generated fundamental group. Under additional topological or geometric assumptions we prove that the foliation is also simple.
It is observed that for complex surfaces, the positivity of the Ricci curvature is preserved by the Kähler-Ricci flow, under the additional assumption that the sum of the two lowest eigenvalues of the traceless curvature operator is non-negative.
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-…
Sparse generalized additive models (GAMs) are an extension of sparse generalized linear models which allow a model's prediction to vary non-linearly with an input variable. This enables the data analyst build more accurate models, especially when the linearity assumption is known to be a poor approximation of reality. …
First order discretizations of Langevin diffusion can achieve better generalization error with additional smoothness assumptions.
Directed graphical models provide a useful framework for modeling causal or directional relationships for multivariate data. Prior work has largely focused on identifiability and search algorithms for directed acyclic graphical (DAG) models. In many applications, feedback naturally arises and directed graphical models …
New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.
Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm ar…
Solves Dirichlet problem for specific PSH functions on Hermitian manifolds.
New algorithm estimates causal effects for non-Gaussian data.
New algorithm reduces bandit problem's regret bound to logarithmic in dimension.
Neural model improves option pricing by calibrating additive process term structure.
In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) structural conditions. Here we generalize this theory to the setting where the mean curvature (of the regular part of the varifold) is prescr…
The paper finds closed hypersurfaces with prescribed mean curvature in non-compact manifolds.
New study shows exponential lower bound for RL even with constant suboptimality gap.
Study of elliptic boundary value problems on non-compact manifolds.
We consider -dimensional hypersurfaces flowing by mean curvature flow with Neumann free boundary conditions supported on a smooth support surface. We show that the Hausdorff -measure of the singular set is zero. In fact, we consider two types of interaction between the support and flowing surfaces. In the case of…
New method tackles OOD robustness with a single additional variable.
We prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions.
In this paper, we study a complete noncompact nonnegatively curved Alexandrov space with a soul of codimension two. We establish some structural results under additional regularity assumptions. As an application, we conclude that in this case Sharafutdinov retraction, , is a submetry.
The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.
We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in with . We further show that under an additional assumption (satisfied in all known cases), the covolumes of these lattices correspond to rational linear combinations of special values of -fun…
By extending Koiso's examples to the non-compact case, we construct complete gradient Kahler-Ricci solitons of various types on certain holomorphic line bundles over compact Kahler-Einstein manifolds. Moreover, a uniformization result on steady gradient Kahler-Ricci solitons with non-negative Ricci curvature is obtaine…