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.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
Study approximates unknown function levels with queries.
In the context of stochastic continuum-armed bandits, we present an algorithm that adapts to the unknown smoothness of the objective function. We exhibit and compute a polynomial cost of adaptation to the H{ö}lder regularity for regret minimization. To do this, we first reconsider the recent lower bound of Locatelli an…
The purpose of these notes is to explain parts of Gromov's survey of Carnot-Carathedory spaces, in the light of subsequent results of M. Rumin. Among the rich material provided by Gromov, most of which pertains to analysis on metric spaces, we choose to concentrate on the H{ö}lder equivalence problem for Carnot manifol…
Efficient algorithms for contextual bandits with smooth regret in continuous action spaces.
Unified approach to discrete and smooth isoperimetric inequalities of arbitrary order.
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero …
We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\t…
A variant of Gromov's H{ö}lder-equivalence problem, motivated by a pinching problem in Riemannian geometry, is discussed. A partial result is given. The main tool is a general coarea inequality satisfied by packing energies of maps.
Paper establishes tight lower bounds for minimizing certain smooth and convex functions.
New algorithms optimize convex functions with high-order derivatives.
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the a…
Paper accelerates diffusion models without retraining, reducing evaluations.
Paper learns hypergraph structures from signals with smoothness priors.
High-order Klein geometries constructed using Lie algebras.
Improved fourth-order compact scheme for option valuation with Robin boundary condition.
Paper tackles high-order inference in structured prediction tasks.
In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher acc…
Exact partitioning of high-order planted models achieved through convex optimization.
Study shows zero-shot super-resolution in neural operators is impossible in many cases.
Paper develops a high-order recombination algorithm for financial modeling.
Paper proposes efficient methods for high-order clustering in tensor block models.
New high-order universal portfolios outperform standard ones.
This paper shows how many samples are needed for smooth functions in high dimensions.
New tests detect high-order interactions without permutations.
New method for pricing options in stochastic volatility models.
New method finds significant high-order interactions efficiently.
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the present paper is to provide a short overview of some results and open problems on s…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines differ…
This paper selects features in deep neural networks with theoretical guarantees.
Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric Embedding (HOPE) approach to data visualization and compression. Compared to deep emb…
Taking into account high-order interactions among covariates is valuable in many practical regression problems. This is, however, computationally challenging task because the number of high-order interaction features to be considered would be extremely large unless the number of covariates is sufficiently small. In thi…
Finding statistically significant high-order interaction features in predictive modeling is important but challenging task. The difficulty lies in the fact that, for a recent applications with high-dimensional covariates, the number of possible high-order interaction features would be extremely large. Identifying stati…
EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.
New deep learning architecture learns martingales efficiently.
We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{ä}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in R n , and through t…
THS-GAN uses tensorizing and high-order pooling for AD diagnosis.
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle (Krener, 1977) must be used in o…
Deep model learns protein interfaces from high-order interactions.
The paper analyzes cryptocurrency trading networks using pairwise and high-order dependencies.
Novel CG-EGNNs learn equivariant functions from Clifford algebras.
AD-HOC simplifies high-order derivative calculations in C++.
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical i…
A new method for embedding sparse high-order interactions.
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, o…
AutoEncoder smooths noisy sensor data and interpolates missing values.