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.
Deep RL algorithms generally generalize better than specialized schemes.
MixUp explained as a special adversarial training technique.
New biharmonic functions created on Lie groups.
We introduce the technique combining the features of integration schemes for SDYM equations and multidimensional dispersionless integrable equations to get SDYM equations on the conformally self-dual background. Generating differential form is defined, the dressing scheme is developed. Some special cases and reductions…
Novel approach ensures stability of compact schemes for variable PDEs.
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…
This paper advances extragradient methods for solving inclusions under co-hypomonotonicity.
New ladder methods improve numerical accuracy in parallel transport on manifolds.
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternativ…
We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrin…
We review properties of so-called special conformal Killing tensors on a Riemannian manifold and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle . We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular La…
Study on error rates for approximating rough volatility models.
Optimal student loan repayment strategies vary based on loan size.
New approach connects stochastic gradient descent to ODE splitting schemes.
We address the problem of classification of hyper-Kähler fourfolds with . In particular we prove some special cases of the Conjecture of O'Grady about hyper-Kähler -folds numerically equivalent to the Hilbert scheme of two points on a surface.
We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for…
We conjecture an expression for the dimensions of the Khovanov-Rozansky HOMFLY homology groups of the link of a plane curve singularity in terms of the weight polynomials of Hilbert schemes of points scheme-theoretically supported on the singularity. The conjecture specializes to our previous conjecture relating the HO…
High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical me…
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the isomorphism classes of metric symplectic Lie algebras and give a complete list …
ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.
A major contributing factor to the recent advances in deep neural networks is structural units that let sensory information and gradients to propagate easily. Gating is one such structure that acts as a flow control. Gates are employed in many recent state-of-the-art recurrent models such as LSTM and GRU, and feedforwa…
This paper explores what causal structures can be distinguished by observational and interventional probing schemes.
This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, wh…
The first part of this article is a general introduction to the the theory of representation spaces of discrete groups into SL(n,C). Special attention is paid to knot groups. In Section 2 we discuss the difference between the tangent space at the representation variety, and the representation scheme. We give an example…
New schemes improve error estimates for sampling from non-log-concave distributions.
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for convex optimization, but it does not work well for nonconvex optimization typic…
The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.
The -dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative -dimensional vectors, and include non-negative matrix factorization, dictionary learning, sparse coding, -means clustering and vector quantization as special cases. Previous generalizat…
SGQuant reduces GNN memory usage without significant accuracy loss.
This article analyzes the weak error of SGD optimization schemes.
We design iterative receiver schemes for a generic wireless communication system by treating channel estimation and information decoding as an inference problem in graphical models. We introduce a recently proposed inference framework that combines belief propagation (BP) and the mean field (MF) approximation and inclu…
Ensemble methods are arguably the most trustworthy techniques for boosting the performance of machine learning models. Popular independent ensembles (IE) relying on naive averaging/voting scheme have been of typical choice for most applications involving deep neural networks, but they do not consider advanced collabora…
The paper calculates bonus values in complex insurance schemes.
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, s…
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. …
The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.
oPoW proposes a new PoW algorithm to reduce mining costs and environmental impact.
Adaptive Monte Carlo schemes developed over the last years usually seek to ensure ergodicity of the sampling process in line with MCMC tradition. This poses constraints on what is possible in terms of adaptation. In the general case ergodicity can only be guaranteed if adaptation is diminished at a certain rate. Import…
Abstract: Generalized reduction methods for symmetries in graded geometry.
We introduce a novel algorithm that computes the -sparse principal component of a positive semidefinite matrix . Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional eigen-subspace of . We obtain provable approximation guarantees that depend on t…
We describe the combinatorial stochastic process underlying a sequence of conditionally independent Bernoulli processes with a shared beta process hazard measure. As shown by Thibaux and Jordan [TJ07], in the special case when the underlying beta process has a constant concentration function and a finite and nonatomic …
Paper proposes efficient GP hyper-parameter optimization methods.
We deal with the problem of description of nonsingular pairs of compatible flat metrics for the general -component case. We describe the scheme of the integrating the nonlinear equations describing nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics). It is based on …
We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point Process (DPP). The DPP relies on a similarity measure between data points and g…
New algorithm improves convergence of gradient boosting trees.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
New methods for cost-sensitive learning in noisy data without needing noise rate.
Efficient Bayesian variable selection for binomial and negative binomial data.