arXiv research

We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.

New method improves nonlinear filtering accuracy with reduced computation.

Study improves BN TTA under distribution shift using higher-order asymptotics.

Edgeworth Accountant calculates privacy loss under differential privacy compositions efficiently.

The paper provides non-asymptotic Edgeworth expansions for neural network outputs.

The study improves volatility model pricing accuracy with new statistical expansions.

The paper improves A/B testing for non-Gaussian data, ensuring reliable results with large sample sizes.

Sharp privacy bounds for sequential analysis of sensitive data.

Paper provides Edgeworth expansions for network moments, improving accuracy of sampling distributions.

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validat…

In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our …

Bayesian inference for wide neural networks using Edgeworth expansion.

There has been a recent surge of interest in modeling neural networks (NNs) as Gaussian processes. In the limit of a NN of infinite width the NN becomes equivalent to a Gaussian process. Here we demonstrate that for an ensemble of large, finite, fully connected networks with a single hidden layer the distribution of ou…

Study finds the number of modes in Gaussian kernel density estimators scales with sqrt(β log β).

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (200…

The paper provides rigorous guarantees for m-out-of-n bootstrap estimators of sample quantiles.

A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary.…

Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First …

We present a flexible approach for the valuation of interest rate derivatives based on Affine Processes. We extend the methodology proposed in Keller-Ressel et al. (2009) by changing the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. We then show that it is possible…

The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.

We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is par…

New bootstraps improve speed and accuracy for graph count functionals.

A new model for pricing ultra-short-term options with complex volatility patterns.

In this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents. The leading idea is to describe the trading of these goods by means of some fundamental rules in price theory, in particular by using Cobb-Douglas utility functions for the bina…

Paper develops a method to compare generative models using KL divergence.

A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a trained classification model by adding a correction procedure to the model prediction. The correction procedure can be coupled with any app…

A new model of learning corrects for chance to improve learning outcomes.

Mathematical study of instanton corrected q-map spaces and their isometries.

Corrected misstatements about invariant rank in ECS manifold papers.

New method combines machine learning with data assimilation for model error correction.

Localized Multidirectional Correction improves non-refusal target-response behavior in foundation models.

Theoretical analysis shows LLMs can self-correct responses through in-context learning.

New algorithms improve boosting by optimizing chance-corrected measures.

Study examines corrections to heterotic geometry on SU(3) manifolds.

A model corrects Lithuanian grammatical errors.

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correcti…

MaxEnt Model Correction improves reinforcement learning model accuracy.

We derive a closed formula for the Heegaard Floer correction terms of lens spaces in terms of the classical Dedekind sum and its generalization, the Dedekind-Rademacher sum. Our proof relies on a reciprocity formula for the correction terms established by Ozsvath and Szabo. A consequence of our result is that the Casso…

New methods correct spectral distortions using known analyte concentrations.

This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.

Bayesian method corrects for model selection multiplicity in regression.

In recent years several trading platforms appeared which provide a backtest engine to calculate historic performance of self designed trading strategies on underlying candle data. The construction of a correct working backtest engine is, however, a subtle task as shown by Maier-Paape and Platen (cf. arXiv:1412.5558 [q-…

This paper corrects the proof of the Theorem 2 from the Gower's paper \cite[page 5]{Gower:1982} as well as corrects the Theorem 7 from Gower's paper \cite{Gower:1986}. The first correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for $k$-means clusterin…

New approach shows AI can adapt like toddlers by correcting old knowledge.

Khovanov homology helps create quantum error-correcting codes.

The study examines methods to correct measurement error in nutritional epidemiology studies.

Post-training corrections boost time-series forecasting accuracy.

This paper improves deep learning model consistency through ensemble methods.