arXiv research

SRRM improves recursive transport surrogates in the small-discrepancy regime.

New dynamics for SGD in small learning rate regime.

A new approach is presented to describe the change in the statistics of the log return distribution of financial data as a function of the timescale. To this purpose a measure is introduced, which quantifies the distance of a considered distribution to a reference distribution. The existence of a small timescale regime…

VAE improves semi-supervised learning in small data.

New examples of deformed Hermitian-Yang-Mills connections found.

GNA optimally identifies the best arm with small gaps.

Sharp stability of Alexandrov's theorem for $C^1$ domains in the small-excess regime

New method detects and clusters market regimes in multidimensional data.

Local minimizers are convex and close to Wulff shapes.

Study identifies change points in piecewise constant reward functions with fixed exploration budget.

Study best arm identification with contextual info, achieving optimal misidentification probability.

The intraday pattern, long memory, and multifractal nature of the intertrade durations, which are defined as the waiting times between two consecutive transactions, are investigated based upon the limit order book data and order flows of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in 2003. An inverse…

Paper analyzes Gibbs and Langevin Monte Carlo for interpolation regime, showing generalization from low errors.

Theoretical analysis explains why models generalize after overfitting in modular addition.

The paper identifies five extreme learning regimes for large linear autoencoders.

Study small perturbations on low energy Laplace eigenfunctions.

Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review of their main properties and show that most of these properties can be analytic…

We find the wealth distribution for an economic agent in the financial market, in analogy with standard derivation of generaliz Boltzman (Tsallis) factor in statistical mechanics. In this respect, Tsallis entropic index separates two different regimes, the large and small size market. The Pareto like wealth distributio…

A model of open economics composed of producers and speculators is investigated by numerical simulations. The capital flows from the environment to the producers and from them to the speculators. The price fluctuations are suppressed by the speculators. When the aggressivity of the speculators grows, there is a transit…

Study finds multiple solutions for Gross-Pitaevskii equations on curved spaces.

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncom…

Analyzes Willmore flow for graphs with boundary data, proving existence and convergence.

The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.

Two distinct phases of deep learning training improve model generalization.

Momentum affects optimization differently at small vs large batch sizes near instability.

The study identifies conditions under which algorithmic stability explains generalization in interpolating learning systems.

We train a network to generate mappings between training sets and classification policies (a 'classifier generator') by conditioning on the entire training set via an attentional mechanism. The network is directly optimized for test set performance on an training set of related tasks, which is then transferred to unsee…

Random learning rate improves neural network training without extra cost.

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options. First and higher order small-time moderate deviation estimates of call prices an…

A new parametric method studies Willmore flows and energy quantization.

Improved SVMs learn from few samples with composition and multiple scales.

We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a deterministic function of the…

Large learning rates prevent memorization in denoising score matching.

ALO-CV approximates leave-one-out error in proportional regime.

Generative models use kernel smoothing for conditioning on small example sets.

We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its asymptotic properties in the limit of a large number of time steps under a certai…

New method for density estimation without approximating posterior distributions.

Deep neural networks have had an enormous impact on image analysis. State-of-the-art training methods, based on weight decay and DropOut, result in impressive performance when a very large training set is available. However, they tend to have large problems overfitting to small data sets. Indeed, the available regulari…

Study shows how large neural networks avoid overfitting through decoupling of feature learning and complexity growth.

Stochastic Gradient Descent phases explained for deep networks.

The vision for precision medicine is to use individual patient characteristics to inform a personalized treatment plan that leads to the best healthcare possible for each patient. Mobile technologies have an important role to play in this vision as they offer a means to monitor a patient's health status in real-time an…

The paper provides generalization bounds for metric learning using neural network embeddings.

We derive a small-time expansion for out-of-the-money call options under an exponential Levy model, using the small-time expansion for the distribution function given in Figueroa-Lopez & Houdre (2009), combined with a change of numéraire via the Esscher transform. In particular, we quantify find that the effect of a no…

We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic sh…

New learner achieves optimal agnostic error in small error regime.

Study compares deep feature methods for anomaly detection in limited data scenarios.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space wit…