arXiv research

Study analyzes FIT schemes under market and regulatory uncertainty.

HAR model outperforms ML in stock forecasting with correct fitting schemes.

In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing PDE. This can be done in a very e…

This paper studies parallelization schemes for stochastic Vector Quantization algorithms in order to obtain time speed-ups using distributed resources. We show that the most intuitive parallelization scheme does not lead to better performances than the sequential algorithm. Another distributed scheme is therefore intro…

Exact LAD line fitting via PALB with linear scaling and speed.

We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of t…

Neural Galerkin schemes use active learning to solve high-dimensional equations.

A new unsupervised learning method calibrates rough volatility models efficiently.

Bayesian optimization speeds up parameter reconstruction in optical nano-metrology.

Regularization is a big issue for training deep neural networks. In this paper, we propose a new information-theory-based regularization scheme named SHADE for SHAnnon DEcay. The originality of the approach is to define a prior based on conditional entropy, which explicitly decouples the learning of invariant represent…

Regularization is a big issue for training deep neural networks. In this paper, we propose a new information-theory-based regularization scheme named SHADE for SHAnnon DEcay. The originality of the approach is to define a prior based on conditional entropy, which explicitly decouples the learning of invariant represent…

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its practical applicability. We provide a scheme for learning a kernel parameterized by …

Study on Metropolis-within-Gibbs schemes for high-dimensional Bayesian models.

Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent works have increased the robustness of DNNs by fitting networks using adversarially…

Efficiently simulates and calibrates the rough Bergomi model using Wasserstein distance.

Paper develops a generative model using Wasserstein-2 loss.

We propose a sampling scheme suitable for reducing a data set prior to selecting a hypothesis with minimum empirical risk. The sampling only considers a subset of the ultimate (unknown) hypothesis set, but can nonetheless guarantee that the final excess risk will compare favorably with utilizing the entire original dat…

Improved Random Forests detect pure interactions better.

If a document is about travel, we may expect that short snippets of the document should also be about travel. We introduce a general framework for incorporating these types of invariances into a discriminative classifier. The framework imagines data as being drawn from a slice of a Levy process. If we slice the Levy pr…

Extends Heston model with local volatility for better fit to market volatilities.

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed …

Proposes using prior variable importance information in high-dimensional regression.

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the…

Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on surface meshes is important and challenging, and some existing methods often produce …

Improves GCNNs with node transition probabilities and DropNode regularization.

Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing

ACV improves structured data CV, handling dependence and noisy initial fits.

Hyper-parameter optimization remains as the core issue of Gaussian process (GP) for machine learning nowadays. The benchmark method using maximum likelihood (ML) estimation and gradient descent (GD) is impractical for processing big data due to its $O(n^3)$ complexity. Many sophisticated global or local approximation m…

New method uses reinforcement learning to sample from complex data structures efficiently.

Adaptive quadrature improves Bayesian inference through active learning.

We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often fit target functions from low to high frequencies -- on high-dimensional benchmark datasets such as MNIST/CIFAR10 and deep neural networks s…

Forecasting a time series from multivariate predictors constitutes a challenging problem, especially using model-free approaches. Most techniques, such as nearest-neighbor prediction, quickly suffer from the curse of dimensionality and overfitting for more than a few predictors which has limited their application mostl…

We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that the case when the curve is reducible and all its irreducible components are rational curves the construction procedure reduces to solving systems of linear equatio…

This paper improves simulation methods for rough Volterra stochastic volatility models.

Unified neural network model for astro-particle physics predictions with coverage, systematics, and goodness-of-fit.

We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polyno…

We solve ReLU regression with efficient approximations for various distributions.

We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility function $U$ is assumed to be smooth and strictly concave, however the resulting utilit…

New method selects best HTE estimator without ground-truth treatment effects.

Earlier work with Robert Gompf and Abigail Thompson classified, via a natural slope indexed by the rationals, all two-component links which contain the square knot and from which $(S^1 \times S^2) \# (S^1 \times S^2)$ can be obtained by surgery. It was argued that a certain family $L_n$ of such links probably contradic…

Fractional porous media equations yield q-Gaussian solutions for stock price returns.

New algorithms improve spectral clustering for finite mixture models.

INFERS PDEs from data samples using learned context.

How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as extreme cases the classical Heston model (when n = 1), and the rough Heston model (w…

We propose theoretical and empirical improvements for two-stage hashing methods. We first provide a theoretical analysis on the quality of the binary codes and show that, under mild assumptions, a residual learning scheme can construct binary codes that fit any neighborhood structure with arbitrary accuracy. Secondly, …

Cross-validation estimates model performance on unseen data, not training data.

Efficient exploration improves large language model performance with fewer queries.

We consider the problem of fitting a linear model to data held by individuals who are concerned about their privacy. Incentivizing most players to truthfully report their data to the analyst constrains our design to mechanisms that provide a privacy guarantee to the participants; we use differential privacy to model in…