arXiv research

We develop a new model for VIX derivatives with closed-form solutions.

Generic model for commodity derivatives pricing.

Law derived for neural networks with sparse connections.

Estimates cross-impact on derivatives markets using E-Mini futures and options.

The Heston model is validated for option pricing using theoretical derivations and empirical market data.

This paper presents a new model for pricing financial derivatives subject to collateralization. It allows for collateral arrangements adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a uni…

We discuss the problem of risk estimation in the classification problem, with specific focus on finding distributions that maximize the confidence intervals of risk estimation. We derived simple analytic approximations for the maximum bias of empirical risk for histogram classifier. We carry out a detailed study on usi…

Paper derives PAC-Bayesian bounds for LTI systems learning from empirical data.

In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literat…

We develop methods to approximate derivatives for causal inference problems using data.

A new DP algorithm for weighted ERM protects sensitive data in predictive models.

Blade uses diffusion priors to accurately and calibratedly infer complex systems.

Recently, a unified model for image-to-image translation tasks within adversarial learning framework has aroused widespread research interests in computer vision practitioners. Their reported empirical success however lacks solid theoretical interpretations for its inherent mechanism. In this paper, we reformulate thei…

This paper addresses anisotropy in Transformer models, providing geometric insights and empirical support.

We investigate LIBOR-based derivatives using a parsimonious field theory interest rate model capable of instilling imperfect correlation between different maturities. Delta and Gamma hedge parameters are derived for LIBOR Caps against fluctuations in underlying forward rates. An empirical illustration of our methodolog…

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-kno…

Batch Active Learning uses derivative information for Gaussian Process regression.

Personal income distributions in Japan are analyzed empirically and a simple stochastic model of the income process is proposed. Based on empirical facts, we propose a minimal two-factor model. Our model of personal income consists of an asset accumulation process and a wage process. We show that these simple processes…

Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair treatment do not result from decision making or predictions made via machine le…

New PAC-Bayes bounds derived using Legendre transform and f-divergences.

The standard probabilistic perspective on machine learning gives rise to empirical risk-minimization tasks that are frequently solved by stochastic gradient descent (SGD) and variants thereof. We present a formulation of these tasks as classical inverse or filtering problems and, furthermore, we propose an efficient, g…

Solves the equity premium puzzle without calibrated values.

Study compares model-free valuation to actual financial outcomes, finds it slightly conservative.

The study provides theoretical guarantees for the statistical performance of optimal decision trees.

Machine learning selects the best prediction rules from noisy data.

Researchers analyze inverse optimal transport, deriving theoretical and empirical insights.

This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as condition…

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. We compare our result with other alterna…

This paper reformulates systemic risk measures and finds new properties and estimators.

This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be solved via a block coordinate descent algorithm. Statistical estimation performance …

We study compressing empirical measures in finite RKHSs using convex optimization.

Empirical median performs well in estimating location with varying scales.

Derives an empirical capacity model for self-attention neural networks.

New algorithm closes empirical gap in PFSGD performance.

The paper analyzes local minima in high-dimensional empirical risk minimization.

Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in the next time period is a measure of the response function of the market particip…

We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph cluste…

New method for efficient inference in large datasets.

Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.

Meta-learning framework improves model performance on few-shot classification tasks.

From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various norms appearing in the context of structured sparsity and multitask dictionary lear…

Reintroduces straight-through estimators for binary neural networks.

Deep neural network with l_1-regularization achieves nearly optimal risk bounds.

The famous Policy Iteration algorithm alternates between policy improvement and policy evaluation. Implementations of this algorithm with several variants of the latter evaluation stage, e.g, $n$-step and trace-based returns, have been analyzed in previous works. However, the case of multiple-step lookahead policy impr…

The paper improves the empirical bootstrap method for non-normal estimators.

A new method estimates the learning coefficient using empirical loss.

Framework for robust control under model uncertainty, improving financial derivatives hedging.

We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some restrictions imposed on the functional class fast convergence rates can be achieved incl…