Related papers: Approximation Rates for Deep Calibration of (Rough…
Stochastic volatility models, where the volatility is a stochastic process, can capture most of the essential stylized facts of implied volatility surfaces and give more realistic dynamics of the volatility smile/skew. However, they come…
Bringing deep neural networks (DNNs) into safety critical applications such as automated driving, medical imaging and finance, requires a thorough treatment of the model's uncertainties. Training deep neural networks is already resource…
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural networks (DNNs). Two important applications of these estimations…
This paper studies the approximation capacity of neural networks with an arbitrary activation function and with norm constraint on the weights. Upper and lower bounds on the approximation error of these networks are computed for smooth…
This paper proposes a sensitivity analysis framework based on set valued mapping for deep neural networks (DNN) to understand and compute how the solutions (model weights) of DNN respond to perturbations in the training data. As a DNN may…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
The quadratic rough Heston model provides a natural way to encode Zumbach effect in the rough volatility paradigm. We apply multi-factor approximation and use deep learning methods to build an efficient calibration procedure for this model.…
We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal…
Optimal decision-making in social settings is often based on forecasts from time series (TS) data. Recently, several approaches using deep neural networks (DNNs) such as recurrent neural networks (RNNs) have been introduced for TS…
Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…
Estimation of a regression function from independent and identically distributed random variables is considered. The $L_2$ error with integration with respect to the design measure is used as an error criterion. Over-parametrized deep…
This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…
Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the performance in tasks with complex-valued inputs, such as in…
We construct a deep learning-based numerical algorithm to solve path-dependent partial differential equations arising in the context of rough volatility. Our approach is based on interpreting the PDE as a solution to an BSDE, building upon…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
We develop a deep learning algorithm for constructing globally accurate approximations to functional rational expectations equilibria of dynamic stochastic economies in the sequence space. We use deep neural networks to parameterize key…
There has been a significant recent surge in deep neural network (DNN) techniques. Most of the existing DNN techniques have restricted model formats/assumptions. To overcome their limitations, we propose the nonparametric transformation…
Understanding deep neural networks (DNNs) is a key challenge in the theory of machine learning, with potential applications to the many fields where DNNs have been successfully used. This article presents a scaling limit for a DNN being…
Deep Neural Networks (DNNs) rely on inherent fluctuations in their internal parameters (weights and biases) to effectively navigate the complex optimization landscape and achieve robust performance. While these fluctuations are recognized…
In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential…