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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…

Deep neural networks (DNNs) exhibit superior performance in various machine learning tasks, e.g., image classification, speech recognition, biometric recognition, object detection, etc. However, it is essential to analyze their sensitivity…

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…

In discrete choice modeling (DCM), model misspecifications may lead to limited predictability and biased parameter estimates. In this paper, we propose a new approach for estimating choice models in which we divide the systematic part of…

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It…

Deep neural networks (DNNs) have become ubiquitous thanks to their remarkable ability to model complex patterns across various domains such as computer vision, speech recognition, robotics, etc. While large DNN models are often more…

The recent surge in Deep Learning (DL) research of the past decade has successfully provided solutions to many difficult problems. The field of quantitative analysis has been slowly adapting the new methods to its problems, but due to…

The deep neural networks (DNNs) have achieved great success in learning complex patterns with strong predictive power, but they are often thought of as "black box" models without a sufficient level of transparency and interpretability. It…

While researchers increasingly use deep neural networks (DNN) to analyze individual choices, overfitting and interpretability issues remain as obstacles in theory and practice. By using statistical learning theory, this study presents a…

Modern deep neural networks (DNNs) are extremely powerful; however, this comes at the price of increased depth and having more parameters per layer, making their training and inference more computationally challenging. In an attempt to…

Selective classification techniques (also known as reject option) have not yet been considered in the context of deep neural networks (DNNs). These techniques can potentially significantly improve DNNs prediction performance by trading-off…

Advances in deep generative and density models have shown impressive capacity to model complex probability density functions in lower-dimensional space. Also, applying such models to high-dimensional image data to model the PDF has shown…

We develop a large-scale deep learning model to predict price movements from limit order book (LOB) data of cash equities. The architecture utilises convolutional filters to capture the spatial structure of the limit order books as well as…

To investigate the theoretical foundations of deep learning from the viewpoint of the minimum description length (MDL) principle, we analyse risk bounds of MDL estimators based on two-stage codes for simple two-layers neural networks (NNs)…

We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$,…

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However,…

This paper is a supplement to our recent paper ``Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models". We introduce the class of regime-switching L\'evy models with memory,…

We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains $\mathrm{D} \subset \mathbb{R}^d$, $d=2,3$. We prove exponential emulation rates in Sobolev spaces in terms of the…

Deep Neural Networks (DNNs) have become increasingly popular in computer vision, natural language processing, and other areas. However, training and fine-tuning a deep learning model is computationally intensive and time-consuming. We…

In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies…