Related papers: Robust Nonparametric Regression with Deep Neural N…
This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…
Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised,…
This article studies deep neural network expression rates for optimal stopping problems of discrete-time Markov processes on high-dimensional state spaces. A general framework is established in which the value function and continuation…
Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…
Adversarial robustness has become an emerging challenge for neural network owing to its over-sensitivity to small input perturbations. While being critical, we argue that solving this singular issue alone fails to provide a comprehensive…
Deep neural networks have achieved impressive performance on a variety of tasks, but their brittleness to distributional shifts remains a significant barrier to real-world deployment. In this paper, we propose a framework to analyse and…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…
Classifiers built with neural networks handle large-scale high dimensional data, such as facial images from computer vision, extremely well while traditional statistical methods often fail miserably. In this paper, we attempt to understand…
We prove a non-asymptotic distribution-independent lower bound for the expected mean squared generalization error caused by label noise in ridgeless linear regression. Our lower bound generalizes a similar known result to the…
Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…
In this paper, we are concerned with the generalization performance of non-parametric estimation for pairwise learning. Most of the existing work requires the hypothesis space to be convex or a VC-class, and the loss to be convex. However,…
Randomized algorithms are used in many state-of-the-art solvers for constraint satisfaction problems (CSP) and Boolean satisfiability (SAT) problems. For many of these problems, there is no single solver which will dominate others. Having…
Deep learning searches for nonlinear factors for predicting asset returns. Predictability is achieved via multiple layers of composite factors as opposed to additive ones. Viewed in this way, asset pricing studies can be revisited using…
The presence of outliers (anomalous values) in synthetic aperture radar (SAR) data and the misspecification in statistical image models may result in inaccurate inferences. To avoid such issues, the Rayleigh regression model based on a…
Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrapolation properties of neural networks yield poor uncertainty…
A key task in actuarial modelling involves modelling the distributional properties of losses. Classic (distributional) regression approaches like Generalized Linear Models (GLMs; Nelder and Wedderburn, 1972) are commonly used, but…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
Anomaly detection is an important problem in many application areas, such as network security. Many deep learning methods for unsupervised anomaly detection produce good empirical performance but lack theoretical guarantees. By casting…
We study the training and generalization of deep neural networks (DNNs) in the over-parameterized regime, where the network width (i.e., number of hidden nodes per layer) is much larger than the number of training data points. We show that,…