Related papers: Deep Regression for Repeated Measurements
We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…
Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do…
Deep Neural Networks (DNNs) are intensively used to solve a wide variety of complex problems. Although powerful, such systems require manual configuration and tuning. To this end, we view DNNs as configurable systems and propose an…
Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and…
Deep neural network (DNN) based approaches hold significant potential for reinforcement learning (RL) and have already shown remarkable gains over state-of-art methods in a number of applications. The effectiveness of DNN methods can be…
Deep neural networks (DNNs) have shown to provide superb performance in many real life applications, but their large computation cost and storage requirement have prevented them from being deployed to many edge and internet-of-things (IoT)…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
Deep neural networks (DNNs) have proven to be highly effective in a variety of tasks, making them the go-to method for problems requiring high-level predictive power. Despite this success, the inner workings of DNNs are often not…
Why do deep neural networks (DNNs) benefit from very high dimensional parameter spaces? Their huge parameter complexities vs stunning performance in practice is all the more intriguing and not explainable using the standard theory of model…
To reduce training costs, several Deep neural networks (DNNs) that can learn from a small set of HF data and a sufficient number of low-fidelity (LF) data have been proposed. In these established neural networks, a parallel structure is…
The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
We propose a novel method to explain trained deep neural networks (DNNs), by distilling them into surrogate models using unsupervised clustering. Our method can be applied flexibly to any subset of layers of a DNN architecture and can…
We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold but is only observable in an infinite-dimensional space. Contamination of the predictor due to discrete/noisy…
Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression problem with inputs on a $d^*$-dimensional manifold that is…
We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…
Deep neural networks (DNNs) have emerged as key enablers of machine learning. Applying larger DNNs to more diverse applications is an important challenge. The computations performed during DNN training and inference are dominated by…
Deep neural networks (DNNs) have achieved significant success in a variety of real world applications, i.e., image classification. However, tons of parameters in the networks restrict the efficiency of neural networks due to the large model…
As deep neural networks (DNNs) are increasingly used in safety-critical applications, there is a growing concern for their reliability. Even highly trained, high-performant networks are not 100% accurate. However, it is very difficult to…
In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…