Related papers: Statistical Properties of Deep Neural Networks wit…
We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…
Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…
The pioneer deep neural networks (DNNs) have emerged to be deeper or wider for improving their accuracy in various applications of artificial intelligence. However, DNNs are often too heavy to deploy in practice, and it is often required to…
The use of Convolutional Neural Networks (CNNs) is widespread in Deep Learning due to a range of desirable model properties which result in an efficient and effective machine learning framework. However, performant CNN architectures must be…
Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed…
We introduce the Schrodinger Neural Network (SNN), a principled architecture for conditional density estimation and uncertainty quantification inspired by quantum mechanics. The SNN maps each input to a normalized wave function on the…
Deep neural networks (DNNs) have been successfully applied to many real-world problems, but a complete understanding of their dynamical and computational principles is still lacking. Conventional theoretical frameworks for analysing DNNs…
A general lack of understanding pertaining to deep feedforward neural networks (DNNs) can be attributed partly to a lack of tools with which to analyze the composition of non-linear functions, and partly to a lack of mathematical models…
This paper is concerned with a special class of deep neural networks (DNNs) where the input and the output vectors have the same dimension. Such DNNs are widely used in applications, e.g., autoencoders. The training of such networks can be…
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…
Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…
Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these…
While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited. Unlike previously proposed local methods which try to explain particular…
We propose a novel deep learning approach to nonparametric statistical inference for the conditional hazard function of survival time with right-censored data. We use a deep neural network (DNN) to approximate the logarithm of a conditional…
In this paper, we provide a novel Model-free approach based on Deep Neural Network (DNN) to accomplish point prediction and prediction interval under a general regression setting. Usually, people rely on parametric or non-parametric models…
Deep neural networks (DNNs) have achieved remarkable empirical success, yet their training dynamics remain understood mainly from optimization rather than statistical principles. Here we develop a statistical framework for DNN training in…
This work presents an in-depth analysis of the majority of the deep neural networks (DNNs) proposed in the state of the art for image recognition. For each DNN multiple performance indices are observed, such as recognition accuracy, model…
In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields…
A key challenge for deploying deep neural networks (DNNs) in safety critical settings is the need to provide rigorous ways to quantify their uncertainty. In this paper, we propose a novel algorithm for constructing predicted classification…
We study the performance of stochastically trained deep neural networks (DNNs) whose synaptic weights are implemented using emerging memristive devices that exhibit limited dynamic range, resolution, and variability in their programming…