Related papers: Testing for Normality with Neural Networks
We use a system of first-order partial differential equations that characterize the moment generating function of the $d$-variate standard normal distribution to construct a class of affine invariant tests for normality in any dimension. We…
Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the…
Transforming a random variable to improve its normality leads to a followup test for whether the transformed variable follows a normal distribution. Previous work has shown that the Anderson Darling test for normality suffers from…
This research is to search for alternatives to the resolution of complex medical diagnosis where human knowledge should be apprehended in a general fashion. Successful application examples show that human diagnostic capabilities are…
Neural networks are increasingly employed to model, analyze and control non-linear dynamical systems ranging from physics to biology. Owing to their universal approximation capabilities, they regularly outperform state-of-the-art…
We consider the link prediction problem in a partially observed network, where the objective is to make predictions in the unobserved portion of the network. Many existing methods reduce link prediction to binary classification problem.…
This paper shows how to train binary networks to within a few percent points ($\sim 3-5 \%$) of the full precision counterpart. We first show how to build a strong baseline, which already achieves state-of-the-art accuracy, by combining…
There is emerging interest in performing regression between distributions. In contrast to prediction on single instances, these machine learning methods can be useful for population-based studies or on problems that are inherently…
Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of…
With the development of neural networks based machine learning and their usage in mission critical applications, voices are rising against the \textit{black box} aspect of neural networks as it becomes crucial to understand their limits and…
Modern neural networks are very powerful predictive models, but they are often incapable of recognizing when their predictions may be wrong. Closely related to this is the task of out-of-distribution detection, where a network must…
When neural networks are employed for high-stakes decision-making, it is desirable that they provide explanations for their prediction in order for us to understand the features that have contributed to the decision. At the same time, it is…
The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…
The robustness and anomaly detection capability of neural networks are crucial topics for their safe adoption in the real-world. Moreover, the over-parameterization of recent networks comes with high computational costs and raises questions…
Various problems in Engineering and Statistics require the computation of the likelihood ratio function of two probability densities. In classical approaches the two densities are assumed known or to belong to some known parametric family.…
How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96%, while other methods, especially kernel methods, fall relatively behind? Can we more provide theoretical justifications for this gap?…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
Abnormal data detection is an important step to ensure the accuracy and reliability of node data in wireless sensor networks. In this paper, a data classification method based on convolutional neural network is proposed to solve the problem…
Current deep neural networks suffer from two problems; first, they are hard to interpret, and second, they suffer from overfitting. There have been many attempts to define interpretability in neural networks, but they typically lack…