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KNN is one of the most popular classification methods, but it often fails to work well with inappropriate choice of distance metric or due to the presence of numerous class-irrelevant features. Linear feature transformation methods have…
The recent success of generative adversarial networks and variational learning suggests training a classifier network may work well in addressing the classical two-sample problem. Network-based tests have the computational advantage that…
Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class…
Certified robustness is a desirable property for deep neural networks in safety-critical applications, and popular training algorithms can certify robustness of a neural network by computing a global bound on its Lipschitz constant.…
Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…
In this paper, we propose another version of help-training approach by employing a Probabilistic Neural Network (PNN) that improves the performance of the main discriminative classifier in the semi-supervised strategy. We introduce the…
The reliable measurement of confidence in classifiers' predictions is very important for many applications and is, therefore, an important part of classifier design. Yet, although deep learning has received tremendous attention in recent…
We examine the stability of loss-minimizing training processes that are used for deep neural networks (DNN) and other classifiers. While a classifier is optimized during training through a so-called loss function, the performance of…
The Lipschitz constant of a network plays an important role in many applications of deep learning, such as robustness certification and Wasserstein Generative Adversarial Network. We introduce a semidefinite programming hierarchy to…
Deep Neural Networks (DNNs), with its promising performance, are being increasingly used in safety critical applications such as autonomous driving, cancer detection, and secure authentication. With growing importance in deep learning,…
We compare different training strategies for the Deep Ritz Method for elliptic equations with Dirichlet boundary conditions and highlight the problems arising from the boundary values. We distinguish between an exact resolution of the…
We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a $d$-dimensional risky asset as functions of the underlying model parameters, payoff parameters and initial conditions. We cover a general…
The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…
We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k…
To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…
Deep learning systems have been reported to acheive state-of-the-art performances in many applications, and one of the keys for achieving this is the existence of well trained classifiers on benchmark datasets which can be used as backbone…
Existing Rademacher complexity bounds for neural networks rely only on norm control of the weight matrices and depend exponentially on depth via a product of the matrix norms. Lower bounds show that this exponential dependence on depth is…
Knowledge distillation has become one of the most important model compression techniques by distilling knowledge from larger teacher networks to smaller student ones. Although great success has been achieved by prior distillation methods…
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…
We build a valid p-value based on a concentration inequality for bounded random variables introduced by Pelekis, Ramon and Wang. The motivation behind this work is the calibration of predictive algorithms in a distribution-free setting. The…