Related papers: Bounds for the VC Dimension of 1NN Prototype Sets
We suggest a robust nearest-neighbor approach to classifying high-dimensional data. The method enhances sensitivity by employing a threshold and truncates to a sequence of zeros and ones in order to reduce the deleterious impact of…
Data structure has a dramatic impact on the properties of neural networks, yet its significance in the established theoretical frameworks is poorly understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine operating on…
Most of the research in convolutional neural networks has focused on increasing network depth to improve accuracy, resulting in a massive number of parameters which restricts the trained network to platforms with memory and processing…
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…
Cross-validation techniques for risk estimation and model selection are widely used in statistics and machine learning. However, the understanding of the theoretical properties of learning via model selection with cross-validation risk…
A new lower bound for the maximal length of a multivector is obtained. It is much closer to the best known upper bound than previously reported lower bound estimates. The maximal length appears to be unexpectedly large for $n$-vectors, with…
Venn Prediction (VP) is a new machine learning framework for producing well-calibrated probabilistic predictions. In particular it provides well-calibrated lower and upper bounds for the conditional probability of an example belonging to…
Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…
We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes…
Although there is extensive literature on the application of artificial neural networks (NNs) in quality control (QC), to monitor the conformity of a process to quality specifications, at least five QC measurements are required, increasing…
Given a hypothesis space, the large volume principle by Vladimir Vapnik prioritizes equivalence classes according to their volume in the hypothesis space. The volume approximation has hitherto been successfully applied to binary learning…
Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…
The architectures of deep neural networks (DNN) rely heavily on the underlying grid structure of variables, for instance, the lattice of pixels in an image. For general high dimensional data with variables not associated with a grid, the…
We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is…
The k-Nearest Neighbors (kNN) classifier is a fundamental non-parametric machine learning algorithm. However, it is well known that it suffers from the curse of dimensionality, which is why in practice one often applies a kNN classifier on…
The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…
Although the variational autoencoder (VAE) and its conditional extension (CVAE) are capable of state-of-the-art results across multiple domains, their precise behavior is still not fully understood, particularly in the context of data (like…
We introduce and study the spherical dimension, a natural topological relaxation of the VC dimension that unifies several results in learning theory where topology plays a key role in the proofs. The spherical dimension is defined by…
In many practical applications it is important to build symmetries into neural network architectures. Consider the important case of permutation symmetry on point clouds consisting of $n$ points in $d$ dimensions. In this case the network…
Breast cancer detection is still an open research field, despite a tremendous effort devoted to work in this area. Effect size is a statistical concept that measures the strength of the relationship between two variables on a numeric scale.…