相关论文: Estimated VC dimension for risk bounds

We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and…

One of the most studied problems in machine learning is finding reasonable constraints that guarantee the generalization of a learning algorithm. These constraints are usually expressed as some simplicity assumptions on the target. For…

We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…

Deep neural networks often contain far more parameters than training examples, yet they still manage to generalize well in practice. Classical complexity measures such as VC-dimension or PAC-Bayes bounds usually become vacuous in this…

In response to a 1997 problem of M. Vidyasagar, we state a necessary and sufficient condition for distribution-free PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain…

Explaining the unreasonable effectiveness of deep learning has eluded researchers around the globe. Various authors have described multiple metrics to evaluate the capacity of deep architectures. In this paper, we allude to the radius…

There has been growing interest in generalization performance of large multilayer neural networks that can be trained to achieve zero training error, while generalizing well on test data. This regime is known as 'second descent' and it…

A fundamental result of statistical learnig theory states that a concept class is PAC learnable if and only if it is a uniform Glivenko-Cantelli class if and only if the VC dimension of the class is finite. However, the theorem is only…

The capacity of a learning machine is measured by its Vapnik-Chervonenkis dimension, and learning machines with a low VC dimension generalize better. It is well known that the VC dimension of SVMs can be very large or unbounded, even though…

Visual representations of data (visualizations) are tools of great importance and widespread use in data analytics as they provide users visual insight to patterns in the observed data in a simple and effective way. However, since…

Following recent work on the VC-dimension of subsets of various pseudorandom graphs, we study the VC-dimension of Hamming graphs, which have proved somewhat resistant to the standard techniques in the literature. Our methods are elementary,…

Degrading performance of indexing schemes for exact similarity search in high dimensions has long since been linked to histograms of distributions of distances and other 1-Lipschitz functions getting concentrated. We discuss this…

The recently proposed Minimal Complexity Machine (MCM) finds a hyperplane classifier by minimizing an exact bound on the Vapnik-Chervonenkis (VC) dimension. The VC dimension measures the capacity of a learning machine, and a smaller VC…

The VC dimension measures the capacity of a learning machine, and a low VC dimension leads to good generalization. While SVMs produce state-of-the-art learning performance, it is well known that the VC dimension of a SVM can be unbounded;…

We investigate the VC-dimension of the perceptron and simple two-layer networks like the committee- and the parity-machine with weights restricted to values $\pm1$. For binary inputs, the VC-dimension is determined by atypical pattern sets,…

In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. The uniform Glivenko--Cantelli property…

The VC dimension of the Ising perceptron with binary patterns is calculated by numerical enumerations for system sizes N <= 31. It is significantly larger than N/2. The data suggest that there is probably no well defined asymptotic…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…

We investigate the Probably Approximately Correct (PAC) property of scenario decision algorithms, which refers to their ability to produce decisions with an arbitrarily low risk of violating unknown safety constraints, provided a sufficient…

The Vapnik-Chervonenkis dimension of a set K in R^n is the maximal dimension of the coordinate cube of a given size, which can be found in coordinate projections of K. We show that the VC dimension of a convex body governs its entropy. This…