相关论文: Estimated VC dimension for risk bounds

We obtain the upper error bounds of robust estimators for mean vector, using the median-of-means (MOM) method. The method is designed to handle data with heavy tails and contamination, with only a finite second moment, which is weaker than…

The main purpose of this paper is to prove that the point-line incidence bound due to Vinh (2011) over arbitrary finite fields can be improved in certain ranges by using tools from the VC-dimension theory. As consequences, a number of…

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…

We present the first nearly optimal differentially private PAC learner for any concept class with VC dimension 1 and Littlestone dimension $d$. Our algorithm achieves the sample complexity of…

We propose a randomized algorithm for training Support vector machines(SVMs) on large datasets. By using ideas from Random projections we show that the combinatorial dimension of SVMs is $O({log} n)$ with high probability. This estimate of…

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic…

One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return…

The design, analysis and application of a volumetric convolutional neural network (VCNN) are studied in this work. Although many CNNs have been proposed in the literature, their design is empirical. In the design of the VCNN, we propose a…

Bayesian deep learning plays an important role especially for its ability evaluating epistemic uncertainty (EU). Due to computational complexity issues, approximation methods such as variational inference (VI) have been used in practice to…

This article deals with the generalization performance of margin multi-category classifiers, when minimal learnability hypotheses are made. In that context, the derivation of a guaranteed risk is based on the handling of capacity measures…

In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We…

Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…

Understanding minimal assumptions that enable learning and generalization is perhaps the central question of learning theory. Several celebrated results in statistical learning theory, such as the VC theorem and Littlestone's…

We control the probability of the uniform deviation between empirical and generalization performances of multi-category classifiers by an empirical L1 -norm covering number when these performances are defined on the basis of the truncated…

Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic…

Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…

We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an…

The geometric dimension $g$ of a Vector Addition System with States (VASS) is the dimension of the vector space generated by cycles in the VASS; this parameter refines the standard dimension $d$, the number of counters. Recently, it was…

We present here a PAC-Bayesian point of view on adaptive supervised classification. Using convex analysis, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior…

We study set systems definable in graphs using variants of logic with different expressive power. Our focus is on the notion of Vapnik-Chervonenkis density: the smallest possible degree of a polynomial bounding the cardinalities of…