Learning with Partially Labeled and Interdependent Data, 2015. ,
Probability inequalities for the sum of independent random variables, Journal of the American Statistical Association, vol.57, issue.297, pp.33-45, 1962. ,
On a modification of Chebyshev's inequality and of the error formula of Laplace, Ann. Sci. Inst. Sav. Ukraine, Sect. Math, vol.1, issue.4, pp.38-49, 1924. ,
Convex Optimization, 2004. ,
Basic properties of strong mixing conditions, a survey and some open questions, Probability Surveys, vol.2, issue.2, pp.107-144, 2005. ,
A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, The Annals of Mathematical Statistics, vol.23, issue.4, pp.493-507, 1952. ,
American mathematical society, vol.107, 2006. ,
, Handbook of Combinatorial Designs, 2010.
Learning Theory: An Approximation Theory Viewpoint, 2007. ,
Problems and results on 3-chromatic hypergraphs and some related questions. Infinite and finite sets, vol.10, pp.609-627, 1975. ,
On the v ? dimension for regression in reproducing kernel hilbert spaces, International Conference on Algorithmic Learning Theory, pp.106-117, 1999. ,
Logical Bayesian networks and their relation to other probabilistic logical models, Inductive Logic Programming, pp.121-135, 2005. ,
Learning probabilistic relational models, IJCAI, vol.99, pp.1300-1309, 1999. ,
Computers and Intractibility, A Guide to the Theory of NP-Completeness, 1979. ,
, Introduction to Statistical Relational Learning, 2007.
Classification with non-iid sampling, Mathematical and Computer Modelling, vol.54, issue.5, pp.1347-1364, 2011. ,
A class of statistics with asymptotically normal distributions, Annals of Statistics, vol.19, issue.3, pp.293-325, 1948. ,
Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association, vol.58, issue.301, pp.13-30, 1963. ,
Relational Bayesian networks, Proceedings of the Thirteenth Conference on Uncertainty in Artificial Intelligence, pp.266-273, 1997. ,
Large deviations for sums of partly dependent random variables, Random Structures & Algorithms, vol.24, issue.3, pp.234-248, 2004. ,
Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Mathematica, vol.30, issue.1, pp.175-193, 1906. ,
Economic networks, 2014. ,
Social networks: A developing paradigm, 2013. ,
Bootstrap procedures under some non-iid models, The Annals of Statistics, vol.16, issue.4, pp.1696-1708, 1988. ,
Learning to rank for information retrieval, Foundations and Trends® in Information Retrieval, vol.3, issue.3, pp.225-331, 2009. ,
Invitation to Discrete Mathematics, 1998. ,
Minimum complexity regression estimation with weakly dependent observations. Information Theory, IEEE Transactions on, vol.42, issue.6, pp.2133-2145, 1996. ,
Pagerank variants in the evaluation of citation networks, Journal of Informetrics, vol.8, issue.3, pp.683-692, 2014. ,
Entropy-Based Concentration Inequalities for Dependent Variables, Proceedings of the 32 nd International Conference on Machine Learning, pp.1-9, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01211199
Chromatic PAC-Bayes Bounds for Non-IID Data: Applications to Ranking and Stationary ?-Mixing Processes, Journal of Machine Learning Research, vol.11, pp.1927-1956, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00415162
Transforming graph data for statistical relational learning, Journal of Artificial Intelligence Research, vol.45, issue.1, pp.363-441, 2012. ,
Fractional graph theory: a rational approach to the theory of graphs, Courier Corporation, 2011. ,
Structural risk minimization over data dependent hierarchies. Information Theory, IEEE Transactions on, vol.44, issue.5, pp.1926-1940, 1998. ,
, First, since H is M -bounded, we have that ?M 2 ? g f (z) ? M 2 holds almost everywhere. It follows that |g f ? E z??