Distribution-free bounds for relational classification

Abstract

Statistical Relational Learning (SRL) is a sub-area in Machine Learning which addresses the problem of performing statistical inference on data that is correlated and not independently and identically distributed (i.i.d.) -as is generally assumed. For the traditional i.i.d. setting, distribution free bounds exist, such as the Hoeffding bound, which are used to provide confidence bounds on the generalization error of a classification algorithm given its hold-out error on a sample size of N . Bounds of this form are currently not present for the type of interactions that are considered in the data by relational classification algorithms. In this paper we extend the Hoeffding bounds to the relational setting. In particular, we derive distribution free bounds for certain classes of data generation models that do not produce i.i.d. data and are based on the type of interactions that are considered by relational classification algorithms that have been developed in SRL. We conduct empirical studies on synthetic and real data which show that these data generation models are indeed realistic and the derived bounds are tight enough for practical use.

Single Network Relational Transductive Learning

“…In such cases, standard relational learning strategies such as collapsing portions of the graph and using aggregation can be applied to reduce to a graph with a single type of node with attributes (Getoor & Taskar, 2007;Dhurandhar & Dobra, 2012). To this new graph the above extended procedure can be applied.…”

A Dependence Stability Bound based on the VC Dimension for Relational Classification

“…However, the Hoeffding bound cannot be directly used on relational data. To overcome this restriction, Dhurandhar and Dobra proposed a distributionfree bound on the generalization error of a non-i.i.d classifier [9][10]. Our study is based on this bound.…”

“…Each independent subgraph is connected. Based on this observation, Dhurandhar and Dobra proposed two measures to characterize the data relation [9][10]: the number of independent subsets k in the range [1 ] N  ( N is number of object in data), and the dependence strength d [1], which measures the dependence of every subset in the range [0 1]  .  The number of independent subsets k capture the subset (subgraphs) property of the object.…”

Online learning of event definitions

“…However, its usage for learning relational models is limited. One reason is that it requires independence of observations, which cannot always be ensured in relational domains, due to dependencies in the data (Jensen 1999;Jensen and Neville 2002;Hulten et al 2003;Dhurandhar and Dobra 2012). An ILP approach that uses the Hoeffding bound for relational learning is HTILDE (Lopes and Zaverucha 2009), an extension of the TILDE system for learning first-order decision trees (Blockeel and De Raedt 1998).…”

“…OLED uses the Hoeffding bound (Hoeffding 1963), a statistical tool that allows to build decision models using only a small subset of the data, by relating the size of this subset to a user-defined confidence level on the error margin of not making a (globally) optimal decision (Dhurandhar and Dobra 2012;Domingos and Hulten 2000;Gama et al 2011). OLED learns a clause in a top-down fashion, by gradually adding literals to its body.…”