Probabilistic setting of information-based complexity

We study the probabilistic (E, b)-complexity for linear problems equipped with Gaussian measures. The probabilistic (E, S)-complexity, comp@“˜(e, 6), is understood as the minimal cost required to compute approximations with error at most e on a set of measure at least 1 - 6. We find estimates of comp@(e, 6) in terms of eigenvalues of the correlation operator of the Gaussian measure over elements which we want to approximate. In particular, we study the approximation and integration problems. The approximation problem is studied for functions of d variables which are continuous after r times differentiation with respect to each variable. For the Wiener measure placed on rth derivatives, the probabilistic comp@(e, S) is estimated by ,((~/,)“(r+~)(ln(~/~))(d-“˜“r+““r‘+~‘), where a = 1 for the lower bound and a = 0.5 for the upper bound. The integration problem is studied for the same class of functions with d = 1. In this case, compPmb(e,6 ) = @((m/E)“@““˜)

The accessibility dimension for structured document retrieval

Structured document retrieval aims at retrieving the document components that best satisfy a query, instead of merely retrieving pre-defined document units. This paper reports on an investigation of a tf-idf-acc approach, where tf and idf are the classical term frequency and inverse document frequency, and acc, a new parameter called accessibility, that captures the structure of documents. The tf-idf-acc approach is defined using a probabilistic relational algebra. To investigate the retrieval quality and estimate the acc values, we developed a method that automatically constructs diverse test collections of structured documents from a standard test collection, with which experiments were carried out. The analysis of the experiments provides estimates of the acc values