Let F be a finite model of cardinality M and denote by conv(F ) its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over conv(F ). Consider the bounded regression model with respect to the squared risk denoted by R(·). If f̂ n denotes the empirical risk minimization procedure over conv(F ) then we prove that for an...

Let F be a finite model of cardinality M and denote by conv(F ) its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over conv(F ). Consider the bounded regression model with respect to the squared risk denoted by R(·). If f̂ ERM-C n denotes the empirical risk minimization procedure over conv(F ), then we prove that...

The measurement and prediction of software reliability require the use of the Software Reliability Growth Models (SRGMs). The predictive quality can be measured by the average end-point projection error [9]. In this paper, the e ects of two orthogonal classes of approaches to improve prediction capability of a SRM have been examined using a large number of data sets. The rst approach is preproc...

To say that positive political theory (PPT) scholarship on the hierarchy of justice is theory rich and data poor is to make a rather uncontroversial claim. For over a decade now, scholars have offered intriguing theoretical accounts aimed at understanding why lower courts defy (comply with) higher courts. But only rarely do they subject the accounts to rigorous empirical interrogation. The chie...

In this paper, we introduce a method of designing optimal time}frequency detectors from training samples, which is potentially of great bene"t when few a priori information on the nonstationary signal to be detected is available. However, achieving good performance with data-driven detectors requires matching their complexity to the available amount of training samples: receivers with a too lar...

In the previous class, we had described a universal learning algorithm, called ERM (Empirical Risk Minimization). Under the ERM principle, we want to learn a function f , and we are promised that this function belongs to the function class H. We are given a training set S, and the ERM algorithm returns a function h ∈ H that minimizes the error on the training sample. That is, h = argming∈H errS...

2 ) converges to zero in probability. Hence, even in the case of multiple minimizers of expected error, as n increases it becomes less and less likely that adding a sample (or a number of samples) to the training set will result in a large jump to a new hypothesis. Moreover, under some assumptions on the entropy of the class, along with an assumption of Komlos-Major-Tusnady type, we derive a po...

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classi…cation framework. We extend Tsybakov’s analysis of the risk of an ERM under margin type conditions by using concentration inequalities for conveniently weighted empirical processes. This allows us to deal with other ways of measuring the ”size”of a clas...

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functions whose growth function is polynomial in the sample size n. The bounds lead us to consider sample variance penalization, a novel learning method which takes into account the empirical variance of the lo...

SAS@offers the option of using hiperspaces as the standard WORK file under MVS/ESA” as a performance en.tiancement. This paper introduces hiperspaces under MVS, and the applicable SAS options to invoke hiperspace use. Also, attention is given to tuning the use of hiperspaces within MVS (i.e. MVS’5 SRM parameters). Performance gains can be astonishing with little or no work on the part of the us...