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...

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 last 30 years have seen enormous progress in the design of algorithms, but comparatively little of it has been put into practice, even within academic laboratories. Indeed, the gap between theory and practice has continuously widened over these years. Moreover, many of the recently developed algorithms are very hard to characterize theoretically and, as initially described, suffer from larg...

For a given test criterion, the number of test-sets satisfying the criterion may be very large, with varying fault detection effectiveness. In recent work [29], the measure of variation in effectiveness of test criterion was defined as ‘tolerance’. This paper presents an experimental evaluation of tolerance for control-flow test criteria. The experimental analysis is done by exhaustive test-set...

This article focuses on the under-researched temporary agency employment in Greece. It shows that the development of the temporary employment agency sector has gone hand in hand with the flow of undocumented and exploitable migrant labour in Greece over the past 25 years, reflecting the segmentation of the Greek labour market along ethnic lines. Using empirical research evidence on the operatio...

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 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...