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...

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...

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...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...