Developed in this article are theories of the so-called linear estimation techniques. The methods are exclusively based on the space-time empirical orthogonal functions which describe nonuniform covariance statistics of background uctuations of investigated variable. Two speciic methods to be discussed are the detection and the estimation algorithms with speciic emphasis on the description of e...

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...

OBJECTIVES To review the extant literature on HIV criminal laws, and to determine the impact of these laws on public health practice. METHODS The available research on this topic was obtained and reviewed. RESULTS The extant literature addressed three main topics: people's awareness of HIV criminal laws; people's perceptions of HIV criminal laws; and the potential effects of HIV criminal la...

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...

Higher education has recently faced new challenges and responsibilities such as higher expectations to contribute to national and regional developments; considerable cuts in public funds, and the highly competitive educational markets. Previous research has suggested a positive association between development of human capitals in higher education institutions and their capacity to deal with the...

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...