Part 1: In this problem we will examine randomized classifiers. Define, for any point x, a probabilty distribution q(c|x) over the class labels c. We define a randomized decision rule given by h r (x; q) = c r , for c r ∼ q(c|x). The risk R(h r ; q) for this classifier is given by the expectation over all possible outcomes such that R(h r ; q) = x C c=1 C c =1 L(c , c)q(c r = c |x)p(x, y = c)dx...

Effect modification occurs in biomedical research when a measure of statistical association between an exposure and a health outcome, as represented on some specific scale, differs according to the levels of a third variable—the effect modifier. The heterogeneity of a measure of association across the levels of a modifying variable has an importance that might be statistical, epidemiologic, and...

To the Editor: The Global Burden of Disease (GBD) collaborators (July 6 issue)1 report that more than two thirds of deaths related to high body-mass index (BMI) were due to cardiovascular disease, which suggests that BMI-defined obesity has a major effect on cardiovascular disease. Some readers may wonder whether the perceived burden of obesity could have been even larger if an accurate measure...

Let’s begin by briefly reviewing the Matlab routines required for VQ-based image compression. First, note that the VQ parameters are set on lines 13-19 of prob1.m. The general VQ framework is implemented by learnVQ.m, which uses the subroutine kmeans.m to implement the k-means algorithm. (Note that, as recommended, we use findnn.m and lpnorm.m within the k-means implementation to allow flexible...

Let’s begin by examining the general structure of trainSVM.m: the skeleton code which implements SVM training. On lines 20-23 the training samples in data are parsed. On lines 25-29 we evaluate an arbitrary kernel matrix (specified by the user as kernel with a single parameter param). Next, on lines 31-61 we apply Matlab’s built-in quadratic programming quadprog routine to determine the support...

"Migration and Mobility in the European Union." Journal of Contemporary Studies, 30(1), pp. 194–195

Experiments: Single molecule Jarzynski [71]; single molecule fluctuation theorems [170]; Hatano and Sasa with optically trapped colloid particle [116]; optically trapped colloid particle, time varying spring constant [100]. Model systems for which the work distributions can be computed analytically: harmonic potentials [41], two level systems [75, 120], ideal gas compression [133, 146, 169, 195...