The previous lecture defined the Nearest Neighbor Algorithm and discussed how it suffers from the curse of dimensionality. This means that as the number of dimensions increase the Nearest Neighbor algorithm performs poorer and poorer. To better understand the curse of dimensionality with regard to the Nearest Neighbor algorithm one must understand what higher dimensions look like. The following...

The dot sign means inner product. If b is forced to be 0, the VC-dimension reduces to n. It is often the case that the VC-dimension is equal to the number of free parameters of a concept (for example, a rectangle’s parameters are its topmost, bottommost, leftmost and rightmost bounds, and its VC-dimension is 4). However, it is not always true; there exists concepts with 1 parameter but an infin...

These are edited lecture notes from a graduate course at the Computer Science department of Princeton University in Fall 2002. The course was my attempt to teach first year graduate students students many mathematical tools useful in theoretical computer science. Of course, the goal was too ambitious for a course with 12 three hour lectures. I had to relegate some topics to homework; these incl...

In linear regression, we need to avoid adding too much richness to the model. Therefore we need feature selection, or regularization to make our fitting curve smoother. Qualitatively, the original linear regression model is an optimization problem of the form min w m i=1 (w · x i − y i) 2 And the corresponding regularized version of the same problem is min w m i=1 (w · x i − y i) 2 + λw 2 2 , w...

In the last few lectures, we talked about various kinds of online learning problems. We started with the simplest case in which there is a perfect expert, who is always right. In the last lecture, we generalize this into the case in which we might not have a “perfect expert”, but instead we have a panel or subcommittee of experts, whose combined prediction is always right. We also introduced th...

BACKGROUND A COS represents an agreed minimum set of outcomes that should be measured and reported in all trials of a specific condition. The COMET (Core Outcome Measures in Effectiveness Trials) initiative aims to collate and stimulate the development and application of COS, by including data on relevant studies within a publically available internet-based resource. In recent years, there has ...

We investigate the effect of the Rashba interaction on two dimensional superconductivity. The presence of the Rashba interaction lifts the spin degeneracy and gives rise to the spectrum of two bands. There are intraband and interband pairs scattering which result in the coupled gap equations. We find that there are isotropic and anisotropic components in the gap function. The latter has the for...

Background A systematic review of core outcome sets (COS) identified 198 COS [1]. A range of methods were used to develop COS. Furthermore, 164/178 studies that described the methods used did not provide an explanation regarding their choice of methodology. There is little guidance about how to conduct or report COS studies and it is currently uncertain which of these methods are the most suita...

abstract leafy vegetables such as lettuce are more susceptible to post harvest losses, thus application desirable treatments can be recommendable. generally, type of packaging, such as modified atmosphere packaging (map) and wrapping can considerably suppress post harvest loss of horticultural products. in this study, the effects of polypropylene film (thickness 30 and 40 micron) wrapping and m...