By Richard Arum, Josipa Roksa

In spite of hovering institution charges, a growing number of scholars visit collage each year. A bachelor’s measure is now required for access right into a growing to be variety of professions. and a few mom and dad start making plans for the price of sending their teenagers to varsity whilst they’re born. virtually each person strives to head, yet nearly nobody asks the elemental query posed by means of *Academically Adrift*: are undergraduates rather studying something when they get there?

For a wide share of scholars, Richard Arum and Josipa Roksa’s resolution to that query is a definitive no. Their large examine attracts on survey responses, transcript info, and, for the 1st time, the state of the art Collegiate studying evaluation, a standardized attempt administered to scholars of their first semester after which back on the finish in their moment yr. in response to their research of greater than 2,300 undergraduates at twenty-four associations, forty five percentage of those scholars show no major development in a number of skills—including serious considering, advanced reasoning, and writing—during their first years of faculty. As troubling as their findings are, Arum and Roksa argue that for lots of college and directors they are going to come as no surprise—instead, they're the anticipated results of a pupil physique distracted via socializing or operating and an institutional tradition that places undergraduate studying with regards to the ground of the concern list.

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Academically Adrift* holds sobering classes for college kids, school, directors, coverage makers, and parents—all of whom are implicated in selling or at the very least ignoring modern campus tradition. greater schooling faces crises on a few fronts, yet Arum and Roksa’s record that schools are failing at their most elementary challenge will call for the eye people all.

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N and μ1 + μ2 + · · · + μn = 1. Let μ = (μ1 , μ2 , . . , μn ). If n ≤ k or k ≤ 1 there is a trivial unique minimizer. Hence we assume that n > k ≥ 2. For a sample S of size m, we denote the number of occurrences of the point xi in S by mi , and use wi = mi /m to denote the empirical frequency (weight ) of the point xi in the sample. The sample is completely determined by the vector of weights w = (w1 , w2 , . . , wn ) . Since the support of P is ﬁnite, there are only ﬁnitely many partitions of F .

M ˜ 0 − d−1 κ x ∈ Iq˜} + (Lq˜ − Lq˜)1{˜ κ + tN M −(d−1)/κ }d−1 = O M d−1 M −α M − =O κ M −α + tN κ d−1 κ + tN M −(d−1)/κ + M −1 κ κ κ ⎞ ⎞ ⎠ + O(M −1 ) ⎠ + O(M −1 ) + O(M −1 ) . Plugging in the choices of M and N given in the theorem statement we obtain ακ R(Gn ) − R(G∗ ) = O (log n/n) α(2κ−2)+d−1 ακ Finally, noticing that 1 − Pr(Ωn ) = O n− α(2κ−2)+d−1 ακ . we have E[R(Gn )] − R(G∗ ) ≤ O (log n/n) α(2κ−2)+d−1 Pr(Ωn ) + 1 · (1 − Pr(Ωn )) ακ = O (log n/n) α(2κ−2)+d−1 concluding the proof. , Stability of k-Means Clustering Shai Ben-David1 , D´ avid P´ al1 , and Hans Ulrich Simon2,⋆ 1 David R.

2 Definitions and Notation Consider the problem of predicting a binary label y based on its corresponding input vector x. As in the standard machine learning formulation, we assume that the data points (x, y) are drawn from an unknown underlying distribution P over X × Y ; X is called the instance space and Y is the label space. In this paper we assume that Y = {±1}. Our goal is to find a classifier f with the property that its expected true loss of err(f ) is as small as possible. Here we assume err(f ) = E(x,y)∼P [ℓ(f (x), y)], where we use E(x,y)∼P to denote the expectation with respect to the true (but unknown) underlying distribution P .