The paper presents an efficient computational method for estimating the tails of a target variable Z which is related to other set of bounded variables X = (Xi,. . . , X,) by an increasing (decreasing) relation Z = h( XI, . . . , X,). To this aim, variables Xi, i = 1,. . . , n are sequentially simulated in such a manner that Z = h( xi, . . . , xi-i, Xi, . . . ,X,) is guaranteed to be in the tai...

For each integer m ≥ 1, consider the graph Gm whose vertex set is the set N = {0, 1, 2, . . . } of natural numbers and whose edges are the pairs xy with y = x + m or y = x − m or y = mx or y = x/m. Our aim in this note is to show that, for each m, the graph Gm contains a Hamilton path. This answers a question of Lichiardopol. For each integer m ≥ 1, consider the graph Gm whose vertex set is the...

There is an error in “Stability and Hypothesis Transfer Learning” (Kuzborskij & Orabona, 2013) which appeared in proceedings of ICML 2013. The Leave-One-Out generalization bound for Hypothesis Transfer Learning algorithm through Regularized Least Squares with biased regularization does not have the right convergence rate with respect to the regularization parameter λ and the source risk on the ...

cov(Xi, Xj) := E(Xi − E(Xi))(Xj − E(Xj)), and cov(X) is the d×d symmetric positive semi-definite (psd) matrix whose (i, j)-th entry is cov(Xi, Xj). For now, we’ll define quantities and procedures with respect to cov(X), even though typically in practice, cov(X) can only be estimated (and we’ll come back to estimation issues later). One may also view X as being uniformly distributed over the dat...

What happens if the Xi ’s take values in a (real) Banach space (B, ‖ · ‖)? In such cases, in particular when the square of the norm ‖ · ‖ is not given by an inner product, we are aiming at inequalities of the following type: Let X1, X2, . . . , Xn be independent random vectors with values in (B, ‖ · ‖) with EXi = 0 and E‖Xi‖2 < ∞. With Sn := ∑n i=1 Xi we want to show that E‖Sn‖ ≤ K n ∑ i=1 E‖Xi...

We report the observation and measurement of the mass of the bottom, strange baryon Xi(b)- through the decay chain Xi(b)- -->J/psiXi-, where J/psi-->mu+mu-, Xi- -->Lambdapi-, and Lambda-->ppi-. A signal is observed whose probability of arising from a background fluctuation is 6.6 x 10(-15), or 7.7 Gaussian standard deviations. The Xi(b)- mass is measured to be 5792.9+/-2.5(stat) +/- 1.7(syst) M...

This supplemental material gives the extended definitions of the tuple operations, lists the definition of some transformation operators, details the examples about DEVIATION, SEQBIN, and LONGESTPLATEAU, and describes the experimental protocol for the experiments. 1 Extended Definitions of Tuple Operations The projection 〈vi1 , . . . , vik〉 of a tuple 〈v1, . . . , vn〉 onto a subset of its compo...

For this problem we assume that the set of training examples {(xi, yi)} are drawn from two classes such that yi = ±1. For such two-class classifcation problems, the form of yihm(xi) is particularly simple; if an example is correctly classified, then yihm(xi) = 1. If an example is misclassified, then yihm(xi) = −1. As a result, Equation 3 can be decomposed as Zm = W (m−1) + e −αm + W (m−1) − e α...

Let Xi,j , i, j = 1, ..., n, be independent, not necessarily identically distributed random variables with finite first moments. We show that the norm of the random matrix (Xi,j) n i,j=1 is up to a logarithmic factor of the order of E max i=1,...,n ∥∥(Xi,j)nj=1∥∥2 +E max i=1,...,n ∥∥(Xi,j)nj=1∥∥2 . This extends (and improves in most cases) the previous results of Seginer and Latała.

x ∈ Σ∗ is a sequence from the alphabet Σ, xi is the ith symbol, where p(xi) is a distribution over Σ independent of i. (Actually, a full model of the empirical distribution would also have to include a model of the length distribution P (n). But let’s neglect that.) On his third level, he distinguished different p(xi) for different parts of the sequence. Distinguishing different p(xi) for every...