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60
On kerneltarget alignment
 Advances in Neural Information Processing Systems 14
, 2002
"... Editor: Kernel based methods are increasingly being used for data modeling because of their conceptual simplicity and outstanding performance on many tasks. However, the kernel function is often chosen using trialanderror heuristics. In this paper we address the problem of measuring the degree of ..."
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Cited by 290 (8 self)
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Editor: Kernel based methods are increasingly being used for data modeling because of their conceptual simplicity and outstanding performance on many tasks. However, the kernel function is often chosen using trialanderror heuristics. In this paper we address the problem of measuring the degree of agreement between a kernel and a learning task. A quantitative measure of agreement is important from both a theoretical and practical point of view. We propose a quantity to capture this notion, which we call Alignment. We study its theoretical properties, and derive a series of simple algorithms for adapting a kernel to the labels and vice versa. This produces a series of novel methods for clustering and transduction, kernel combination and kernel selection. The algorithms are tested on two publicly available datasets and are shown to exhibit good performance.
Randomized distributed edge coloring via an extension of the ChernoffHoeffding bounds
 SIAM Journal on Computing
, 1997
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Generating Random Regular Graphs Quickly
, 1999
"... this paper we examine an algorithm which, although it does not generate uniformly at random, is provably close to a uniform generator when the degrees are relatively small. Moreover, it is easy to implement and quite fast in practice. The most interesting case is the regular one, when all degrees ar ..."
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Cited by 56 (2 self)
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this paper we examine an algorithm which, although it does not generate uniformly at random, is provably close to a uniform generator when the degrees are relatively small. Moreover, it is easy to implement and quite fast in practice. The most interesting case is the regular one, when all degrees are equal to d = d(n) say. Moreover, methods for the regular case of this problem usually extend to arbitrary degree sequences, although the analysis can become more complicated and it may be needed to impose restrictions on the variation in the degrees (such as is analyzed by Jerrum et al. [4]). The rst algorithm for generating dregular graphs uniformly at random was implicit in the paper of Bollobas [2] and also in the approaches to counting regular graphs by Bender and Caneld [1] and in [13] (see also [14] for explicit algorithms). The
A sharp threshold in proof complexity
 PROCEEDINGS OF STOC 2001
, 2001
"... We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small � and � � �, random formulas consisting of 2clauses and 3clauses, which are known to be unsatisfiable almost certainly, almost certainly require resolution and DavisPutnam ..."
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Cited by 54 (14 self)
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We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small � and � � �, random formulas consisting of 2clauses and 3clauses, which are known to be unsatisfiable almost certainly, almost certainly require resolution and DavisPutnam proofs of unsatisfiability of exponential size, whereas it is easily seen that random formulas with 2clauses (and 3clauses) have linear size proofs of unsatisfiability almost certainly. A consequence of our result also yields the first proof that typical random 3CNF formulas at ratios below the generally accepted range of the satisfiability threshold (and thus expected to be satisfiable almost certainly) cause natural DavisPutnam algorithms to take exponential time to find satisfying assignments.
AlmostEverywhere Algorithmic Stability and Generalization Error
 In UAI2002: Uncertainty in Artificial Intelligence
, 2002
"... We introduce a new notion of algorithmic stability, which we call training stability. ..."
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Cited by 54 (8 self)
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We introduce a new notion of algorithmic stability, which we call training stability.
Concentration inequalities using the entropy method
"... We investigate a new methodology, worked out by Ledoux and Massart, to prove concentrationofmeasure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We provide some very simple and general readytouse inequalities. One of these inequalities may be considered ..."
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Cited by 54 (3 self)
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We investigate a new methodology, worked out by Ledoux and Massart, to prove concentrationofmeasure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We provide some very simple and general readytouse inequalities. One of these inequalities may be considered as an exponential version of the EfronStein inequality. The main purpose of this paper is to point out the simplicity and the generality of the approach. We show how the new method can recover many of Talagrand’s revolutionary inequalities and provide new applications in a variety of problems including Rademacher averages, Rademacher chaos, the number of certain small subgraphs in a random graph, and the minimum of the empirical risk in some statistical estimation problems.
On the Spanning Ratio of Gabriel Graphs and βSkeletons
, 2001
"... The spanning ratio of a graph de ned on n points in the Euclidean plane is the maximal ratio over all pairs of data points (u; v), of the minimum graph distance between u and v, over the Euclidean distance between u and v. A connected graph is said to be a kspanner if the spanning ratio does n ..."
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Cited by 50 (0 self)
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The spanning ratio of a graph de ned on n points in the Euclidean plane is the maximal ratio over all pairs of data points (u; v), of the minimum graph distance between u and v, over the Euclidean distance between u and v. A connected graph is said to be a kspanner if the spanning ratio does not exceed k. For example, for any k, there exists a point set whose minimum spanning tree is not a kspanner. At the other end of the spectrum, a Delaunay triangulation is guaranteed to be a 2:42spanner [11]. For proximity graphs inbetween these two extremes, such as Gabriel graphs[8], relative neighborhood graphs[16] and skeletons[12] with 2 [0; 2] some interesting questions arise. We show that the spanning ratio for Gabriel graphs (which are skeletons with = 1) is ( in the worst case. For all skeletons with 2 [0; 1], we prove that the spanning ratio is at most O(n ) where = (1 log 2 (1 + ))=2.
Risk bounds for Statistical Learning
"... 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 weig ..."
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Cited by 50 (2 self)
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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 class of classi…ers than entropy with bracketing as in Tsybakov’s work. In particular we derive new risk bounds for the ERM when the classi…cation rules belong to some VCclass under margin conditions and discuss the optimality of those bounds in a minimax sense.