Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is poorly understood. In a seminal paper, Bickel and Levina [Bernoulli 10 (2004) 989–1010] show that the Fisher discriminant performs poorly due to diverging spectra ...

Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is largely poorly understood. In a seminal paper, Bickel and Levina (2004) show that the Fisher discriminant performs poorly due to diverging spectra and they propose...

We examine patterns of human choice in a passphrase-based authentication system deployed by Amazon, a large online merchant. We tested the availability of a large corpus of over 100,000 possible phrases at Amazon’s registration page, which prohibits using any phrase already registered by another user. A number of large, readily-available lists such as movie and book titles prove effective in gu...

We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can be solved by a quantum algorithm using a single query; we show that such infinity-vs-one separations between classical and quantum query complexities can be c...

The most basic property of the boosting algorithm is its ability to reduce the training error, subject to the critical assumption that the base learners generate weak hypotheses that are better that random guessing. We exploit analogies between regression and classiication to give a characterization on what base learners generate weak hypotheses, by introducing a geometric concept called the an...

Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is largely poorly understood. In a seminal paper, Bickel and Levina (2004) show that the Fisher discriminant performs poorly due to diverging spectra and they propose...

Witsenhausen's hyperbola bound for the multiple description problem without excess rate in case of a binary source is not right for exact joint reproductions. However, this bound is tight for almost{exact joint reproductions (Theorem 1, conjectured by Witsenhausen). The proof is based on an approximative form of the team guessing lemma for sequences of random variables. (This result may be of i...

We consider the problem of inferring an ancestral state from observations at leaves a tree, assuming evolves along tree according to two-state symmetric Markov process. establish general branching rate condition under which maximum parsimony, common reconstruction method requiring only knowledge topology (but not substitution rates or other parameters), succeeds better than random guessing unif...

The notion of public key encryption with keyword search (PEKS) was put forth by Boneh et al. to enable a server to search from a collection of encrypted emails given a “trapdoor” (i.e., an encrypted keyword) provided by the receiver. The nice property in this scheme allows the server to search for a keyword, given the trapdoor. Hence, the verifier can merely use an untrusted server, which makes...