Beyond N formalism

Beyond Word N-Grams

We describe, analyze, and experimentally evaluate a new probabilistic model for wordsequence prediction in natural languages, based on prediction suffi~v trees (PSTs). By using efficient data structures, we extend the notion of PST to unbounded vocabularies. We also show how to use a Bayesian approach based on recursive priors over all possible PSTs to efficiently maintain tree mixtures. These ...

Beyond N in N-gram Tagging

The Hidden Markov Model (HMM) for part-of-speech (POS) tagging is typically based on tag trigrams. As such it models local context but not global context, leaving long-distance syntactic relations unrepresented. Using n-gram models for n > 3 in order to incorporate global context is problematic as the tag sequences corresponding to higher order models will become increasingly rare in training d...

Reduction formalism for dimensionally regulated one - loop N - point integrals

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional external momenta to box integrals in (4 − 2ǫ) dimensions. We derive a formula valid for arbitrary N and give an explicit expression for N = 6. Further a tensor red...

Inductive Pairwise Ranking: Going Beyond the n log(n) Barrier

We study the problem of ranking a set of items from nonactively chosen pairwise preferences where each item has feature information with it. We propose and characterize a very broad class of preference matrices giving rise to the Feature Low Rank (FLR) model, which subsumes several models ranging from the classic Bradley–Terry–Luce (BTL) (Bradley and Terry 1952) and Thurstone (Thurstone 1927) m...

BEYOND PROBABILITY 1 Running head: BEYOND PROBABILITY The N-Effect: Beyond Winning Probabilities