37,690 research outputs found
Maximal theorems and square functions for analytic operators on Lp-spaces
Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity,
and assume that T is analytic, that is, there exists a constant K such that
n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T
is positive (or contractively regular), we establish the boundedness of various
Littlewood-Paley square functions associated with T. As a consequence we show
maximal inequalities of the form \norm{\sup_{n\geq 0}\, (n+1)^m\bigl
|T^n(T-I)^m(x) \bigr |}_p\,\lesssim\, \norm{x}_p, for any nonnegative integer
m. We prove similar results in the context of noncommutative Lp-spaces. We also
give analogs of these maximal inequalities for bounded analytic semigroups, as
well as applications to R-boundedness properties
Strong q-variation inequalities for analytic semigroups
Let T : Lp --> Lp be a positive contraction, with p strictly between 1 and
infinity. Assume that T is analytic, that is, there exists a constant K such
that \norm{T^n-T^{n-1}} < K/n for any positive integer n. Let q strictly
betweeen 2 and infinity and let v^q be the space of all complex sequences with
a finite strong q-variation. We show that for any x in Lp, the sequence
([T^n(x)](\lambda))_{n\geq 0} belongs to v^q for almost every \lambda, with an
estimate \norm{(T^n(x))_{n\geq 0}}_{Lp(v^q)}\leq C\norm{x}_p. If we remove the
analyticity assumption, we obtain a similar estimate for the ergodic averages
of T instead of the powers of T. We also obtain similar results for strongly
continuous semigroups of positive contractions on Lp-spaces
NPRF: A Neural Pseudo Relevance Feedback Framework for Ad-hoc Information Retrieval
Pseudo-relevance feedback (PRF) is commonly used to boost the performance of
traditional information retrieval (IR) models by using top-ranked documents to
identify and weight new query terms, thereby reducing the effect of
query-document vocabulary mismatches. While neural retrieval models have
recently demonstrated strong results for ad-hoc retrieval, combining them with
PRF is not straightforward due to incompatibilities between existing PRF
approaches and neural architectures. To bridge this gap, we propose an
end-to-end neural PRF framework that can be used with existing neural IR models
by embedding different neural models as building blocks. Extensive experiments
on two standard test collections confirm the effectiveness of the proposed NPRF
framework in improving the performance of two state-of-the-art neural IR
models.Comment: Full paper in EMNLP 201
Document Clustering Based On Max-Correntropy Non-Negative Matrix Factorization
Nonnegative matrix factorization (NMF) has been successfully applied to many
areas for classification and clustering. Commonly-used NMF algorithms mainly
target on minimizing the distance or Kullback-Leibler (KL) divergence,
which may not be suitable for nonlinear case. In this paper, we propose a new
decomposition method by maximizing the correntropy between the original and the
product of two low-rank matrices for document clustering. This method also
allows us to learn the new basis vectors of the semantic feature space from the
data. To our knowledge, we haven't seen any work has been done by maximizing
correntropy in NMF to cluster high dimensional document data. Our experiment
results show the supremacy of our proposed method over other variants of NMF
algorithm on Reuters21578 and TDT2 databasets.Comment: International Conference of Machine Learning and Cybernetics (ICMLC)
201
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