Weak Dimension-Free Concentration of Measure
نویسندگان
چکیده
منابع مشابه
Measure Concentration and the Weak Pinsker Property
Let pX,μq be a standard probability space. An automorphism T of this space has the weak Pinsker property if for every ε ą 0 it is isomorphic to a direct product of a Bernoulli shift and an automorphism of entropy less than ε. This property was introduced by Thouvenot, who conjectured that it holds for all measure-preserving systems. This paper proves Thouvenot’s conjecture. The proof applies wi...
متن کاملDimension-free Information Concentration via Exp-Concavity
Information concentration of probability measures have important implications in learning theory. Recently, it is discovered that the information content of a log-concave distribution concentrates around their differential entropy, albeit with an unpleasant dependence on the ambient dimension. In this work, we prove that if the potentials of the log-concave distribution are exp-concave, which i...
متن کاملDimension-free Concentration Bounds on Hankel Matrices for Spectral Learning
Learning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an unknown target distribution. These methods rely on a singular value decomposition of a matrix HS , called the Hankel matrix, that records the frequencies of (s...
متن کاملWeak Measure Extension Axioms
We consider axioms asserting that Lebesgue measure on the real line may be extended to measure a few new non-measurable sets. Strong versions of such axioms, such as real-valued measurability, involve large cardinals, but weak versions do not. We discuss weak versions which are suucient to prove various combinatorial results, such as the non-existence of Ramsey ultraalters, the existence of ccc...
متن کاملdedekind modules and dimension of modules
در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bernoulli
سال: 2000
ISSN: 1350-7265
DOI: 10.2307/3318510