Min- and Max-Entropy in Infinite Dimensions
نویسندگان
چکیده
منابع مشابه
Max-Margin Min-Entropy Models
We propose a new family of latent variable models called max-margin min-entropy (m3e) models, which define a distribution over the output and the hidden variables conditioned on the input. Given an input, an m3e model predicts the output with the smallest corresponding Rényi entropy of generalized distribution. This is equivalent to minimizing a score that consists of two terms: (i) the negativ...
متن کاملFirst-Order Algorithms for Generalized Semi-Infinite Min-Max Problems
We present a first-order algorithm for solving semi-infinite generalized min-max problems which consist of minimizing a function f0(x) = F (ψ1(x), ...., ψm(x)), where F is a smooth function and each ψi is the maximum of an infinite number of smooth functions. In Section 3.3 of [17] Polak finds a methodology for solving infinite dimensional problems by expanding them into an infinite sequence of...
متن کاملMin, Max, and Sum
This paper provides characterization theorems for preferences that can be represented by U(x1, ..., xn)=min{xk}, U(x1, ..., xn)=max{xk}, U(x1, ..., xn)=; u(xk), or combinations of these functionals. The main assumption is partial separability, where changing a common component of two vectors does not reverse strict preferences, but may turn strict preferences into indifference. We discuss appli...
متن کاملEntropy of infinite systems and transformations
The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...
متن کاملMax and min limiters
If A ⊆ ω, n ≥ 2, and the function max({x1, . . . , xn} ∩ A) is partial recursive, it is easily seen that A is recursive. In this paper, we weaken this hypothesis in various ways (and similarly for “min” in place of “max”) and investigate what effect this has on the complexity of A. We discover a sharp contrast between retraceable and coretraceable sets, and we characterize sets which are the un...
متن کاملذخیره 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: Communications in Mathematical Physics
سال: 2011
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-011-1282-1