Minimax Rates of Entropy Estimation on Large Alphabets via Best Polynomial Approximation
نویسندگان
چکیده
منابع مشابه
Minimax Polynomial Approximation
Some new methods for obtaining the minimax polynomial approximation of degree n to a continuous function are introduced, and applied to several simple functions. The amount of computation required is substantially reduced compared with that of previous methods.
متن کاملApproximating the entropy of large alphabets
We consider the problem of approximating the entropy of a discrete distribution P on a domain of size q, given access to n independent samples from the distribution. It is known that n ≥ q is necessary, in general for a good additive estimate of the entropy. A problem of multiplicative entropy estimate was recently addressed by Batu, Dasgupta, Kumar, and Rubinfeld. They show that n = q suffices...
متن کاملAn Approximation Error Lower Bound for Integer Polynomial Minimax Approximation
The need to solve a polynomial minimax approximation problem appears often in science. It is especially common in signal processing and in particular in filter design. The results presented in this paper originated from a study of the finite wordlength restriction in the FIR digital filter design problem. They are, however, much more general and can be applied to any polynomial minimax approxim...
متن کاملThe best uniform polynomial approximation of two classes of rational functions
In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.
متن کاملPermutation estimation and minimax rates of identifiability
The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical analysis of the accuracy of several natural estimators. To this end, the notion of the minimax rate of identifiability is introduced and its expression is ob...
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: IEEE Transactions on Information Theory
سال: 2016
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2016.2548468