Fano’s inequality is a mistake
نویسنده
چکیده
for every i. One can remark that for the first time, these inequalities were indicated by Margherita Piazzola-Beloch in [1]. She was a pupil of G. Castelnuovo, her paper presents the text of her thesis , G. Castelnuovo was the adviser of the thesis. Thus all (including G. Fano ) the subsequent authors of the variants or generalizations of the Fano inequality are out of the historical responsibility for the mistake explained below.
منابع مشابه
Arimoto-Rényi conditional entropy and Bayesian hypothesis testing
This paper gives upper and lower bounds on the minimum error probability of Bayesian M -ary hypothesis testing in terms of the Arimoto-Rényi conditional entropy of an arbitrary order α. The improved tightness of these bounds over their specialized versions with the Shannon conditional entropy (α = 1) is demonstrated. In particular, in the case where M is finite, we show how to generalize Fano’s...
متن کاملFano’s inequality is false for a simple Cremona transformation of five-dimensional projective space
A Cremona transformation of five-dimensional projective space is constructed. The degree of the transformation is 7. The inequalities of Fano are not fulfilled for this transformation. MSC : 14E07. Acknowledgement. I would like to thank Miles Reid for helpful correspondence on the subject. Introduction It was shown in [3] and [4] that Fano’s inequalities are false for tree-dimensional projectiv...
متن کاملEqual-image-size source partitioning: Creating strong Fano's inequalities for multi-terminal discrete memoryless channels
This paper introduces equal-image-size source partitioning, a new tool for analyzing channel and joint source-channel coding in a multi-terminal discrete memoryless channel environment. Equal-image-size source partitioning divides the source (combination of messages and codewords) into a sub-exponential number of subsets. Over each of these subsets, the exponential orders of the minimum image s...
متن کاملDistance-based and continuum Fano inequalities with applications to statistical estimation
In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano’s inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a discrete quantity is within some distance t of the quantity. The second inequality extends our bound to a continuum setting and provides a volume-based bound. We i...
متن کاملA strong converse bound for multiple hypothesis testing, with applications to high-dimensional estimation
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to do this involves the use of Fano’s inequality. However, recent work in an information-theoretic setting has shown that an argument based on binary hypothesis testing gives tighter converse results (error lower bounds) than Fan...
متن کامل