Corrections to "Blind source separation using renyi's mutual information"
IEEE Signal Processing Letters · 2003
In the above paper [1], the authors have found that it contains an incorrect statement. The introductory section includes the sentence “However, both (1) and (2) are nonnegative [6], and both evaluate to zero when and only when the joint PDF can be written as a product of the marginals. ” As it is written, reference [6] in the letter appears to apply to both (1) and (2); however, it should only apply to (1). Furthermore, the previously held belief that the estimator of Renyi’s Mutual Information, given by (2), can never be negative has since been determined to be in error. This is the case, for example, for sub-Gaussian sources. Although it has been proven that (2) has a minimum value of zero for the case that there are two Laplacian sources, there is no known proof that generalizes this result for any combination of super-Gaussian sources and/or for any number of sources. It does appear that, for sub-Gaussian sources, there is a local minimum at the location corresponding to separation (which evaluates to zero), but it may not be the global minimum. Therefore, the sentence above should be corrected to read “... (1) is nonnegative and evaluates to zero when and only when the joint PDF can be written as a product of the marginals [6]. In addition, for super-Gaussian sources there is experimental evidence that (2) is also nonnegative and evaluates to zero only when the joint PDF can be written as a product of the marginals. ” The end result is that the criterion must be slightly modified in order for it to also separate sub-Gaussian sources. The details of the modification may be found in a paper by the same authors [2]. The authors wish to extend an apology for any inconvenience this may have caused.