BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Raymond W. Yeung (The Chinese University of Hong Kong) DTSTART:20230510T140000Z DTEND:20230510T151500Z DTSTAMP:20260423T035957Z UID:AAIT/12 DESCRIPTION:Title: En tropy Inequalities: My Personal Journey.\nby Raymond W. Yeung (The Chi nese University of Hong Kong) as part of Seminar on Algorithmic Aspects of Information Theory\n\n\nAbstract\nShannon's information measures\, namely entropy\, mutual information\, and their conditional versions\, where eac h of them can be expressed as a linear combination of unconditional joint entropies. These measures are central in information theory\, and constrai nts on these measures\, in particular in the form of inequalities\, are of fundamental interest. It is well-known that all Shannon's information mea sures are nonnegative\, forming a set of inequalities on entropy. However\ , whether these are all the constraints on entropy was unknown\, and the p roblem had been rather evasive until the introduction of the entropy funct ion region in the late 1990s.\n\nThis talk consists of two part. The first part is about how I became interested in this subject in the late 1980s. It began with my PhD thesis in which I needed to use inequalities on Shann on's information measures (viz. information inequalities\, or equivalently entropy inequalities) to prove converse coding theorems. During that time I was also intrigued by the underlying set-theoretic structure of Shannon 's information measures\, namely their representation by diagrams that res emble the Venn diagram. In 1991 I introduced the I-Measure to formally est ablish the one-to-one correspondence between set theory and Shannon's info rmation measures. In the mid-1990s\, I introduced the entropy function reg ion Γ* that provides a geometrical interpretation of entropy inequalities . Shortly after\, Zhen Zhang and I discovered so-called non-Shannon-type i nequalities which are beyond the nonnegativity of Shannon's information me asures. Since then this subject has been under active research\n\nA byprod uct of the entropy function region and the associated geometrical interpre tation is the machine-proving of entropy inequalities. In the second part of this talk\, I will discuss the research along this line\, including som e recent results.\n LOCATION:https://researchseminars.org/talk/AAIT/12/ END:VEVENT END:VCALENDAR