By Topic

Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Haim H. Permuter ; Electrical & Computer Engineering Department, Ben Gurion University, Beer-Sheva, Israel ; Young-Han Kim ; Tsachy Weissman

We investigate the role of directed information in portfolio theory, data compression, and statistics with causality constraints. In particular, we show that directed information is an upper bound on the increment in growth rates of optimal portfolios in a stock market due to causal side information. This upper bound is tight for gambling in a horse race, which is an extreme case of stock markets. Directed information also characterizes the value of causal side information in instantaneous compression and quantifies the benefit of causal inference in joint compression of two stochastic processes. In hypothesis testing, directed information evaluates the best error exponent for testing whether a random process Y causally influences another process X or not. These results lead to a natural interpretation of directed information I(YnXn) as the amount of information that a random sequence Yn = (Y1,Y2,..., Yn) causally provides about another random sequence Xn = (X1,X2,...,Xn). A new measure, directed lautum information, is also introduced and interpreted in portfolio theory, data compression, and hypothesis testing.

Published in:

IEEE Transactions on Information Theory  (Volume:57 ,  Issue: 6 )