Computer Science – Information Theory
Scientific paper
2009-12-24
Computer Science
Information Theory
Scientific paper
We investigate the role of Massey's 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 give a natural interpretation of directed information $I(Y^n \to X^n)$ as the amount of information that a random sequence $Y^n = (Y_1,Y_2,..., Y_n)$ {causally} provides about another random sequence $X^n = (X_1,X_2,...,X_n)$. A new measure, {\em directed lautum information}, is also introduced and interpreted in portfolio theory, data compression, and hypothesis testing.
Kim Young-Han
Permuter Haim H.
Weissman Tsachy
No associations
LandOfFree
Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-555896