Related papers: On Directed Information and Gambling
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…
We study the capital growth in gambling with (and without) side information and memory effects. We derive several equalities for gambling, which are of similar form to the Jarzynski equality and its extension to systems with feedback…
Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…
For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kelly's logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived,…
The problem of estimating the directed information rate between two discrete processes $\{X_n\}$ and $\{Y_n\}$ via the plug-in (or maximum-likelihood) estimator is considered. When the joint process $\{(X_n,Y_n)\}$ is a Markov chain of a…
Directed information theory deals with communication channels with feedback. When applied to networks, a natural extension based on causal conditioning is needed. We show here that measures built from directed information theory in networks…
An attempt to obtain market directional information from non-stationary solution of the dynamic equation: "future price tends to the value maximizing the number of shares traded per unit time" is presented. A remarkable feature of the…
We extend the Blahut-Arimoto algorithm for maximizing Massey's directed information. The algorithm can be used for estimating the capacity of channels with delayed feedback, where the feedback is a deterministic function of the output. In…
A notion of directed information between two continuous-time processes is proposed. A key component in the definition is taking an infimum over all possible partitions of the time interval, which plays a role no less significant than the…
Directed information and its causally conditioned variations are often used to measure causal influences between random processes. In practice, these quantities must be measured from data. Non-asymptotic error bounds for these estimates are…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…
We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the…
Probabilistic graphical models are a fundamental tool in statistics, machine learning, signal processing, and control. When such a model is defined on a directed acyclic graph (DAG), one can assign a partial ordering to the events occurring…
Faced with data-driven policies, individuals will manipulate their features to obtain favorable decisions. While earlier works cast these manipulations as undesirable gaming, recent works have adopted a more nuanced causal framing in which…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
A source sequence is to be guessed with some fidelity based on a rate-limited description of an observed sequence with which it is correlated. The trade-off between the description rate and the exponential growth rate of the least power…
We propose a sequential optimizing betting strategy in the multi-dimensional bounded forecasting game in the framework of game-theoretic probability of Shafer and Vovk (2001). By studying the asymptotic behavior of its capital process, we…
Directed information (DI) is an information measure that attempts to capture directionality in the flow of information from one random process to another. It is closely related to other causal influence measures, such as transfer entropy,…
This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger (2002) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy…
In this work, we proposed a new $N$-person game in which the players can bet on two options, for example represented by two boxers. Some of the players have privileged information about the boxers and part of them can provide this…