Computing the Unique Information

Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has proposed to quantify the unique component of the decomposition as the minimum value of the conditional mutual information over a constrained set of information channels. We present an efficient iterative divergence minimization algorithm to solve this optimization problem with convergence guarantees and evaluate its performance against other techniques.Comment: To appear in 2018 IEEE International Symposium on Information Theory (ISIT); 18 pages; 4 figures, 1 Table; Github link to source code: https://github.com/infodeco/computeU

Unique Information and Secret Key Decompositions

The unique information ($UI$) is an information measure that quantifies a deviation from the Blackwell order. We have recently shown that this quantity is an upper bound on the one-way secret key rate. In this paper, we prove a triangle inequality for the $UI$, which implies that the $UI$ is never greater than one of the best known upper bounds on the two-way secret key rate. We conjecture that the $UI$ lower bounds the two-way rate and discuss implications of the conjecture.Comment: 7 page

Optimal Asset Pricing

We describe an R package for determining the optimal price of an asset which is “perishable” in a certain sense, given the intensity of customer arrivals and a time-varying price sensitivity function which specifies the probability that a customer will purchase an asset offered at a given price at a given time. The package deals with the case of customers arriving in groups, with a probability distribution for the group size being specified. The methodology and software allow for both discrete and continuous pricing. The class of possible models for price sensitivity functions is very wide, and includes piecewise linear models. A mechanism for constructing piecewise linear price sensitivity functions is provided