Learning the joint probability of random variables (RVs) is cornerstone statistical signal processing and machine learning. However, direct nonparametric estimation for high-dimensional in general impossible, due to curse dimensionality. Recent work has proposed recover mass function (PMF) an arbitrary number RVs from three-dimensional marginals, leveraging algebraic properties low-rank tensor ...

The conditional in conditional Kolmogorov complexity commonly is taken to be a finite binary string. The Coding Theorem of L.A. Levin connects unconditional prefix Kolmogorov complexity with the discrete universal distribution. The least upper semicomputable code-length is up to a constant equal to the negative logarithm of the greatest lower semicomputable probability mass function. We investi...

We consider a bipartite quantum conductor and discuss the joint probability distribution of particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multi-contour Keldysh Green function technique, we calculate the Rényi entropy of a positive integer order M subjected to the particle number constraint, from which we der...

Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a fully specified joint probability distribution is available, and conclude that it is not suitable for application in AI systems. Probability intervals, however, constitute a means for expressing incompleteness of information. We present a method for computing probability interval!...

In the discrete case a joint probability mass function tells you the probability of any combination of events X = a and Y = b: pX ,Y (a,b) = P(X = a,Y = b) This function tells you the probability of all combinations of events (the “,” means “and”). If you want to back calculate the probability of an event only for one variable you can calculate a “marginal” from the joint probability mass funct...

Conventional noncooperative game theory hypothesizes that the joint (mixed) strategy of a set of reasoning players in a game will necessarily satisfy an “equilibrium concept”. The number of joint strategies satisfying that equilibrium concept has measure zero, and all other joint strategies are considered impossible. Under this hypothesis the only issue is what equilibrium concept is “correct”....

Conventional noncooperative game theory hypothesizes that the joint (mixed) strategy of a set of reasoning players in a game will necessarily satisfy an “equilibrium concept”. The number of joint strategies satisfying that equilibrium concept has measure zero, and all other joint strategies are considered impossible. Under this hypothesis the only issue is what equilibrium concept is “correct”....