Various supervised inference methods can be analyzed as convex duals of a generalized maximum entropy framework, where the goal is to find a distribution with maximum entropy subject to the moment matching constraints on the data. We extend this framework to semi-supervised learning using two approaches: 1) by incorporating unlabeled data into the data constraints and 2) by imposing similarity ...

The maximum entropy noise under a lag autocorrelation constraint is known by Burg’s theorem to be the th order Gauss–Markov process satisfying these constraints. The question is, what is the worst additive noise for a communication channel given these constraints? Is it the maximum entropy noise? The problem becomes one of extremizing the mutual information over all noise processes with covaria...

To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such "horizon constraints" allow the use of conformal field theory techniques to compute the density of states, reproducing the Bekenstein-Hawking entropy in a nearly model-independent manner. One standard string t...

We provide a new inequality that links two important entropy notions: Shannon Entropy H1 and collision entropy H2. Our formula gives the worst possible amount of collision entropy in a probability distribution, when its Shannon Entropy is fixed. While in practice it is easier to evaluate Shannon entropy than other entropy notions, it is well known in folklore that it does not provide a good est...

A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. An eoptimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Sin...

We present the learning system Maccent which addresses the novel task of stochastic MAximum ENTropy modeling with Clausal Constraints. Maximum Entropy method is a Bayesian method based on the principle that the target stochastic model should be as uniform as possible, subject to known constraints. Maccent incorporates clausal constraints that are based on the evaluation of Prolog clauses in exa...

A question about a black hole in quantum gravity is a conditional question: to obtain an answer, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity—and probably for a much wider class of theories—I show that the imposition of a spacelike “stretched horizon” constraint modifies the algebra of symmetries, inducing a cent...

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...

Abstract In this paper, we propose a new spatial interaction model for trip-chaining behavior that consists of a sequence of movements. Particularly, including the origin-destination constraints, we generalize the traditional entropy maximizing model to deal with trip-chaining behaviors. Traditional entropy models should be noted in terms of a theoretical derivation of the gravity model and its...