Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper solves the problem of minimization of the Kullback divergence beten a partially known and a completely known probability distribution.#N#It considers two probability distributions of a random vector $(u_1, x_1, \ldots, u_T, x_T )$ on a sample space of $2T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_\tau$ given $u_1, x_1, \ldots, u_{\tau-1}, x_{\tau-1}, u_{\tau}$ are known for $\tau = 1, \ldots, T$. Our objective is to determine the remaining conditional probability distributions of $u_\tau$ given $u_1, x_1, \ldots, u_{\tau-1}, x_{\tau-1}$ such that the Kullback divergence of the partially known distribution with respect to the completely known distribution is minimal. Explicit solution of this problem has been found previously for Markovian systems in Karný [Karny:96a]. The general solution is given in this paper.
['Igor Vajda']
I am writing a research paper on a idea STOCHASTIC CONTROL OPTIMAL IN THE KULLBACK SENSE
[{"from": "human", "value": "I am writing a research paper on a idea STOCHASTIC CONTROL OPTIMAL IN THE KULLBACK SENSE"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper solves the problem of minimization of the Kullback divergence beten a partially known and a completely known probability distribution.#N#It considers two probability distributions of a random vector $(u_1, x_1, \\ldots, u_T, x_T )$ on a sample space of $2T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_\\tau$ given $u_1, x_1, \\ldots, u_{\\tau-1}, x_{\\tau-1}, u_{\\tau}$ are known for $\\tau = 1, \\ldots, T$. Our objective is to determine the remaining conditional probability distributions of $u_\\tau$ given $u_1, x_1, \\ldots, u_{\\tau-1}, x_{\\tau-1}$ such that the Kullback divergence of the partially known distribution with respect to the completely known distribution is minimal. Explicit solution of this problem has been found previously for Markovian systems in Karn\u00fd [Karny:96a]. The general solution is given in this paper."}]