Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The mutual information beten two jointly distributed random variables    $X$    and    $Y$    is a functional of the joint distribution    $P_{XY}$   , which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of    $(X,Y)$    is given by the marginal distributions    $P_{X}, P_{Y}$    and the  adjacency  relation induced by the joint distribution, where    $x$    and    $y$    are adjacent if    $P(x,y)>0$   .  derive a lor bound on the mutual information in terms of these entities. The bound is obtained by viewing the channel from    $X$    to    $Y$    as a probability distribution on a set of possible  actions , where an action determines the output for any possible input, and is independently drawn.  also provide an alternative proof based on convex optimization that yields a generally tighter bound. Finally,  derive an upper bound on the mutual information in terms of adjacency events beten the action and the pair    $(X,Y)$   , where in this case, an action    $a$    and a pair    $(x,y)$    are adjacent if    $y=a(x)$   . As an example,  apply our bounds to the binary deletion channel and show that for the special case of an independent identically distributed input distribution and a range of deletion probabilities, our lor and upper bounds both outperform the best known bounds for the mutual information.
['Yanjun Han', 'Or Ordentlich', 'Ofer Shayevitz']
I am writing a research paper on a idea Mutual Information Bounds via Adjacency Events
[{"from": "human", "value": "I am writing a research paper on a idea Mutual Information Bounds via Adjacency Events"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The mutual information beten two jointly distributed random variables    $X$    and    $Y$    is a functional of the joint distribution    $P_{XY}$   , which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of    $(X,Y)$    is given by the marginal distributions    $P_{X}, P_{Y}$    and the  adjacency  relation induced by the joint distribution, where    $x$    and    $y$    are adjacent if    $P(x,y)>0$   .  derive a lor bound on the mutual information in terms of these entities. The bound is obtained by viewing the channel from    $X$    to    $Y$    as a probability distribution on a set of possible  actions , where an action determines the output for any possible input, and is independently drawn.  also provide an alternative proof based on convex optimization that yields a generally tighter bound. Finally,  derive an upper bound on the mutual information in terms of adjacency events beten the action and the pair    $(X,Y)$   , where in this case, an action    $a$    and a pair    $(x,y)$    are adjacent if    $y=a(x)$   . As an example,  apply our bounds to the binary deletion channel and show that for the special case of an independent identically distributed input distribution and a range of deletion probabilities, our lor and upper bounds both outperform the best known bounds for the mutual information."}]