Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper considers sequential prediction of individual sequences with log loss (online density estimation) using an exponential family of distributions.  rst analyze the regret of the maximum likelihood (\follow the leader") strategy.  nd that this strategy is (1) suboptimal and (2) requires an additional assumption about boundedness of the data sequence.  then show that both problems can be be addressed by adding the currently predicted outcome to the calculation of the maximum likelihood, follod by normalization of the distribution. The strategy obtained in this way is known in the literature as the sequential normalized maximum likelihood or last-step minimax strategy.  show for the rst time that for general exponential families, the regret is bounded by the familiar (k=2) logn and thus optimal up to O(1).  also show the relationship to the Bayes strategy with Jereys’ prior.
['Wojciech Kotłowski', 'Peter Grünwald']
I am writing a research paper on a idea Maximum Likelihood vs. I am writing a research paper on a idea Sequential Normalized Maximum Likelihood in On-line Density Estimation
[{"from": "human", "value": "I am writing a research paper on a idea Maximum Likelihood vs. I am writing a research paper on a idea Sequential Normalized Maximum Likelihood in On-line Density Estimation"}, {"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 considers sequential prediction of individual sequences with log loss (online density estimation) using an exponential family of distributions.  rst analyze the regret of the maximum likelihood (\\follow the leader\") strategy.  nd that this strategy is (1) suboptimal and (2) requires an additional assumption about boundedness of the data sequence.  then show that both problems can be be addressed by adding the currently predicted outcome to the calculation of the maximum likelihood, follod by normalization of the distribution. The strategy obtained in this way is known in the literature as the sequential normalized maximum likelihood or last-step minimax strategy.  show for the rst time that for general exponential families, the regret is bounded by the familiar (k=2) logn and thus optimal up to O(1).  also show the relationship to the Bayes strategy with Jereys\u2019 prior."}]