Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions

@article{Azoury1999RelativeLB,
  title={Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions},
  author={Katy S. Azoury and Manfred K. Warmuth},
  journal={Machine Learning},
  year={1999},
  volume={43},
  pages={211-246}
}
We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After receiving an example the algorithm incurs a loss, which is the negative log-likelihood of the example with respect to the current parameter of the algorithm. An off-line algorithm can choose the best parameter based on all the examples. We prove bounds on the… CONTINUE READING

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