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Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions
Open accessAbstract
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 additional total loss of the on-line algorithm over the total loss of the best off-line parameter. These relative loss bounds hold for an arbitrary sequence of examples. The goal is to design algorithms with the best possible relative loss bounds. We use a Bregman divergence to derive and analyze each algorithm. These divergences are relative entropies between two exponential distributions. We also use our methods to prove relative loss bounds for linear regression.
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Differential-Geometrical Methods in Statistics
Amari, S.-I. (1985) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-5056-2 · Cited by 1,673
Metadata
- Authors
- Azoury, K. S., & Warmuth, M. K.
- Venue
- Machine Learning
- Published
- 2001-06
- Volume
- 43
- Issue
- 3
- Pages
- 211-246
- ISSN
- 0885-6125 (ISSN-L)
- 1573-0565
- OpenAlex
- W1506313179
- Cited by
- 298
- References
- 1
- FWCI
- 16.61
- Type
- journal article
- Language
- en
- Open access
- bronze
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- CoChat. (2026). Citation check: Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions. https://app.cochat.ai/papers/10.1023/a:1010896012157
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- Azoury, K. S., & Warmuth, M. K. (2001). Relative Loss Bounds for On-Line Density Estimation with the Exponential Family of Distributions. Machine Learning. https://doi.org/10.1023/a%3A1010896012157
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