#### DMCA

## The minimax strategy for gaussian density estimation (2000)

### Cached

### Download Links

Venue: | In COLT |

Citations: | 10 - 2 self |

### Citations

356 |
Fisher information and stochastic complexity.
- Rissanen
- 1996
(Show Context)
Citation Context ...s the same as the minimax regret for Bernoulli density estimation. Our work on the minimax regret is different from a large body of work that has its roots in the Minimum Description Length community =-=[6, 7, 12, 9, 10, 13]-=-. In short we require the learner to choose its on-line parameters from the same model class from which the best off-line parameter is chosen. We will discuss the differences in Section 3. In this pap... |

207 | Universal portfolios.
- Cover
- 1991
(Show Context)
Citation Context ...izon T is X2 T∑ ct = 2 1 2 X2 (ln T − ln ln T + O(ln ln T/ ln T )). (1) t=1 The − ln ln T term is surprising because many on-line games were shown to have O(ln T ) upper bounds for the minimax regret =-=[2, 5, 3, 11, 1, 13, 14]-=-. There are some intriguing properties of the optimal strategies of both parties. First, the learner does not need to know the upper bound X on the 2-norm of the instances. Second, the strategies we g... |

171 |
Universal Sequential Coding of Single Messages,
- Shtarkov
- 1987
(Show Context)
Citation Context ... it. For the analogous problem of density estimation over a discrete domain w.r.t. log loss, Shtarkov gave the minimax strategy and an implicit form of the value of the game called the minimax regret =-=[8]-=-. Freund [3] gives an explicit formula for the minimax regret for Bernoulli density estimation: (1/2) ln(T + 1) + ln(π/2) − O(1/ √ T ). The minimax strategy has also been computed for the universal po... |

152 | M.K.: Relative loss bounds for on-line density estimation with the exponential family of distributions.
- Azoury, Warmuth
- 2001
(Show Context)
Citation Context ...izon T is X2 T∑ ct = 2 1 2 X2 (ln T − ln ln T + O(ln ln T/ ln T )). (1) t=1 The − ln ln T term is surprising because many on-line games were shown to have O(ln T ) upper bounds for the minimax regret =-=[2, 5, 3, 11, 1, 13, 14]-=-. There are some intriguing properties of the optimal strategies of both parties. First, the learner does not need to know the upper bound X on the 2-norm of the instances. Second, the strategies we g... |

78 | Approximate Solutions to Markov Decision Processes.
- Gordon
- 1999
(Show Context)
Citation Context ...e. The initial instance is chosen to be zero for Gaussian density estimation. This prediction algorithm is the forward algorithm of [1]. The same algorithm was investigated in parallel work by Gordon =-=[4]-=-. The forward algorithm was inspired by a similar related algorithm of Vovk for linear regression [11]. We show that the regret of the forward algorithm is larger than 1 2X2 (ln T − O(1)) regardless o... |

78 |
Asymptotic minimax regret for data compression,”
- Xie, Barron
- 2000
(Show Context)
Citation Context ...s the same as the minimax regret for Bernoulli density estimation. Our work on the minimax regret is different from a large body of work that has its roots in the Minimum Description Length community =-=[6, 7, 12, 9, 10, 13]-=-. In short we require the learner to choose its on-line parameters from the same model class from which the best off-line parameter is chosen. We will discuss the differences in Section 3. In this pap... |

51 |
A decision-theoretic extension of stochastic complexity and its applications to learning
- Yamanishi
- 1998
(Show Context)
Citation Context ...s the same as the minimax regret for Bernoulli density estimation. Our work on the minimax regret is different from a large body of work that has its roots in the Minimum Description Length community =-=[6, 7, 12, 9, 10, 13]-=-. In short we require the learner to choose its on-line parameters from the same model class from which the best off-line parameter is chosen. We will discuss the differences in Section 3. In this pap... |

49 | Predicting a binary sequence almost as well as the optimal biased coin
- Freund
- 1996
(Show Context)
Citation Context ... analogous problem of density estimation over a discrete domain w.r.t. log loss, Shtarkov gave the minimax strategy and an implicit form of the value of the game called the minimax regret [8]. Freund =-=[3]-=- gives an explicit formula for the minimax regret for Bernoulli density estimation: (1/2) ln(T + 1) + ln(π/2) − O(1/ √ T ). The minimax strategy has also been computed for the universal portfolio prob... |

23 |
Competitive on-line linear regression.
- Vovk
- 1997
(Show Context)
Citation Context ...izon T is X2 T∑ ct = 2 1 2 X2 (ln T − ln ln T + O(ln ln T/ ln T )). (1) t=1 The − ln ln T term is surprising because many on-line games were shown to have O(ln T ) upper bounds for the minimax regret =-=[2, 5, 3, 11, 1, 13, 14]-=-. There are some intriguing properties of the optimal strategies of both parties. First, the learner does not need to know the upper bound X on the 2-norm of the instances. Second, the strategies we g... |

22 | The cost of achieving the best portfolio in hindsight
- Ordentlich, Cover
- 1996
(Show Context)
Citation Context ...es an explicit formula for the minimax regret for Bernoulli density estimation: (1/2) ln(T + 1) + ln(π/2) − O(1/ √ T ). The minimax strategy has also been computed for the universal portfolio problem =-=[5]-=-. In this case the strategy is not ef£ciently computable, but the minimax regret for the universal portfolio problem is the same as the minimax regret for Bernoulli density estimation. Our work on the... |

21 | Stochastic Complexity in Learning - Rissanen |

13 |
Asymptotically minimax regret by Bayes mixtures,”
- Takeuchi, Barron
- 1998
(Show Context)
Citation Context |

11 |
Asymptotically minimax regret for exponential and curved exponential families,”
- Takeuchi, Barron
- 1997
(Show Context)
Citation Context |

6 | Extended stochastic complexity and minimax relative loss analysis - Yamanishi - 1999 |

1 |
Extended stochastic complexity and minimax relative loss analysis
- Yamanshi
- 1999
(Show Context)
Citation Context |