TY - GEN

T1 - On MDL Estimation for Simple Contaminated Gaussian Location Families

AU - Miyamoto, Kohei

AU - Takeuchi, Jun'Ichi

N1 - Funding Information:
This research was partially supported by JSPS KAKENHI Grant Number JP18H03291.
Publisher Copyright:
© 2020 IEICE.

PY - 2020/10/24

Y1 - 2020/10/24

N2 - The performance of MDL density estimators defined as the minimizer of two part code lengths isguaranteed in terms of the redundancy of the two part code [2], [3]. When the true density belongs to the assumed model, the redundancy of a code can be bounded by the regret (pointwise redundancy) of the code. Then, the construction of two part codes which achieve small regret based on quantization of parametric family is developed. For exponential families, it is known that we can achieve sufficiently small regret by using this construction [4]. For non-exponential families, the evaluation of the regret achieved by using this construction breaks. However, for non-exponential families under certain assumptions, by enhancing this construction using local exponentially family bundles [1], we can design efficient two part codes [9]. In this paper, we show that we can apply this coding method to contamination model [5] with simple settings and give the guarantee of performance of MDL estimators for them.

AB - The performance of MDL density estimators defined as the minimizer of two part code lengths isguaranteed in terms of the redundancy of the two part code [2], [3]. When the true density belongs to the assumed model, the redundancy of a code can be bounded by the regret (pointwise redundancy) of the code. Then, the construction of two part codes which achieve small regret based on quantization of parametric family is developed. For exponential families, it is known that we can achieve sufficiently small regret by using this construction [4]. For non-exponential families, the evaluation of the regret achieved by using this construction breaks. However, for non-exponential families under certain assumptions, by enhancing this construction using local exponentially family bundles [1], we can design efficient two part codes [9]. In this paper, we show that we can apply this coding method to contamination model [5] with simple settings and give the guarantee of performance of MDL estimators for them.

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M3 - Conference contribution

AN - SCOPUS:85102615090

T3 - Proceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020

SP - 587

EP - 591

BT - Proceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 16th International Symposium on Information Theory and its Applications, ISITA 2020

Y2 - 24 October 2020 through 27 October 2020

ER -