Online regression with partial information

Generalization and linear projection

Shinji Ito, Daisuke Hatano, Hanna Sumita, Akihiro Yabe, Takuro Fukunaga, Naonori Kakimura, Ken ichi Kawarabayashi

Research output: Contribution to conferencePaper

Abstract

We investigate an online regression problem in which the learner makes predictions sequentially while only the limited information on features is observable. In this paper, we propose a general setting for the limitation of the available information, where the observed information is determined by a function chosen from a given set of observation functions. Our problem setting is a generalization of the online sparse linear regression problem, which has been actively studied. For our general problem, we present an algorithm by combining multi-armed bandit algorithms and online learning methods. This algorithm admits a sublinear regret bound when the number of observation functions is constant. We also show that the dependency on the number of observation functions is inevitable unless additional assumptions are adopted. To mitigate this inefficiency, we focus on a special case of practical importance, in which the observed information is expressed through linear combinations of the original features. We propose efficient algorithms for this special case. Finally, we also demonstrate the efficiency of the proposed algorithms by simulation studies using both artificial and real data.

Original languageEnglish
Pages1599-1607
Number of pages9
Publication statusPublished - 2018 Jan 1
Event21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018 - Playa Blanca, Lanzarote, Canary Islands, Spain
Duration: 2018 Apr 92018 Apr 11

Conference

Conference21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018
CountrySpain
CityPlaya Blanca, Lanzarote, Canary Islands
Period18/4/918/4/11

Fingerprint

Linear Projection
Partial Information
Regression
Observed Information
Multi-armed Bandit
Regret
Online Learning
Linear regression
Linear Combination
Efficient Algorithms
Simulation Study
Generalization
Prediction
Demonstrate
Observation

ASJC Scopus subject areas

  • Statistics and Probability
  • Artificial Intelligence

Cite this

Ito, S., Hatano, D., Sumita, H., Yabe, A., Fukunaga, T., Kakimura, N., & Kawarabayashi, K. I. (2018). Online regression with partial information: Generalization and linear projection. 1599-1607. Paper presented at 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, Spain.

Online regression with partial information : Generalization and linear projection. / Ito, Shinji; Hatano, Daisuke; Sumita, Hanna; Yabe, Akihiro; Fukunaga, Takuro; Kakimura, Naonori; Kawarabayashi, Ken ichi.

2018. 1599-1607 Paper presented at 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, Spain.

Research output: Contribution to conferencePaper

Ito, S, Hatano, D, Sumita, H, Yabe, A, Fukunaga, T, Kakimura, N & Kawarabayashi, KI 2018, 'Online regression with partial information: Generalization and linear projection' Paper presented at 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, Spain, 18/4/9 - 18/4/11, pp. 1599-1607.
Ito S, Hatano D, Sumita H, Yabe A, Fukunaga T, Kakimura N et al. Online regression with partial information: Generalization and linear projection. 2018. Paper presented at 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, Spain.
Ito, Shinji ; Hatano, Daisuke ; Sumita, Hanna ; Yabe, Akihiro ; Fukunaga, Takuro ; Kakimura, Naonori ; Kawarabayashi, Ken ichi. / Online regression with partial information : Generalization and linear projection. Paper presented at 21st International Conference on Artificial Intelligence and Statistics, AISTATS 2018, Playa Blanca, Lanzarote, Canary Islands, Spain.9 p.
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