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Extended Stochastic Complexity and Minimax Relative Loss Analysis [chapter]

Kenji Yamanishi
1999 Lecture Notes in Computer Science  
An eective performance measure is the minimax relative cumulative loss (RCL), which is the minimum of the worst-case dierence between the cumulative loss for any prediction algorithm and that for the best  ...  We are concerned with the problem of sequential prediction using a given hypothesis class of continuously-many prediction strategies.  ...  For any sequential prediction algorithm A, we dene the worst-case relative cumulative loss (RCL is equivalent with the minimax regret (3).  ... 
doi:10.1007/3-540-46769-6_3 fatcat:bn7t5e36uvh4tnj233anr2khgm

Page 6621 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
Warmuth, Tracking the best re- gressor (24-31 (electronic)); Kenji Yamanishi, Minimax relative loss analysis for sequential prediction algorithms using parametric hypotheses (32-43 (electronic)); John  ...  (1-11 (electronic)); Nicold Cesa-Bianchi and Gabor Lugosi, Minimax regret under log loss for general classes of experts (12-18 (electronic)); Tsachy Weissman and Neri Merhay, On prediction of individual  ... 

Universal prediction

N. Merhav, M. Feder
1998 IEEE Transactions on Information Theory  
This paper consists of an overview on universal prediction from an information-theoretic perspective.  ...  Special attention is given to the notion of probability assignment under the self-information loss function, which is directly related to the theory of universal data compression.  ...  mechanism, which is useful for prediction.  ... 
doi:10.1109/18.720534 fatcat:iuadncat2nbvvbln5q3omquqxm

PAC-Bayes with Minimax for Confidence-Rated Transduction [article]

Akshay Balsubramani, Yoav Freund
2015 arXiv   pre-print
We derive minimax optimal rules for confidence-rated prediction in this setting.  ...  We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance.  ...  Conclusion We have presented an analysis of aggregating an ensemble for binary classification, using minimax worstcase techniques to formulate it as an game and suggest an optimal prediction strategy g  ... 
arXiv:1501.03838v1 fatcat:zk5o4sz2gfglbo3mpsobtbligy

Online Nonparametric Regression [article]

Alexander Rakhlin, Karthik Sridharan
2014 arXiv   pre-print
In addition to a non-algorithmic study of minimax regret, we exhibit a generic forecaster that enjoys the established optimal rates.  ...  loss and online nonparametric regression are the same.  ...  Any algorithm derived from the above schema using relaxation Rel n enjoys a bound Reg n ≤ 1 n Rel n (·) on regret.  ... 
arXiv:1402.2594v1 fatcat:vpfkepd2zjchvemp4ceu7iohl4

How the twain can meet: Prospect theory and models of heuristics in risky choice

Thorsten Pachur, Renata S. Suter, Ralph Hertwig
2017 Cognitive Psychology  
In computer simulations, we estimated CPT's parameters for choices produced by various heuristics.  ...  Finally, we show, both in an empirical and a model recovery study, how CPT parameter profiles can be used to detect the operation of heuristics.  ...  There are good arguments for either choice of range. The most important point is to consistently use one range within an analysis or to conduct a comparative analysis.  ... 
doi:10.1016/j.cogpsych.2017.01.001 pmid:28189037 fatcat:33q25zcpafgntphctvl3t6qp2m

Sequential (Quickest) Change Detection: Classical Results and New Directions [article]

Liyan Xie, Shaofeng Zou, Yao Xie, Venugopal V. Veeravalli
2021 arXiv   pre-print
This survey starts with the basics of sequential change detection, and then moves on to generalizations and extensions of sequential change detection theory and methods.  ...  Online detection of changes in stochastic systems, referred to as sequential change detection or quickest change detection, is an important research topic in statistics, signal processing, and information  ...  ACKNOWLEDGEMENT The authors are grateful to the Guest Editor and the anonymous reviewers for their helpful comments.  ... 
arXiv:2104.04186v1 fatcat:ypxkrjyyf5dprpsc5b4kxxrnhm

Luckiness and Regret in Minimum Description Length Inference [chapter]

Steven de Rooij, Peter D. Grünwald
2011 Philosophy of Statistics  
We then discuss how data compression relates to performance in various learning tasks, including parameter estimation, parametric and nonparametric model selection and sequential prediction of outcomes  ...  Minimum Description Length (MDL) inference is based on the intuition that understanding the available data can be defined in terms of the ability to compress the data, i.e. to describe it in full using  ...  Prediction To use MDL for sequential prediction, we have to use codes that can be rendered as prequential forecasting systems.  ... 
doi:10.1016/b978-0-444-51862-0.50029-0 fatcat:ygm33cgeibfkpgb7m57lftxtju

Learning to learn from data: Using deep adversarial learning to construct optimal statistical procedures

Alex Luedtke, Marco Carone, Noah Simon, Oleg Sofrygin
2020 Science Advances  
We use tools from deep learning to develop a new approach, adversarial Monte Carlo meta-learning, for constructing optimal statistical procedures.  ...  Statistical problems are framed as two-player games in which Nature adversarially selects a distribution that makes it difficult for a statistician to answer the scientific question using data drawn from  ...  Gilbert for helpful discussions.  ... 
doi:10.1126/sciadv.aaw2140 pmid:32166115 pmcid:PMC7051830 fatcat:7vc6actnljh7vdm5y6j3nzj5nq

Methodology and Application of Adaptive and Sequential Approaches in Contemporary Clinical Trials

Zhengjia Chen, Yichuan Zhao, Ye Cui, Jeanne Kowalski
2012 Journal of Probability and Statistics  
Many adaptive and sequential approaches have been proposed for use in clinical trials to allow adaptations or modifications to aspects of a trial after its initiation without undermining the validity and  ...  adaptive and sequential approaches and their applications in Phase I, II, and III clinical trials and discuss future directions in this field of research.  ...  The design has two subtypes, optimal and minimax.  ... 
doi:10.1155/2012/527351 fatcat:lzi6aquxajepjjmovwa24uncd4

PAC-Bayesian aggregation and multi-armed bandits [article]

Jean-Yves Audibert
2010 arXiv   pre-print
This habilitation thesis presents several contributions to (1) the PAC-Bayesian analysis of statistical learning, (2) the three aggregation problems: given d functions, how to predict as well as (i) the  ...  I would also like to thank Yuri Golubev for having accepted to participate and chair the habilitation committee.  ...  Another solution is to use the exponentiated gradient algorithm introduced and studied by Kivinen and Warmuth [74] in the context of sequential prediction for the quadratic loss, and then extended to  ... 
arXiv:1011.3396v1 fatcat:oix5eiydzvat7oaqt6uwxxd6vy

A tutorial introduction to the minimum description length principle [article]

Peter Grunwald
2004 arXiv   pre-print
It serves as a basis for the technical introduction given in the second chapter, in which all the ideas of the first chapter are made mathematically precise.  ...  Log Loss for Universal Models Let M be some parametric model and letP be some universal model/code relative to M. What do the individual predictions P (X i | x i−1 ) look like?  ...  prequential probability universal models, non−predictive including use general for log loss only predictive universal models with log loss universal models, .  ... 
arXiv:math/0406077v1 fatcat:zhxexym4vbh2zpyko6pkawszly

Item Response Theory – A Statistical Framework for Educational and Psychological Measurement [article]

Yunxiao Chen, Xiaoou Li, Jingchen Liu, Zhiliang Ying
2021 arXiv   pre-print
The IRT models are latent factor models tailored to the analysis, interpretation, and prediction of individuals' behaviors in answering a set of measurement items that typically involve categorical response  ...  We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation, and sequential analysis  ...  These models typically impose relatively strong parametric assumptions on the copula function.  ... 
arXiv:2108.08604v1 fatcat:4qkgd6wc4zfc3fn6zxy5mq2xsm

Active Learning: Problem Settings and Recent Developments [article]

Hideitsu Hino
2020 arXiv   pre-print
In particular, research on learning acquisition functions to select samples from the data for labeling, theoretical work on active learning algorithms, and stopping criteria for sequential data acquisition  ...  Active learning is a method of obtaining predictive models with high precision at a limited cost through the adaptive selection of samples for labeling.  ...  Masanari Kimura for their valuable comments on the draft of this paper.  ... 
arXiv:2012.04225v2 fatcat:rbtg2kvi6vhj3odzayph4floum

Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles [article]

Dylan J. Foster, Alexander Rakhlin
2020 arXiv   pre-print
We characterize the minimax rates for contextual bandits with general, potentially nonparametric function classes, and show that our algorithm is minimax optimal whenever the oracle obtains the optimal  ...  We show how to transform any oracle for online regression with a given value function class into an algorithm for contextual bandits with the induced policy class, with no overhead in runtime or memory  ...  Acknowledgements We thank Akshay Krishnamurthy and Haipeng Luo for helpful discussions. We acknowledge the support of ONR award #N00014-20-1-2336.  ... 
arXiv:2002.04926v2 fatcat:5iepwb62fjbmjjgd4y2bi6utku
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