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Maximum Likelihood Estimation for Learning Populations of Parameters [article]

Ramya Korlakai Vinayak, Weihao Kong, Gregory Valiant, Sham M. Kakade
2019 arXiv   pre-print
Our main result shows that, in the regime where t ≪ N, the maximum likelihood estimator (MLE) is both statistically minimax optimal and efficiently computable.  ...  In contrast, regardless of how large N is, the naive "plug-in" estimator for this problem only achieves the sub-optimal error of Θ(1/√(t)).  ...  We use the lens of sparse regime analysis for this problem of learning a population of parameters.  ... 
arXiv:1902.04553v1 fatcat:qfds4fg4xzhffbshrqmyli2maq

Trial-by-trial data analysis using computational models [chapter]

Nathaniel D. Daw
2011 Decision Making, Affect, and Learning  
I am very grateful to Peter Dayan, John O'Doherty, Yael Niv, Aaron Bornstein, Sam Gershman, Dylan Simon, and Larry Maloney for many helpful conversations about the issues covered here.  ...  the most probable value for θ M is the maximum likelihood estimate: the setting of the parameters that maximizes the likelihood function, P(D | M, θ M ).  ...  More precisely, if H is the Hessian of the negative log of the likelihood function at the maximum likelihood pointθ M , then a standard estimator for the covariance of the parameter estimates is its matrix  ... 
doi:10.1093/acprof:oso/9780199600434.003.0001 fatcat:w2orwbvjlze37csoj6rnhgq7k4

Max: a Computer Program for the Validation of Learning Hierarchies

Ronald D. Owston
1981 Educational and Psychological Measurement  
Caution must be exercised, however, to ensure that successive maximum likelihood parameter estimates result in convergence at ab- solute maxima.  ...  Output For each iteration the output consists of each of the eight parameter estimates together with estimates of their variance.  ... 
doi:10.1177/001316448104100123 fatcat:m5sm4zp6dnbsxmgtqgzabar47a

A Generalized Discriminant Rule When Training Population and Test Population Differ on Their Descriptive Parameters

Christophe Biernacki, Farid Beninel, Vincent Bretagnolle
2002 Biometrics  
Estimation of the non-labeled sample discriminant rule is then obtained by estimating parameters of this linear relationship.  ...  Several models describing this relation are proposed, and associated estimated parameters are given.  ...  Michel Weil and the two reviewers for contributing to improve the paper.  ... 
doi:10.1111/j.0006-341x.2002.00387.x pmid:12071412 fatcat:56al6rmklrawblidzbet2illd4

A semi-supervised learning method for remote sensing data mining

R.R. Vatsavai, S. Shekhar, T.E. Burk
2005 17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'05)  
Our objectives are to understand the impact of parameter estimation with small learning samples on classification accuracy, and to augment the parameter estimation with unlabeled training samples to improve  ...  We have developed a semi-supervised learning method based on the Expectation-Maximization (EM) algorithm, and maximum likelihood and maximum a posteriori classifiers.  ...  Joydeep Ghosh for useful conversations and critical inputs. We would like to thank Kim Koffolt for improving the readability of this report.  ... 
doi:10.1109/ictai.2005.17 dblp:conf/ictai/VatsavaiSB05 fatcat:da2bvow7k5bixlqw3lowebklwy

Evolution Strategies for Cosmology: A Comparison of Nested Sampling Methods [article]

M. Axiak, T. D. Kitching, J. I. van Hemert
2011 arXiv   pre-print
This quickly finds the maximum for complex likelihoods and provides an accurate measure of the Bayesian evidence, with no prior assumptions about the shape of the likelihood surface.  ...  We compare the performance of ESNested with the publicly available MultiNest and CosmoNest algorithms, in i) finding the maximum likelihood ii) calculating confidence contours in projected parameter spaces  ...  We thank Bob Mann for encouraging inter-disciplinary links between Astronomy and Informatics at the University of Edinburgh. We thank Alan Heavens for comments on a first draft.  ... 
arXiv:1101.0717v2 fatcat:vl42ryehsbdntkk5al3xfd2nxa

Parameter Estimation Model of Weibull Distribution on Students' Achievement of Mathematic Education Program, Cenderawasih University

Yan Dirk, Mayor M., Halomoan Edy
2020 International Journal of Computer Applications  
One of continual distribution used is Weibull distribution. The distribution attained is estimated by the Maximum Likelihood Estimation (MLE) method using Newton Raphson iteration.  ...  This research is supposed to deepen the statistical concept and numerical method particularly Weibull distribution using Maximum Likelihood Estimation along with Newton Raphson iteration and their application  ...  Two-parameter Weibull distribution Methods of Maximum Likelihood Estimations MLE method is one of parameter estimation methods that can be used to evaluate a model parameter of the already known distribution  ... 
doi:10.5120/ijca2020919987 fatcat:jyb66o4chbcmha5uhlqeua2gea

A Bayesian Network Model of the Relationships between Chronic Disease Indicators

Mengru Yuan, David Buckeridge
2018 International Journal of Population Data Science  
ResultsBNs were developed using constraint-based and score-based algorithms for structure learning, and maximum likelihood for parameter estimation.  ...  We found that the BN structures and parameters learned from individual-level data differed from the one estimated from data aggregated by community health centers.  ...  Results BNs were developed using constraint-based and score-based algorithms for structure learning, and maximum likelihood for parameter estimation.  ... 
doi:10.23889/ijpds.v3i4.823 fatcat:4skgv6hb4zbbtkox2b6bbgdcai

Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

Fan Yang, Hu Ren, Zhili Hu
2019 Mathematical Problems in Engineering  
The maximum likelihood estimation is a widely used approach to the parameter estimation.  ...  The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.  ...  Acknowledgments This work is supported by the Fundamental Research Funds for the Central Universities, NO. NS2018004.  ... 
doi:10.1155/2019/6281781 fatcat:ncl6x73rrrdmzltgfnlk4hmedq

A LATENT CLASS MODEL FOR ASSESSING LEARNING STRUCTURES

Nobuoki Eshima, Chooichiro Asano, Eisuke Obana
1990 Behaviormetrika  
A parameter estimation procedure is derived by use of the EM algorithm. A numerical example is also included to illustrate the estimation procedure.  ...  In the present paper, we discuss a latent structure analysis for assessing learning structures of acquiring two kinds of skill.  ...  Acknowledgement The authors wish to thank the referees for their useful comments and suggestions.  ... 
doi:10.2333/bhmk.17.28_23 fatcat:mmv2nxbmrzfw7ljrwjtghdigsu

Parameter cross-validation and early-stopping in univariate marginal distribution algorithm

Hao Wu, Jonathan L. Shapiro
2007 Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07  
Our hypothesis is that the well-known problem of diversity loss in UMDA is a consequence of overfitting during the parameter estimation step at each generation.  ...  In this paper, a cross-validation and early-stopping algorithm is devised for parameter updating in the Univariate Marginal Distribution Algorithm (UMDA) to reduce overftting.  ...  For parameter learning, most of EDAs choose the parameters which maximize the likelihood of the data.  ... 
doi:10.1145/1276958.1277092 dblp:conf/gecco/WuS07 fatcat:6pjvue5ponhodpttvsnd6zu4em

A Unified Bayesian Framework for Evolutionary Learning and Optimization [chapter]

Byoung-Tak Zhang
2003 Natural Computing Series  
Theoretical foundations of Bayesian evolutionary computation are given and its generality is demonstrated by showing specific Bayesian evolutionary algorithms for learning and optimization.  ...  In this framework, evolutionary computation is viewed as Bayesian inference that iteratively updates the posterior distribution of a population from the prior knowledge and observation of new individuals  ...  The parameters of the BEA with the Helmholtz machine were: maximum generation = 10 5 , population size = 50, learning rate = 0.5, and number of iterations = 1000.  ... 
doi:10.1007/978-3-642-18965-4_15 fatcat:koqkik2mybehxkcricjgvwixve

What is the expectation maximization algorithm?

Chuong B Do, Serafim Batzoglou
2008 Nature Biotechnology  
(a) Maximum likelihood estimation. For each set of ten tosses, the maximum likelihood procedure accumulates the counts of heads and tails for coins A and B separately.  ...  data to maximum likelihood estimation with complete data.  ... 
doi:10.1038/nbt1406 pmid:18688245 fatcat:mjtp2ahufrfclearaaxndn3yf4

A Fuzzy Logistic Neural Network for Binary Classification

Dandan Chi, Degang Wang, Hongxing Li
2016 ICIC Express Letters  
The constrained gradient descent algorithm is used to determine the center and width of membership function and maximum likelihood estimation method is applied to identifying the parameters of logistic  ...  Accordingly, a hybrid learning strategy is applied to determining the parameters of FLNN.  ...  This work is supported by the Fundamental Research Funds for the Central Universities (DUT14QY30), the National Natural Science Foundation of China (61374118) and the Special Fund for NHFPC Scientific  ... 
doi:10.24507/icicel.10.08.1865 fatcat:6ophymf3rnbkzg7se2up5tovfy

Estimating the hidden learning representations

Andrea Brovelli, Pierre-Arnaud Coquelin, Driss Boussaoud
2007 Journal of Physiology - Paris  
More precisely, we use Sequential Monte Carlo methods for state estimation and the maximum likelihood principle (MLP) for model selection and parameter estimation.  ...  ' parameters (parameter estimation) and the class of behavioral model (model selection) that are most likely to have generated a given sequence of actions and outcomes.  ...  To do so, we use a bayesian methodology for state estimation and the maximum likelihood principle (MLP) for model selection and parameter estimation.  ... 
doi:10.1016/j.jphysparis.2007.10.002 pmid:18024092 fatcat:zgd6ztfn3rac3dn2oav2neuhvu
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