162 6.2.1 Population approach and hierarchical models, vol.163, p.160 ,
, Fast Stochastic Approximation of the EM
164 6.3.1 The conditional distribution of the individual parameters ,
167 6.4.1 Proposal based on Laplace approximation ,
, 172 6.5.2 Time-to-event Data Model
,
192 7.2.2 Convergence of the iSAEM for curved exponential family, p.195 ,
,
203 complete model (y, z) where the realisations of y are observed and z is the latent data ,
214 8.3 A Repeated Time-To-Event Data Model ,
, A Categorical Data Model with Regression Variables
of the Stochastic Approximation Expectation Maximization algorithm developed by Kuhn and Lavielle, 2004. ,
, , p.1
, On the Global Convergence of (Fast) Incremental Expectation Maximization Methods, Advances in Neural Information Processing Systems, 2019.
Analysis of Biased Stochastic Approximation Scheme, Proceedings of Conference on Learning Theory, 2019. ,
Articles in peer-reviewed journals f-SAEM: A fast Stochastic Approximation of the EM algorithm, Belhal Karimi, Marc Lavielle and Eric Moulines, Computational Statistics and Data Analysis (CSDA), 2019. Preprints A Doubly Stochastic Surrogate Optimization Scheme for Non-convex Finite-sum Problems, Proceedings, 2018. ,
, Software R package, extension of saemix, 2019.
, Awards Visiting Student Researcher Grant from the Jacques Hadamard Foundation, HSE-Samsung AI Lab in Moscow (RUSSIA) with Dr. Dmitry Vetrov (2 months)
, Student award, 32nd Conference on Learning Theory, 2019.
,
TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. ,
, Regret bounds for model-free linear quadratic control, 2018.
, EM algorithms for ICA, 2018.
A lower bound for the optimization of finite sums, 2014. ,
The generalization ability of online algorithms for dependent data, IEEE Transactions on Information Theory, vol.59, issue.1, pp.573-587, 2013. ,
Finding approximate local minima faster than gradient descent, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pp.1195-1199, 2017. ,
Categorical data analysis. A Wiley-Interscience publication, 1990. ,
A New Class of EM Algorithms. Escaping Local Minima and Handling Intractable Sampling, 2019. ,
Convergent Stochastic Expectation Maximization algorithm with efficient sampling in high dimension, Application to deformable template model estimation, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00720617
Variance reduction for faster non-convex optimization, International Conference on Machine Learning, pp.699-707, 2016. ,
Survival Analysis, Wiley Reference Series in Biostatistics, 2006. ,
Particle markov chain monte carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.72, issue.3, pp.269-342, 2010. ,
On the ergodicity properties of some adaptive mcmc algorithms, The Annals of Applied Probability, vol.16, issue.3, pp.1462-1505, 2006. ,
, Bibliography 229
The pseudo-marginal approach for efficient monte carlo computations, The Annals of Statistics, vol.37, issue.2, pp.697-725, 2009. ,
A tutorial on adaptive mcmc, Statistics and computing, vol.18, issue.4, pp.343-373, 2008. ,
On adaptive markov chain monte carlo algorithms, Bernoulli, vol.11, issue.5, pp.815-828, 2005. ,
Statistical guarantees for the EM algorithm: From population to sample-based analysis, Ann. Statist, vol.45, issue.1, pp.77-120, 2017. ,
Infinite-horizon policy-gradient estimation, Journal of Artificial Intelligence Research, vol.15, pp.319-350, 2001. ,
, The NONMEM system. The American Statistician, vol.34, pp.118-119, 1980.
Adaptive Algorithms and Stochastic Approximations, 1990. ,
Pharmacogenetics and population pharmacokinetics: impact of the design on three tests using the saem algorithm, Journal of pharmacokinetics and pharmacodynamics, vol.36, issue.4, pp.317-339, 2009. ,
URL : https://hal.archives-ouvertes.fr/inserm-00406739
Nonlinear programming, 1999. ,
Incremental gradient, subgradient, and proximal methods for convex optimization: A survey. Optimization for Machine Learning, p.3, 2010. ,
A conceptual introduction to Hamiltonian Monte Carlo, 2017. ,
A finite time analysis of temporal difference learning with linear function approximation, Conference On Learning Theory, pp.1691-1692, 2018. ,
Pattern recognition and machine learning, 2006. ,
Variational inference: A review for statisticians, Journal of the American Statistical Association, vol.112, issue.518, pp.859-877, 2017. ,
Variational Inference: A Review for Statisticians, Journal of the American statistical Association, vol.112, issue.518, pp.859-877, 2017. ,
Weight uncertainty in neural network, International Conference on Machine Learning, vol.230, pp.1613-1622, 2015. ,
, Chapter
Stochastic approximation with two time scales, Systems & Control Letters, vol.29, issue.5, pp.291-294, 1997. ,
Stochastic approximation: a dynamical systems viewpoint, vol.48, 2009. ,
Stochastic gradient learning in neural networks, Proceedings of Neuro-N?mes, vol.91, p.12, 1991. ,
Online learning and stochastic approximations, vol.17, p.142, 1998. ,
The tradeoffs of large scale learning, Advances in Neural Information Processing Systems, vol.20, pp.161-168, 2008. ,
Optimization methods for large-scale machine learning, SIAM Review, vol.60, issue.2, pp.223-311, 2018. ,
On-line learning for very large data sets. Applied stochastic models in business and industry, vol.21, pp.137-151, 2005. ,
Concentration inequalities: A nonasymptotic theory of independence, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00794821
, Convex optimization, 2004.
Differentiable germs and catastrophes, vol.17, 1975. ,
Handbook of markov chain monte carlo, 2011. ,
, The tamed unadjusted langevin algorithm, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01648667
On-line Expectation Maximization algorithm for latent data models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.71, issue.3, pp.593-613, 2009. ,
Convex until proven guilty: Dimension-free acceleration of gradient descent on non-convex functions, Proceedings of the 34th International Conference on Machine Learning, vol.70, pp.654-663, 2017. ,
,
Stan: A probabilistic programming language, Journal of Statistical Software, issue.1, p.76, 2017. ,
, , 2011.
, The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects, Journal of Pharmacokinetics and Pharmacodynamics, vol.38, issue.1, pp.41-61
Stochastic Expectation Maximization with variance reduction, Advances in Neural Information Processing Systems, pp.7978-7988, 2018. ,
Parameter estimation in nonlinear mixed effect models using saemix, an r implementation of the saem algorithm, Journal of Statistical Software, vol.80, issue.3, pp.1-42, 2017. ,
URL : https://hal.archives-ouvertes.fr/inserm-01502767
Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints, SIAM Journal on Optimization, vol.3, issue.1, pp.164-221, 1993. ,
Information geometry and alternating minimization procedures, Statist. Decisions, suppl, vol.1, pp.205-237, 1984. ,
Finite sample analyses for td (0) with function approximation, Thirty-Second AAAI Conference on Artificial Intelligence, 2018. ,
Finite sample analysis of two-timescale stochastic approximation with applications to reinforcement learning, Conference On Learning Theory, 2018. ,
Nonlinear models for repeated measurement data, 2017. ,
, Variational mcmc. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, pp.120-127, 2001.
Saga: A fast incremental gradient method with support for non-strongly convex composite objectives, Advances in neural information processing systems, pp.1646-1654, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01016843
Off-policy actor-critic, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00764021
Convergence of a stochastic approximation version of the EM algorithm, Ann. Statist, vol.27, issue.1, pp.94-128, 1999. ,
Convergence of a stochastic approximation version of the EM algorithm, Ann. Statist, vol.27, issue.1, pp.94-128, 1999. ,
Maximum likelihood from incomplete data via the EM algorithm, Journal of the royal statistical society. Series B (methodological), pp.1-38, 1977. ,
, , 2017.
Using pmcmc in EM algorithm for stochastic mixed models: theoretical and practical issues, Journal de la Société Française de Statistique, vol.155, issue.1, pp.49-72, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00950760
, Nonlinear Time Series: Theory, Methods and Applications with R examples, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01263245
On sequential monte carlo sampling methods for bayesian filtering, Statistics and computing, vol.10, issue.3, pp.197-208, 2000. ,
Invariance principles for absolutely regular empirical processes, Annales de l'IHP Probabilités et statistiques, vol.31, pp.393-427, 1995. ,
Ergodic mirror descent, SIAM Journal on Optimization, vol.22, issue.4, pp.1549-1578, 2012. ,
Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator, Advances in Neural Information Processing Systems, pp.687-697, 2018. ,
Global convergence of policy gradient methods for the linear quadratic regulator, International Conference on Machine Learning, pp.1466-1475, 2018. ,
Theory of statistical estimation, Mathematical Proceedings of the Cambridge Philosophical Society, vol.22, pp.700-725, 1925. ,
Convergence of adaptive and interacting Markov chain monte carlo algorithms, The Annals of Statistics, vol.39, issue.6, pp.3262-3289, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00695649
Bayesian regularization for normal mixture estimation and model-based clustering, Journal of classification, vol.24, issue.2, pp.155-181, 2007. ,
, Bibliography 233
Stochastic first-and zeroth-order methods for nonconvex stochastic programming, SIAM Journal on Optimization, vol.23, issue.4, pp.2341-2368, 2013. ,
Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization, Mathematical Programming, vol.155, issue.1-2, pp.267-305, 2016. ,
Probabilistic machine learning and artificial intelligence, Nature, vol.521, issue.7553, pp.452-459, 2015. ,
SGD: general analysis and improved rates, 2019. ,
Evaluating derivatives: principles and techniques of algorithmic differentiation, vol.105, 2008. ,
Convergence theorems for generalized alternating minimization procedures, Journal of Machine Learning Research, vol.6, pp.2049-2073, 2005. ,
An adaptive metropolis algorithm, Bernoulli, vol.7, issue.2, pp.223-242, 2001. ,
Martingale limit theory and its application, 2014. ,
A fast learning algorithm for deep belief nets, Neural computation, vol.18, issue.7, pp.1527-1554, 2006. ,
The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research, vol.15, issue.1, pp.1593-1623, 2014. ,
Probabilistic latent semantic indexing, Proceedings of the 22Nd, 1999. ,
, Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, SIGIR '99, pp.50-57
Nonconvex variance reduced optimization with arbitrary sampling, 2018. ,
Proximal stochastic methods for nonsmooth nonconvex finite-sum optimization, Advances in Neural Information Processing Systems, vol.29, pp.1145-1153, 2016. ,
Convergence of stochastic iterative dynamic programming algorithms, Advances in Neural Information Processing Systems, pp.703-710, 1994. ,
, Chapter
Genetic analysis of growth curves using the saem algorithm, Genetics Selection Evolution, vol.38, issue.6, p.583, 2006. ,
Logistic regression with missing covariatesparameter estimation, model selection and prediction, 2018. ,
Accelerating stochastic gradient descent using predictive variance reduction, Advances in neural information processing systems, pp.315-323, 2013. ,
An introduction to variational methods for graphical models, Mach. Learn, vol.37, issue.2, pp.183-233, 1999. ,
Control system analysis and design via the "second method" of lyapunov: I-continuous-time systems, Journal of Basic Engineering, vol.82, issue.2, pp.371-393, 1960. ,
Efficient Metropolis-Hastings sampling for nonlinear mixed effects models, Proceedings, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01958247
f-saem: A fast stochastic approximation of the em algorithm for nonlinear mixed effects models, Computational Statistics & Data Analysis, vol.141, pp.123-138, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-01958248
Non-asymptotic analysis of biased stochastic approximation scheme, Proceedings of the Thirty-Second Conference on Learning Theory, vol.99, pp.1944-1974, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02127750
A doubly stochastic surrogate optimization scheme for non-convex finite-sum problems, 2019. ,
On the global convergence of (fast) incremental expectation maximization methods, Advances in Neural Information Processing Systems, 2019. ,
Adam: A method for stochastic optimization, 3rd International Conference on Learning Representations, 2015. ,
Auto-encoding variational bayes, 2nd International Conference on Learning Representations, 2014. ,
On actor-critic algorithms, SIAM journal on Control and Optimization, vol.42, issue.4, pp.1143-1166, 2003. ,
, Bibliography 235
Automatic variational inference in stan, Advances in Neural Information Processing Systems, vol.28, pp.568-576, 2015. ,
Coupling a stochastic approximation version of EM with an MCMC procedure, ESAIM: Probability and Statistics, vol.8, pp.115-131, 2004. ,
Stochastic approximation and recursive algorithms and applications, vol.35, 2003. ,
Stochastic approximation methods for constrained and unconstrained systems, vol.26, 2012. ,
Linear stochastic approximation: How far does constant step-size and iterate averaging, International Conference on Artificial Intelligence and Statistics, pp.1347-1355, 2018. ,
MM Optimization Algorithms, 2016. ,
A stochastic algorithm for parametric and non-parametric estimation in the case of incomplete data, Signal Processing, vol.42, issue.1, pp.3-17, 1995. ,
Monolix (modèles non linéaires à effets mixtes), 2005. ,
Mixed effects models for the population approach: models, tasks, methods and tools, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01122873
mlxR: Simulation of Longitudinal Data, 2019. ,
Estimation of population pharmacokinetic parameters of saquinavir in hiv patients with the monolix software, Journal of pharmacokinetics and pharmacodynamics, vol.34, issue.2, pp.229-249, 2007. ,
URL : https://hal.archives-ouvertes.fr/inserm-00156907
Enhanced method for diagnosing pharmacometric models: random sampling from conditional distributions, Pharmaceutical research, vol.33, issue.12, pp.2979-2988, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01365532
The mnist database of handwritten digits, 1998. ,
Gradient-based learning applied to document recognition, Proceedings of the IEEE, vol.86, issue.11, pp.2278-2324, 1998. ,
Dropout inference in bayesian neural networks with alphadivergences, Proceedings of the 34th International Conference on Machine Learning, vol.70, pp.2052-2061, 2017. ,
Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society, Series B: Methodological, vol.44, pp.226-233, 1982. ,
Incremental majorization-minimization optimization with application to large-scale machine learning, SIAM Journal on Optimization, vol.25, issue.2, pp.829-855, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00948338
Incremental majorization-minimization optimization with application to large-scale machine learning, SIAM J. Optim, vol.25, issue.2, pp.829-855, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00948338
Using saem to estimate parameters of models of response to applied fertilizer, Journal of Agricultural, Biological, and Environmental Statistics, vol.11, issue.1, pp.45-60, 2006. ,
Joint modeling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the SAEM algorithm, Journal of Statistical Computation and Simulation, vol.85, issue.8, pp.1512-1528, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01122140
The EM algorithm and extensions, vol.382, 2007. ,
, The EM algorithm and extensions. Wiley Series in Probability and Statistics, 2008.
Human-competitive automatic topic indexing, 2009. ,
Rates of convergence of the hastings and metropolis algorithms, Ann. Statist, vol.24, issue.1, pp.101-121, 1996. ,
Equation of state calculations by fast computing machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953. ,
Markov chains and stochastic stability, 2012. ,
Statistical Inference: An Integrated Approach, Second Edition. Chapman & Hall/CRC Texts in Statistical Science, 2014. ,
Non-asymptotic analysis of stochastic approximation Bibliography 237, 2011. ,
, algorithms for machine learning, Advances in Neural Information Processing Systems, pp.451-459
Bayesian learning for neural networks, vol.118, 2012. ,
Mcmc using hamiltonian dynamics. Handbook of Markov Chain Monte Carlo, vol.2, p.2, 2011. ,
A view of the EM algorithm that justifies incremental, sparse, and other variants, Learning in graphical models, pp.355-368, 1998. ,
,
Problem complexity and method efficiency in optimization, 1983. ,
Introductory Lectures on Convex Optimization: A Basic Course, 2004. ,
On the choice of the number of blocks with the incremental EM algorithm for the fitting of normal mixtures, Statistics and Computing, vol.13, issue.1, pp.45-55, 2003. ,
Studies on coumarin anticoagulant drugs initiation of warfarin therapy without a loading dose, Circulation, vol.38, issue.1, pp.169-177, 1968. ,
Variational bayesian inference with stochastic search, ICML. icml.cc / Omnipress, 2012. ,
Stochastic variance-reduced policy gradient, Proceedings of the 35th International Conference on Machine Learning, vol.80, pp.4026-4035, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01940394
Madness: a package for Multivariate Automatic Differentiation, 2016. ,
Natural actor-critic, Neurocomputing, vol.71, issue.7-9, pp.1180-1190, 2008. ,
Deep learning: a bayesian perspective, Bayesian Analysis, vol.12, issue.4, pp.1275-1304, 2017. ,
Acceleration of stochastic approximation by averaging, SIAM Journal on Control and Optimization, vol.30, issue.4, pp.838-855, 1992. ,
, Miso is making a comeback with better proofs and rates, 2019.
, Chapter
, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, 2008.
A unified convergence analysis of block successive minimization methods for nonsmooth optimization, SIAM Journal on Optimization, vol.23, issue.2, pp.1126-1153, 2013. ,
A generic approach for escaping saddle points, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01652150
, Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, vol.84, pp.1233-1242
Stochastic variance reduction for nonconvex optimization, International conference on machine learning, pp.314-323, 2016. ,
Fast incremental method for nonconvex optimization, 2016. ,
Stochastic backpropagation and approximate inference in deep generative models, International Conference on Machine Learning, pp.1278-1286, 2014. ,
A stochastic approximation method, The Annals of Mathematical Statistics, vol.22, issue.3, pp.400-407, 1951. ,
Metropolis-Hastings Algorithms, pp.167-197, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-01067920
Weak convergence and optimal scaling of random walk metropolis algorithms, Ann. Appl. Probab, vol.7, issue.1, pp.110-120, 1997. ,
Optimal scaling of discrete approximations to langevin diffusions, J. R. Statist. Soc. B, vol.60, pp.255-268, 1997. ,
Quantitative non-geometric convergence bounds for independence samplers, Methodology and Computing in Applied Probability, vol.13, issue.2, pp.391-403, 2011. ,
Exponential convergence of langevin distributions and their discrete approximations, Bernoulli, vol.2, issue.4, pp.341-363, 1996. ,
A stochastic gradient method with an exponential convergence _rate for finite training sets, Advances in Neural Information Processing Systems, vol.25, pp.2663-2671, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00674995
Complexity analysis of second-order linesearch algorithms for smooth nonconvex optimization, SIAM Journal on Optimization, vol.28, issue.2, pp.1448-1477, 2018. ,
Approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations, Journal of the royal statistical society: Series b (statistical methodology), vol.71, issue.2, pp.319-392, 2009. ,
Extension of the saem algorithm to leftcensored data in nonlinear mixed-effects model: Application to hiv dynamics model, Computational Statistics & Data Analysis, vol.51, issue.3, pp.1562-1574, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00263506
Implementation and evaluation of the SAEM algorithm for longitudinal ordered categorical data with an illustration in pharmacokinetics-pharmacodynamics, The AAPS Journal, vol.13, issue.1, pp.44-53, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00637400
Minimizing finite sums with the stochastic average gradient, Mathematical Programming, vol.162, issue.1-2, pp.83-112, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-00860051
Lectures on stochastic programming: modeling and theory, 2009. ,
A comprehensive hepatitis c viral kinetic model explaining cure, Clinical Pharmacology & Therapeutics, vol.87, issue.6, pp.706-713, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00637434
, RStan: the R interface to Stan, Stan Development Team, 2018.
Langevin-type models i: Diffusions with given stationary distributions and their discretizations*, Methodology And Computing In Applied Probability, vol.1, issue.3, pp.283-306, 1999. ,
On Markov chain gradient descent, Advances in Neural Information Processing Systems, vol.31, pp.9918-9927, 2018. ,
On the importance of initialization and momentum in deep learning, International conference on machine learning, pp.1139-1147, 2013. ,
Reinforcement Learning: An Introduction, 2018. ,
Policy gradient methods for reinforcement learning with function approximation, Advances in Neural Information Processing Systems, pp.1057-1063, 2000. ,
Asymptotic bias of stochastic gradient search, The Annals of Applied Probability, vol.27, issue.6, pp.3255-3304, 2017. ,
Accelerating EM for large databases, Machine Learning, vol.45, issue.3, pp.279-299, 2001. ,
Auxiliary gradient?Ä?based sampling algorithms, Journal of the Royal Statistical Society: Series B (Statistical Methodology, issue.0, p.0, 2018. ,
Global convergence rate of proximal incremental aggregated gradient methods, SIAM Journal on Optimization, vol.28, issue.2, pp.1282-1300, 2018. ,
The nature of statistical learning theory, 2013. ,
Linear mixed models for longitudinal data, 1997. ,
Robust adaptive metropolis algorithm with coerced acceptance rate, Statistics and Computing, vol.22, issue.5, pp.997-1008, 2012. ,
Graphical models, exponential families, and variational inference. Foundations and Trends® in Machine Learning, vol.1, pp.1-305, 2008. ,
Derivation of various nonmem estimation methods, Journal of Pharmacokinetics and pharmacodynamics, vol.34, issue.5, pp.575-593, 2007. ,
High dimensional EM algorithm: Statistical optimization and asymptotic normality, Advances in Neural Information Processing Systems, vol.28, pp.2521-2529, 2015. ,
High dimensional em algorithm: Statistical optimization and asymptotic normality, Advances in neural information processing systems, pp.2521-2529, 2015. ,
A monte carlo implementation of the EM algorithm and the poor man's data augmentation algorithms, Journal of the American Statistical Association, vol.85, issue.411, pp.699-704, 1990. ,
A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms, Journal of the American Statistical Association, vol.85, issue.411, pp.699-704, 1990. ,
Simple statistical gradient-following algorithms for connectionist reinforcement learning, Machine Learning, vol.8, pp.229-256, 1992. ,
, Bibliography
On the convergence properties of the EM algorithm, The Annals of Statistics, p.11, 1983. ,
On the convergence properties of the EM algorithm, The Annals of statistics, vol.11, issue.1, pp.95-103, 1983. ,
Global analysis of expectation maximization for mixtures of two gaussians, Advances in Neural Information Processing Systems, vol.29, pp.2676-2684, 2016. ,
Global analysis of Expectation Maximization for mixtures of two gaussians, Advances in Neural Information Processing Systems, pp.2676-2684, 2016. ,
First-order stochastic algorithms for escaping from saddle points in almost linear time, Advances in Neural Information Processing Systems, pp.5530-5540, 2018. ,
Parametric regression model for survival data: Weibull regression model as an example, Ann Transl Med, vol.24, 2016. ,
25 1.2 Metropolis-Hastings (MH) algorithm: representation of a proposal q(z) and the target ?(z) distributions in one dimension, p.33 ,
, Viral load of four patients with hepatitis C (taken from, p.35, 2014.
, Algorithme MH: représentation d'une distribution de proposition et d'une distribution cible en dimension 1
, Charge virale pour 4 patients atteints d'hepatitis C (tiré de [Lavielle, p.54, 2014.
, Convergence of first component of the vector of parameters ? and ? for the SAEM, the MCEM and the MISSO methods. The convergence is plotted against the number of passes over the data
71 5.1 Performance of stochastic EM methods for fitting a GMM. (Left) Precision (|µ (k) ? µ | 2 ) as a function of the epoch elapsed. (Right) Number of iterations to reach a precision of 10 ?3, Incremental Variational Inference) Negated ELBO versus epochs elapsed for fitting the Bayesian LeNet-5 on MNIST using different algorithms ,
174 1.1 ERM methods: Table comparing the complexity, measured in terms of iterations, of different algorithms for non-convex optimization. MC stands for Monte Carlo integration of the drift term and Step. for stepsize, Warfarin concentration (mg/l) over time (h) for 32, p.26 ,
Tableau de comparaison de complexité, mesuré en termes d'iterations, de différents algorithmes d'optimisation non convexe. MC siginifie Intégration de Monte Carlo du terme de dérive, p.45 ,
,
,
,
,
, , p.181
,