419 research outputs found
Automatic Differentiation Tools in Optimization Software
We discuss the role of automatic differentiation tools in optimization
software. We emphasize issues that are important to large-scale optimization
and that have proved useful in the installation of nonlinear solvers in the
NEOS Server. Our discussion centers on the computation of the gradient and
Hessian matrix for partially separable functions and shows that the gradient
and Hessian matrix can be computed with guaranteed bounds in time and memory
requirementsComment: 11 page
Scalable Rejection Sampling for Bayesian Hierarchical Models
Bayesian hierarchical modeling is a popular approach to capturing unobserved
heterogeneity across individual units. However, standard estimation methods
such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling
outcomes from a large number of units. We develop a new method to sample from
posterior distributions of Bayesian models, without using MCMC. Samples are
independent, so they can be collected in parallel, and we do not need to be
concerned with issues like chain convergence and autocorrelation. The algorithm
is scalable under the weak assumption that individual units are conditionally
independent, making it applicable for large datasets. It can also be used to
compute marginal likelihoods
Generalized Direct Sampling for Hierarchical Bayesian Models
We develop a new method to sample from posterior distributions in
hierarchical models without using Markov chain Monte Carlo. This method, which
is a variant of importance sampling ideas, is generally applicable to
high-dimensional models involving large data sets. Samples are independent, so
they can be collected in parallel, and we do not need to be concerned with
issues like chain convergence and autocorrelation. Additionally, the method can
be used to compute marginal likelihoods
Book of Abstracts of the Sixth SIAM Workshop on Combinatorial Scientific Computing
Book of Abstracts of CSC14 edited by Bora UçarInternational audienceThe Sixth SIAM Workshop on Combinatorial Scientific Computing, CSC14, was organized at the Ecole Normale Supérieure de Lyon, France on 21st to 23rd July, 2014. This two and a half day event marked the sixth in a series that started ten years ago in San Francisco, USA. The CSC14 Workshop's focus was on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. The workshop featured three invited talks, 27 contributed talks and eight poster presentations. All three invited talks were focused on two interesting fields of research specifically: randomized algorithms for numerical linear algebra and network analysis. The contributed talks and the posters targeted modeling, analysis, bisection, clustering, and partitioning of graphs, applied in the context of networks, sparse matrix factorizations, iterative solvers, fast multi-pole methods, automatic differentiation, high-performance computing, and linear programming. The workshop was held at the premises of the LIP laboratory of ENS Lyon and was generously supported by the LABEX MILYON (ANR-10-LABX-0070, Université de Lyon, within the program ''Investissements d'Avenir'' ANR-11-IDEX-0007 operated by the French National Research Agency), and by SIAM
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