177,899 research outputs found
Declarative Modeling and Bayesian Inference of Dark Matter Halos
Probabilistic programming allows specification of probabilistic models in a
declarative manner. Recently, several new software systems and languages for
probabilistic programming have been developed on the basis of newly developed
and improved methods for approximate inference in probabilistic models. In this
contribution a probabilistic model for an idealized dark matter localization
problem is described. We first derive the probabilistic model for the inference
of dark matter locations and masses, and then show how this model can be
implemented using BUGS and Infer.NET, two software systems for probabilistic
programming. Finally, the different capabilities of both systems are discussed.
The presented dark matter model includes mainly non-conjugate factors, thus, it
is difficult to implement this model with Infer.NET.Comment: Presented at the Workshop "Intelligent Information Processing",
EUROCAST2013. To appear in selected papers of Computer Aided Systems Theory -
EUROCAST 2013; Volumes Editors: Roberto Moreno-D\'iaz, Franz R. Pichler,
Alexis Quesada-Arencibia; LNCS Springe
Global convergence rate analysis of unconstrained optimization methods based on probabilistic models
We present global convergence rates for a line-search method which is based
on random first-order models and directions whose quality is ensured only with
certain probability. We show that in terms of the order of the accuracy, the
evaluation complexity of such a method is the same as its counterparts that use
deterministic accurate models; the use of probabilistic models only increases
the complexity by a constant, which depends on the probability of the models
being good. We particularize and improve these results in the convex and
strongly convex case.
We also analyze a probabilistic cubic regularization variant that allows
approximate probabilistic second-order models and show improved complexity
bounds compared to probabilistic first-order methods; again, as a function of
the accuracy, the probabilistic cubic regularization bounds are of the same
(optimal) order as for the deterministic case
Probabilistic structural analysis algorithm development for computational efficiency
The PSAM (Probabilistic Structural Analysis Methods) program is developing a probabilistic structural risk assessment capability for the SSME components. An advanced probabilistic structural analysis software system, NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), is being developed as part of the PSAM effort to accurately simulate stochastic structures operating under severe random loading conditions. One of the challenges in developing the NESSUS system is the development of the probabilistic algorithms that provide both efficiency and accuracy. The main probability algorithms developed and implemented in the NESSUS system are efficient, but approximate in nature. In the last six years, the algorithms have improved very significantly
Approximate inference methods in probabilistic machine learning and Bayesian statistics
This thesis develops new methods for efficient approximate inference in probabilistic models. Such models are routinely used in different fields, yet they remain computationally challenging as they involve high-dimensional integrals. We propose different approximate inference approaches addressing some challenges in probabilistic machine learning and Bayesian statistics. First, we present a Bayesian framework for genome-wide inference of DNA methylation levels and devise an efficient particle filtering and smoothing algorithm that can be used to identify differentially methylated regions between case and control groups. Second, we present a scalable inference approach for state space models by combining variational methods with sequential Monte Carlo sampling. The method is applied to self-exciting point process models that allow for flexible dynamics in the latent intensity function. Third, a new variational density motivated by copulas is developed. This new variational family can be beneficial compared with Gaussian approximations, as illustrated on examples with Bayesian neural networks. Lastly, we make some progress in a gradient-based adaptation of Hamiltonian Monte Carlo samplers by maximizing an approximation of the proposal entropy
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