602 research outputs found
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
Geometric ergodicity of the Random Walk Metropolis with position-dependent proposal covariance
We consider a Metropolis-Hastings method with proposal kernel
, where is the current state. After discussing
specific cases from the literature, we analyse the ergodicity properties of the
resulting Markov chains. In one dimension we find that suitable choice of
can change the ergodicity properties compared to the Random Walk
Metropolis case , either for the better or worse. In
higher dimensions we use a specific example to show that judicious choice of
can produce a chain which will converge at a geometric rate to its
limiting distribution when probability concentrates on an ever narrower ridge
as grows, something which is not true for the Random Walk Metropolis.Comment: 15 pages + appendices, 4 figure
A framework for the construction of generative models for mesoscale structure in multilayer networks
Multilayer networks allow one to represent diverse and coupled connectivity patterns—such as time-dependence, multiple subsystems, or both—that arise in many applications and which are difficult or awkward to incorporate into standard network representations. In the study of multilayer networks, it is important to investigate mesoscale (i.e., intermediate-scale) structures, such as dense sets of nodes known as communities, to discover network features that are not apparent at the microscale or the macroscale. The ill-defined nature of mesoscale structure and its ubiquity in empirical networks make it crucial to develop generative models that can produce the features that one encounters in empirical networks. Key purposes of such models include generating synthetic networks with empirical properties of interest, benchmarking mesoscale-detection methods and algorithms, and inferring structure in empirical multilayer networks. In this paper, we introduce a framework for the construction of generative models for mesoscale structures in multilayer networks. Our framework provides a standardized set of generative models, together with an associated set of principles from which they are derived, for studies of mesoscale structures in multilayer networks. It unifies and generalizes many existing models for mesoscale structures in fully ordered (e.g., temporal) and unordered (e.g., multiplex) multilayer networks. One can also use it to construct generative models for mesoscale structures in partially ordered multilayer networks (e.g., networks that are both temporal and multiplex). Our framework has the ability to produce many features of empirical multilayer networks, and it explicitly incorporates a user-specified dependency structure between layers. We discuss the parameters and properties of our framework, and we illustrate examples of its use with benchmark models for community-detection methods and algorithms in multilayer networks
Predicting Flavonoid UGT Regioselectivity with Graphical Residue Models and Machine Learning.
Machine learning is applied to a challenging and biologically significant protein classification problem: the prediction of flavonoid UGT acceptor regioselectivity from primary protein sequence. Novel indices characterizing graphical models of protein residues are introduced. The indices are compared with existing amino acid indices and found to cluster residues appropriately. A variety of models employing the indices are then investigated by examining their performance when analyzed using nearest neighbor, support vector machine, and Bayesian neural network classifiers. Improvements over nearest neighbor classifications relying on standard alignment similarity scores are reported
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