48,747 research outputs found
Probabilistic Graphical Model Representation in Phylogenetics
Recent years have seen a rapid expansion of the model space explored in
statistical phylogenetics, emphasizing the need for new approaches to
statistical model representation and software development. Clear communication
and representation of the chosen model is crucial for: (1) reproducibility of
an analysis, (2) model development and (3) software design. Moreover, a
unified, clear and understandable framework for model representation lowers the
barrier for beginners and non-specialists to grasp complex phylogenetic models,
including their assumptions and parameter/variable dependencies.
Graphical modeling is a unifying framework that has gained in popularity in
the statistical literature in recent years. The core idea is to break complex
models into conditionally independent distributions. The strength lies in the
comprehensibility, flexibility, and adaptability of this formalism, and the
large body of computational work based on it. Graphical models are well-suited
to teach statistical models, to facilitate communication among phylogeneticists
and in the development of generic software for simulation and statistical
inference.
Here, we provide an introduction to graphical models for phylogeneticists and
extend the standard graphical model representation to the realm of
phylogenetics. We introduce a new graphical model component, tree plates, to
capture the changing structure of the subgraph corresponding to a phylogenetic
tree. We describe a range of phylogenetic models using the graphical model
framework and introduce modules to simplify the representation of standard
components in large and complex models. Phylogenetic model graphs can be
readily used in simulation, maximum likelihood inference, and Bayesian
inference using, for example, Metropolis-Hastings or Gibbs sampling of the
posterior distribution
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Power Flow Modelling of Dynamic Systems - Introduction to Modern Teaching Tools
As tools for dynamic system modelling both conventional methods such as
transfer function or state space representation and modern power flow based
methods are available. The latter methods do not depend on energy domain, are
able to preserve physical system structures, visualize power conversion or
coupling or split, identify power losses or storage, run on conventional
software and emphasize the relevance of energy as basic principle of known
physical domains. Nevertheless common control structures as well as analysis
and design tools may still be applied. Furthermore the generalization of power
flow methods as pseudo-power flow provides with a universal tool for any
dynamic modelling. The phenomenon of power flow constitutes an up to date
education methodology. Thus the paper summarizes fundamentals of selected power
flow oriented modelling methods, presents a Bond Graph block library for
teaching power oriented modelling as compact menu-driven freeware, introduces
selected examples and discusses special features.Comment: 12 pages, 9 figures, 4 table
Visual analytics for supply network management: system design and evaluation
We propose a visual analytic system to augment and enhance decision-making processes of supply chain managers. Several design requirements drive the development of our integrated architecture and lead to three primary capabilities of our system prototype. First, a visual analytic system must integrate various relevant views and perspectives that highlight different structural aspects of a supply network. Second, the system must deliver required information on-demand and update the visual representation via user-initiated interactions. Third, the system must provide both descriptive and predictive analytic functions for managers to gain contingency intelligence. Based on these capabilities we implement an interactive web-based visual analytic system. Our system enables managers to interactively apply visual encodings based on different node and edge attributes to facilitate mental map matching between abstract attributes and visual elements. Grounded in cognitive fit theory, we demonstrate that an interactive visual system that dynamically adjusts visual representations to the decision environment can significantly enhance decision-making processes in a supply network setting. We conduct multi-stage evaluation sessions with prototypical users that collectively confirm the value of our system. Our results indicate a positive reaction to our system. We conclude with implications and future research opportunities.The authors would like to thank the participants of the 2015 Businessvis Workshop at IEEE VIS, Prof. Benoit Montreuil, and Dr. Driss Hakimi for their valuable feedback on an earlier version of the software; Prof. Manpreet Hora for assisting with and Georgia Tech graduate students for participating in the evaluation sessions; and the two anonymous reviewers for their detailed comments and suggestions. The study was in part supported by the Tennenbaum Institute at Georgia Tech Award # K9305. (K9305 - Tennenbaum Institute at Georgia Tech Award)Accepted manuscrip
High-Dimensional Dependency Structure Learning for Physical Processes
In this paper, we consider the use of structure learning methods for
probabilistic graphical models to identify statistical dependencies in
high-dimensional physical processes. Such processes are often synthetically
characterized using PDEs (partial differential equations) and are observed in a
variety of natural phenomena, including geoscience data capturing atmospheric
and hydrological phenomena. Classical structure learning approaches such as the
PC algorithm and variants are challenging to apply due to their high
computational and sample requirements. Modern approaches, often based on sparse
regression and variants, do come with finite sample guarantees, but are usually
highly sensitive to the choice of hyper-parameters, e.g., parameter
for sparsity inducing constraint or regularization. In this paper, we present
ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning,
which estimates an edge specific parameter in the first step,
and uses these parameters to learn the structure in the second step. Both steps
of our algorithm use (inexact) ADMM to solve suitable linear programs, and all
iterations can be done in closed form in an efficient block parallel manner. We
compare ACLIME-ADMM with baselines on both synthetic data simulated by partial
differential equations (PDEs) that model advection-diffusion processes, and
real data (50 years) of daily global geopotential heights to study information
flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and
competitive, usually better than the baselines especially on difficult
problems. On real data, ACLIME-ADMM recovers the underlying structure of global
atmospheric circulation, including switches in wind directions at the equator
and tropics entirely from the data.Comment: 21 pages, 8 figures, International Conference on Data Mining 201
Probabilistic Intra-Retinal Layer Segmentation in 3-D OCT Images Using Global Shape Regularization
With the introduction of spectral-domain optical coherence tomography (OCT),
resulting in a significant increase in acquisition speed, the fast and accurate
segmentation of 3-D OCT scans has become evermore important. This paper
presents a novel probabilistic approach, that models the appearance of retinal
layers as well as the global shape variations of layer boundaries. Given an OCT
scan, the full posterior distribution over segmentations is approximately
inferred using a variational method enabling efficient probabilistic inference
in terms of computationally tractable model components: Segmenting a full 3-D
volume takes around a minute. Accurate segmentations demonstrate the benefit of
using global shape regularization: We segmented 35 fovea-centered 3-D volumes
with an average unsigned error of 2.46 0.22 {\mu}m as well as 80 normal
and 66 glaucomatous 2-D circular scans with errors of 2.92 0.53 {\mu}m
and 4.09 0.98 {\mu}m respectively. Furthermore, we utilized the inferred
posterior distribution to rate the quality of the segmentation, point out
potentially erroneous regions and discriminate normal from pathological scans.
No pre- or postprocessing was required and we used the same set of parameters
for all data sets, underlining the robustness and out-of-the-box nature of our
approach.Comment: Accepted for publication in Medical Image Analysis (MIA), Elsevie
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