10,872 research outputs found
Bayesian Robust Tensor Factorization for Incomplete Multiway Data
We propose a generative model for robust tensor factorization in the presence
of both missing data and outliers. The objective is to explicitly infer the
underlying low-CP-rank tensor capturing the global information and a sparse
tensor capturing the local information (also considered as outliers), thus
providing the robust predictive distribution over missing entries. The
low-CP-rank tensor is modeled by multilinear interactions between multiple
latent factors on which the column sparsity is enforced by a hierarchical
prior, while the sparse tensor is modeled by a hierarchical view of Student-
distribution that associates an individual hyperparameter with each element
independently. For model learning, we develop an efficient closed-form
variational inference under a fully Bayesian treatment, which can effectively
prevent the overfitting problem and scales linearly with data size. In contrast
to existing related works, our method can perform model selection automatically
and implicitly without need of tuning parameters. More specifically, it can
discover the groundtruth of CP rank and automatically adapt the sparsity
inducing priors to various types of outliers. In addition, the tradeoff between
the low-rank approximation and the sparse representation can be optimized in
the sense of maximum model evidence. The extensive experiments and comparisons
with many state-of-the-art algorithms on both synthetic and real-world datasets
demonstrate the superiorities of our method from several perspectives.Comment: in IEEE Transactions on Neural Networks and Learning Systems, 201
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
Fuzzy Fibers: Uncertainty in dMRI Tractography
Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI)
allows for noninvasive reconstruction of fiber bundles in the human brain. In
this chapter, we discuss sources of error and uncertainty in this technique,
and review strategies that afford a more reliable interpretation of the
results. This includes methods for computing and rendering probabilistic
tractograms, which estimate precision in the face of measurement noise and
artifacts. However, we also address aspects that have received less attention
so far, such as model selection, partial voluming, and the impact of
parameters, both in preprocessing and in fiber tracking itself. We conclude by
giving impulses for future research
Emotion Recognition in the Wild using Deep Neural Networks and Bayesian Classifiers
Group emotion recognition in the wild is a challenging problem, due to the
unstructured environments in which everyday life pictures are taken. Some of
the obstacles for an effective classification are occlusions, variable lighting
conditions, and image quality. In this work we present a solution based on a
novel combination of deep neural networks and Bayesian classifiers. The neural
network works on a bottom-up approach, analyzing emotions expressed by isolated
faces. The Bayesian classifier estimates a global emotion integrating top-down
features obtained through a scene descriptor. In order to validate the system
we tested the framework on the dataset released for the Emotion Recognition in
the Wild Challenge 2017. Our method achieved an accuracy of 64.68% on the test
set, significantly outperforming the 53.62% competition baseline.Comment: accepted by the Fifth Emotion Recognition in the Wild (EmotiW)
Challenge 201
A Bayesian - Deep Learning model for estimating Covid-19 evolution in Spain
This work proposes a semi-parametric approach to estimate Covid-19
(SARS-CoV-2) evolution in Spain. Considering the sequences of 14 days
cumulative incidence of all Spanish regions, it combines modern Deep Learning
(DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma
model for counts. DL model provides a suitable description of observed
sequences but no reliable uncertainty quantification around it can be obtained.
To overcome this we use the prediction from DL as an expert elicitation of the
expected number of counts along with their uncertainty and thus obtaining the
posterior predictive distribution of counts in an orthodox Bayesian analysis
using the well known Poisson-Gamma model. The overall resulting model allows us
to either predict the future evolution of the sequences on all regions, as well
as, estimating the consequences of eventual scenarios.Comment: Related to: https://github.com/scabras/covid19-bayes-d
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