51,846 research outputs found
Bayesian Reconstruction of Missing Observations
We focus on an interpolation method referred to Bayesian reconstruction in
this paper. Whereas in standard interpolation methods missing data are
interpolated deterministically, in Bayesian reconstruction, missing data are
interpolated probabilistically using a Bayesian treatment. In this paper, we
address the framework of Bayesian reconstruction and its application to the
traffic data reconstruction problem in the field of traffic engineering. In the
latter part of this paper, we describe the evaluation of the statistical
performance of our Bayesian traffic reconstruction model using a statistical
mechanical approach and clarify its statistical behavior
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
While nonlinear stochastic partial differential equations arise naturally in
spatiotemporal modeling, inference for such systems often faces two major
challenges: sparse noisy data and ill-posedness of the inverse problem of
parameter estimation. To overcome the challenges, we introduce a strongly
regularized posterior by normalizing the likelihood and by imposing physical
constraints through priors of the parameters and states. We investigate joint
parameter-state estimation by the regularized posterior in a physically
motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate
reconstruction. The high-dimensional posterior is sampled by a particle Gibbs
sampler that combines MCMC with an optimal particle filter exploiting the
structure of the SEBM. In tests using either Gaussian or uniform priors based
on the physical range of parameters, the regularized posteriors overcome the
ill-posedness and lead to samples within physical ranges, quantifying the
uncertainty in estimation. Due to the ill-posedness and the regularization, the
posterior of parameters presents a relatively large uncertainty, and
consequently, the maximum of the posterior, which is the minimizer in a
variational approach, can have a large variation. In contrast, the posterior of
states generally concentrates near the truth, substantially filtering out
observation noise and reducing uncertainty in the unconstrained SEBM
Conditional Random Field Autoencoders for Unsupervised Structured Prediction
We introduce a framework for unsupervised learning of structured predictors
with overlapping, global features. Each input's latent representation is
predicted conditional on the observable data using a feature-rich conditional
random field. Then a reconstruction of the input is (re)generated, conditional
on the latent structure, using models for which maximum likelihood estimation
has a closed-form. Our autoencoder formulation enables efficient learning
without making unrealistic independence assumptions or restricting the kinds of
features that can be used. We illustrate insightful connections to traditional
autoencoders, posterior regularization and multi-view learning. We show
competitive results with instantiations of the model for two canonical NLP
tasks: part-of-speech induction and bitext word alignment, and show that
training our model can be substantially more efficient than comparable
feature-rich baselines
Predicting trend reversals using market instantaneous state
Collective behaviours taking place in financial markets reveal strongly
correlated states especially during a crisis period. A natural hypothesis is
that trend reversals are also driven by mutual influences between the different
stock exchanges. Using a maximum entropy approach, we find coordinated
behaviour during trend reversals dominated by the pairwise component. In
particular, these events are predicted with high significant accuracy by the
ensemble's instantaneous state.Comment: 18 pages, 15 figure
Scanner Invariant Representations for Diffusion MRI Harmonization
Purpose: In the present work we describe the correction of diffusion-weighted
MRI for site and scanner biases using a novel method based on invariant
representation.
Theory and Methods: Pooled imaging data from multiple sources are subject to
variation between the sources. Correcting for these biases has become very
important as imaging studies increase in size and multi-site cases become more
common. We propose learning an intermediate representation invariant to
site/protocol variables, a technique adapted from information theory-based
algorithmic fairness; by leveraging the data processing inequality, such a
representation can then be used to create an image reconstruction that is
uninformative of its original source, yet still faithful to underlying
structures. To implement this, we use a deep learning method based on
variational auto-encoders (VAE) to construct scanner invariant encodings of the
imaging data.
Results: To evaluate our method, we use training data from the 2018 MICCAI
Computational Diffusion MRI (CDMRI) Challenge Harmonization dataset. Our
proposed method shows improvements on independent test data relative to a
recently published baseline method on each subtask, mapping data from three
different scanning contexts to and from one separate target scanning context.
Conclusion: As imaging studies continue to grow, the use of pooled multi-site
imaging will similarly increase. Invariant representation presents a strong
candidate for the harmonization of these data
An Empirical Study of Stochastic Variational Algorithms for the Beta Bernoulli Process
Stochastic variational inference (SVI) is emerging as the most promising
candidate for scaling inference in Bayesian probabilistic models to large
datasets. However, the performance of these methods has been assessed primarily
in the context of Bayesian topic models, particularly latent Dirichlet
allocation (LDA). Deriving several new algorithms, and using synthetic, image
and genomic datasets, we investigate whether the understanding gleaned from LDA
applies in the setting of sparse latent factor models, specifically beta
process factor analysis (BPFA). We demonstrate that the big picture is
consistent: using Gibbs sampling within SVI to maintain certain posterior
dependencies is extremely effective. However, we find that different posterior
dependencies are important in BPFA relative to LDA. Particularly,
approximations able to model intra-local variable dependence perform best.Comment: ICML, 12 pages. Volume 37: Proceedings of The 32nd International
Conference on Machine Learning, 201
One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks
This paper formulates and studies a general distributed field reconstruction
problem using a dense network of noisy one-bit randomized scalar quantizers in
the presence of additive observation noise of unknown distribution. A
constructive quantization, coding, and field reconstruction scheme is developed
and an upper-bound to the associated mean squared error (MSE) at any point and
any snapshot is derived in terms of the local spatio-temporal smoothness
properties of the underlying field. It is shown that when the noise, sensor
placement pattern, and the sensor schedule satisfy certain weak technical
requirements, it is possible to drive the MSE to zero with increasing sensor
density at points of field continuity while ensuring that the per-sensor
bitrate and sensing-related network overhead rate simultaneously go to zero.
The proposed scheme achieves the order-optimal MSE versus sensor density
scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review
format), 4 figures. Submitted to IEEE Transactions on Signal Processing.
Current version is updated for journal submission: revised author list,
modified formulation and framework. Previous version appeared in Proceedings
of Allerton Conference On Communication, Control, and Computing 200
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