Our previous work developed an online learning Bayesian framework (dynamic tree) for data organization and
clustering. To continuously adapt the system during operation, we concurrently seek to perform outlier detection
to prevent them from incorrectly modifying the system. We propose a new Bayesian surprise metric to differentiate
outliers from the training data and thus help to selectively adapt the model parameters. The metric is
calculated based on the difference between the prior and the posterior distributions on the model when a new
sample is introduced. A good training datum would sufficiently but not excessively change the model; consequently,
the difference between the prior and the posterior distributions would be reasonable to the amount of
new information present on the datum. However, an outlier carries an element of surprise that would significantly
change the model. In such a case, the posterior distribution would greatly differ from the prior resulting in a large
value for the surprise metric. We categorize this datum as an outlier and other means (e.g. human operator) will
have to be used to handle such cases. The surprise metric is calculated based on the model distribution, and as
such, it adapts with the model. The surprise factor is dependent on the state of the system. This speeds up the
learning process by considering only the relevant new data. Both the model parameters and even the structure
of the dynamic tree can be updated under this approach.
KEYWORDS: Data modeling, Data fusion, Statistical modeling, Visual process modeling, Annealing, Algorithms, Statistical inference, Machine vision, Computer vision technology, Chemical elements
In this work, we propose DEformable BAyesian Networks (DEBAN), a probabilistic graphical model framework
where model selection and statistical inference can be viewed as two key ingredients in the same iterative
process. While this concept has shown successful results in computer vision community,1-4 our proposed approach
generalizes the concept such that it is applicable to any data type. Our goal is to infer the optimal structure/model
to fit the given observations. The optimal structure conveys an automatic way to find not only the number of
clusters in the data set, but also the multiscale graph structure illustrating the dependence relationship among
the variables in the network. Finally, the marginal posterior distribution at each root node is regarded as the
fused information of its corresponding observations, and the most probable state can be found from the maximum
a posteriori (MAP) solution with the uncertainty of the estimate in the form of a probability distribution which
is desired for a variety of applications.
KEYWORDS: LIDAR, Data modeling, Motion measurement, Data centers, Data analysis, Motion models, Error analysis, Laser scanners, 3D scanning, Vegetation
Land surface elevation measurements from airborne laser swath mapping (ALSM) data can be irregularly spaced due to occlusion by forest canopy or scanner and aircraft motion. The measurements are usually interpolated into a regularly spaced grid using techniques such as Kriging or spline-interpolation. In this paper a probabilistic
graphical model called a Bayesian network (BN) is employed to interpolate missing data. A grid of nodes is imposed over ALSM measurements and the elevation information at each node is estimated using two methods: 1) a simple causal method, similar to a Markov mesh random field (MMRF), and 2) BN belief propagation. The interpolated results of both algorithms using the maximum a posteriori (MAP) estimates are presented and compared. Finally, uncertainty measures are introduced and evaluated against the final estimates from the BN belief propagation algorithm.
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