PSEUDOGRAPHOID AXIOMS AND THE COVARIANCE GLOBAL MARKOV PROPERTY
The covariance and the concentration graphs are two undirected graphs associated with a random vector X. Each vertex... more
The covariance and the concentration graphs are two undirected graphs associated with a random vector X. Each vertex in these graphs corresponds to a variable in the vector X. The absence
of an edge in the covariance graph between any pair of vertices encodes pairwise marginal independence between the variables represented by these vertices. The absence of an edge between any pair of vertices in the concentration graph encodes onditional independence between these two variables given the rest. More complex conditional independence relationships at the level of sets of variables can also be deduced from separation tatements from these two graphs by using the global Markov property with respect to the graph. The equivalence of the pairwise and global Markov property for concentration graphs is valid under a general condition called the pseudographoid axiom. The analogous result for the covariance global Markov property however requires the verification of a longer list of properties. One typical set of conditions are the so-called weak transitivity composition(WTC) graphoid axioms. Hence the global Markov property cannot be invoked as easily for covariance graphs. The aim of this paper is to prove that the covariance global Markov property can be established under simpler conditions, in particular when the converse of the pseudographoid axiom is satisfied. The result therefore significantly reduces the conditions that need to
verified for the application of the covariance global Markov property, and in the process establishes a duality
between the covariance and concentration global Markov properties.
Efficient Markov Network Structure Discovery from Independence Tests.
Bromberg, F., Margaritis, D., and Honavar, V. (2009). Efficient Markov Network Structure Discovery from Independence Tests. Journal of Artificial Intelligence Research. Vol. 35. pp. 449-485.
A Classic and Neural Probabilistic Approach to the Dust Storm Detection Problem
This paper address the problem of dust storm detection based on multispectral image analysis from a probabilistic... more This paper address the problem of dust storm detection based on multispectral image analysis from a probabilistic point of view. Two classifiers are designed, one based on classic probability theory and other based on a probabilistic computational intelligence approach. The first classifier is designed under the Maximum Likelihood Estimation (MLE) model, and the second with a Probabilistic Neural Network (PNN) model. The data set used in this work consists of MODIS instrument at the NASA’s Terra satellite data, generating 75 millions of samples used in the design and validation of the classifiers. Findings indicated that the PNN presents a better classification performance than the MLE classifier. The proposed models are suitable for near real-time applications, and provide with an output at a resolution of 1km, which is an improvement over the methods based on the MODIS AOT product which has a 10km resolution.
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Seen by:A Probabilistic Model for Stratospheric Soil-Independent Dust Aerosol Detection
We present a simple probabilistic model for dust aerosol detection, analysing MODIS 11.3µm and 12.02µm thermal... more We present a simple probabilistic model for dust aerosol detection, analysing MODIS 11.3µm and 12.02µm thermal emissive bands. We introduce a dust aerosol probabilistic visualization, and a feasible extension to classification.
Automatic Dust Storm Detection Based on Supervised Classification of Multispectral Data
This paper address the detection of dust storms based on a probabilistic analysis of multispectral images. We develop... more This paper address the detection of dust storms based on a probabilistic analysis of multispectral images. We develop a feature set based on the analysis of spectral bands reported in the literature. These studies have focused on the visual identification of the image channels that reflect the presence of dust storms through correlation with meteorological reports. Using this feature set we develop a Maximum Likelihood classifier and a Probabilistic Neural Network (PNN) to automate the dust storm detection process. The data sets are MODIS multispectral bands from NASA Terra satellite. Findings indicate that the PNN provides improved classification performance with reference to the ML classifier. Furthermore, the proposed schemes allow real-time processing of satellite data at 1 km resolutions which is an improvement compared to the 10 km resolution currently provided by other detection methods.
A Classic and Neural Probabilistic Approach to Remote Sensing: The Dust Storm Detection Problem
Dust storms are a natural severe weather condition. A recent study in 2009 found correlation between lung diseases and... more
Dust storms are a natural severe weather condition. A recent study in 2009 found correlation between lung diseases and dust storm events. Since then, more research has been done for dust air-borne suspended particle (aerosol) analysis. However, there is paucity of formal methods in machine learning. Particularly, we study a classic and hybrid neural probabilistic approach to alleviate the lack of specialized classification methods. The maximum Likelihood Estimator (MLE) and the hybrid Probabilistic Neural Network (PNN) approaches are discussed.
The features utilized are Moderate Resolution Imaging Spectroradiometer (MODIS) thermal emissive spectral bands. We utilized four near infrared bands: B20, B29, B31, and B32. Numerical performance evaluation show that the hybrid approach (PNN) performed better than the classic (MLE). Visually, both accurately detect dust storms. The classifiers demonstrated a strong ability to find non-trivial relationships within the spectral bands. Both methods demonstrated to be soil-independent and surface-invariant detection methods. The proposed methods can be effectively utilized in understanding dust storm phenomena.

