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Register a new userSampling Spatially Correlated Clutter
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Added by
Georgina Flesia MS
Publication date
2008
fields
Mathematical Statistics
and research's language is
English
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Correlated ${cal G}$ distributions can be used to describe the clutter seen in images obtained with coherent illumination, as is the case of B-scan ultrasound, laser, sonar and synthetic aperture radar (SAR) imagery. These distributions are derived using the square root of the generalized inverse Gaussian distribution for the amplitude backscatter within the multiplicative model. A two-parameters particular case of the amplitude ${mathcal G}$ distribution, called ${mathcal G}_{A}^{0}$, constitutes a modeling improvement with respect to the widespread ${mathcal K}_{A}$ distribution when fitting urban, forested and deforested areas in remote sensing data. This article deals with the modeling and the simulation of correlated ${mathcal G}_{A}^{0}$-distributed random fields. It is accomplished by means of the Inverse Transform method, applied to Gaussian random fields with spatial correlation. The main feature of this approach is its generality, since it allows the introduction of negative correlation values in the resulting process, necessary for the proper explanation of the shadowing effect in many SAR images.
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Sampling errors in nested sampling parameter estimation differ from those in Bayesian evidence calculation, but have been little studied in the literature. This paper provides the first explanation of the two main sources of sampling errors in nested sampling parameter estimation, and presents a new diagrammatic representation for the process. We find no current method can accurately measure the parameter estimation errors of a single nested sampling run, and propose a method for doing so using a new algorithm for dividing nested sampling runs. We empirically verify our conclusions and the accuracy of our new method.
Spatial regression or geographically weighted regression models have been widely adopted to capture the effects of auxiliary information on a response variable of interest over a region. In contrast, relationships between response and auxiliary variables are expected to exhibit complex spatial patterns in many applications. This paper proposes a new approach for spatial regression, called spatially clustered regression, to estimate possibly clustered spatial patterns of the relationships. We combine K-means-based clustering formulation and penalty function motivated from a spatial process known as Potts model for encouraging similar clustering in neighboring locations. We provide a simple iterative algorithm to fit the proposed method, scalable for large spatial datasets. Through simulation studies, the proposed method demonstrates its superior performance to existing methods even under the true structure does not admit spatial clustering. Finally, the proposed method is applied to crime event data in Tokyo and produces interpretable results for spatial patterns. The R code is available at https://github.com/sshonosuke/SCR.
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based samplings world.
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Nandish Chattopadhyay
, Lionell Yip En Zhi
, Bryan Tan Bing Xing andn Anupam Chattopadhyay
2020
Adversarial attacks have proved to be the major impediment in the progress on research towards reliable machine learning solutions. Carefully crafted perturbations, imperceptible to human vision, can be added to images to force misclassification by an otherwise high performing neural network. To have a better understanding of the key contributors of such structured attacks, we searched for and studied spatially co-located patterns in the distribution of pixels in the input space. In this paper, we propose a framework for segregating and isolating regions within an input image which are particularly critical towards either classification (during inference), or adversarial vulnerability or both. We assert that during inference, the trained model looks at a specific region in the image, which we call Region of Importance (RoI); and the attacker looks at a region to alter/modify, which we call Region of Attack (RoA). The success of this approach could also be used to design a post-hoc adversarial defence method, as illustrated by our observations. This uses the notion of blocking out (we call neutralizing) that region of the image which is highly vulnerable to adversarial attacks but is not important for the task of classification. We establish the theoretical setup for formalising the process of segregation, isolation and neutralization and substantiate it through empirical analysis on standard benchmarking datasets. The findings strongly indicate that mapping features into the input space preserves the significant patterns typically observed in the feature-space while adding major interpretability and therefore simplifies potential defensive mechanisms.
The coherent potential approximation (CPA) is extended to describe satisfactorily the motion of particles in a random potential which is spatially correlated and smoothly varying. In contrast to existing cluster-CPA methods, the present scheme preserves the simplicity of the conventional CPA in using a single self-energy function. Its accuracy is checked by a comparison with the exact moments of the Greens function, and with the spectral function from numerical simulations. The scheme is applied to excitonic absorption spectra in different spatial dimensions.
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