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38
Dependency networks for inference, collaborative filtering, and data visualization
 Journal of Machine Learning Research
"... We describe a graphical model for probabilistic relationshipsan alternative tothe Bayesian networkcalled a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of ..."
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Cited by 157 (10 self)
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We describe a graphical model for probabilistic relationshipsan alternative tothe Bayesian networkcalled a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of conditional distributions, one for each nodegiven its parents. We identify several basic properties of this representation and describe a computationally e cient procedure for learning the graph and probability components from data. We describe the application of this representation to probabilistic inference, collaborative ltering (the task of predicting preferences), and the visualization of acausal predictive relationships.
Structure from motion causally integrated over time
 IEEE Trans Pattern Analysis & Machine Intelligence
"... AbstractÐWe describe an algorithm for reconstructing threedimensional structure and motion causally, in real time from monocular sequences of images. We prove that the algorithm is minimal and stable, in the sense that the estimation error remains bounded with probability one throughout a sequence ..."
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Cited by 79 (4 self)
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AbstractÐWe describe an algorithm for reconstructing threedimensional structure and motion causally, in real time from monocular sequences of images. We prove that the algorithm is minimal and stable, in the sense that the estimation error remains bounded with probability one throughout a sequence of arbitrary length. We discuss a scheme for handling occlusions �point features appearing and disappearing) and drift in the scale factor. These issues are crucial for the algorithm to operate in real time on real scenes. We describe in detail the implementation of the algorithm, which runs on a personal computer and has been made available to the community. We report the performance of our implementation on a few representative long sequences of real and synthetic images. The algorithm, which has been tested extensively over the course of the past few years, exhibits honest performance when the scene contains at least 2040 points with high contrast, when the relative motion is ªslowº compared to the sampling frequency of the frame grabber �30Hz), and the lens aperture is ªlarge enoughº �typically more than 30 o of visual field). Index TermsÐStructure from motion, realtime vision, shape, geometry. æ 1
Towards a Theory of Landscapes
, 1995
"... this paper), spanned by eigenvectors f` y g of the graph Laplacian, the familiar properties of Fourier series, such as Parseval's equation kfk ..."
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Cited by 59 (6 self)
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this paper), spanned by eigenvectors f` y g of the graph Laplacian, the familiar properties of Fourier series, such as Parseval's equation kfk
A semidirect approach to structure from motion
 Vis. Comput. 2003
"... The problem of structure form motion is often decomposed into two steps: feature correspondence and threedimensional reconstruction. This separation often causes gross errors when establishing correspondence fails. Therefore, we advocate the necessity to integrate visual information not only in tim ..."
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Cited by 30 (1 self)
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The problem of structure form motion is often decomposed into two steps: feature correspondence and threedimensional reconstruction. This separation often causes gross errors when establishing correspondence fails. Therefore, we advocate the necessity to integrate visual information not only in time (i.e. across different views), but also in space, by matching regions – rather than points – using explicit photometric deformation models. We present an algorithm that integrates image region tracking and threedimensional motion estimation into a closed loop, while detecting and rejecting outlier regions that do not fit the model. Due to occlusions and the causal nature of our algorithm, a drift in the estimates accumulates over time. We describe a method to perform global registration of local estimates of motion and structure by matching the appearance of feature regions stored over long time periods. We use image intensities to construct a score function that takes into account changes in brightness and contrast. Our algorithm is recursive and suitable for realtime implementation. 1
3D Motion and Structure from 2D Motion Causally Integrated over Time: Implementation
 In IEEE Trans. Robotics and Automation
, 2000
"... The causal estimation of threedimensional motion from a sequence of twodimensional images can be posed as a nonlinear filtering problem. We describe the implementation of an algorithm whose uniform observability, minimal realization and stability have been proven analytically in [5]. We discuss a ..."
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Cited by 20 (1 self)
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The causal estimation of threedimensional motion from a sequence of twodimensional images can be posed as a nonlinear filtering problem. We describe the implementation of an algorithm whose uniform observability, minimal realization and stability have been proven analytically in [5]. We discuss a scheme for handling occlusions, drift in the scale factor and tuning of the lter. We also present an extension to partially calibrated camera models and prove its observability. We report the performance of our implementation on a few long sequences of real images. More importantly, however, we have made our realtime implementation  which runs on a personal computer  available to the public for firsthand testing.
Philosophy and the practice of Bayesian statistics
, 2010
"... A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually ..."
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Cited by 15 (6 self)
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A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypotheticodeductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.
Multiply stochastic representations for K distributions and their Poisson transforms
 Journal of the Optical Society of America A
, 1989
"... The K distribution is used in a number of areas of scientific endeavor. In optics, it provides a useful statistical description for fluctuations of the irradiance (and the electric field) of light that has been scattered or transmitted through random media (e.g., the turbulent atmosphere). The Poiss ..."
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Cited by 4 (3 self)
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The K distribution is used in a number of areas of scientific endeavor. In optics, it provides a useful statistical description for fluctuations of the irradiance (and the electric field) of light that has been scattered or transmitted through random media (e.g., the turbulent atmosphere). The Poisson transform of the K distribution describes the photoncounting statistics of light whose irradiance is K distributed. The Kdistribution family can be represented in a multiply stochastic (compound) form whereby the mean of a gamma distribution is itself stochastic and is described by a member of the gamma family of distributions. Similarly, the family of Poisson transforms of the K distributions can be represented as a family of negativebinomial transforms of the gamma distributions or as Whittaker distributions. The K distributions have heretofore had their origins in randomwalk models; the multiply stochastic representations provide an alternative interpretation of the genesis of these distributions and their Poisson transforms. By multiple compounding, we have developed a new transform pair as a possibly useful addition to the Kdistribution family. All these distributions decay slowly and are difficult to calculate accurately by conventional formulas. A recursion relation, together with a generalized method of steepest descent, has been developed to evaluate numerically the photoncounting distributions and their factorial moments with excellent accuracy. 1.
GIS and spatial data analysis: converging perspectives
 Papers in Regional Science
, 2004
"... We take as our starting point the state of geographic information systems (GIS) and spatial data analysis 50 years ago when regional science emerged as a new field of enquiry. In the late 1950s and 1960s advances in computing technology were making possible forms of automated cartography that in due ..."
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Cited by 3 (0 self)
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We take as our starting point the state of geographic information systems (GIS) and spatial data analysis 50 years ago when regional science emerged as a new field of enquiry. In the late 1950s and 1960s advances in computing technology were making possible forms of automated cartography that in due course would lead to the
Fluctuations of the impulse rate in Limulus eccentric cells
 J. Gen
, 1971
"... ABSTRACT Fluctuations in the discharge of impulses were studied in eccentric cells of the compound eye of the horseshoe crab, Limulus polyphemus. A theory is presented which accounts for the variability in the response of the eccentric cell to light. The main idea of this theory is that the source o ..."
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Cited by 3 (1 self)
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ABSTRACT Fluctuations in the discharge of impulses were studied in eccentric cells of the compound eye of the horseshoe crab, Limulus polyphemus. A theory is presented which accounts for the variability in the response of the eccentric cell to light. The main idea of this theory is that the source of randomness in the impulse rate is "noise " in the generator potential. Another essential aspect of the theory is that the process which transforms the generator potential "noise" into the impulse rate fluctuations may be treated as a linear filter. These ideas lead directly to Fourier analysis of the fluctuations. Experimental verification of theoretical predictions was obtained by calculation of the variance spectrum of the impulse rate. The variance spectrum of the impulse rate is shown to be the filtered variance spectrum of the generator potential.
Evolution of the Statistical Properties of Photons Passed through a TravelingWave Laser Amplifier
 IEEE J. Quantum Electron
, 1992
"... We determine the evolution of the photon statistics of a light beam as it passes through a travelingwave laser amplifier, modeled as a birthdeathimmigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but p ..."
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Cited by 2 (1 self)
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We determine the evolution of the photon statistics of a light beam as it passes through a travelingwave laser amplifier, modeled as a birthdeathimmigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but possibly varying) birth, death, and immigration rates for arbitrary input statistics is obtained. The case of constant birth, death, and immigration rates is considered in particular detail. The photon statistics at the output of a general BDI travelingwave amplifier are always broader than those at the input, and they can take many forms. Our most general solution can be applied when the input distribution to the amplifier takes the form of a negativebinomial transform. The results are expected to be useful in calculating the performance characteristics of lightwave systems using optical amplifiers in which the object is to detect light with a broad range of statistical properties, including scattered light, spontaneousemission light, and light emitted from a laser. In the latter case the input is Poisson, and the output distribution assumes the form of a noncentralnegativebinomial (Laguerre) distribution which is usually associated with a multimode (phasepreserving) superposition of coherent and chaotic fields.