397,178 research outputs found
Distance Measures for Probabilistic Patterns
Numerical measures of pattern dissimilarity are at the heart of pattern recognition and
classification. Applications of pattern recognition grow more sophisticated every year, and
consequently we require distance measures for patterns not easily expressible as feature
vectors. Examples include strings, parse trees, time series, random spatial fields, and
random graphs [79] [117].
Distance measures are not arbitrary. They can only be effective when they incorporate
information about the problem domain; this is a direct consequence of the Ugly Duckling
theorem [37].
This thesis poses the question: how can the principles of information theory and statistics guide us in constructing distance measures? In this thesis, I examine distance functions
for patterns that are maximum-likelihood model estimates for systems that have random
inputs, but are observed noiselessly. In particular, I look at distance measures for histograms, stationary ARMA time series, and discrete hidden Markov models.
I show that for maximum likelihood model estimates, the L2 distance involving the
information matrix at the most likely model estimate minimizes the type II classification
error, for a fixed type I error. I also derive explicit L2 distance measures for ARMA(p, q)
time series and discrete hidden Markov models, based on their respective information
matrices
Infotropism as the underlying principle of perceptual organization
Whether perceptual organization favors the simplest or most likely interpretation of a distal stimulus has long been debated. An unbridgeable gulf has seemed to separate these, the Gestalt and Helmholtzian viewpoints. But in recent decades, the proposal that likelihood and simplicity are two sides of the same coin has been gaining ground, to the extent that their equivalence is now widely assumed. What then arises is a desire to know whether the two principles can be reduced to one. Applying Occam's Razor in this way is particularly desirable given that, as things stand, an account referencing one principle alone cannot be completely satisfactory. The present paper argues that unification of the two principles is possible, and that it can be achieved in terms of an incremental notion of `information seeking' (infotropism). Perceptual processing that is infotropic can be shown to target both simplicity and likelihood. The ability to see perceptual organization as governed by either objective can then be explained in terms of it being an infotropic process. Infotropism can be identified as the principle which underlies, and thus generalizes the principles of likelihood and simplicity
Multiscale Discriminant Saliency for Visual Attention
The bottom-up saliency, an early stage of humans' visual attention, can be
considered as a binary classification problem between center and surround
classes. Discriminant power of features for the classification is measured as
mutual information between features and two classes distribution. The estimated
discrepancy of two feature classes very much depends on considered scale
levels; then, multi-scale structure and discriminant power are integrated by
employing discrete wavelet features and Hidden markov tree (HMT). With wavelet
coefficients and Hidden Markov Tree parameters, quad-tree like label structures
are constructed and utilized in maximum a posterior probability (MAP) of hidden
class variables at corresponding dyadic sub-squares. Then, saliency value for
each dyadic square at each scale level is computed with discriminant power
principle and the MAP. Finally, across multiple scales is integrated the final
saliency map by an information maximization rule. Both standard quantitative
tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating
the proposed multiscale discriminant saliency method (MDIS) against the
well-know information-based saliency method AIM on its Bruce Database wity
eye-tracking data. Simulation results are presented and analyzed to verify the
validity of MDIS as well as point out its disadvantages for further research
direction.Comment: 16 pages, ICCSA 2013 - BIOCA sessio
Bayesian Inference in Processing Experimental Data: Principles and Basic Applications
This report introduces general ideas and some basic methods of the Bayesian
probability theory applied to physics measurements. Our aim is to make the
reader familiar, through examples rather than rigorous formalism, with concepts
such as: model comparison (including the automatic Ockham's Razor filter
provided by the Bayesian approach); parametric inference; quantification of the
uncertainty about the value of physical quantities, also taking into account
systematic effects; role of marginalization; posterior characterization;
predictive distributions; hierarchical modelling and hyperparameters; Gaussian
approximation of the posterior and recovery of conventional methods, especially
maximum likelihood and chi-square fits under well defined conditions; conjugate
priors, transformation invariance and maximum entropy motivated priors; Monte
Carlo estimates of expectation, including a short introduction to Markov Chain
Monte Carlo methods.Comment: 40 pages, 2 figures, invited paper for Reports on Progress in Physic
MaxEnt assisted MaxLik tomography
Maximum likelihood estimation is a valuable tool often applied to inverse
problems in quantum theory. Estimation from small data sets can, however, have
non unique solutions. We discuss this problem and propose to use Jaynes maximum
entropy principle to single out the most unbiased maximum-likelihood guess.Comment: 10 pages, 5 figures, presented at MaxEnt conference in Jackson, WY,
200
Multi-scale Discriminant Saliency with Wavelet-based Hidden Markov Tree Modelling
The bottom-up saliency, an early stage of humans' visual attention, can be
considered as a binary classification problem between centre and surround
classes. Discriminant power of features for the classification is measured as
mutual information between distributions of image features and corresponding
classes . As the estimated discrepancy very much depends on considered scale
level, multi-scale structure and discriminant power are integrated by employing
discrete wavelet features and Hidden Markov Tree (HMT). With wavelet
coefficients and Hidden Markov Tree parameters, quad-tree like label structures
are constructed and utilized in maximum a posterior probability (MAP) of hidden
class variables at corresponding dyadic sub-squares. Then, a saliency value for
each square block at each scale level is computed with discriminant power
principle. Finally, across multiple scales is integrated the final saliency map
by an information maximization rule. Both standard quantitative tools such as
NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed
multi-scale discriminant saliency (MDIS) method against the well-know
information based approach AIM on its released image collection with
eye-tracking data. Simulation results are presented and analysed to verify the
validity of MDIS as well as point out its limitation for further research
direction.Comment: arXiv admin note: substantial text overlap with arXiv:1301.396
Some procedures for computerized ability testing
For computerized test systems to be operational, the use of item response theory is a prerequisite. As opposed to classical test theory, in item response models the abilities of the examinees and the properties of the items are parameterized separately. Hence, when measuring the abilities of examinees, the model implicitly corrects for the item properties, and measurement on an item-independent scale is possible. In addition, item response theory offers the use of test and item information as local reliability indices defined on the ability scale. In this chapter, it is shown how the main features of item response theory have given rise to the development of promising procedures for computerized testing. Among the topics discussed are procedures for item bank calibration, automated test construction, adaptive test administration, generating norm distributions, and diagnosing test scores
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