Learning Filters for Optimum Pattern Recognition

Braverman, David

doi:10.1109/tit.1962.1057722

Cited by 26 publications

(9 citation statements)

References 6 publications

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“…This test is optimal for noise distributions (i.e., conditional probabilities of the response given stimulus) of any shape (Dhingra and Smith, 2004). Our procedure is equivalent to a Bayesian discriminant, or maximum likelihood method for stimuli occurring with equal probability (Braverman, 1962;Geisler et al, 1991;Duda et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

Design of a Neuronal Array

et al. 2008

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Retinal ganglion cells of a given type overlap their dendritic fields such that every point in space is covered by three to four cells. We investigated what function is served by such extensive overlap. Recording from pairs of ON or OFF brisk-transient ganglion cells at photopic intensities, we confirmed that this overlap causes the Gaussian receptive field centers to be spaced at ϳ2 SDs (). This, together with response nonlinearities and variability, was just sufficient to provide an ideal observer with uniform contrast sensitivity across the retina for both threshold and suprathreshold stimuli. We hypothesized that overlap might maximize the information represented from natural images, thereby optimizing retinal performance for many tasks. Indeed, tested with natural images (which contain statistical correlations), a model ganglion cell array maximized information represented in its population responses with ϳ2 spacing, i.e., the overlap observed in the retina. Yet, tested with white noise (which lacks statistical correlations), an array maximized its information by minimizing overlap. In both cases, optimal overlap balanced greater signal-to-noise ratio (from larger receptive fields) against greater redundancy (because of larger receptive field overlap). Thus, dendritic overlap improves vision by taking optimal advantage of the statistical correlations of natural scenes.

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Section: Introductionmentioning

confidence: 99%

Design of a Neuronal Array

et al. 2008

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“…[7][8][9][10] has been based on the computation of p(XJi) when some parameter e. in this probability-density function is unknown. The basic equations are slight modifications of Eqs.…”

Section: Sel-63-099mentioning

confidence: 99%

“…It is again desired to find a decision rule minimizing the probability of error in recognition. Equation (8) and the discussion that accompanies it indicate that the optimum decision rule picks the pattern for which p(Xli)P(i) is maximum.…”

Section: Consider a Variation Of The Pattern-recognition Problem Discmentioning

confidence: 99%

Reproducing Distributions for Machine Learning

Spragins¹

1963

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A model is proposed for learning the nature and value of an unknown parameter, or unknown parameters, in a probability distribution which forms part of a body of statistics related to some system or process.The model is Bayesian, involving the assumption of an a priori probability distribution over the possible values of the unknown parameters; the performance of experiments to gain information about the parameters; and the alteration of the a priori probabilities by Bayes' rule.In the limit, as the number of experiments approaches infinity, the a posteriori distribution in most cases encountered in practice approaches a delta function at the true values of the unknown parameters, so the system learns the values of the parameters exactly.

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“…Further progress has been made in the last few years (see, e.g. [2,4,5,7]). In this paper, we report some results concerning the above and similar types of optimal decision functions.…”

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confidence: 99%

Optimal Decision Functions for Computer Character Recognition

Chu

1965

J. ACM

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The use of statistical decision functions with computers for character recognition is investigated. The three eases considered are (1) where both the losses due to incorrect decisions and the a priori probability of the characters are known, (2) where the a priori probability is known, but the losses are not, and (3) the reverse of the second ease. For the first ease, Bayes decision functions are reviewed. A theorem about the advantage of using rejection is proved. For the second ease, minimum error and minimum rejection decision functions are defined and obtained. For the third ease, admissible, and a complete class of, decision functions are discussed. Illustrative ex'~mples are given. Introd~telionThe use of statistical decision functions is one of the many possible approaches to the problem of character recognition by computer. Decision functions which minimize respectively the average risk and the probability of error anmng those whose probability of rejection is equal to a prescribed limit were considered by Chow [3]. Further progress has been made in the last few years (see, e.g. [2,4,5,7]). In this paper, we report some results concerning the above and similar types of optimal decision functions. The three eases considered are (1) where both the losses due to incorrect decisions and the a priori probability of the characters are known, (2) where the a priori probability is known, but the losses are not, and (3) the reverse of this ease.For the first ease Bayes decision functions which minimize the average risk are reviewed. A special ease is also discussed, where tile losses due to incorrect recognition and rejection (as unrecognizable) are independent of the characters (Equation 7). For that special ease an advantage due to the inclusion of rejection as a possible decision is proved. It is shown that the proportional reduction in Bayes risk, by such a provision, increases as the relative cost of rejection to error decreases (Theorem 1 ). This means that if the cost of rejection is 10w, then the use of rejection to dispose of unrecognizable characters could provide worthwhile savings. On the other hand, if the cost of rejection is not much smaller (or even greater) than that of making an error, Bayes decision functions will never exercise that. option of rejection (Section 2, Remark 2). A similar result is also obtained for the proportional reduction of a posteriori risk (Theorem 1'). For the second ease two types of optimal decision functions are introduced, as generalizations of Chow's work [3]. These are, namely, decision functions which minimize the probability of rejection (error) among those whose probabilities of error (rejection) do not exceed a prescribed limit a (Section 3, Definition 1). ~linimum rejection decision functions may well be of more practical importance, since the probability of making errors which often have more serious consequences

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Learning Filters for Optimum Pattern Recognition

Cited by 26 publications

References 6 publications

Design of a Neuronal Array

Design of a Neuronal Array

Reproducing Distributions for Machine Learning

Optimal Decision Functions for Computer Character Recognition

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