Neural network learning system inferring an input-output relationship from a set of given input and output samples
First Claim
1. A neural network learning system for inferring an input-output relationship from a set of given input and output samples, comprising:
- a) probability density means for determining a probability density on a sum space of an input space and an output space from the set of given input and output samples by learning a value of a parameter through a prescribed maximum likelihood method;
b) inference means for determining a probability density function based on the probability density from said probability density means, to infer the input-output relationship of the samples from the probability density function;
wherein the learning a value of the parameter is repeated by said inference means until a value of a predefined parameter differential function using the prescribed maximum likelihood method is smaller than a prescribed value, thereby determining said parameter value;
c) conditional probability distribution means for computing a conditional probability distribution from either the given input samples or the given output samples in accordance with the probability density function determined by said inference means; and
d) output means for obtaining an inference value based on the conditional probability distribution from said conditional probability distribution means and for outputting said inference value.
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Abstract
A neural network learning system in which an input-output relationship is inferred. The system includes a probability density part for determining a probability density on a sum space of an input space and an output space from a set of given input and output samples by learning, the probability density on the sum space being defined to have a parameter, and an inference part for inferring a probability density function based on the probability density from the probability density part, so that an input-output relationship of the samples is inferred from the probability density function having a parameter value determined by learning, the learning of the parameter being repeated until the value of a predefined parameter differential function using a prescribed maximum likelihood method is smaller than a prescribed reference value.
69 Citations
27 Claims
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1. A neural network learning system for inferring an input-output relationship from a set of given input and output samples, comprising:
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a) probability density means for determining a probability density on a sum space of an input space and an output space from the set of given input and output samples by learning a value of a parameter through a prescribed maximum likelihood method; b) inference means for determining a probability density function based on the probability density from said probability density means, to infer the input-output relationship of the samples from the probability density function;
wherein the learning a value of the parameter is repeated by said inference means until a value of a predefined parameter differential function using the prescribed maximum likelihood method is smaller than a prescribed value, thereby determining said parameter value;c) conditional probability distribution means for computing a conditional probability distribution from either the given input samples or the given output samples in accordance with the probability density function determined by said inference means; and d) output means for obtaining an inference value based on the conditional probability distribution from said conditional probability distribution means and for outputting said inference value. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
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15. A neural network learning system for inferring an input-output relationship from a set of given input and output samples, comprising:
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a) probability density means for determining a probability density on a sum space of an input space and an output space from the set of given input and output samples by learning a value of a parameter through a prescribed maximum likelihood method; b) inference means for determining a probability density function based on the probability density from said probability density means, to infer the input-output relationship of the samples from the probability density function;
wherein the learning a value of the parameter is repeated by said inference means until a value of a predefined parameter differential function using the prescribed maximum likelihood method is smaller than a prescribed value, thereby determining said parameter value;c) conditional probability distribution means for computing a conditional probability distribution from either the given input samples or the given output samples in accordance with the probability density function determined by said inference means; and d) output means for obtaining an inference value based on the conditional probability distribution from said conditional probability distribution means and for outputting said inference value; wherein; 1) said conditional probability distribution computed in accordance with the probability density function is an input distribution function P(w;
x|y),2) x|y indicates a relationship between x and y, and 3) said output means determines and outputs a set of inputs x in accordance with said function P(w;
x|y) for a given output y, and a set of values of said function P(w;
x|y) corresponding to the respective inputs x.
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16. A neural network learning system for inferring an input-output relationship from a set of given input and output samples, comprising:
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a) probability density means for determining a probability density on a sum space of an input space and an output space from the set of given input and output samples by learning a value of a parameter through a prescribed maximum likelihood method; b) inference means for determining a probability density function based on the probability density from said probability density means, to infer the input-output relationship of the samples from the probability density function;
wherein the learning a value of the parameter is repeated by said inference means until a value of a predefined parameter differential function using the prescribed maximum likelihood method is smaller than a prescribed value, thereby determining said parameter value;c) conditional probability distribution means for computing a conditional probability distribution from either the given input samples or the given output samples in accordance with the probability density function determined by said inference means; and d) output means for obtaining an inference value based on the conditional probability distribution from said conditional probability distribution means and for outputting said inference value; wherein; 1) a set of outputs and a probability of occurrence for each one of the outputs are determined for a given input, a probability density to determine the probability of occurrence being approximated by a linear combination of predetermined exponential functions according to a prescribed probability distribution function and being learned repeatedly using the prescribed maximum likelihood method; and 2) when the probability of occurrence for the given input is obtained, a determination is made whether the given input is known or unknown based on said probability of occurrence for the given input.
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17. A neural network learning system for inferring an input-output relationship from a set of given input and output samples, comprising:
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a) probability density means for determining a probability density on a sum space of an input space and an output space from the set of given input and output samples by learning a value of a parameter through a prescribed maximum likelihood method; b) inference means for determining a probability density function based on the probability density from said probability density means, to infer the input-output relationship of the samples from the probability density function;
wherein the learning a value of the parameter is repeated by said inference means until a value of a predefined parameter differential function using the prescribed maximum likelihood method is smaller than a prescribed value, thereby determining said parameter value;c) conditional probability distribution means for computing a conditional probability distribution from either the given input samples or the given output samples in accordance with the probability density function determined by said inference means; and d) output means for obtaining an inference value based on the conditional probability distribution from said conditional probability distribution means and for outputting said inference value; wherein an inference value for each of a set of outputs and a variance of the inference values are determined by said learning performed based on the probability density on the sum space for the given input and output samples. - View Dependent Claims (18, 19, 20, 21, 23, 24, 25, 26)
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22. A neural network learning system in which an input-output relationship for a set of input and output samples is predetermined, said system comprising:
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a) output probability means for determining output probabilities for given inputs in accordance with probability distributions on a sum space of an input space and an output space; and b) parameter learning means for carrying out a learning of parameters, the parameters respectively defining the probability distributions of said output probability means, wherein said parameter learning means includes; 1) clustering means for classifying the given data on the sum space into a set of clusters to determine statistical quantities of data in each of the clusters, and 2) parameter computing means for determining values of the parameters for the probability distributions of the output probability means based on the statistical quantities of the data from the clustering means. - View Dependent Claims (11, 12, 13, 14, 27)
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Specification