Device, method, and medium for predicting a probability of an occurrence of a data
First Claim
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1. A Bayes mixture density calculator operable in response to a sequence of vectors xn=(x1, x2, . . . , xn) selected from a vector value set x to produce a Bayes mixture density on occurrence of the xn, comprising:
- a probability density calculator, supplied with a sequence of data xt and a vector value parameter u, for calculating a probability density for the xt, p(xt|u);
a Bayes mixture calculator for calculating a first approximation value of a Bayes mixture density pw(xn) on the basis of a prior distribution w(u) predetermined by the probability density calculator to produce the first approximation value;
an enlarged mixture calculator for calculating a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle in cooperation with the probability density calculator to produce the second approximation value; and
a whole mixture calculator for calculating (1−
e) pw(xn)+e·
m(xn) to produce a calculation result by mixing the first approximation value of the Bayes mixture density pw(xn) with a part of the second approximation value of the Bayes mixture m(xn) at a rate of 1−
e;
e to produce the calculation result where e is a value smaller than unity, said Bayes mixture density calculator including a device for applying said calculation result to perform data compression using arithmetic coding.
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Abstract
In a Bayes mixture probability density calculator for calculating Bayes mixture probability density which reduces a logarithmic loss A modified Bayes mixture probability density is calculated by mixing raditional Bayes mixture probability density calculated on given model S with a small pary of Bayes mixture probability density for exponential fiber bundle on the S. Likewise, a prediction probability calculator is configured by including the Bayes mixture probability density calculator, and by using Jeffredys prior distribution in traditional Bayes procedure on the S.
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Citations
12 Claims
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1. A Bayes mixture density calculator operable in response to a sequence of vectors xn=(x1, x2, . . . , xn) selected from a vector value set x to produce a Bayes mixture density on occurrence of the xn, comprising:
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a probability density calculator, supplied with a sequence of data xt and a vector value parameter u, for calculating a probability density for the xt, p(xt|u);
a Bayes mixture calculator for calculating a first approximation value of a Bayes mixture density pw(xn) on the basis of a prior distribution w(u) predetermined by the probability density calculator to produce the first approximation value;
an enlarged mixture calculator for calculating a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle in cooperation with the probability density calculator to produce the second approximation value; and
a whole mixture calculator for calculating (1−
e) pw(xn)+e·
m(xn) to produce a calculation result by mixing the first approximation value of the Bayes mixture density pw(xn) with a part of the second approximation value of the Bayes mixture m(xn) at a rate of 1−
e;
e to produce the calculation result where e is a value smaller than unity, said Bayes mixture density calculator including a device for applying said calculation result to perform data compression using arithmetic coding.- View Dependent Claims (3)
a joint probability calculator structured by the Bayes mixture density calculator claimed in claim 1 for calculating a modified Bayes mixture density q(ε
)(xn) and q(ε
)(xn+1) based on predetermined prior distribution to produce first calculation results; and
a divider responsive to the calculation results for calculating probability density (ε
)(xn+1)/q(ε
)(xn) to produce a second calculation result with the first calculation results kept intact.
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2. A Jeffreys mixture density calculator operable in response to a sequence of vectors xn=(x1, x2, . . . , xn) selected from a vector value set x to produce a Bayes mixture density on occurrence of the xn, comprising:
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a probability density calculator, supplied with a sequence of data xt and a vector value parameter u, for calculating a probability density for the xt, p(xt|u);
a Jeffreys mixture calculator for calculating a first approximation value of a Bayes mixture density pJ(xn) on the basis of a prior distribution wJ(u) predetermined by the probability density calculator to produce the first approximation value;
an enlarged mixture calculator for calculating a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle in cooperation with the probability density calculator to produce the second approximation value; and
a whole mixture calculator for calculating (1−
e) pJ(xn)+e·
m(xn) to produce a calculation result by mixing the first approximation value of the Bayes mixture density pJ(xn) with a part of the second approximation value of the Bayes mixture m(xn) at a rate of 1−
e;
e to produce the calculation result where e is a value smaller than unity, said Jeffreys mixture density calculator including a device for applying said calculation result to perform data compression using arithmetic coding.- View Dependent Claims (4)
a joint probability calculator structured by the Jeffreys mixture density calculator claimed in claim 2 for calculating a modified Jeffreys mixture density q(ε
)(xn) and q(ε
)(xn+1) to produce first calculation results; and
a divider response to the calculation results for calculating a probability density q(ε
)(xn−
1)/q(ε
)(xn) to produce a second calculation result with the first calculation results kept intact.
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5. A Bayes mixture density calculating means for operation in response to a sequence of vectors xn=(x1, x2, . . . , xn) selected from a vector value set χ
- to produce a Bayes mixture density on occurrence of the xn, comprising;
a probability density calculating means, supplied with a sequence of data xt and a vector value parameter u, for calculating a probability density for the xt, p(xt|u);
a Bayes mixture calculating means for calculating a first approximation value of a Bayes mixture density pw(xn) on the basis of a prior distribution w(u) predetermined by the probability density calculating means to produce the first approximation value;
an enlarged mixture calculating means for calculating a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle in cooperation with the probability density calculating means to produce the second approximation value; and
a whole mixture calculating means for calculating (1−
ε
)pw(xn)+ε
·
m(xn) to produce a calculation result by mixing the first approximation value of the Bayes mixture density pw(xn) with a part of the second approximation value of the Bayes mixture m(xn) at a rate of 1−
ε
;
ε
to produce the calculation result where ε
is a value smaller than unity, said Bayes mixture density calculating means including means for applying said calculation result to perform data compression using arithmetic coding.- View Dependent Claims (6)
a joint probability calculating means structured by the Bayes mixture density calculating means claimed in claim 5 for calculating a modified Bayes mixture density q(ε
)(xn) and q(ε
)(xn+1) based on predetermined prior distribution to produce first calculation results; and
a divider responsive to the calculation results for calculating probability density q(ε
)(xn+1)/q(ε
)(xn) to produce a second calculation result with the first calculation results kept intact.
- to produce a Bayes mixture density on occurrence of the xn, comprising;
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7. A Jeffreys mixture density calculating means for operation in response to a sequence of vector xn=(x1, x2, . . . , xn) selected from a vector value set χ
- to produce a Bayes mixture density on occurrence of the xn, comprising;
a probability density calculating means responsive to a sequence of data xt and a vector value parameter u for calculating a probability density p(xt|u) for the xt;
a Jeffreys mixture calculating means for calculating a first approximation value of a Bayes mixture density pj(xn) based on a Jeffreys prior distribution wJ(u) in cooperation with the probability density calculating means to produce the first approximation value;
an enlarged mixture calculating means for calculating a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle in cooperation with the probability density calculating means to produce the second approximation value; and
a whole mixture calculating means for calculating (1−
ε
)pw(xn)+ε
·
m(xn) to produce a calculation result by mixing the first approximation value of the Bayes mixture density pJ(xn) with a part of the second approximation value of the Bayes mixture m(xn) at a rate of 1−
ε
;
ε
to produce the calculation result where ε
is a value smaller than unity, said Jeffreys mixture density calculating means including means for applying said calculation result to perform data compression using arithmetic coding.- View Dependent Claims (8)
a joint probability calculating means structured by the Jeffreys mixture density calculating means claimed in claim 7 for calculating a modified Jeffreys mixture density q(ε
)(xn) and q(ε
)(xn+1) to produce first calculation results; and
a dividing means, responsive to the calculation results for calculating a probability density q(ε
)(xn+1)/q(ε
)(xn) to produce a second calculation result with the first calculation results kept intact.
- to produce a Bayes mixture density on occurrence of the xn, comprising;
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9. A Bayes mixture density calculator, comprising:
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a probability density calculator having an input that includes a sequence of vectors xn=(x1, x2, . . . , xn) selected from a vector value set χ
to produce a Bayes mixture density on occurrence of the xn, supplied with a sequence of data xt and a vector value parameter u, that calculates a probability density for the xt, p(xt|u), and a first output;
a Bayes mixture calculator that is coupled to the first output and generates a first approximation value of a Bayes mixture density pw(xn) on the basis of a prior distribution w(u) predetermined by the probability density calculator to produce the first approximation value as a second output;
an enlarged mixture calculator having an input that receives the first output from the probability density calculator to calculate a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle and produce the second approximation value; and
a whole mixture calculator that mixes the first approximation value, received from the Bayes mixture calculator, of the Bayes mixture density pw(xn) with a part of the second approximation value received from the enlarged mixture calculator, of the Bayes mixture m(xn) at a rate of 1−
ε
;
ε
to generate (1−
ε
)pw(xn)+·
m(xn) and produce the calculation result where ε
is a value smaller than unity, said Bayes mixture density calculator including a device for applying said calculation result to perform data compression using arithmetic coding.- View Dependent Claims (10)
a joint probability calculator that is structured by the Bayes mixture density calculator of claim 9 and calculates a modified Bayes mixture density q(ε
)(xn) and q(ε
)(xn+1) based on an input that comprises a predetermined prior distribution to produce first calculation results at a first output; and
a divider, coupled to the joint probability calculator and responsive to the calculation results at said output that generates probability density q(ε
)(xn+1)/q(ε
)(xn+1) to produce a second calculation result at a second output, with the first calculation results kept intact.
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11. A Jeffreys mixture density calculator, comprising:
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a probability density calculator having an input that includes a sequence of vector xn=(x1, x2, . . . , xn) selected from a vector value set χ
to produce a Bayes mixture density on occurrence of the xn, responsive to a sequence of data xt and a vector value parameter u that calculates a probability density p(xt|u) for the xt at a first output and a second output;
a Jeffreys mixture calculator that calculates a first approximation value of a Bayes mixture density pj(xn) based on a Jeffreys prior distribution wJ(u) in cooperation with the input and first output of the probability density calculator to produce the first approximation value;
an enlarged mixture calculator that calculates a second approximation value of a Bayes mixture m(xn) on exponential fiber bundle in cooperation with the second output of the probability density calculator to output the second approximation value; and
a whole mixture calculator that calculates (1−
ε
)pw(xn)+ε
·
m(xn) to produce a calculation result by mixing the first approximation value, from an output of the Jeffreys mixture calculator, of the Bayes mixture density pJ(xn) with a part of the second approximation value, output by the enlarged mixture calculator, of the Bayes mixture m(xn) at a rate of 1−
ε
;
ε
to produce the calculation result wherein ε
is a value smaller than unity, said Jeffreys mixture density calculator including a device for applying said calculation result to perform data compression using arithmetic coding.- View Dependent Claims (12)
a joint probability calculator structured by the Jeffreys mixture density calculator of claim 11 that calculates a modified Jeffreys mixture density q(ε
)(xn) and q(ε
)(xn+1) to produce first calculation results; and
a divider, responsive to the calculation results, that calculates a probability density q(ε
)(xn+1)/q(ε
)(xn) to produce a second calculation result with the first calculation results kept intact.
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Specification
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Current AssigneeNEC Corporation, Yale University
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Original AssigneeNEC Corporation, Yale University
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InventorsBarron, Andrew R., Takeuchi, Jun-Ichi
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Primary Examiner(s)Hoff, Marc S.
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Assistant Examiner(s)TSAI, CAROL S W
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Application NumberUS09/099,405Publication NumberTime in Patent Office1,580 DaysField of Search702/179, 702/181, 702/198, 700/91, 700/93, 341/50, 341/107US Class Current702/181CPC Class CodesG06F 17/18 for evaluating statistical ...
