Device, method, and medium for predicting a probability of an occurrence of a data
First Claim
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1. An apparatus for processing 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 Bayes mixture density calculator having an input that receives a sequence of data xt and a vector value parameter u, and an output, the Bayes mixture density calculator comprising;
a first calculator that calculates, from the sequence of data xt received at the input of the Bayes mixture density calculator, a probability density p(xt|u) for the data xt on curved exponential family;
a second calculator, coupled to the first calculator, that calculates a first approximation value of a Bayes mixture density pw(xn) on the basis of a prior distribution w(u) predetermined by the first calculator to produce the first approximation value;
a third calculator, coupled to the first calculator, that calculates a second approximation value of a Bayes mixture m(xn) on exponential family including curved exponential family in cooperation with the first calculator to produce the second approximation value; and
a fourth calculator, coupled to the second and third calculators, that calculates (1−
ε
)pw(xn)−
ε
·
m(xn) 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
, where ε
is a value smaller than unity, to produce the Bayes mixture density on occurrence of the xn for arithmetic coding during data compression, the Bayes mixture density being output from the Bayes mixture density calculator.
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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 traditional Bayes mixture probability density calculated on given model S with a small part of Bayes mixture probability density for exponential fiber bundle on the S. Likewise, a prediction probability density calculator is configured by including the Bayes mixture probability density calculator, and by using Jeffreys prior distribution in traditional Bayes procedure on the S.
31 Citations
18 Claims
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1. An apparatus for processing 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 Bayes mixture density calculator having an input that receives a sequence of data xt and a vector value parameter u, and an output, the Bayes mixture density calculator comprising;
a first calculator that calculates, from the sequence of data xt received at the input of the Bayes mixture density calculator, a probability density p(xt|u) for the data xt on curved exponential family;
a second calculator, coupled to the first calculator, that calculates a first approximation value of a Bayes mixture density pw(xn) on the basis of a prior distribution w(u) predetermined by the first calculator to produce the first approximation value;
a third calculator, coupled to the first calculator, that calculates a second approximation value of a Bayes mixture m(xn) on exponential family including curved exponential family in cooperation with the first calculator to produce the second approximation value; and
a fourth calculator, coupled to the second and third calculators, that calculates (1−
ε
)pw(xn)−
ε
·
m(xn) 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
, where ε
is a value smaller than unity, to produce the Bayes mixture density on occurrence of the xn for arithmetic coding during data compression, the Bayes mixture density being output from the Bayes mixture density calculator.- View Dependent Claims (3)
a joint probability calculator structured by the apparatus claimed in claim 1 for calculating a modified Bayes mixture density q(ε
)(xn) and q(ε
)(xn+1) based on a predetermined prior distribution to produce first calculation results; and
a divider coupled to receive an output of the joint probability calculator and responsive to the calculation results for calculating a probability density q(ε
)(xn+1)/q(ε
)(xn) to produce as an output 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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2. An apparatus for processing of 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 Jeffreys mixture density calculator having an input that receives a sequence of data xt and a vector value parameter u, and an output, the Jeffreyss mixture density calculator comprising;
a first calculator that calculates, from the sequence of data xt received at the input of the Bayes mixture density calculator, a probability density p(xt|u) for the data xt on curved exponential family;
a second calculator, coupled to the first 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 first calculator to produce the first approximation value;
a third calculator, coupled to the first calculator, that calculates a second approximation value of a Bayes mixture m(xn) on exponential family including curved exponential family in cooperation with the first calculator to produce the second approximation value; and
a fourth calculator, coupled to the second and third calculators, that calculates (1−
ε
)pJ(xn) 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 ratio of 1−
ε
;
ε
, where ε
is a value smaller than unity, to produce the Bayes mixture density on occurrence of the xn for arithmetic coding during data compression, the Bayes mixture density being output from the Jeffreys mixture density calculator.- View Dependent Claims (4)
a joint probability calculator structured by the apparatus 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 coupled to receive an output of the joint probability calculator and responsive to the calculation results for calculating a probability density q(ε
)(xn+1)/q(ε
)(xn) to produce as an output 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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5. A means for processing a sequence of data xn=(x1, x2, . . . , xn) to produce a mixture density on occurrence of the xn, comprising:
-
means for calculating the mixture density having an input that receives the sequence of data xn, and an output, the Bayes mixture density calculating means comprising;
means for calculating a first Bayes mixture density on a hypothesis class;
means for calculating a second Bayes mixture density on an enlarged hypothesis class; and
means for mixing the first Bayes mixture density with the second Bayes mixture density in a predetermined proportion to produce a the modified Bayes mixture density, wherein the means for calculating the mixture density outputs the modified Bayes mixture density as the mixture density on occurrence of the xn for arithmetic coding during data compression. - View Dependent Claims (6, 7, 8, 9)
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10. A means for processing a sequence of data xn=(x1, x2, . . . , xn) and a data xn+1 to produce a prediction probability density on occurrence of the xn+1 comprising:
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means for calculating a prediction probability density having an input that receives the sequence of data xn and data xn+1, and an output, the means for calculating a prediction probability density comprising;
means for calculating first Bayes mixture densities, on a hypothesis class, for the sequence of data xn and a sequence of data xn+1 which representing (x1, x2, . . . , xn, xn+1);
means for calculating second Bayes mixture densities, on an enlarged hypothesis class, for the sequence of data xn and the sequence of data xn+1;
means for mixing the first Bayes mixture densities for the sequence of data xn and the sequence of data xn+1 with the second Bayes mixture densities for the sequence of data xn and the sequence of data xn+1, in a predetermined proportion to produce the modified Bayes mixture densities for the sequence of data xn and the sequence of data xn+1, respectively; and
means for dividing the modified Bayes mixture density for the sequence of data xn+1 by the modified Bayes mixture density for the sequence of data xn, wherein the means for calculating a prediction probability density outputs the result as the prediction probability density on occurrence of the xn+1 for arithmetic coding during data compression. - View Dependent Claims (11, 12, 13, 14)
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15. A method for processing a sequence of data xn=(x1, x2, . . . , xn) to produce a mixture density on occurrence of the xn, wherein the method comprises:
-
receiving the sequence of data xn;
calculating a first Bayes mixture density on a hypothesis class;
calculating a second Bayes mixture density on an enlarged hypothesis class; and
mixing the first Bayes mixture density with the second Bayes mixture density in a predetermined proportion to produce the mixture density on occurrence of the xn for arithmetic coding during data compression.
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16. A method for processing a sequence of data xn=(x1, x2, . . . , xn) and a data xn+1 to produce a prediction probability density on occurrence of the xn+1, wherein the method comprises:
-
receiving the sequence of data xn and data xn+1; and
repeating, for each sequence of data xn and each sequence of data xn+1 representing (x1, x2, . . . , xn, xn+1), the following first through third substeps of;
(1) calculating a first Bayes mixture density, on a hypothesis class, for the sequence of data xn and the sequence of data xn+1;
(2) calculating a second Bayes mixture density, on an enlarged hypothesis class, for the sequence of data xn and the sequence of data xn+1; and
(3) mixing the first Bayes mixture densities for the sequence of data xn and the sequence of data xn+1 with the second Bayes mixture densities for the sequence of data xn and the sequence of data xn+1 in a predetermined proportion to produce modified Bayes mixture densities for the sequence of data xn and the sequence of data xn+1; and
dividing the modified Bayes mixture density for the sequence of data xn+1 by the modified Bayes mixture density for the sequence of data xn, wherein the result is output as the prediction probability density on occurrence of the xn+1 for arithmetic coding during data compression.
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17. A computer readable medium which stores a program for processing a sequence of data xn=(x1, x2, . . . , xn) to produce a mixture density on occurrence of the xn, the program comprising the steps of:
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receiving the sequence of data xn;
calculating a first Bayes mixture density on a hypothesis class;
calculating a second Bayes mixture density on an enlarged hypothesis class; and
mixing the first Bayes mixture density with the second Bayes mixture density in a predetermined proportion to produce the mixture density on occurrence of the xn for arithmetic coding during data compression.
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18. A computer readable medium which stores a program which is for processing a sequence of data xn=(x1, x2, . . . , xn) and a data xn+1 to produce a prediction probability density on occurrence of the xn+1 the program comprising the steps of:
-
receiving the sequence of data xn and xn+1;
repeating, for each sequence of data xn and each sequence of data xn+1 which representing (x1, x2, . . . , xn, xn+1), the following substeps;
(1) calculating a first Bayes mixture density, on a hypothesis class, for the sequence of data xn and the sequence of data xn+1;
(2) calculating a second Bayes mixture density, on an enlarged hypothesis class, for the sequence of data xn and the sequence of data xn+1 data (3) mixing the first Bayes mixture densities for the sequence of data xn and the sequence of data xn+1 with the second Bayes mixture densities for the sequence of data xn and the sequence of data xn+1, in a predetermined proportion to produce modified Bayes mixture densities for the sequence of data xn and the sequence of data xn+1; and
dividing the modified Bayes mixture density for the sequence of data xn+1 by the modified Bayes mixture density for the sequence of data xn, wherein the result is output as the prediction probability density on occurrence of the xn+1 for arithmetic coding during data compression.
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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 NumberUS10/227,461Publication NumberTime in Patent Office694 DaysField of Search702/179, 702/181, 702/198, 700/91, 700/93, 341/50, 341/107, 703/2US Class Current702/189CPC Class CodesG06F 17/18 for evaluating statistical ...
