Methods and apparatus to determine characteristics of media audiences

1. A method to determine characteristics of media audiences, the method comprising:

creating, by executing an instruction via a processor, a constraint matrix in computer memory based on a first activity being associated with a first characteristic of a population, the first activity being associated with a second characteristic of the population, and a first combination being associated with at least one of the first activity, the first characteristic, and the second characteristic;

creating, by executing an instruction via the processor, a combination total set in the computer memory based on a first measurement for the first activity being associated with the first characteristic and a second measurement for the first activity being associated with the second characteristic;

computing, by executing an instruction via the processor, a first entropy probability based on an equality constraint including the constraint matrix and the combination total set; and

reducing an amount of data collected by the processor by estimating, by executing an instruction via the processor, a first portion of the population that matches the first combination based on the first entropy probability.

2. The method as defined in claim 1 , wherein the creating of the constraint matrix is further based on the first activity being associated with a third characteristic of the population.

3. The method as defined in claim 1 , wherein the creating of the constraint matrix is further based on a second activity being associated with the first characteristic and the second activity being associated with the second characteristic.

4. The method as defined in claim 1 , wherein the creating of the constraint matrix is further based on a second combination being associated with at least one of the first activity, the first characteristic, and the second characteristic, the second combination being different than the first combination.

5. The method as defined in claim 1 , wherein the creating of the constraint matrix includes assigning the first activity being associated with the first characteristic as a first row of the constraint matrix, assigning the first activity being associated with the second characteristic as a second row of the constraint matrix, and assigning the first combination as a column of the constraint matrix.

6. The method as defined in claim 1 , wherein the calculating of the first entropy probability includes performing non-linear optimization of the constraint matrix and the combination total set using a Jacobian and multivariate Newton's method.

7. The method as defined in claim 1 , wherein the computing of the first entropy probability includes approximating a first maximum entropy probability.

8. The method as defined in claim 1 , further including identifying an audience characteristic of the population by utilizing the first portion of the population as partial panelist data to determine the audience characteristic.

9. The method as defined in claim 1 , wherein the processor includes at least a first processor of a first hardware computer system and a second processor of a second hardware computer system.

10. The method as defined in claim 1 , further including:

identifying the first characteristic;

identifying the second characteristic; and

identifying an association between the first activity and the first characteristic and an association between the first activity and the second characteristic.

11. The method as defined in claim 1 , further including:

collecting the first measurement for the first activity being associated with the first characteristic; and

collecting the second measurement for the first activity being associated with the second characteristic.

12. The method as defined in claim 1 , further including calculating a lower bound of the first portion and an upper bound of the first portion.

13. The method as defined in claim 1 , further including determining an audience characteristic of the population based on the first portion.

14. The method as defined in claim 1 , wherein the first characteristic and the second characteristic include at least one of panelist households having a first quantity of members, panelist households having a second quantity of television sets, and all panelist households.

15. The method as defined in claim 1 , wherein the first activity includes total tuning minutes or total presentation minutes.

16. The method of claim 4 , further including:

computing, by executing an instruction via the processor, a second entropy probability based on the constraint matrix and the combination total set; and

estimating, by executing an instruction via the processor, a second portion of the population that matches the second combination based on the second entropy probability.

17. An apparatus to determine characteristics of media audiences, the apparatus comprising:

a constraint constructor to:

create a constraint matrix in computer memory based on a first activity being associated with a first characteristic of a population, the first activity being associated with a second characteristic of the population, and a first combination being associated with at least one of the first activity, the first characteristic, and the second characteristic; and

create a combination total set in the computer memory based on a first measurement for the first activity being associated with the first characteristic and a second measurement being associated with the second characteristic; and

a probability calculator to:

compute a first entropy probability based on an equality constraint including the constraint matrix and the combination total set; and

reduce an amount of data collected by the constraint constructor by estimating a first portion of the population that matches the first combination based on the first entropy probability.

18. The apparatus as defined in claim 17 , wherein the probability calculator is to calculate a lower bound of the first portion and an upper bound of the first portion.

19. The apparatus as defined in claim 17 , further including a characteristic determiner to determine an audience characteristic of the population based on the first portion.

20. The apparatus as defined in claim 17 , wherein the first characteristic and the second characteristic include at least one of panelist households having a first quantity of members, panelist households having a second quantity of television sets, and all panelist households.

21. The apparatus as defined in claim 17 , wherein the first activity includes total tuning minutes or total presentation minutes.

22. The apparatus as defined in claim 17 , wherein, to create the constraint matrix, the constraint constructor is to:

assign the first activity being associated with the first characteristic as a first row of the constraint matrix;

assign the first activity being associated with the second characteristic as a second row of the constraint matrix; and

assign the first combination as a column of the constraint matrix.

23. The apparatus as defined in claim 17 , wherein, to calculate the first entropy probability, the probability calculator is to perform non-linear optimization of the constraint matrix and the combination total set using a Jacobian and multivariate Newton's method.

24. The apparatus as defined in claim 17 , wherein the constraint constructor is to create the constraint matrix further based on the first activity being associated with a third characteristic of the population.

25. The apparatus as defined in claim 17 , wherein the constraint constructor is to create the constraint matrix further based on a second activity being associated with the first characteristic and the second activity being associated with the second characteristic.

26. The apparatus as defined in claim 17 , wherein the constraint constructor is to create the constraint matrix further based on a second combination being associated with at least one of the first activity, the first characteristic, and the second characteristic, the second combination being different than the first combination.

27. The apparatus as defined in claim 17 , wherein, to compute the first entropy probability, the probability calculator is to approximate a first maximum entropy probability.

28. The apparatus as defined in claim 17 , wherein the probability calculator is to estimate an audience characteristic of the population by utilizing the first portion of the population as partial panelist data to determine the audience characteristic.

29. The apparatus as defined in claim 17 , wherein the constraint constructor is to:

identify the first characteristic;

identify the second characteristic; and

identify an association between the first activity and the first characteristic and an association between the first activity and the second characteristic.

30. The apparatus as defined in claim 17 , wherein the constraint constructor is to:

collect the first measurement for the first activity being associated with the first characteristic; and

collect the second measurement for the first activity being associated with the second characteristic.

31. The apparatus of claim 26 , wherein the probability calculator further is to:

compute a second entropy probability based on the constraint matrix and the combination total set; and

estimate a second portion of the population that matches the second combination based on the second entropy probability.

32. A tangible computer readable storage medium to determine characteristics of media audiences, the tangible computer readable storage medium comprising instructions which, when executed, cause a machine to at least:

create a constraint matrix in computer memory based on a first activity being associated with a first audience characteristic of a population, the first activity being associated with a second audience characteristic of the population, and a first combination being associated with at least one of the first activity, the first characteristic, and the second characteristic;

create a combination total set in the computer memory based on a first measurement for the first activity being associated with the first characteristic and a second measurement for the first activity being associated with the second characteristic;

compute a first entropy probability based on an equality constraint including the constraint matrix and the combination total set; and

reduce an amount of data collected by a processor by estimating a first portion of the population that matches the first combination based on the first entropy probability.

33. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to create the constraint matrix is further based on the first activity being associated with a third characteristic of the population.

34. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to create the constraint matrix further based on a second activity being associated with the first characteristic and the second activity being associated with the second characteristic.

35. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to create the constraint matrix further based on a second combination being associated with at least one of the first activity, the first characteristic, and the second characteristic, the second combination being different than the first combination.

36. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to compute the first entropy probability by approximating a first maximum entropy probability.

37. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to estimate an audience characteristic of the population by utilizing the first portion of the population as partial panelist data to determine the audience characteristic.

38. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to calculate a lower bound of the first portion and an upper bound of the first portion.

39. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to determine an audience characteristic of the population based on the first portion.

40. The tangible computer readable storage medium as defined in claim 32 , wherein the first characteristic and the second characteristic include at least one of panelist households having a first quantity of members, panelist households having a second quantity of television sets, and all panelist households.

41. The tangible computer readable storage medium as defined in claim 32 , wherein the first activity includes total tuning minutes or total presentation minutes.

42. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to create the constraint matrix by:

assigning the first activity being associated with the first characteristic as a first row of the constraint matrix;

assigning the first activity being associated with the second characteristic as a second row of the constraint matrix; and

assigning the first combination as a column of the constraint matrix.

43. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to calculate the first entropy probability by performing non-linear optimization of the constraint matrix and the combination total set using a Jacobian and multivariate Newton's method.

44. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine to:

identify the first characteristic;

identify the second characteristic; and

identify an association between the first activity and the first characteristic and an association between the first activity and the second characteristic.

45. The tangible computer readable storage medium as defined in claim 32 , wherein the instructions cause the machine:

collect the first measurement for the first activity being associated with the first characteristic; and

collect the second measurement for the first activity being associated with the second characteristic.

46. The tangible computer readable storage medium of claim 25 , wherein the instructions cause the machine to:

compute a second entropy probability based on the constraint matrix and the combination total set; and

estimate a second portion of the population that matches the second combination based on the second entropy probability.