Methods and apparatus to estimate large scale audience deduplication
An example apparatus includes an association controller to generate a tree structure association for a total audience size that accessed a plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size, a matrix generator to generate a matrix by selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item and storing the sum of probabilities value in an element of the matrix, and a commercial solver to estimate a deduplicated audience size of the total audience size using the matrix.
1. An apparatus comprising:
interface circuitry to collect, via a network, impression data indicative of accesses to a plurality of media items for a total audience size, the impression data including audience sizes for the plurality of media items, the total audience size including a computer-generated inaccuracy causing a misrepresentation of a deduplicated audience size of the plurality of media items;
association controller circuitry to generate a tree structure association for the total audience size that accessed the plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size;
matrix generator circuitry to improve functionality of a computer by generating a matrix without using processing power to solve a partial derivative equation for the first node or the second node, the matrix generator circuitry to generate the matrix by:
selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item; and
storing the sum of probabilities value in an element of the matrix; and
commercial solver circuitry to increase an accuracy of the computer to reduce the computer-generated inaccuracy of the total audience size by estimating the deduplicated audience size of the total audience size using the matrix.
2. The apparatus of claim 1 , wherein the first node includes a first index value, the second node includes a second index value, and the element includes a third index value and a fourth index value.
3. The apparatus of claim 2 , wherein, when the third index value of the element equals the fourth index value of the element, the sum of probabilities value corresponds to:
the first node when the first index value of the first node equals the third index value of the element; and
the second node when the second index value of the second node equals the fourth index value of the element.
4. The apparatus of claim 2 , wherein the tree structure association further includes a union node representative of a union of the first node and the second node, the union node having a fifth index value, and when (1) the third index value of the element equals the fifth index value of the union, and (2) the fourth index value of the element equals the first index value of the first node, the sum of probabilities value corresponds to the first node.
5. The apparatus of claim 2 , wherein, when the third index value of the element equals the first index value of the first node, the fourth index value of the element equals the second index value of the second node, the sum of probabilities value is equivalent to a quotient of:
a second sum of probabilities value of the first node multiplied by a third sum of probabilities value of the second node; and
a fourth sum of probabilities value of an ancestor node of the first node and the second node.
6. The apparatus of claim 1 , wherein the commercial solver circuitry is to determine Lagrange multipliers using the matrix.
7. The apparatus of claim 6 , wherein the commercial solver circuitry is to use the Lagrange multipliers to solve a maximum entropy problem to estimate the deduplicated audience size.
8. A non-transitory computer readable storage medium comprising instructions to cause programmable circuitry to at least:
cause collection, via a network, of impression data indicative of accesses to a plurality of media items for a total audience size, the impression data including audience sizes for the plurality of media items, the total audience size including a processor-generated inaccuracy causing a misrepresentation of a deduplicated audience size of the plurality of media items;
generate a tree structure association for the total audience size that accessed the plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size;
generate a matrix without using processing power to solve a partial derivative equation for the first node or the second node by:
selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item; and
storing the sum of probabilities value in an element of the matrix; and
increase an accuracy of a computer by determining the deduplicated audience size of the total audience size using the matrix to reduce the processor-generated inaccuracy of the total audience size.
9. The computer readable storage medium of claim 8 , wherein the first node includes a first index value, the second node includes a second index value, and the element includes a third index value and a fourth index value.
10. The computer readable storage medium of claim 9 , wherein the instructions are to cause the programmable circuitry to, when the third index value of the element equals the fourth index value of the element, select the sum of probabilities value as corresponding to:
the first node when the first index value of the first node equals the third index value of the element; and
the second node when the second index value of the second node equals the fourth index value of the element.
11. The computer readable storage medium of claim 9 , wherein the instructions are to cause the programmable circuitry to:
generate the tree structure association to include a union node representative of a union of the first node and the second node, the union node having a fifth index value; and
when (1) the third index value of the element equals the fifth index value of the union, and (2) the fourth index value of the element equals the first index value of the first node, select the sum of probabilities value as corresponding to the first node.
12. The computer readable storage medium of claim 9 , wherein the instructions are to cause the programmable circuitry to, when the third index value of the element equals the first index value of the first node and the fourth index value of the element equals the second index value of the second node, select the sum of probabilities value as equivalent to a quotient of:
a second sum of probabilities value of the first node multiplied by a third sum of probabilities value of the second node; and
a fourth sum of probabilities value of an ancestor node of the first node and the second node.
13. The computer readable storage medium of claim 9 , wherein the instructions are to cause the programmable circuitry to determine Lagrange multipliers using the matrix.
14. The computer readable storage medium of claim 13 , wherein the instructions are to cause the programmable circuitry to use the Lagrange multipliers to solve a maximum entropy problem for use in determining the deduplicated audience size.
15. A method comprising:
collecting, via a network, impression data indicative of accesses to a plurality of media items for a total audience size, the impression data including audience sizes for the plurality of media items, the total audience size including a computer-generated error causing a misrepresentation of a deduplicated audience size of the plurality of media items;
generating, by executing an instruction with programmable circuitry, a tree structure association for the total audience size that accessed the plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size;
improving functionality of a computer by generating, by executing an instruction with the programmable circuitry, a matrix without using processing power to solve a partial derivative equation for the first node or the second node by:
selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item; and
storing the sum of probabilities value in an element of the matrix; and
increasing an accuracy of the computer to reduce the computer-generated error of the total audience size by estimating the deduplicated audience size of the total audience size using the matrix.
16. The method of claim 15 , wherein the first node includes a first index value, the second node includes a second index value, and the element includes a third index value and a fourth index value.
17. The method of claim 16 , further including, when the third index value of the element equals the fourth index value of the element, selecting the sum of probabilities value as corresponding to:
the first node when the first index value of the first node equals the third index value of the element; and
the second node when the second index value of the second node equals the fourth index value of the element.
18. The method of claim 16 , further including:
generating the tree structure association to include a union node representative of a union of the first node and the second node, the union node having a fifth index value; and
when (1) the third index value of the element equals the fifth index value of the union, and (2) the fourth index value of the element equals the first index value of the first node, selecting the sum of probabilities value as corresponding to the first node.
19. The method of claim 16 , further including, when the third index value of the element equals the first index value of the first node and the fourth index value of the element equals the second index value of the second node, selecting the sum of probabilities value as equivalent to a quotient of:
a second sum of probabilities value of the first node multiplied by a third sum of probabilities value of the second node; and
a fourth sum of probabilities value of an ancestor node of the first node and the second node.
20. The method of claim 16 , further including determining Lagrange multipliers using the matrix.
21. The method of claim 20 , further including using the Lagrange multipliers to solve a maximum entropy problem for use in determining the deduplicated audience size.
22. A system comprising:
memory;
programmable circuitry; and
instructions to cause the programmable circuitry to:
cause collection, via a network, of impression data indicative of accesses to a plurality of media items for a total audience size, the impression data including audience sizes for the plurality of media items, the total audience size including a computer-generated inaccuracy causing a misrepresentation of a deduplicated audience size of the plurality of media items;
generate a tree structure association for the total audience size that accessed the plurality of media items, the tree structure association including a first node representative of a first media item accessed by first audience members of the total audience size and a second node representative of a second media item accessed by second audience members of the total audience size;
improve functionality of a computer by generating a matrix without using processing power to solve a partial derivative equation for the first node or the second node, the generating of the matrix by:
selecting a sum of probabilities value corresponding to the tree structure association, the sum of probabilities value representative of a probability of the first audience members accessing the first media item; and
storing the sum of probabilities value in an element of the matrix; and
increase an accuracy of the computer to reduce the computer-generated inaccuracy of the total audience size by estimating the deduplicated audience size of the total audience size using the matrix.
23. The system of claim 22 , wherein the first node includes a first index value, the second node includes a second index value, and the element includes a third index value and a fourth index value.
24. The system of claim 23 , wherein when the third index value of the element equals the fourth index value of the element, the programmable circuitry is to select the sum of probabilities value as corresponding to:
the first node when the first index value of the first node equals the third index value of the element; and
the second node when the second index value of the second node equals the fourth index value of the element.
25. The system of claim 23 , wherein the programmable circuitry is to:
generate the tree structure association to include a union node representative of a union of the first node and the second node, the union node having a fifth index value; and
when (1) the third index value of the element equals the fifth index value of the union, and (2) the fourth index value of the element equals the first index value of the first node, select the sum of probabilities value as corresponding to the first node.
26. The system of claim 23 , wherein the programmable circuitry is to, when the third index value of the element equals the first index value of the first node and the fourth index value of the element equals the second index value of the second node, select the sum of probabilities value as equivalent to a quotient of:
a second sum of probabilities value of the first node multiplied by a third sum of probabilities value of the second node; and
a fourth sum of probabilities value of an ancestor node of the first node and the second node.
27. The system of claim 22 , wherein the programmable circuitry is to determine Lagrange multipliers using the matrix.
28. The system of claim 27 , wherein the programmable circuitry is to use the Lagrange multipliers to solve a maximum entropy problem for use in determining the deduplicated audience size.