Methods and systems for cross-platform overlap modeling
A multivariate probit model is used to determine overlaps for reach and impressions for a plurality of different platforms.
1 . A computer-implemented method for determining a proportion of a population that is exposed during a time interval to a content item by one or a combination of a plurality of platforms, the computer-implemented method comprising:
receiving, by an aggregation server from a plurality of automatic content recognition (ACR) systems integrated into a first plurality of television sets, first reach statistics comprising the proportion of the population exposed during the time interval to the content item by a first platform, wherein the first platform includes a linear television platform, the plurality of ACR systems sample audio and/or video from the content item and compare the sampled audio and/or video with a database of content items to identify the content item by its unique characteristics, the first reach statistics identify at least one of a household or device that displayed the content item using the first platform;
receiving, by the aggregation server from a plurality of pixel tag tracking systems integrated into a second plurality of television sets, second reach statistics comprising the proportion of the population exposed during the time interval to the content item by a second platform, wherein the second platform includes a streaming platform, the plurality of pixel tracking systems search for pixel tags embedded in the content item to identify the content item, and the second reach statistics identify the at least one of the household or the device that displayed the content item using the second platform;
receiving, by the aggregation server from a video sharing system, third reach statistics comprising the proportion of the population exposed during the time interval to the content item by a third platform, the third platform including the video sharing system and the content item including a video displayed by the video sharing system, wherein the third platform does not identify the at least one of the household or the device that displayed the content item using the third platform;
calculating, by at least one processor in operable communication with the aggregation server, overlap reach statistics comprising the proportion of the population exposed to the content item during the time interval by both the first platform and the second platform;
calculating, by the at least one processor, using a multivariate probit model with the first reach statistics, the second reach statistics, the third reach statistics, and the overlap reach statistics to calculate proportion information including at least one of:
the proportion of the population that is not exposed to the content item during the time interval by any of the platforms;
the proportion of the population that is exposed to the content item during the time interval by only one of the platforms;
the proportion of the population that is exposed to the content item during the time interval by at least two of the platforms but not by one of the platforms;
or
the proportion of the population that is exposed to the content item during the time interval by all of the platforms;
generating, by the at least one processor, a report including the proportion information; and
transmitting, by a network interface, the report for display on a display device.
2 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is not exposed to the content item during the time interval by the first, second, or third platform.
3 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is exposed to the content item during the time interval by only the third platform.
4 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is exposed to the content item during the time interval by only the second platform or by only the first platform.
5 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is exposed to the content item during the time interval by both the second platform and the third platform, but not on the first platform.
6 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is exposed to the content item during the time interval by both the first platform and the third platform, but by the second platform.
7 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is exposed to the content item on both the first platform and the second platform, but not on the third platform.
8 . The computer-implemented method of claim 1 , wherein using the multivariate probit model comprises using the multivariate probit model to calculate the proportion of the population that is exposed to the first platform, the second platform, and the third platform.
9 . The computer-implemented method of claim 1 , wherein calculating the overlap reach statistics comprises calculating the overlap reach statistics using an Internet Protocol (IP) address.
10 . The computer-implemented method of claim 1 , wherein the first platform comprises a linear platform.
11 . The computer-implemented method of claim 1 , wherein the second platform comprises over-the-top (OTT) platform.
12 . The computer-implemented method of claim 1 , wherein the multivariate probit model takes as input a mean vector corresponding to a total reach of the first platform, the second platform, and the third platform, respectively, as well as correlation matrix including correlation parameters relating a probability of an individual watching a first content item on both the first platform and the second platform, a probability of the individual watching the first content item on both the first platform and the third platform, and the probability of the individual watching the first content item on both the second platform and the third platform.
13 . The computer-implemented method of claim 1 , wherein the multivariate probit model is expressed by:
(
u
1
u
2
u
3
)
∼
MVN
(
[
μ
1
μ
2
μ
3
]
,
[
1
r
v
r
1
w
v
w
1
]
)
[
z
i
=
1
]
⇔
[
u
i
>
0
]
where:
MVN is a multivariate normal distribution;
z 1 , z 2 , and z 3 are indicator variables for exposure to the content item by the first platform, the second platform, and the third platform, respectively, and take a value of 1 if exposure occurs during the time interval or is 0 otherwise;
u 1 , u 2 , and u 3 are latent variables;
μ 1 , μ 2 , and μ 3 are mean parameters and correspond to total reach for the first platform, total reach for the second platform, and total reach for the third platform and are obtained from the first reach statistics, second reach statistics, and third reach statistics, respectively;
r is a correlation parameter between the first platform and the second platform;
v is a correlation parameter between the first platform and the third platform; and
w is a correlation parameter between the first platform and the third platform.
14 . The computer-implemented method of claim 13 , wherein r is estimated by:
r
=
arg
min
r
(
❘
"\[LeftBracketingBar]"
O
-
∫
0
∞
∫
0
∞
f
μ
^
1
,
μ
^
2
,
r
(
u
1
,
u
2
)
du
1
du
2
❘
"\[RightBracketingBar]"
)
where the argmin is taken with respect to r, over a range (−1, +1), and
O is the proportion of the population exposed to the content item during the time interval by both the first platform and the second platform.
15 . The computer-implemented method of claim 13 , wherein v is estimated by:
v
=
arg
min
v
(
❘
"\[LeftBracketingBar]"
O
-
∫
0
∞
∫
0
∞
f
μ
^
1
,
μ
^
3
,
v
(
u
1
,
u
3
)
du
1
du
3
❘
"\[RightBracketingBar]"
)
where the argmin is taken with respect to v, over a range (−1, +1), and
O is the proportion of the population exposed to the content item during the time interval by both the first platform and the third platform.
16 . The computer-implemented method of claim 13 , wherein w is estimated by:
w
=
arg
min
w
(
❘
"\[LeftBracketingBar]"
O
-
∫
0
∞
∫
0
∞
f
μ
^
2
,
μ
^
3
,
v
(
u
2
,
u
3
)
du
2
du
3
❘
"\[RightBracketingBar]"
)
where the argmin is taken with respect to v, over a range (−1, +1), and
O is the proportion of the population exposed to the content item during the time interval by both the second platform and the third platform.
17 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by only the third platform (π 001 ) is calculated by:
π
001
=
∫
-
∞
0
∫
-
∞
0
∫
0
∞
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f Θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
18 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by only the second platform (π 010 ) is calculated by:
π
010
=
∫
-
∞
0
∫
0
∞
∫
-
∞
0
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
19 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by only the first platform (π 100 ) is calculated by:
π
100
=
∫
0
∞
∫
-
∞
0
∫
-
∞
0
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
20 . The computer-implemented method of claim 13 , wherein the proportion of the population that is not exposed to the content item during the time interval by the first platform, the second platform, or the third platform (π 000 ) is calculated by:
π
000
=
∫
-
∞
0
∫
-
∞
0
∫
-
∞
0
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
21 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by all three platforms (π 111 ) is calculated by:
π
111
=
∫
0
∞
∫
0
∞
∫
0
∞
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
22 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by both the first platform and the second platform, but not the third platform (π 110 ) is calculated by:
π
110
=
∫
0
∞
∫
0
∞
∫
-
∞
0
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
23 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by both the first platform and the third platform, but not the second platform (π 101 ) is calculated by:
π
101
=
∫
0
∞
∫
-
∞
0
∫
0
∞
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
24 . The computer-implemented method of claim 13 , wherein the proportion of the population that is exposed to the content item during the time interval by both the second platform and the third platform, but not the first platform (π 011 ) is calculated by:
π
011
=
∫
-
∞
0
∫
0
∞
∫
0
∞
f
Θ
(
u
1
,
u
2
,
u
3
)
du
1
du
2
du
3
where f θ (u 1 , u 2 , u 3 ) denotes a probability density function (PDF) of the multivariate Gaussian distribution with parameter vector θ, wherein:
f
Θ
(
u
→
)
=
(
2
π
)
-
3
/
2
⌈
∑
⌉
-
1
/
2
exp
(
-
1
2
(
u
→
-
μ
→
)
′
∑
-
1
(
u
→
-
μ
→
)
)
.
25 . A system for determining a proportion of a population that is exposed during a time interval to a content item by one or a combination of a plurality of platforms, the system comprising:
an aggregation server configured to:
receive, from a plurality of automatic content recognition (ACR) systems integrated into a first plurality of television sets, first reach statistics comprising the proportion of the population exposed during the time interval to the content item by a first platform, wherein the first platform includes a linear television platform, the plurality of ACR systems sample audio and/or video from the content item and compare the sampled audio and/or video with a database of content items to identify the content item by its unique characteristics, the first reach statistics identify at least one of a household or device that displayed the content item using the first platform;
receive, from a plurality of pixel tag tracking systems integrated into a second plurality of television sets, second reach statistics comprising the proportion of the population exposed during the time interval to the content item by a second platform, wherein the second platform includes a streaming platform, the plurality of pixel tracking systems search for pixel tags embedded in the content item to identify the content item, and the second reach statistics identify the at least one of the household or the device that displayed the content item using the second platform; and
receive, from a video sharing system, third reach statistics comprising the proportion of the population exposed during the time interval to the content item by a third platform, the third platform including the video sharing system and the content item including a video displayed by the video sharing system, wherein the third platform does not identify the at least one of the household or the device that displayed the content item using the third platform;
at least one processor in operable communication with the aggregation server and configured to:
calculate overlap reach statistics comprising the proportion of the population exposed to the content item during the time interval by both the first platform and the second platform; and
use a multivariate probit model with the first reach statistics, the second reach statistics, the third reach statistics, and the overlap reach statistics to generate a report including proportion information at least one of:
the proportion of the population that is not exposed to the content item during the time interval by any of the platforms;
the proportion of the population that is exposed to the content item during the time interval by only one of the platforms;
the proportion of the population that is exposed to the content item during the time interval by at least two of the platforms but not by one of the platforms; or
the proportion of the population that is exposed to the content item during the time interval by all of the platforms; and
a network interface configured to transmit the report for display on a display device.