ANALYZING SOCIAL BEHAVIOR
A relational event history is determined based on a data set, the relational event history including a set of relational events that occurred in time among a set of actors. Data is populated in a probability model based on the relational event history, where the probability model is formulated as a series of conditional probabilities that correspond to a set of sequential decisions by an actor for each relational event. The set of sequential decisions includes a decision to send a communication, and one or more decisions as to recipients. For a relational event in the relational event history, one or more possible sequences in which the actor decided to include the recipients of the communication are determined. A baseline communications behavior for the relational event history is determined, and departures from the baseline communications behavior within the relational event history are determined.
1 . A method comprising:
determining a relational event history based on a data set, the relational event history comprising a set of relational events that occurred in time among a set of actors;
populating data in a probability model based on the relational event history, wherein the probability model is formulated as a series of conditional probabilities that correspond to a set of sequential decisions by an actor for each relational event, wherein the set of sequential decisions comprises a decision to send a communication, and one or more decisions as to recipients of the communication included within a set of recipients of the communication, the probability model including one or more statistical parameters and corresponding statistics that relate to one or more of senders of relational events or recipients of relational events;
determining, for a relational event in the relational event history, one or more possible sequences in which the actor decided to include the recipients in the set of recipients of the communication;
determining, by one or more processing devices, a baseline communications behavior for the relational event history based on the populated probability model and the determined possible sequences, wherein the baseline comprises a first set of values for the one or more statistical parameters; and
determining departures from the baseline communications behavior within the relational event history.
2 . The method of claim 1 , wherein the first set of values for the one or more statistical parameters is determined using a maximum-likelihood method.
3 . The method of claim 1 , wherein the first set of values for the one or more statistical parameters is determined through iterative optimization.
4 . The method of claim 3 , wherein determining the first set of values for the one or more statistical parameters comprises:
determining an expectation of a function evaluated using a first estimate of values for the one or more statistical parameters; and
determining a second estimate of values for the one or more statistical parameters, wherein the second estimate of values maximizes the determined expectation of the function.
5 . The method of claim 4 , further comprising determining a number of recipients included in a set of recipients of a relational event.
6 . The method of claim 5 , wherein, when the number of recipients included in the set of recipients of the relational event is greater than a threshold number, the first set of values for the one or more statistical parameters is determined using simulation.
7 . The method of claim 3 , wherein determining the first set of values for the one or more statistical parameters comprises:
determining a first derivative and a second derivative of a log-likelihood function about a first estimate of values for the one or more statistical parameters; and
determining, based on the first derivative, the second derivative, and the first estimate of values for the one or more statistical parameters, a second estimate of values for the one or more statistical parameters.
8 . The method of claim 7 , wherein the second estimate of values for the one or more statistical parameters maximizes an expectation of the log-likelihood function.
9 . The method of claim 8 , wherein the expectation of the log-likelihood function is determined using Markov chain Monte Carlo sampling.
10 . The method of claim 1 , wherein the first set of values for the one or more statistical parameters is determined using a distributed computing platform.
11 . A system comprising:
one or more processing devices; and
one or more non-transitory computer-readable media coupled to the one or more processing devices having instructions stored thereon which, when executed by the one or more processing devices, cause the one or more processing devices to perform operations comprising:
determining a relational event history based on a data set, the relational event history comprising a set of relational events that occurred in time among a set of actors;
populating data in a probability model based on the relational event history, wherein the probability model is formulated as a series of conditional probabilities that correspond to a set of sequential decisions by an actor for each relational event, wherein the set of sequential decisions comprises a decision to send a communication, and one or more decisions as to recipients of the communication included within a set of recipients of the communication, the probability model including one or more statistical parameters and corresponding statistics that relate to one or more of senders of relational events or recipients of relational events;
determining, for a relational event in the relational event history, one or more possible sequences in which the actor decided to include the recipients in the set of recipients of the communication;
determining, by one or more processing devices, a baseline communications behavior for the relational event history based on the populated probability model and the determined possible sequences, wherein the baseline comprises a first set of values for the one or more statistical parameters; and
determining departures from the baseline communications behavior within the relational event history.
12 . The system of claim 11 , wherein the first set of values for the one or more statistical parameters is determined using a maximum-likelihood method.
13 . The system of claim 11 , wherein the first set of values for the one or more statistical parameters is determined through iterative optimization.
14 . The system of claim 13 , wherein determining the first set of values for the one or more statistical parameters comprises:
determining an expectation of a function evaluated using a first estimate of values for the one or more statistical parameters; and
determining a second estimate of values for the one or more statistical parameters, wherein the second estimate of values maximizes the determined expectation of the function.
15 . The system of claim 14 , further comprising determining a number of recipients included in a set of recipients of a relational event.
16 . The system of claim 15 , wherein, when the number of recipients included in the set of recipients of the relational event is greater than a threshold number, the first set of values for the one or more statistical parameters is determined using simulation.
17 . The system of claim 13 , wherein determining the first set of values for the one or more statistical parameters comprises:
determining a first derivative and a second derivative of a log-likelihood function about a first estimate of values for the one or more statistical parameters; and
determining, based on the first derivative, the second derivative, and the first estimate of values for the one or more statistical parameters, a second estimate of values for the one or more statistical parameters.
18 . The system of claim 17 , wherein the second estimate of values for the one or more statistical parameters maximizes an expectation of the log-likelihood function.
19 . The system of claim 18 , wherein the expectation of the log-likelihood function is determined using Markov chain Monte Carlo sampling.
20 . The system of claim 19 , wherein the first set of values for the one or more statistical parameters is determined using a distributed computing platform.
21 . A non-transitory computer-readable medium embodying one or more instructions thereon which, when executed, cause one or more computer processors to perform steps comprising:
determining a relational event history based on a data set, the relational event history comprising a set of relational events that occurred in time among a set of actors;
populating data in a probability model based on the relational event history, wherein the probability model is formulated as a series of conditional probabilities that correspond to a set of sequential decisions by an actor for each relational event, wherein the set of sequential decisions comprises a decision to send a communication, and one or more decisions as to recipients of the communication included within a set of recipients of the communication, the probability model including one or more statistical parameters and corresponding statistics that relate to one or more of senders of relational events or recipients of relational events;
determining, for a relational event in the relational event history, one or more possible sequences in which the actor decided to include the recipients in the set of recipients of the communication;
determining, by one or more processing devices, a baseline communications behavior for the relational event history based on the populated probability model and the determined possible sequences, wherein the baseline comprises a first set of values for the one or more statistical parameters; and
determining departures from the baseline communications behavior within the relational event history.