Point process learning method, point process learning apparatus and program

1 . A point process learning method executed by a computer, the point process learning method comprising:

inputting a learning data set including at least first event data representing a series of occurrences of first events and auxiliary data representing environment information or attribute information associated with the first events;

dividing the first event data included in the learning data set by using a prediction time observation area including at least a time series when predicting future event occurrence to obtain a divided learning data set, said dividing being performed by (i) randomly determining a start point of time for a learning observation area; and (ii) simulating a low-data prediction environment by extracting a first data group of a specific time scale from the learning data set, thereby adapting the learning process to specific time-scale constraints at a time of prediction by matching a time scale of the learning observation area with a time scale of the prediction time observation area;

transforming, by a neural network, the extracted first data group and the auxiliary data into a latent vector that represents a compressed spatiotemporal feature of the events, thereby integrating heterogeneous data sources while optimizing a computational load of the point process model through reduction of data dimensionality;

parameterizing an intensity function of a point process model specifically as a joint function of the latent vector and a continuous-time state of the point process; and

learning a model parameter including a parameter of the intensity function of a predetermined point process model by using the divided learning data set, thereby updating the model parameter to minimize a prediction error relative to teacher data.

2 . The point process learning method according to claim 1 , further comprising:

inputting a prediction data set including at least second event data representing a series of occurrences of second events to be predicted, and

predicting a series of occurrences of second events in a prediction target area that is an area later than the prediction time observation area by the point process model by using the prediction data set and the learned model parameter.

3 . The point process learning method according to claim 2 , wherein the learning data set and the prediction data set include one or more pieces of auxiliary data that is auxiliary information other than an event occurrence series.

4 . The point process learning method according to claim 2 , wherein a mark for each of the first events and the second events is added to the first event data and the second event data.

5 . The point process learning method according to claim 1 , wherein

the point process model includes a function implemented by one or more neural networks and the intensity function, and

the learning includes learning model parameters including a parameter of the neural network and a parameter of the intensity function.

6 . The point process learning method according to claim 1 , wherein

the dividing of the first event data includes:

creating a learning observation area in which a time series included in the prediction time observation area is changed; and

dividing the first event data included in the learning data set into a first data group corresponding to the learning observation area, a second data group corresponding to a time series later than the time series included in the learning observation area, and a remaining data group.

7 . A point process learning apparatus comprising:

a memory; and

a processor coupled to the memory and configured to

input a learning data set including at least first event data representing a series of occurrences of first events and auxiliary data representing environment information or attribute information associated with the first events;

divide the first event data included in the learning data set by using a prediction time observation area including at least a time series when predicting future event occurrence to obtain a divided learning data set, said first event data being divided by (i) randomly determining a start point of time for a learning observation area; and (ii) simulating a low-data prediction environment by extracting a first data group of a specific time scale from the learning data set, thereby adapting the learning process to specific time-scale constraints at a time of prediction by matching a time scale of the learning observation area with a time scale of the prediction time observation area;

transform, by a neural network, the extracted first data group and the auxiliary data into a latent vector that represents a compressed spatiotemporal feature of the events, thereby integrating heterogeneous data sources while optimizing a computational load of the point process model through reduction of data dimensionality;

parameterize an intensity function of a point process model specifically as a joint function of the latent vector and a continuous-time state of the point process; and

learn a model parameter including a parameter of the intensity function of a predetermined point process model by using the divided learning data set, thereby updating the model parameter to minimize a prediction error relative to teacher data.

8 . A non-transitory computer-readable recording medium storing a program for causing a computer to execute the point process learning method according to claim 1 .

9 . The point process learning method according to claim 1 , further comprising:

repeatedly executing the learning procedure until a predetermined termination condition is satisfied, wherein the predetermined termination condition includes that a value of the model parameter has converged; and

controlling, by the processor, the repetition of the learning procedure to minimize a computational update amount of the model parameter before and after each repetition, thereby optimizing a computational resource of the computer required to reach the converged value of the model parameter.

10 . The point process learning method according to claim 1 , further comprising:

normalizing, by the processor, a value of the first event data and a value of the auxiliary data to have a common domain across different data sets prior to the transforming into the latent vector,

wherein the normalizing includes representing a time element of the first events as an elapsed time from a reference observation start time point and representing latitude and longitude elements of the first events as values within a range of [ 0 , 1 ] to reduce a computational bias of the neural network.

11 . The point process learning method according to claim 1 , wherein the joint function of the intensity function is defined as an extension of a Hawkes process comprising:

(i) a first neural network that generates a positive scalar background intensity based on the latent vector; and

(ii) a second neural network that calculates a triggering effect between past events and a future event time based on the latent vector, thereby enabling the computer to model non-linear self-exciting or inhibiting dynamics that are not captured by a standard additive Hawkes process.