39 research outputs found
Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks
Event sequence, asynchronously generated with random timestamp, is ubiquitous
among applications. The precise and arbitrary timestamp can carry important
clues about the underlying dynamics, and has lent the event data fundamentally
different from the time-series whereby series is indexed with fixed and equal
time interval. One expressive mathematical tool for modeling event is point
process. The intensity functions of many point processes involve two
components: the background and the effect by the history. Due to its inherent
spontaneousness, the background can be treated as a time series while the other
need to handle the history events. In this paper, we model the background by a
Recurrent Neural Network (RNN) with its units aligned with time series indexes
while the history effect is modeled by another RNN whose units are aligned with
asynchronous events to capture the long-range dynamics. The whole model with
event type and timestamp prediction output layers can be trained end-to-end.
Our approach takes an RNN perspective to point process, and models its
background and history effect. For utility, our method allows a black-box
treatment for modeling the intensity which is often a pre-defined parametric
form in point processes. Meanwhile end-to-end training opens the venue for
reusing existing rich techniques in deep network for point process modeling. We
apply our model to the predictive maintenance problem using a log dataset by
more than 1000 ATMs from a global bank headquartered in North America.Comment: Accepted at Thirty-First AAAI Conference on Artificial Intelligence
(AAAI17
Dirichlet-Survival Process: Scalable Inference of Topic-Dependent Diffusion Networks
Information spread on networks can be efficiently modeled by considering
three features: documents' content, time of publication relative to other
publications, and position of the spreader in the network. Most previous works
model up to two of those jointly, or rely on heavily parametric approaches.
Building on recent Dirichlet-Point processes literature, we introduce the
Houston (Hidden Online User-Topic Network) model, that jointly considers all
those features in a non-parametric unsupervised framework. It infers dynamic
topic-dependent underlying diffusion networks in a continuous-time setting
along with said topics. It is unsupervised; it considers an unlabeled stream of
triplets shaped as \textit{(time of publication, information's content,
spreading entity)} as input data. Online inference is conducted using a
sequential Monte-Carlo algorithm that scales linearly with the size of the
dataset. Our approach yields consequent improvements over existing baselines on
both cluster recovery and subnetworks inference tasks
The limits of statistical significance of Hawkes processes fitted to financial data
Many fits of Hawkes processes to financial data look rather good but most of
them are not statistically significant. This raises the question of what part
of market dynamics this model is able to account for exactly. We document the
accuracy of such processes as one varies the time interval of calibration and
compare the performance of various types of kernels made up of sums of
exponentials. Because of their around-the-clock opening times, FX markets are
ideally suited to our aim as they allow us to avoid the complications of the
long daily overnight closures of equity markets. One can achieve statistical
significance according to three simultaneous tests provided that one uses
kernels with two exponentials for fitting an hour at a time, and two or three
exponentials for full days, while longer periods could not be fitted within
statistical satisfaction because of the non-stationarity of the endogenous
process. Fitted timescales are relatively short and endogeneity factor is high
but sub-critical at about 0.8
Shaping Social Activity by Incentivizing Users
Events in an online social network can be categorized roughly into endogenous
events, where users just respond to the actions of their neighbors within the
network, or exogenous events, where users take actions due to drives external
to the network. How much external drive should be provided to each user, such
that the network activity can be steered towards a target state? In this paper,
we model social events using multivariate Hawkes processes, which can capture
both endogenous and exogenous event intensities, and derive a time dependent
linear relation between the intensity of exogenous events and the overall
network activity. Exploiting this connection, we develop a convex optimization
framework for determining the required level of external drive in order for the
network to reach a desired activity level. We experimented with event data
gathered from Twitter, and show that our method can steer the activity of the
network more accurately than alternatives