Bayesian networks for static and temporal data fusion2018
Prediction and inference on temporal data is very frequently performed using time
series data alone. We believe that these tasks could benefit from leveraging the contex-
tual metadata associated to time series - such as location, type, etc. Conversely, tasks
involving prediction and inference on metadata could benefit from information held
within time series. However, there exists no standard way of jointly modeling both
time series data and descriptive metadata. Moreover, metadata frequently contains
highly correlated or redundant information, and may contain errors and missing values.
We first consider the problem of learning the inherent probabilistic graphical structure
of metadata as a Bayesian Network. This has two main benefits: (i) once structured
as a graphical model, metadata is easier to use in order to improve tasks on temporal
data and (ii) the learned model enables inference tasks on metadata alone, such
as missing data imputation. However, Bayesian network structure learning is a
tremendous mathematical challenge, that involves a NP-Hard optimization problem.
We present a tailor-made structure learning algorithm, inspired from novel theoretical
results, that exploits (quasi)-determinist dependencies that are typically present in
descriptive metadata. This algorithm is tested on numerous benchmark datasets
and some industrial metadatasets containing deterministic relationships. In both
cases it proved to be significantly faster than state of the art, and even found more
performant structures on industrial data. Moreover, learned Bayesian networks are
consistently sparser and therefore more readable.
We then focus on designing a model that includes both static (meta)data and dynamic
data. Taking inspiration from state of the art probabilistic graphical models for tem-
poral data (Dynamic Bayesian Networks) and from our previously described approach
for metadata modeling, we present a general methodology to jointly model metadata
and temporal data as a hybrid static-dynamic Bayesian network. We propose two
main algorithms associated to this representation: (i) a learning algorithm, which
while being optimized for industrial data, still generalizes to any task of static and
dynamic data fusion, and (ii) an inference algorithm, enabling both usual tasks on
temporal or static data alone, and tasks using the two types of data.
Finally, we discuss some of the notions introduced during the thesis, including ways
to measure the generalization performance of a Bayesian network by a score inspired
from the cross-validation procedure from supervised machine learning. We also
propose various extensions to the algorithms and theoretical results presented in the
previous chapters, and formulate some research perspectives.
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