Learning using Privileged Time Series
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Examensarbete för masterexamen
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Modellbyggare
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Sammanfattning
In this thesis, we study the impact of having privileged information, in the form
of intermediate time series, available during the training of models for long-term
prediction. An algorithm which incorporates these time series is presented, and
we prove that it is more efficient when the time series are drawn from a Gaussian Linear dynamical system in comparison to a linear baseline model without access
to the privileged information. Notably, the main analysis tool which we use is Rao Blackwell’s theorem. Using synthetically generated data, we validate the theoretical
results and characterize the algorithm’s behavior, but also test the limits of the
algorithm by evaluating it on synthetic data where the assumptions of the theoretical
analysis are violated. Furthermore, the applicability of the algorithm is investigated
on real-world datasets for forecasting air quality in Chinese cities and predicting
Alzheimer’s disease progression. We show that our approach is preferable to classical
learning in most settings, especially when data is scarce. Furthermore, empirical
results are used to discuss the trade-off between bias and variance when using the
proposed algorithm. We conclude that learning with privileged information in time
series data for long-term prediction is beneficial and a highly interesting subject
for further research. Proposals are given for future work, such as extensions to
non-linear models or investigating how privileged time series could be beneficial for
latent variable systems.
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Ämne/nyckelord
Machine learning, linear dynamical systems, privileged information, time series, Alzheimer’s disease, Rao-Blackwellization.