  We consider a sequence of related multivariate time series learning tasks,
such as predicting failures for different instances of a machine from time
series of multi-sensor data, or activity recognition tasks over different
individuals from multiple wearable sensors. We focus on two under-explored
practical challenges arising in such settings: (i) Each task may have a
different subset of sensors, i.e., providing different partial observations of
the underlying 'system'. This restriction can be due to different manufacturers
in the former case, and people wearing more or less measurement devices in the
latter (ii) We are not allowed to store or re-access data from a task once it
has been observed at the task level. This may be due to privacy considerations
in the case of people, or legal restrictions placed by machine owners.
Nevertheless, we would like to (a) improve performance on subsequent tasks
using experience from completed tasks as well as (b) continue to perform better
on past tasks, e.g., update the model and improve predictions on even the first
machine after learning from subsequently observed ones. We note that existing
continual learning methods do not take into account variability in input
dimensions arising due to different subsets of sensors being available across
tasks, and struggle to adapt to such variable input dimensions (VID) tasks. In
this work, we address this shortcoming of existing methods. To this end, we
learn task-specific generative models and classifiers, and use these to augment
data for target tasks. Since the input dimensions across tasks vary, we propose
a novel conditioning module based on graph neural networks to aid a standard
recurrent neural network. We evaluate the efficacy of the proposed approach on
three publicly available datasets corresponding to two activity recognition
tasks (classification) and one prognostics task (regression).
