  In this paper, we propose a novel approach to tackle the multiple instance
regression (MIR) problem. This problem arises when the data is a collection of
bags, where each bag is made of multiple instances corresponding to the same
unique real-valued label. Our goal is to train a regression model which maps
the instances of an unseen bag to its unique label. This MIR setting is common
to remote sensing applications where there is high variability in the
measurements and low geographical variability in the quantity being estimated.
Our approach, in contrast to most competing methods, does not make the
assumption that there exists a prime instance responsible for the label in each
bag. Instead, we treat each bag as a set (i.e, an unordered sequence) of
instances and learn to map each bag to its unique label by using all the
instances in each bag. This is done by implementing an order-invariant
operation characterized by a particular type of attention mechanism. This
method is very flexible as it does not require domain knowledge nor does it
make any assumptions about the distribution of the instances within each bag.
We test our algorithm on five real world datasets and outperform previous
state-of-the-art on three of the datasets. In addition, we augment our feature
space by adding the moments of each feature for each bag, as extra features,
and show that while the first moments lead to higher accuracy, there is a
diminishing return.
