Learning with Sets in Multiple Instance Regression Applied to Remote Sensing
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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.
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