Cost Sensitive Sequential Classification

In many decision systems, sensing modalities have different acquisition costs. It is often unnecessary to use every sensor to classify a majority of examples. We study a multi-stage system in a prediction time cost reduction setting, where all the modalities are available for training, but for a test example, measurements in a new modality can be acquired at each stage for an additional cost. We seek decision rules to reduce the average acquisition cost. We construct an empirical risk minimization problem (ERM) for a multi-stage reject classifier, wherein the stage $k$ classifier either classifies a sample using only the measurements acquired so far or rejects it to the next stage where more attributes can be acquired for a cost. To solve the ERM problem, we factorize the loss function into classification and rejection decisions. We then transform reject decisions into a binary classification problem. We formulate stage-by-stage global surrogate risk and introduce an iterative algorithm in the boosting framework. We present convergence results for our algorithm and derive generalization guarantees. We evaluate our work on synthetic, medical and explosives detection datasets. Our results show that substantial cost reduction without a significant sacrifice in accuracy is possible.