In many classification systems, sensing modalities have different acquisition costs. It is often unnecessary to use every modality to classify a majority of examples. We study a multi-stage system in a prediction time cost reduction setting, where the full data is 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 measurement acquisition cost. We formulate 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 cost function into classification and rejection decisions. We then transform reject decisions into a binary classification problem. We construct stage-by-stage global surrogate risk, develop an iterative algorithm in the boosting framework and present convergence results. We test our work on synthetic, medical and explosives detection datasets. Our results demonstrate that substantial cost reduction without a significant sacrifice in accuracy is achievable.

Budget constraints arise in many computer vision problems. Computational costs limit many automated recognition systems while crowdsourced systems are hindered by monetary costs. We leverage wide variability in image complexity and learn adaptive model selection policies. Our learnt policy maximizes performance under average budget constraints by selecting "cheap" models for low complexity instances and utilizing descriptive models only for complex ones. During training, we assume access to a set of models that utilize features of different costs and types. We consider a binary tree architecture where each leaf corresponds to a different model. Internal decision nodes adaptively guide model-selection process along paths on a tree. The learning problem can be posed as an empirical risk minimization over training data with a non-convex objective function. Using hinge loss surrogates we show that adaptive model selection reduces to a linear program thus realizing substantial computational efficiencies and guaranteed convergence properties.

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