Sensing-aware classification with high-dimensional data
In many applications decisions must be made about the state of an object based on indirect noisy observation of high-dimensional data. An example is the determination of the presence or absence of stroke from tomographic projections. Conventionally, the sensing process is inverted and a classifier is built in the reconstructed domain, which requires complete knowledge of the sensing mechanism. Alternatively, a direct data domain classifier might be constructed, but the constraints imposed by the sensing process are then lost. In this work we study the behavior of a third path we term “sensing-aware classification.” Our aim is to contribute to the development of a rigorous theory for such challenging problems. To this end, we consider an abstracted binary classification problem with very high dimensional observations, a restricting sensing configuration, and unknown statistical models of noise and object which must be learned from constrained training data. We analyze the impact of different levels of prior knowledge concerning the sensing mechanism for various classification strategies. In particular we prove that the strategies based on the naive estimation of all model elements results in a classification performance asymptotically no better than guessing whereas sensing-aware, projection-based classification rules attain Bayes-optimal risk. Simulation results are also provided.