Sequential Classification with Empirically Observed Statistics Motivated by realworld machine learning applications, we consider the binary statistical classification task in the sequential setting where the generating distributions are unknown and only empirically sampled sequences are available to the decision maker. Then, the decision maker is tasked to classify a test sequence which is known to be generated according to either one of two distributions. The decision maker wishes to perform the classification task with minimum number of the test samples, so, at each step, it declares either xe2x80x9c1xe2x80x9d, xe2x80x9c2xe2x80x9d or xe2x80x9cgive me one more test samplexe2x80x9d. We propose a classifier and analyze the typeI and typeII error probabilities. Also, we show the advantage of our sequential scheme compared to the existing nonsequential classifiers.

Distributed Detection with Empirically Observed Statistics. We consider a binary distributed detection problem in which the distributions of the sensor observations are unknown and only empirically observed statistics are available to the fusion center. The source (test) sequences are transmitted through different channels to the fusion center, which also observes noisy versions of labelled training sequences generated independently from the two underlying distributions. The fusion center decides which distribution the source sequence is sampled from based on the observed statistics, i.e., the noisy training data. We derive the optimal typeII error exponent given that the typeI error decays exponentially fast. We further maximize the typeII error exponent over the proportions of channels for both source and training sequences and conclude that as the ratio of the lengths of training to test sequences tends to infinity, using only one channel is optimal. Finally, we relate our results to the distributed detection problem studied by Tsitsiklis.