Class imbalance and concept drift are two problems commonly exist in sequential learning Most of the existing sequential learning methods for class imbalance learn data in chunks. We propose a weighted online sequential extreme learning machine (WOS-ELM) algorithm that has a distinctive feature to tackle the class imbalance problem in both chunk-by-chunk and one-by-one learning. In one-by-one learning of WOS-ELM, a new sample can update the classification model without waiting for a chunk to be completed. To alleviate the class imbalance problem in concept drifting data streams, a computationally efficient framework, referred to as ensemble of subset online sequential extreme learning machine (ESOS-ELM) is also proposed. It comprises a main ensemble representing short-term memory, an information storage module representing long-term memory and a change detection mechanism to promptly detect concept drifts. Using ELM theory, a computationally efficient storage scheme is proposed to leverage the prior knowledge of recurring concepts.

In this talk, we discuss signal detection in compressed sensing (CS). We first consider the theoretical bound of the probability of error by detecting the signal reconstructed in CS with the Bayesian approach. Utilizing the oracle estimator in CS, a theoretical bound of the probability of error is provided when the noise in CS is white Gaussian noise. We then consider the Bayesian approach to signal detection in CS using compressed measurements directly. It is shown that with an additive Gaussian noise, the probability of error for unequal prior probabilities of the hypotheses is always smaller than the one with equal prior probability. A general expression is obtained for the probability of error where the prior probabilities could be equal or unequal. Performance bounds for the probability of error using the restricted isometry property constant and then the computationally more feasible mutual coherence of a given sampling matrix in CS are also derived. Numerical simulations are given to verify the new theoretical results.