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Informed speaker extraction aims to extract a target speech signal from a mixture of sources given prior knowledge about the desired speaker. Recent deep learning-based methods leverage a speaker discriminative model that maps a reference snippet uttered by the target speaker into a single embedding vector that encapsulates the characteristics of the target speaker. However, such modeling deliberately neglects the time-varying properties of the reference signal. In this work, we assume that a reference signal is available that is temporally correlated with the target signal. To take this correlation into account, we propose a time-varying source discriminative model that captures the temporal dynamics of the reference signal. We also show that existing methods and the proposed method can be generalized to non-speech sources as well. Experimental results demonstrate that the proposed method significantly improves the extraction performance when applied in an acoustic echo reduction scenario.