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In this paper, we present a supervised graph-based framework for sequential processing and employ it to the problem of transient interference suppression. Transients typically consist of an initial peak followed by decaying short-duration oscillations. Such sounds, e.g., keyboard typing and door knocking, often arise as an interference in everyday applications: hearing aids, hands-free accessories, mobile phones, and conference-room devices. We describe a graph construction using a noisy speech signal and training recordings of typical transients. The main idea is to capture the transient interference structure, which may emerge from the construction of the graph. The graph parametrization is then viewed as a data-driven model of the transients and utilized to define a filter that extracts the transients from noisy speech measurements. Unlike previous transient interference suppression studies, in this work the graph is constructed in advance from training recordings. Then, the graph is extended to newly acquired measurements, providing a sequential filtering framework of noisy speech.