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Data streams are prevalent in current manufacturing and service systems where real-time data arrive progressively. A quick distribution inference from such data streams at their early stages is extremely useful for prompt decision making in many industrial applications. For example, a quality monitoring scheme can be quickly started if the process data distribution is available and the optimal inventory level can be determined early once the customer demand distribution is estimated. To this end, this article proposes a novel online recursive distribution inference method for stationary data streams that can respond as soon as the streaming data are generated and update as regularly as the data accumulate. A major challenge is that the data size might be too small to produce an accurate estimation at the early stage of data streams. To solve this, we resort to an instance-based transfer learning approach which integrates a sufficient amount of auxiliary data from similar processes or products to aid the distribution inference in our target task. Particularly, the auxiliary data are reweighted automatically by a density ratio fitting model with a prior-belief-guided regularization term to alleviate data scarcity. Our proposed distribution inference method also possesses an efficient online algorithm with recursive formulas to update upon every incoming data point. Extensive numerical simulations and real case studies verify the advantages of the proposed method.

Distribution inference from early-stage stationary data streams by transfer learning