Statistical language modeling (LM) that intends to quantify the acceptability of a given piece of text has long been an interesting yet challenging research area. In particular, language modeling for information retrieval (IR) has enjoyed remarkable empirical success; one emerging stream of the LM approach for IR is to employ the pseudo-relevance feedback process to enhance the representation of an input query so as to improve retrieval effectiveness. This paper presents a continuation of such a general line of research and the major contributions are three-fold. First, we propose a principled framework which can unify the relationships among several widely-cited query modeling formulations. Second, on top of this successfully developed framework, two extensions have been proposed. On one hand, we present an extended query modeling formulation by incorporating critical query-specific information cues to guide the model estimation. On the other hand, a word-based relevance modeling has also been leveraged to overcome the obstacle of time-consuming model estimation when the framework is being utilized for practical applications. In addition, we further adopt and formalize such a framework to the speech recognition and summarization tasks. A series of experiments reveal the empirical potential of such an LM framework and the performance merits of the deduced models on these two tasks.
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