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### 3.4 Parameter Settings

Bennett et al. [30] find that the level of smoothing has a significant influence on the resulting retrieval performance and that optimal smoothing parameters are dependent on the query set as well as the collection. They also observe that longer queries require more aggressive smoothing, a finding corroborated by Zhai and Lafferty [355]. In later chapters we need to set values for the smoothing parameter associated with our retrieval model presented in Chapter 2. In particular, we set $\mu$ (cf. Eq. 2.7 on page 32) to the average length of documents in the collection.

Some of the (pseudo) relevance feedback models in use and under investigation in later chapters require additional parameter settings. The models that we evaluate have the following parameters in common:

• $|{\mathsc{V}}_{Q}|$ (the number of terms with the highest probability to be included in the query model),
• $|R|$ (the number of feedback documents used), and
• ${\lambda }_{Q}$ (the value of the query interpolation factor, cf. Eq. 2.10).

There are various approaches that may be used to estimate these parameters. One can optimize the set of parameters on one test collection and evaluate on the other, use some kind of cross-validation, or designate a set of topics as training topics which are subsequently excluded from the final evaluation. Ideally, we would like to use a form of gradient ascent on the retrieval metric we aim to optimize. None of these measures are continuous, differentiable functions of the set of parameters, however, and many local optima exist [262]. A possible solution is to define another function that does have these properties [54], but typically, a grid or line search is employed to find the optimal values for the parameters, see e.g. [119173189196223224235262356]. This is also the approach we employ in later chapters. While computationally expensive (exponential in the number of parameters), it does provide us with an upper bound on the retrieval performance that one might achieve using the described models.

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