Probabilistic Autocomplete Suggestion Ranking with Localization and Personalization A Quick Notes for Geosearch

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1 Probabilistic Autocomplete Suggestion Ranking with Localization and Personalization A Quick Notes for Geosearch Xugang Ye Introduction We aim to formulate the problem of the autocomplete suggestion ranking in a general probabilistic way with localization and personalization. The common formulation is based on the relevance probability of the suggestion given the prefix. We now add the search location and user profile into the conditions so that the top ranked suggestion results are not only relevant to the user s typed input, but also relevant to user s location context and historical activities. 1. Formulation We denote P(sug pre, l, u) as the relevance probability of the suggestion sug given the prefix pre, the search location l, and the user u. In order to calculate this probability, we consider the Bayes rule: P(sug pre, l, u) =.(/01,l,2 324). Assume that (pre, l) and u are independent with or.(/01,l,2) without given sug, then P(sug pre, l, u).(/01,l 324).(2 324).(/01,l).(2) = P(sug pre, l).(324 2). (1) Therefore, the probability can be approximately factorized into two factors: P(sug pre, l) and.(324 2). The first one quantifies the relevance of sug for general user with location context; the second one quantifies the dependence of sug on u, i.e. personalization. For P(sug pre, l), we calculate it via conditioning on the geo-partition i. That is P(sug pre, l) = P(sug pre, l, i)p(i pre, l) 9 = P(sug pre, i)p(i l) 9, (2) where P(sug pre, i) is the local relevance probability for the partition i, and P(i l) is the weight of partition i given the search location l. To calculate P(sug pre, i) for a particular i, we expand it via conditioning on the synonym-space of the partition i. That is P(sug pre, i) = 3<=? (@) P(sug pre, i, syn)p(syn pre, i) = 3<=? (@) P(sug syn, i)p(syn pre, i), (3) where P(sug syn, i) is the local relevance probability of sug given the synonym syn and the partition number i, P(syn pre, i) is the probability of the synonym syn given the prefix pre and the partition number i, and S (9) is the synonym space of the partition i.

2 For.(324 2), we calculate P(sug u) via conditioning on a set of features f, that is P(sug u) = PDsug f EPDf ue =.DF 324E PDf ue.de = P(sug).DF 324E PDf ue.de P(sug).( 324) P(f 9 u) 9 = P(sug).( 324) 9 P(f 9 u), (4) where we have applied the Bayes rule and also assumed that f are independent with and without given sug. This yields.(324 2).( 324) 9 P(f 9 u). (5) 2. Implementation We adopt the two-phase greedy ranking for runtime efficiency. In phase 1, we calculate P(sug pre, l). In this phase, there is no personalization. That requires us to calculate P(i l) and P(sug pre, i) for all i. For P(i l), the formula could be distance-based, for example, P(i l) = HIJ N HIJ (LM(9 N,l)), where d(i, l) is a (relative) distance measure of partition i and the search location l. In practice, l can be geo-hashed so that in runtime P(i l) can be looked up from previous computed (geo-code, geopartition)-probability table. For P(sug pre, i), we need P(sug syn, i) and P(syn pre, i). Note that P(sug syn, i) can be precomputed and stored in the (synonym, suggestion)-probability table for the partition i. However, P(syn pre, i) has to be computed in runtime from the pre-built synonym-trie data structure of the partition i. In summary, in the phase 1, we need to build those things into the memory: 1) (geo-code, geopartition)-probability table; 2) (synonym, suggestion)-probability tables for all partitions, and 3) synonym-trie data structures for all partitions. Upon the completion of the phase 1, we would have retrieved a list of suggestions for the input pair (pre, l), and ranked them by the phase 1 ranking score as P(sug pre, l). In phase 2, for each suggestion sug, we calculate.(324 2) against the user u, which, by (5), can be.( 324) approximated by 9 P(f 9 u). We define a phase 2 ranking score as s(sug, u) = ln.( 324) 9 P(f 9 u) = ln.( 324) 9 P(f 9 u). To be able to calculate this, we need a pre-

3 built user-profile DB that stores P(f 9 u) and P(f 9 ) and a (suggestion, feature)-value table that stores P(f 9 sug). For runtime requirement, those values may be pre-sent to the user-cache so that the scoring function can read from in-memory. Upon the completion of the phase 2, we would have reranked the list returned in the phase Evaluation Metrics We use five click-based metrics: 1) Typing effort, which is measured by number of chars typed upon click. 2) Clicked position. 3) Click-recall of top k positions, defined as CR T = UVWXHY Z[ \]^\_` ^a [^Y`b T JZ`^b^Za` UVWXHY Z[ \]^\_` 4) Click-precision of top k positions, defined as CP T = UVWXHY Z[ \]^\_` c (e) fg k, ]Zh i Dcj9 (e) E. where i (k) is the clicked position of the click c, I 9 (e) nt is the indicator of whether i(k) k. 5) Session success, which is measured by number of chars entered upon click on search button. 4. Result demo typehead = sea, location = POINT( , ), user = general user Seattle Hill-Silver Firs, WA CITY Seattle Center - King County,WA LOCALE Capitol Hill, Seattle, WA NEIGHBORHOOD Magnolia, Seattle, WA NEIGHBORHOOD POINT( ) POINT( ) POINT( ) ) POINT( ) POINT( ) POINT( ) typehead = sea, location = POINT( , ), user = user *** Seattle Hill-Silver Firs, WA CITY POINT( ) Seatac, WA CITY POINT( ) Seattle Center - King County,WA LOCALE Capitol Hill, Seattle, WA NEIGHBORHOOD POINT( ) POINT( ) POINT( ) POINT( ) POINT( )

4 typehead = sea, location = POINT( , ), user = general user Seabrook, NH CITY POINT( ) Sea Street Beach - Barnstable County,MA BEACH POINT( ) Cape Cod National Seashore - Barnstable County,MA PARK POINT( ) Sea Gull Beach - Barnstable County,MA BEACH POINT( ) POINT( ) typehead = sea, location = POINT( , ), user = user *** Seabrook, NH CITY POINT( ) Sea Street Beach - Barnstable County,MA BEACH POINT( ) Cape Cod National Seashore - Barnstable County,MA PARK POINT( ) Seaside Park - Essex County,MA PARK POINT( ) POINT( ) 5. Running time We randomly generated 5000 typeheads or abbreviations from the synonym space. Length of typehead = 2: Length of typehead =

5 Length of typehead = Length of typehead = A/B Test Results Evaluation metrics are calculated from the three months user click-logs for the three types of settings: general ranking (GR), localized ranking (LR), localized and personalized ranking (LPR).

Probabilistic Autocomplete Suggestion Ranking with Localization and Personalization A Quick Notes for Geosearch

Probabilistic Autocomplete Suggestion Ranking with Localization and Personalization A Quick Notes for Geosearch Xugang Ye Introduction We aim to formulate the problem of the autocomplete suggestion ranking