Abstract:
A method for efficiently choosing optimal weights in a distributed manner may include optimizing weights in a predefined order while preventing or reducing the likelihood that interacting weights are concurrently optimized. In this manner, divergence and deadlock during optimization may be avoided.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates generally to efficiently optimizing multivariate functions created from large data sets and, more particularly, to systems and methods for efficiently optimizing very large logistic regression models used in a ranking function used to rank documents. 
   2. Description of Related Art 
   Generally speaking, search engines attempt to return hyperlinks to relevant web documents in which a user may be interested. Search engines may base their determination of the documents&#39; relevancy on search terms (called a search query) entered by the user as well as additional non-query related features such as geographical location, language, etc. The goal of the search engine is to provide links to high quality, relevant results to the user based on the search query and additional information. Typically, the search engine accomplishes this by matching the terms in the search query to a corpus of pre-stored web documents. Web documents that contain the user&#39;s search terms are “hits” and are returned to the user. The search engine often ranks the documents using a ranking function based on the documents&#39; perceived relevance to the user&#39;s search terms. Optimization techniques may be employed in determining this ranking function. 
   Efficiently optimizing models of large amounts of information however, such as data on the World Wide Web (“web”), is a challenging task. One requirement for such optimizations is that the resulting optimization converge rather that diverge. Unfortunately, it has been found that, for certain optimization tasks, variables to be optimized share some relationship or interaction with one or more additional variables. Accordingly, convergence of such tasks may only be guaranteed when the variables are optimized one at a time, so as to eliminate the possibility of divergence. 
   For very sparse problems, one can optimize non-interacting variables concurrently. However, this approach does not work well when the optimization is distributed. Additionally, naive implementations may optimize a small number of weights at once, controlled by a parameter. This approach can work for specific settings of the parameter controlling the number of rules. Unfortunately, it isn&#39;t possible to predict what value is right, and a future data may cause divergence. Additionally, because efficiency hinges on the parameter, it tends to be set as high as possible, making the system more likely to fail. 
   SUMMARY OF THE INVENTION 
   According to one aspect consistent with principles of the invention, a system for ranking documents is provided. The system may include a repository configured to store training data that includes a group of features called an “instance”. A group of distributed devices may be configured to select a current condition that includes one or more of the features associated with an instance, identify a number of other conditions associated with the instances that are currently being optimized, and determine whether the number of other conditions currently being optimized is less than a predetermined value. When it is determined that the number of other conditions currently being optimized is less than a predetermined value, the group of distributed devices may be further configured to estimate a weight for the current condition. 
   According to a further aspect, a method for optimizing a large data set may include identifying at least one instance in the large data set, the at least one instance including a combination of features. A group of conditions may be identified within the large data set, where each of the group of conditions is a subset of the features included within the at least one instance. A candidate condition associated with a selected instance may be identified. The candidate condition may be assigned to a designated device among a group of devices. It may be determined whether a number of conditions associated with the selected instance being currently optimized by others of the group of devices is less than a predetermined value. A weight associated with the candidate condition may be optimized when it is determined that the number of conditions associated with the selected instance is less than a predetermined value. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and, together with the description, explain the invention. In the drawings, 
       FIG. 1  is a diagram of an exemplary information retrieval network in which systems and methods consistent with principles of the invention may be implemented; 
       FIG. 2  is a diagram of an exemplary model generation system according to an implementation consistent with principles of the invention; 
       FIG. 3  is an exemplary diagram of a device according to an implementation consistent with principles of the invention; 
       FIG. 4  is a diagram of another exemplary model generation system according to an implementation consistent with principles of the invention; 
       FIG. 5  is a flowchart of exemplary processing for generating a ranking model according to another implementation consistent with principles of the invention; 
       FIG. 6  is a flowchart of exemplary processing for concurrently optimizing data according to yet another implementation consistent with principles of the invention; and 
       FIG. 7  is a flowchart of exemplary processing for ranking documents according to an implementation consistent with principles of the invention. 
   

   DETAILED DESCRIPTION 
   The following detailed description of the invention refers to the accompanying drawings. The same reference numbers in different drawings may identify the same or similar elements. Also, the following detailed description does not limit the invention. 
   Systems and methods consistent with principles of the invention may be used to rapidly optimize large data sets by enabling concurrent or parallel processing of multiple data elements without an undue risk of divergence. In one implementation, the optimized data may be used to generate a ranking model based, at least in part, on prior information retrieval data, such as data relating to users, queries previously provided by these users, documents retrieved based on these queries, and documents that were selected and not selected in relation to these queries. 
   Exemplary Information Retrieval Network 
     FIG. 1  is an exemplary diagram of a network  100  in which systems and methods consistent with principles of the invention may be implemented. Network  100  may include multiple clients  110  connected to multiple servers  120 - 140  via a network  150 . Network  150  may include a local area network (LAN), a wide area network (WAN), a telephone network, such as the Public Switched Telephone Network (PSTN), an intranet, the Internet, a memory device, another type of network, or a combination of networks. Two clients  110  and three servers  120 - 140  have been illustrated as connected to network  150  for simplicity. In practice, there may be more or fewer clients and servers. Also, in some instances, a client may perform the functions of a server and a server may perform the functions of a client. 
   Clients  110  may include client entities. An entity may be defined as a device, such as a wireless telephone, a personal computer, a personal digital assistant (PDA), a lap top, or another type of computation or communication device, a thread or process running on one of these devices, and/or an object executable by one of these devices. Servers  120 - 140  may include server entities that gather, process, search, and/or maintain documents in a manner consistent with principles of the invention. Clients  110  and servers  120 - 140  may connect to network  150  via wired, wireless, and/or optical connections. 
   In an implementation consistent with principles of the invention, server  120  may optionally include a search engine  125  usable by clients  110 . Server  120  may crawl documents (e.g., web pages) and store information associated with these documents in a repository of crawled documents. Servers  130  and  140  may store or maintain documents that may be crawled by server  120 . While servers  120 - 140  are shown as separate entities, it may be possible for one or more of servers  120 - 140  to perform one or more of the functions of another one or more of servers  120 - 140 . For example, it may be possible that two or more of servers  120 - 140  are implemented as a single server. It may also be possible that a single one of servers  120 - 140  is implemented as multiple, possibly distributed, devices. 
   A “document,” as the term is used herein, is to be broadly interpreted to include any machine-readable and machine-storable work product. A document may include, for example, an e-mail, a web site, a file, a combination of files, one or more files with embedded links to other files, a news group posting, a blog, a web advertisement, etc. In the context of the Internet, a common document is a web page. Web pages often include textual information and may include embedded information (such as meta information, images, hyperlinks, etc.) and/or embedded instructions (such as Javascript, etc.). A “link,” as the term is used herein, is to be broadly interpreted to include any reference to/from a document from/to another document or another part of the same document. 
   Exemplary Model Generation System 
     FIG. 2  is an exemplary diagram of a model generation system  200  consistent with principles of the invention. System  200  may include devices  210   a ,  210   b ,  210   c , and  210   n  (collectively, “devices  210 ”) and a repository  220 . Repository  220  may include one or more logical or physical memory devices that may store a large data set (e.g., tens of millions of instances and millions of features) that may be used, as described in more detail below, to create and train a ranking model. The data may include information retrieval data, such as query data, user information, and document information, that may be used to create a model that may be used to rank a particular document. The query data may include, for example, search terms previously provided by users to retrieve documents. The user information may include, for example, Internet Protocol (IP) addresses, cookie information, query languages, and/or geographical information associated with the users. The document information may include, for example, information relating to the documents presented to the users and the documents that were selected and not selected by the users. In other exemplary implementations, other types of data may alternatively or additionally be stored by repository  220 . 
   Device(s)  210  may include any type of computing device capable of accessing repository  220  via any type of connection mechanism. According to one implementation consistent with principles of the invention, system  200  may include multiple devices  210 . According to another implementation, system  200  may include a single device  210 . Device(s)  210  may correspond to or be included within one or more of servers  120 - 140 . 
     FIG. 3  is an exemplary diagram of a device  300  according to an implementation consistent with principles of the invention. Device  300  may correspond to one or more of clients  110 , servers  120 - 140 , and device(s)  210 . Device  300  may include a bus  310 , a processor  320 , a main memory  330 , a read only memory (ROM)  340 , a storage device  350 , one or more input devices  360 , one or more output devices  370 , and a communication interface  380 . Bus  310  may include one or more conductors that permit communication among the components of device  300 . 
   Processor  320  may include any type of processor or microprocessor that interprets and executes instructions. Main memory  330  may include a random access memory (RAM) or another type of dynamic storage device that stores information and instructions for execution by processor  320 . ROM  340  may include a conventional ROM device or another type of static storage device that stores static information and instructions for use by processor  320 . Storage device  350  may include a magnetic and/or optical recording medium and its corresponding drive. 
   Input device(s)  360  may include one or more mechanisms that permit an operator to input information to device  300 , such as a keyboard, a mouse, a pen, voice recognition and/or biometric mechanisms, etc. Output device(s)  370  may include one or more mechanisms that output information to the operator, including a display, a printer, a speaker, etc. Communication interface  380  may include any transceiver-like mechanism that enables device  300  to communicate with other devices and/or systems. 
   As will be described in detail below, device  300 , consistent with principles of the invention, may perform certain data-related operations. Device  300  may perform these operations in response to processor  320  executing software instructions contained in a computer-readable medium, such as memory  330 . A computer-readable medium may be defined as one or more physical or logical memory devices and/or carrier waves. 
   The software instructions may be read into memory  330  from another computer-readable medium, such as data storage device  350 , or from another device via communication interface  380 . The software instructions contained in memory  330  causes processor  320  to perform processes that will be described later. Alternatively, hardwired circuitry may be used in place of or in combination with software instructions to implement processes consistent with principles of the invention. Thus, implementations consistent with principles of the invention are not limited to any specific combination of hardware circuitry and software. 
   Exemplary Model Generation Processing 
   For purposes of the discussion to follow, the set of data in repository  220  ( FIG. 2 ) may include multiple elements, called instances. It may be possible for repository  220  to store more than 50 million instances. Each instance may include a triple of data: (u, q, d), where u refers to user information, q refers to query data provided by the user, and d refers to document information relating to documents retrieved as a result of the query data and which documents the user selected and did not select. 
   Several features may be extracted for any given (u, q, d). In one exemplary implementation, these features may include one or more of the following: the country in which user u is located, the time of day that user u provided query q, the language of the country in which user u is located, each of the previous three queries that user u provided, the language of query q, the exact string of query q, the word(s) in query q, the number of words in query q, each of the words in document d, each of the words in the Uniform Resource Locator (URL) of document d, the top level domain in the URL of document d, each of the prefixes of the URL of document d, each of the words in the title of document d, each of the words in the links pointing to document d, each of the words in the title of the documents shown above and below document d for query q, the number of times a word in query q matches a word in document d, the number of times user u has previously accessed document d, and other information. In one implementation, repository  220  may store more than 5 million distinct features. 
   To facilitate fast identification of correspondence between features and instances, a feature-to-instance index may be generated that links features to the instances in which they are included. For example, for a given feature f, the set of instances that contain that feature may be listed. The list of instances for a feature f is called the “hitlist for feature f.” Thereafter, given a set of features f 0 , . . . , f n , the set of instances that contains those features can be determined by intersecting the hitlist for each of the features f 0 , . . . , f n . 
   Other information may also be determined for a given (u, q, d). This information may include, for example, the position that document d was provided within search results presented to user u for query q, the number of documents above document d that were selected by user u for query q, and a score (“old score”) that was assigned to document d for query q. The old score may have been assigned by search engine  125  or by another search engine. 
   A ranking model may be created from this data. The model uses the data in repository  220  as a way of evaluating how good the model is. The model may include rules that maximize the log likelihood of the data in repository  220 . In one implementation consistent with principles of the invention, the model may be a logistic model. The general idea of the model is that, given a new (u, q, d), the model may predict whether user u will select a particular document d for query q. As will be described in more detail below, this information may be used to rank document d for query q and user u. 
   To facilitate generation of the ranking model, a prior probability of selection may be determined. This “prior” probability of selection may provide the initial probability of document selection without considering any of the features. It uses the position, the old score, and the number of selections of documents above this document. 
   A set of instances based on the same or a different set of instances may be used as “training data” D. For each instance (u, q, d) in the training data D, its features (f 0 , f 1 , . . . , f n ) may be extracted. For example, f o  may be the feature corresponding to “the word ‘tree’ appears in the query.” In this implementation, the feature f 0  may include a boolean value, such that if “tree” appears in query q then the value of f 0  is one, otherwise the value of f 0  is zero. In other implementations, the features may include discrete values. It may be assumed that many of the features will have values of zero. Accordingly, a sparse representation for the features of each instance may be used. In this case, each instance may store only features that have non-zero values. Therefore, for each instance (u, q, d), the following information is available: 1.) its set of features, 2.) whether document d was selected by user u for query q, and 3.) its prior probability of selection. 
   A “condition” C is a conjunction of various features and possibly their complements. For example, a condition that includes two distinct features may be: “tree” is in query q and the domain of document d is “trees.com.” Further, an exemplary condition that includes a feature and a complement of a feature may be: “football” is in query q and the user did not provide the query from “www.google.co.uk.” Accordingly, for a given instance (u, q, d), the value of its features may determine the set of conditions C that apply to the instance. 
   In addition to conditions and features, a “rule” may be defined by a condition C and a weight w, represented as (C, w). The ranking model M may include a set of rules (e.g., (C 1 ,w 1 ), (C 2 ,w 2 ), etc.) and a prior probability of selection. To generate the model M the values of the weights w 1 , . . . , w n  need to first be determined. Based on this information, a function may be created that maps the set of conditions to a probability of selection. 
   To generate the model M, processing may start with an empty model M that includes the prior probability of selection. A candidate condition C may initially be selected. In one implementation, candidate conditions may be selected from the training data D. For example, for each instance in the training data D, combinations of features that are present in that instance (or, alternatively, complements of these features) may be chosen as candidate conditions. In another implementation, random sets of conditions may be selected as candidate conditions. In yet another implementation, single feature conditions may be considered for candidate conditions. In a further implementation, existing conditions in the model M may be augmented by adding extra features and these augmented conditions may be considered as candidate conditions. 
   A weight w for condition C may then be estimated. The weight w may be estimated by attempting to maximize a function of the training data D and the model M, such as the log likelihood of the training data D given the model M augmented with rule (C, w)—that is, find the weight that maximizes Log P(D|M, (C, w)), where “M, (C, w)” denotes the model M with rule (C, w) added if condition C is not already part of the model M, and w is the weight for condition C. 
   Large Data Sets 
     FIG. 4  is an exemplary diagram of a model generation system  400  consistent with principles of the invention. System  400 , as with system  200  described above, may include devices  410   a ,  410   b , and  410   n  (collectively, “devices  410 ”), devices  420   a ,  420   b , and  420   m  (collectively, “devices  420 ”), and a repository  430 . Devices  410 - 420  and repository  430  are substantially similar in function to devices  210  and repository  220  described above. When the data set within repository  430  becomes very large (e.g., substantially more than a few million instances), devices  410  and devices  420  may be configured as a distributed system. It should be fully understood that devices  410  and  420  may, in fact, represent multiple physical machines or may represent multiple processing threads or other types of parallel processing performed on a single or smaller number of physical machines. For example, devices  410  and  420  may be capable of communicating with each other and with repository  430 , as illustrated in  FIG. 4 . 
   Unfortunately, as multiple devices  410  and  420  become responsible for handling or otherwise contributing to the generation of model M, it may be possible for various candidate conditions to be correlated in such a manner that parallel processing of the conditions may deadlock and fail to result in an accurate optimization of the conditions, and hence, the model as a whole. In such a circumstance, the deadlock may be caused by interdependencies between the conditions that may prevent the necessary optimization and may result in eventual divergence of the model. In accordance with one implementation consistent with principles of the invention, such correlated conditions may be adequately addressed, such that an optimized model is created and deadlock may be avoided. 
   According to one exemplary implementation of the distributed system, devices  410  (e.g., “instance machines”) may each be responsible for a subset of the instances within repository  430 . Each instance machine  410  may possibly store its subset of instances in local memory. Additionally, devices  420  (e.g., “condition machines”) may be responsible for optimizing the various candidate conditions that may apply to each instance and returning the optimized results to instance machines  410 . In one embodiment, each device  410  and  420  may build its own feature-to-instance index for its subset of instances or conditions. 
   As described above, each instance (u, q, d) in repository  430  may include or correspond to one or more features. Additionally, each instance may have one or more conditions that apply to it, where the conditions relate to features or combinations of features found in the instance.  FIG. 5  is a flowchart of exemplary processing for generating a ranking model according to an implementation consistent with principles of the invention. Initially, processing may begin by assigning each instance to one of the instance machines  410  and assigning each condition to one of the condition machines  420  in a sorted manner (act  510 ). It should be noted that multiple instances may be assigned to a single instance machine  410  and multiple conditions may be assigned to a single condition machine  420 . 
   Once the instances and conditions have been assigned, processing of the various instances and conditions may begin. Initially, for each instance being processed, a concurrency counter may be initialized indicating the number of concurrently processed conditions depending on the instance (act  512 ). A next available condition may then be identified for optimization (act  514 ). Prior to optimizing the identified condition, the concurrency counters associated with each instance related to the condition are checked to determine whether they are each less than a maximum concurrency cap (act  516 ). Because each condition to be optimized may be associated with multiple instances, multiple concurrency counters may need to be examined. In one exemplary implementation, such a concurrency cap may be 2. However, it should be noted that divergence of optimized data may be completely avoided by setting the cap equal to 1. In this case, the conditions associated with each instance are processed one at a time. Increases to the concurrency cap aid in enabling concurrent processing of conditions. Such concurrent processing increases the speed in which the optimization is completed. However, such increased concurrency may result in an increased risk of divergence. 
   If it is determined that the concurrency counter for any instance associated with the current condition is less than the concurrency cap, the concurrency counter associated with each relevant instance is incremented and the weight associated with the current condition is optimized in the manner set forth above in  FIG. 4  (act  518 ). Upon completion of the optimization, optimized weights are passed to instance machines  410  responsible for the associated instances (act  520 ). Upon receipt of optimized weights, the associated concurrency counters at instance machines  410  may be decremented (act  522 ). The process then returns to act  514  for processing of the next available condition. 
   If it is determined that a concurrency counter for any instance associated with the current condition is not less than the concurrency cap, optimization of the models associated with the current condition may be suspended (act  524 ). Upon suspension of processing, a message may be sent to each condition machine  420  indicating that processing of the current condition has been blocked at the associated instance machine  410  (act  526 ). The message and any processing to create it may be at low priority. 
   This notification serves to inform each condition machine  420  that all conditions prior to the current condition in the sorted list of conditions have either been processed by the instance machine  410  sending the message or are not associated with the instance being processed by the instance machine  410  sending the message. Accordingly, any other instance machine waiting for input from the condition machine sending the message relating to a condition below the current condition may determine the message to be an indication that the instance machine sending the message is not providing information regarding any other condition. The process then returns to act  516  where it is again determined whether the applicable concurrency counters are at least one less than the concurrency cap. As described above, return of optimized values for conditions serve to decrement the concurrency counters associated with the condition currently being processed. As should be clear from the above description, adherence to the concurrency cap significantly reduces the likelihood that the processing of correlated or interacting conditions may result in an optimization deadlock. 
   It should be noted that determining whether applicable counters are at least one less than the concurrency cap (act  516 ) may be performed concurrently with the act of sending messages indicating that processing of the current condition has been blocked (act  526 ). Moreover, sending messages indicating that processing of the current condition has been blocked may cease as soon as applicable counters are less than the concurrency cap. 
   Consider the following example: model generation system  400  includes two instance machines  410   a  and  410   b , two condition machines  420   a  and  420   b , and a repository  430  containing data having the following features: f 1 =(query contains: “thanks”); f 2 =(query is in English); f 3 =(query contains: “abrigado”); and f 4 =(query is in Portugese). Further consider that a first instance i 1  includes features f 1  and f 2  and is assigned to instance machine  410   a  and a second instance i 2  includes features f 3  and f 4  and is assigned to instance machine  410   b . Further, four feature-specific candidate conditions are identified, where condition c 1 =feature f 1  and is assigned to condition machine  420   a ; condition c 2 =feature f 3  and is assigned to condition machine  420   b ; condition c 3 =feature f 2  and is assigned to condition machine  420   a ; and condition c 4 =feature f 4  and is assigned to condition machine  420   b . In this example, conditions c 1  and c 3  apply to instance i 1  and conditions c 2  and c 4  apply to instance i 2 . As noted by the feature definitions, conditions c 1  and c 3  may be considered correlated in that each condition depends from or applies to instance i 1 . Similarly, conditions c 2  and c 4  may be considered correlated in that each condition depends from or applies to instance i 2 . Further, assume that the concurrency cap for this example is 1, meaning that no more than one condition relating to an instance may be optimized at any one time. 
     FIG. 6  is a flow chart of exemplary processing for generating a concurrently optimizing data in the system  400  of the present example. Initially, instance machine  410   a  begins by incrementing its concurrency counter to 1 and processing condition c 1 , resulting in instance machine  410   a  sending information for optimizing condition c 1  to condition machine  420   a  responsible for optimizing condition c 1  (act  610 ). Next, instance machine  410   b  begins incrementing its concurrency counter to 1 and sending information for optimizing condition c 2  to condition machine  420   b  responsible for optimizing condition c 2  (act  612 ). 
   Upon receipt of the information for optimizing condition c 1  from instance machine  410   a , condition machine  420   a  waits to perform optimization of c 1  until it hears from instance machine  410   b , in case the instance under process by instance machine  410   b  also applies to instance c 1  (act  614 ). Similarly, upon receipt of the information for optimizing condition c 2  from instance machine  410   b , condition machine  420   b  waits to perform optimization of c 2  until it hears from instance machine  410   a , in case the instance under process by instance machine  410   a  also applies to instance c 2  (act  616 ). 
   At this point, while instance machine  410   a  awaits an optimized weight for condition c 1 , it considers processing condition c 3 . However, instance machine  410   a  determines that the concurrency cap for instance i 1  has been reached, since condition c 1  also associated with instance i 1  is currently being optimized (act  618 ). Accordingly, as described above, instance machine  410   a  sends a message to condition machines  420   a  and  420   b  indicating that it is blocked at condition c 3  (act  620 ). 
   Upon receipt of this message, condition machine  420   b  determines that it no longer needs to wait for input from instance machine  410   a  relating to condition c 2 , since c 3  (the current stopping point) is greater than (i.e., after) condition c 2  (act  622 ). Accordingly, condition machine  420   b  then finalizes optimization of condition c 2  (act  624 ) and sends its optimized weight back to instance machine  410   b  (act  626 ). 
   Upon receipt of the optimized weight for condition c 2  the concurrency counter is decremented (act  628 ). Instance machine  410   b  then processes the next available condition c 4  associated with its instance i 2  by sending an information for optimizing condition c 4  to condition machine  420   a  responsible for optimizing condition c 4  (act  630 ). Condition machine  420   a  then determines that it no longer needs to wait for instance machine  410   b  to process condition c 1  and finalizes optimization of condition c 1  since condition c 4  is greater than (i.e., after) condition c 1  and that condition c 1  is associated with instance machine  410   a  (act  632 ). Condition machine  420   a  then sends an optimized weight for condition c 1  back to instance machine  410   a  (act  634 ). Upon receipt of the optimized weight for condition c 1  the concurrency counter associated with instance i 1  is decremented (act  636 ). 
   Upon decrementing the concurrency counter associated with instance i 1 , condition machine  410   a  is unblocked regarding condition c 3 . Information for optimizing condition c 3  is then sent to condition machine  420   b  (act  638 ). Condition machine  420   b  processes condition c 3  and finalizes optimization of condition c 3  (act  640 ). Condition machine  420   b  then sends an optimized weight for condition c 3  back to instance machine  410   a  (act  642 ). It should be noted that condition c 4  must wait until it is determined whether instance machine  410   a  has any instances to which condition c 4  may apply. This determination is made upon receipt of a message about condition c 4  from instance machine  410   a  or a message from instance machine  410   a  regarding a later condition. As discussed above, a message regarding a later condition indicates that instance machine  410   a  does not apply to condition c 4  and that processing may continue. 
   In this example, instance machine  410   a  does not affect condition c 4  and there are no late instances. Accordingly, instance machines  410   a  and  410   b  send a message to condition machines  420   a  and  420   b  indicating that they have no more instances (act  644 ). In this way, any remaining conditions may be optimized. 
   Exemplary Process for Ranking Documents 
     FIG. 7  is a flowchart of exemplary processing for ranking documents according to an implementation consistent with principles of the invention. Processing may begin with a user providing one or more search terms as a search query for searching a document corpus. In one implementation, the document corpus is the Internet and the vehicle for searching this corpus is a search engine, such as search engine  125  ( FIG. 1 ). The user may provide the search query to search engine  125  via web browser software on a client, such as client  110  ( FIG. 1 ). 
   Search engine  125  may receive the search query and act upon it to identify documents (e.g., web pages) related to the search query (acts  710  and  720 ). A number of techniques exist for identifying documents related to a search query. One such technique might include identifying documents that contain the one or more search terms as a phrase. Another technique might include identifying documents that contain the one or more search terms, but not necessarily together. Other techniques might include identifying documents that contain less than all of the one or more search terms, or synonyms of the one or more search terms. Yet other techniques are known to those skilled in the art. 
   Search engine  125  may then score the documents based on the ranking model described above (act  730 ). With regard to each document, search engine  125  may identify a new instance (u, q, d) that corresponds to this user search, where u refers to the user, q refers to the search query provided by the user, and d refers to the document under consideration. Search engine  125  may extract the features from the new instance and determine which rules of the ranking model apply. Search engine  125  may then combine the weight of each rule with the prior probability of selection for (u, q, d) to determine the final posterior probability of the user u selecting this document d for query q. Search engine  125  may use the final posterior probability as the score for the document. Alternatively, search engine  125  might use the final posterior probability as one of multiple factors in determining the score of the document. 
   Search engine  125  may sort the documents based on their scores (act  740 ). Search engine  125  may then formulate search results based on the sorted documents (act  750 ). In an implementation consistent with principles of the invention, the search results may include references to the documents, such as links to the documents and possibly a textual description of the links. In another implementation, the search results may include the documents themselves. In yet other implementations, the search results may take other forms. 
   Search engine  125  may provide the search results as a HyperText Markup Language (HTML) document, similar to search results provided by conventional search engines. Alternatively, search engine  125  may provide the search results according to a protocol agreed upon by search engine  125  and client  110  (e.g., Extensible Markup Language (XML)). 
   Search engine  125  may further provide information concerning the user, the query provided by the user, and the documents provided to the user to help improve the ranking model. For example, server  120  may store this information in repository  220  (or repository  430 ) or provide it to one of devices  210  (or devices  410  and/or  420 ) to be used as training data for training the model. 
   CONCLUSION 
   Systems and methods consistent with principles of the invention may facilitate functions. In one implementation consistent with principles of the invention, a concurrency counter or counters may be used to limit the number of concurrently optimized variables. 
   The foregoing description of preferred embodiments of the present invention provides illustration and description, but is not intended to be exhaustive or to limit the invention to the precise form disclosed. Modifications and variations are possible in light of the above teachings or may be acquired from practice of the invention. For example, while series of acts have been described with regard to  FIGS. 5-7 , the order of the acts may be modified in other implementations consistent with principles of the invention. Also, non-dependent acts may be performed in parallel. Further, the acts may be modified in other ways. 
   It will also be apparent to one of ordinary skill in the art that aspects of the invention, as described above, may be implemented in many different forms of software, firmware, and hardware in the implementations illustrated in the figures. The actual software code or specialized control hardware used to implement aspects consistent with the present invention is not limiting of the present invention. Thus, the operation and behavior of the aspects were described without reference to the specific software code—it being understood that one of ordinary skill in the art would be able to design software and control hardware to implement the aspects based on the description herein. 
   No element, act, or instruction used in the description of the invention should be construed as critical or essential to the invention unless explicitly described as such. Also, as used herein, the article “a” is intended to include one or more items. Where only one item is intended, the term “one” or similar language is used. Further, the phrase “based on” is intended to mean “based, at least in part, on” unless explicitly stated otherwise.