Patent Publication Number: US-9418335-B1

Title: Method and apparatus for selecting links to include in a probabilistic generative model for text

Description:
This application is a continuation of U.S. patent application Ser. No. 12/176,621, filed Jul. 21, 2008 now U.S. Pat. No. 8,180,725, which claims priority under 35 U.S.C. §119 to U.S. Provisional Patent Application No. 60/953,295 filed Aug. 1, 2007, the contents of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     1. Field 
     The present invention relates to techniques for modeling textual documents. More specifically, the present invention relates to techniques for selecting links in a probabilistic generative model for textual documents, wherein the model characterizes textual documents based on clusters of conceptually related words. 
     2. Related Art 
     Processing text in a way that captures its underlying meaning—its semantics—is an often-performed but poorly understood task. This function is most often performed in the context of search engines, which attempt to match documents in some repository to queries by users. It is sometimes also used by other library-like sources of information, for example to find documents with similar content. In general, understanding the semantics of text is an extremely useful functionality in such systems. Unfortunately, most systems written in the past have only a rudimentary understanding of text, focusing only on the words used in the text, and not the underlying meaning behind them. 
     One existing system captures some of this underlying meaning by characterizing a document with respect to clusters of conceptually related words. For example, see U.S. Pat. No. 7,231,393 entitled, “Method and Apparatus for Learning a Probabilistic Generative Model for Text,” by inventors Georges Harik and Noam Shazeer. This system builds and maintains a model which uses clusters of conceptually related words to capture a significant amount of semantic meaning within text. More specifically, the model contains terminal nodes representing words and cluster nodes representing clusters of conceptually related words. In this model, nodes are coupled together by weighted links, wherein if a node fires, a link from the node to another node causes the other node to fire with a probability proportionate to the weight of the link. 
     In this type of model, it is desirable to keep track of the probability of every word given every cluster. Unfortunately, this can generate too many links to fit into main memory. For example, if there exist millions of words and hundreds of thousands of clusters, the system must keep track of hundreds of billions of links, and it is not practical to store this many links in main memory. It is therefore desirable to be able to selectively retain the most important links and delete the others. Unfortunately, existing systems provide no satisfactory mechanisms for automatically selecting links to include in such a model. 
     Hence, what is needed is a method and an apparatus that facilitates automatically selecting links to be included in a generative model for textual documents. 
     SUMMARY 
     Some embodiments of the present invention provide a system that selects links while updating a probabilistic generative model for textual documents. During operation, the system receives a current model, which contains terminal nodes representing words and cluster nodes representing clusters of conceptually related words, wherein nodes in the current model are coupled together by weighted links, wherein if a node fires, a link from the node to another node is activated and causes the other node to fire with a probability proportionate to the weight of the link. Next, the system applies a set of training documents containing words to the current model to produce a new model. While doing so, the system: determines expected counts for activations of links and prospective links; determines link-ratings for the links and the prospective links based on the expected counts, and selects links to be included in the new model based on the determined link-ratings. Finally, the system makes the new model the current model. 
     In some embodiments, selecting the links to be included in the new model involves ensuring source diversity by selecting links which are associated with at least a minimum number of sources. In some embodiments, the minimum number of sources is three sources. 
     In some embodiments, determining the link-rating for a given link between a parent (always a cluster) and a child (either a terminal or a cluster) involves: determining an expected count for the given link which indicates an expected number of times the given link was activated; calculating a significance for the given link by dividing a probability of the child given the parent by a probability of the child, significance=p(child|parent)/p(child); and calculating the link-rating for the given link as a function of the significance and the expected count for the given link. 
     In some embodiments, the function for the link-rating is significance 2 ×expected count. 
     In some embodiments, determining the expected count for the given link involves reducing the value of the expected count if the given link is a prospective link. 
     In some embodiments, selecting links to be included in the new model based on the determined link-ratings involves: ranking the links and prospective links based on the determined link ratings and selecting the N top-ranked links and prospective links to be included in the new model. 
     In some embodiments, applying the set of training documents to the current model involves: applying the set of training documents to the links defined in the current model to produce expected counts for corresponding links and prospective new links in the new model; and using these expected counts to produce weights for links in the new model. 
     In some embodiments, producing the new model additionally involves selectively introducing new cluster nodes into the current model. 
     In some embodiments, producing the new model additionally involves selectively deleting nodes from the new model. 
     In some embodiments, the system selectively merges nodes in the current model. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  illustrates a probabilistic model in accordance with an embodiment of the present invention. 
         FIG. 2  illustrates a state of the probabilistic model in accordance with an embodiment of the present invention. 
         FIG. 3  illustrates a model representing states in the United States in accordance with an embodiment of the present invention. 
         FIG. 4  illustrates global nodes and a number of local networks in accordance with an embodiment of the present invention. 
         FIG. 5  illustrates a reworked model in accordance with an embodiment of the present invention. 
         FIG. 6  illustrates the crawling, ranking and searching processes in accordance with an embodiment of the present invention. 
         FIG. 7  illustrates data structures involved in characterizing a document in accordance with an embodiment of the present invention. 
         FIG. 8  presents a flow chart of the characterization process in accordance with an embodiment of the present invention. 
         FIG. 9  presents of a flow chart of the process for selecting candidate clusters in accordance with an embodiment of the present invention. 
         FIG. 10  presents a flow chart of the process of approximating probabilities for candidate clusters in accordance with an embodiment of the present invention. 
         FIG. 11  presents a flow chart illustrating how states for the probabilistic model are selected in accordance with an embodiment of the present invention. 
         FIG. 12  presents a flow chart summarizing the learning process in accordance with an embodiment of the present invention. 
         FIG. 13  presents a flow chart of the process of selectively deleting cluster nodes in accordance with an embodiment of the present invention. 
         FIG. 14  presents a flow chart illustrating the process of identifying and merging similar cluster nodes in accordance with an embodiment of the present invention. 
         FIG. 15  presents a flow chart illustrating the process of determining whether cluster nodes explain each other in accordance with an embodiment of the present invention. 
         FIG. 16  presents a flow chart illustrating the process of merging two cluster nodes to form a combined cluster node in accordance with an embodiment of the present invention. 
         FIG. 17  presents a flow chart, illustrating the process of selecting links in accordance with an embodiment of the present invention. 
         FIG. 18  presents a flow chart illustrating the process of determining link-ratings in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the present invention. Thus, the present invention is not limited to the embodiments shown, but is to be accorded the widest scope consistent with the claims. 
     The data structures and code described in this detailed description are typically stored on a computer-readable storage medium, which may be any device or medium that can store code and/or data for use by a computer system. This includes, but is not limited to, volatile memory, non-volatile memory, magnetic and optical storage devices such as disk drives, magnetic tape, CDs (compact discs), DVDs (digital versatile discs or digital video discs), or other media capable of storing computer readable media. 
     The System 
     One embodiment of the present invention provides a system that learns concepts by learning an explanatory model of text. In the system&#39;s view, small pieces of text are generated in a fairly simple, but incredibly powerful way, through the execution of a probabilistic network. The system learns the parameters of this network by examining many examples of small pieces of text. 
     One embodiment of the system considers the important information in a piece of text to be the words (and compounds) used in the text. For example in the query “cooking classes palo alto” the words are “cooking” and “classes”, and the compounds consist of the simple compound “palo alto”. Distinguishing compounds from words is done on the basis of compositionality. For example, “cooking classes” is not a compound because it is about both cooking and classes. However “palo alto” is not about “palo” and “alto” separately. This is sometimes a hard distinction to make, but good guesses can make such a system better than no guesses at all. 
     What this means is that the system simplifies the analysis of text by not considering the order of the words in the text. For example, one embodiment of the present invention does not distinguish the above from “palo-alto classes cooking” (we use dashes in this specification to connect the components of compounds). We will refer to both words and compounds as “terminals”. (We will see later that this is because, in our model of the world, they do not generate words, as opposed to concepts, which do generate words.) This simplification means that the system treats segments of text as a set of terminals. 
     Probabilistic Model for Text Generation as a Set of Terminals 
     Let&#39;s look at what a system that generated text as a set of words might look like.  FIG. 1  shows one such model. Here, the circles are called model nodes. These nodes represent random variables, each of which models the existence or non-existence of concepts or terminals. The only terminals we are considering in this model are “elephant”, “grey” and “skies”. There are two concepts, called C 1  and C 2  (because they are used to generate related words, concepts are sometimes referred to as clusters). 
     This model might be used, for example, to explain why the words “grey” and “skies” often occur together, why the words “grey” and “elephant” often occur together, but yet why the words “elephant” and “skies” rarely occur together. It is because when people are generating text with these words, they have ideas in mind. The system&#39;s concepts are supposed to model the ideas in a person&#39;s mind before they generate text. 
     Note that there is a darker node at the top of the figure without a name. This is the universal node, U, which is always active. When modeling text, it is always active, and all concepts come from it. The arrows exiting any concept are called links. These links imply that when a user thinks of one concept, they are likely to think of another concept or write another terminal afterwards. For example, the concept C 1  links to the words “elephant” and “grey”. That means that after a user thinks of C 1 , they often write out the words “elephant” and/or “grey”. In particular, the numbers on the links are important. They represent the probabilities of certain events. The link between C 1  and “elephant” means that after thinking of C 1 , a user thinks of the word “elephant” with probability 0.5. These numbers are often referred to as the “weights” on the links. 
     This model can be used or “executed” to generate text. When we are doing this, we begin at the universal node (often called U), and consider it to exist in the mind of the generator. We will often say that the node is “active” or has “fired” to imply this. For concepts, firing means that the idea of that concept is active, and is able to fire terminals. For terminals, the idea of firing is that the terminals exist in the text to be generated. 
     Let us run through an example of how one such piece of text could be generated. In the example in  FIG. 1 , we would start out by assuming that the universal node is active. Then C 1  would fire with 0.1 probability. At this point, some random process would decide whether or not C 1  would fire. For this random process you could throw dice or use any random information. Usually, if this were taking place on a computational machine, a random number generator would be used. Many methods are adequate so long as we have some way of producing a decision that turns out 9 out of 10 times to be no (0.9) and 1 out of 10 times to be yes (0.1). When it turns out to be yes, the concept C 1  is activated. When it turns out no, C 1  is not activated. A similar process is applied to C 2 . 
     We will assume that for our example now, the random number generator has produced YES for the link U→C 1  and NO for the link U→C 2 . At this point, C 1  is active. When a concept is active, we can then pick random numbers for the other concepts or terminals which have links originating from that active concept. In this example, now the words “elephant” and “grey” have a possibility of becoming active with probabilities of 0.5 and 0.4. Now let us assume that we get more random numbers (to make a simple analogy we will now refer to this as throwing dice) and decide that both “elephant” and “grey” are active. This means that we have our piece of text; it is the words “elephant” and “grey””. Note that because in one embodiment of the present invention the word order is not modeled, we cannot distinguish “grey elephant” from “elephant grey” (unless they form a compound). In this way, we have generated a small piece of text. 
       FIG. 2  shows this particular execution of the model detailed in  FIG. 1 . In this figure, we see the concept C 1  becoming active (we illustrate this graphically by darkening the node) and the words “elephant” and “grey” becoming active. This idea of graphically viewing the execution model of a piece of text is important from the standpoint of examining the whole system to see if it is operating correctly, and we will use it later on. 
     This seems like a lot of work to generate a grey elephant Note, however, that the words we came up with have some meaning to us as people. This is because elephants are grey. In some small way, even this model in  FIG. 1  captures a little bit about the state of the world. If only on the surface, this model captures the correlation between the words “grey” and “elephant”, “grey” and “skies”, but not “elephant” and “skies”. 
     Our system learns the intermediate concepts, the links and the link weights in order to explain the co-occurrence of words and compounds in small pieces of text. In addition, its generative model is slightly more complicated than that described above, in order to be better able to generate and explain text of various sizes (for example, queries are often 2-3 words, while documents are 1000 words or so). 
     Adjusting for Text of Various Sizes 
     For various reasons, the type of simple model above is slightly inadequate for dealing with text. A simple explanation for this is that each of the concepts produces a certain number of words, but finds it much more difficult, for example, to produce many words if the weights on the links are small. It would be desirable, for example, if a concept could produce either a few or many words from the terminals it points at. 
       FIG. 3  shows an example concept representing the states of the United States of America. In following our earlier model, the concept can fire terminals representing each of the 50 states, each with probability 1/50. Now, for this model to generate the word “California” alone is not that improbable. That probability is roughly (1/50)*(49/50) 49 , which is approximately 0.7%. For this concept to fire all the states would be (1/50) 50  which is incredibly small. However, should we develop such a concept that covers the idea of the states of the United States, we would want it to explain pieces of text where all the states occur. 
     In order to address this problem, before it fires other terminals, each concept picks an activation level. Conceptually, this activation level chooses “how many” terminals are to be picked from this concept. Note that this activation level is not a quality of our model. In fact, it is only chosen when the model is being executed. What activation does is to modify the probability that this concept fires each of its terminals (but not its sub-concepts, i.e., concept-to-concept linking is unaffected by activation). 
     The exact numerical adjustment can be as follows. If a link has a weight W and the cluster chooses activation A in its execution, and the link points between a concept and a terminal, then the concept fires the terminal with probability (1−e −AW ). Here “e” is the common mathematical number approximately 2.71. At first glance, this formulation seems odd, but it has the following useful properties: When W is very small (&lt;0.01) and A is a small number (say 2), the probability is approximately equal to AW—so these numbers are easy to approximate in general. The reason they have an odd exponential form is because probabilities have to have an upper limit of 1. So, having a link weight of 0.02 (1/50) and an activation of 100 should not give you a probability of 2.0. The exponential form also has a number of other useful theoretical properties from a mathematical standpoint. 
     At this point, we have detailed almost all the individual pieces comprising our model. One detail is the interaction between two or more clusters trying to fire the same terminal or cluster. In this case, each interaction is independent of the other. In particular, the probability that the result does NOT fire is the product of the probability that each case does NOT fire it. For example, if three clusters C 1 , C 2  and C 3  link to a fourth cluster C 4  with weights 0.1, 0.2, 0.3 and C 1 , C 2  and C 3  are active: C 4  does not fire with probability (1-0.1)*(1-0.2)*(1-0.3) or (0.9)*(0.8)*(0.7) or 0.504. Therefore, the chance it DOES fire is 1-(1-0.1)*(1-0.2)*(1-0.3) or 1-0.504=0.496. 
     Bayesian Networks 
     At this point and before we proceed, it is worthwhile to talk about a certain duality between the model we have been talking about and a certain class of probabilistic models called Bayesian networks. 
     Bayesian networks are well-understood probabilistic modeling techniques in which conditional independences are asserted between various random variables in a joint distribution. As in the model above, Bayesian networks have nodes and directed links. These networks compactly represent a joint distribution over a number of random variables while structurally representing conditional independence assumptions about these variables. 
     In a Bayesian network, the set of nodes pointing to a node is called its “parents”. The set of nodes reachable from a node via following links is called its “descendants” or “children”, and the structure implies that a node is independent of its non-descendants given its parents. The entire distribution is therefore encoded in the conditional probability tables of a child given its parents (nodes with no parents have their own distributions). The probability of a particular instantiation of the entire network is simply the product of the probabilities of each child given its parents. 
     Bayesian networks are related to our model in the following way: if each node in the execution of our model is considered to be a random variable, then the joint distribution over the set of nodes that are turned on is exactly that which arises from considering our model as a Bayesian network with noisy-or combination functions. Noisy-or conditional probabilities turn a Boolean child on independently from each parent. That is, the probability of a child being off is the product of the probability that each parent does not fire it. Note this is exactly the combination function used in our model to decide if multiple active concepts that link to a terminal fire it. Note that Bayesian networks are themselves a subclass of more general probabilistic models. 
     Learning 
     At this point, we have gone over how an existing model could be used to generate text. We have not detailed several aspects of this work: (1) how our model is learned; (2) how our model is used to estimate the concepts present in text; and (3) how our model is used in practical situations. In this section, we will attempt to detail how our model is learned, and the various techniques that can be used for this purpose. 
     In learning a generative model of text, in one embodiment of the present invention some source of text must be chosen. Some considerations in such a choice are as follows: (1) it should have related words in close proximity; (2) it should present evidence that is independent, given the model we are trying to learn (more on this later); and (3) it should be relevant to different kinds of text. For this reason, the implementation of the model which follows uses exemplary “query sessions” from a search engine as its small pieces of text. We have also implemented and run our model on web pages and other sources of text, but for the purposes of making this exposition more concrete, we focus on the analysis of query sessions. 
     To be more precise, we generally define a query session (also referred to as a user session or a session) as any set of queries that are deemed to be relevant. For example, a query session can include a set of queries issued by a single user on a search engine over a fixed period of time. Note that while issuing queries, a user will often search for related material, issuing several queries in a row about a particular topic. Sometimes, these queries are interspersed with queries associated with other random topics. An example query session (not an actual one) might appear as follows: 
     the graduate 
     dustin hoffman 
     rain man 
     autism 
     cool junk 
     fast cars 
     tom cruise nicole kidman 
     Each query here is on a separate line. Note that most of the words are related in some way. The first is a movie by Dustin Hoffman, as is the third. The second is Dustin Hoffman himself. The fourth deals with an issue brought up in the movie. The fifth query “cool junk” is not related to the main topic of the session, neither is the sixth “fast cars”. The last is a little related because Tom Cruise acted in Rain Man with Dustin Hoffman. In general, there is a lot of information in such a small piece of text, from which we can draw conclusions, but there is also a lot of uncorrelated junk. The main task of our system is to cull the proper correlations from the junk, while looking at a large number (billions) of such pieces of text. 
     Learning a probabilistic model that can explain all the words that occur together in queries is difficult. Note that in the explanation of the session above, we used information we had about the world in general to explain the query session. This is the nature of the information that our model learns in order to come up with a world model in which the session above is more than infinitesimally likely. Our approach to this problem is to use the well-known Expectation Maximization (EM) algorithm. 
     Assume we do not know the model but we have a current guess (possibly very inaccurate) about it. We use this guess to go over the training data and generate expected counts, e.g., how many times a certain link was active. By dividing this count by the total number of training instances, we can transform the count to the probability that the link is active in any training instance. We then use these probabilities to update the model itself and iterate. We now explain this algorithm in more details in the context of our model. 
     Thus, we first need to come up with expected counts. To do so we create a local network for every training instance.  FIG. 4  illustrates a number of local networks. In each local network, the terminals for a particular user session are assumed to be active. Note that our model is replicated for each such session. This is because what we observe for each session is only the words that the user used and not, in fact, the concepts that were active in the user&#39;s mind when those words came about! The local nodes here represent our uncertainty about these concepts. Because the user may have been thinking of anything when they wrote each word, all concepts have to be considered in each local network. 
       FIG. 5  shows a slightly reworked version of the model, where variables exist to show explicitly whether or not each concept triggers another concept or terminal. Note that the joint distributions implied by both are the same, once they are projected to the original variables we are interested in (i.e., C 1  and C 2 ). The triangles in this figure represent extra “trigger” variables, and it is often helpful to think about the model with them because they simplify the number of conditional probabilities that are required. 
     For example, in  FIG. 5 , the “trigger” variable between U and C 2  only needs to know the distributions of U and the weight of the link from U to C 2  to decide the probability that C 2  gets fired from U. Similarly the other trigger into C 2  only needs to know the values of the C 1  and weight of the link from C 1  to C 2 . 
     During the training process, the system maintains counters for links and prospective links in the current model to count the expected number of times they are activated during the training process, where the expectation is over the probability that the trigger variables are activated given the training data Next, the system applies Expectation Maximization (EM) to the expected counts to produce weights for links in the new model. 
     Crawling Ranking and Searching Processes 
       FIG. 6  illustrates the crawling, ranking and searching processes in accordance with an exemplary embodiment of the present invention. During the crawling process, a web crawler  604  crawls or otherwise searches through websites on web  602  to select web pages to be stored in indexed form in data center  608 . The selected web pages are then compressed, indexed and ranked in module  605  (using the ranking process described above) before being stored in data center  608 . 
     During a subsequent searching process, a search engine  612  receives a query  613  from a user  611  through a web browser  614 . This query  613  specifies a number of terms to be searched for in the set of documents. In response to query  613 , search engine  612  uses search terms specified in the query to identify highly-ranked documents that satisfy the query. Search engine  612  then returns a response  615  through web browser  614 , wherein the response  615  contains matching pages along with ranking information and references to the identified documents. 
     Note that during the searching and/or ranking processes, the system can characterize the documents (and query phrases) based on the clusters of conceptually related words to improve the searching and/or ranking processes. 
     Process of Characterizing a Document 
       FIG. 7  illustrates data structures involved in characterizing a document in accordance with an embodiment of the present invention. These data structures include order one probability table  702 , parent table  704 , child table  706  and link table  708 . 
     Order one probability table  702  includes entries for each node in the probabilistic model that approximate the order one (unconditional) probability that the node is active in generating a given set of words. Hence, an entry in order one probability table  702  indicates how common an associated word or cluster is in sets of words that are generated by the probabilistic model. In one embodiment of the present invention, order one priority table  702  also includes an “activation” for each cluster node indicating how many links from the candidate cluster to other nodes are likely to fire. 
     Parent table  704  includes entries that identify parents of associated nodes in the probabilistic model, as well as the link weights from the identified parents. 
     Similarly, child table  706  includes entries that identify children of associated nodes in the probabilistic model, as well as the link weights to the identified children. (Note that child table  706  is optional; it is not necessary for most of the operations we discuss.) 
     Note that order one probability table  702 , parent table  704  and child table  706  are pre-computed for the probabilistic model, prior to characterizing the document. On the other hand, link table  708  is populated during the process of characterizing a document. 
     Link table  708  includes entries for links to consider as evidence while constructing an evidence tree as is discussed below with reference to  FIGS. 8-11 . Each entry in link table  708  contains the weight for an associated link as well as the identifier for the associated parent node. Moreover, link table  708  can be sorted by parent identifier as is discussed below. 
       FIG. 8  presents a flow chart of the characterization process in accordance with an embodiment of the present invention. The system starts by receiving a document containing a set of words (step  802 ). Note that this document can include a web page or a set of terms (words) from a query. 
     Next, the system selects a set of “candidate clusters” from the probabilistic model that are likely to be active in generating the set of words (step  804 ). This process is described in more detail below with reference to  FIG. 9 . Note that by selecting a set of candidate clusters, the system limits the number of clusters that are considered in subsequent computational operations, thereby reducing the amount of computation involved in characterizing the document. 
     The system then constructs a vector (set of components) to characterize the document (step  806 ). This vector includes components for candidate clusters, wherein each component of the vector indicates a degree to which the corresponding candidate cluster was active in generating the set of words in the document. This process is described in more detail below with reference to  FIGS. 10-11 . 
     Finally, the system can use this vector to facilitate a number of different operations related to the document (step  808 ). Some of these uses are listed below in a following section of this specification entitled “Uses of the Model”. 
       FIG. 9  presents a flow chart of the process for selecting candidate clusters in accordance with an embodiment of the present invention. This flow chart describes in more detail the operations involved in performing step  804  in  FIG. 8 . The system starts by constructing an “evidence tree” starting from terminal nodes associated with the set of words in the document and following links to parent nodes (step  902 ). As a node is selected to be part of the evidence tree, links to the node from parent nodes are inserted into link table  808 . 
     During the process of constructing the evidence tree, the system uses the evidence tree to estimate the likelihood that each parent cluster is active in generating the set of words (step  904 ). More specifically, in one embodiment of the present invention, for a cluster node C i  that only points to terminal nodes, the system estimates the likelihood that C i  was involved in generating the set of words (we refer to this estimated likelihood as the “Guess of C i ”) using the following formula, 
               Guess   ⁡     (     C   i     )       =     O   ⁢           ⁢   1   ⁢     (     C   i     )     ⁢       ∏   j     ⁢           ⁢         P   ~     ⁡     (       C   i     →     w   j       )           P   ~     ⁡     (     w   j     )                   
wherein
 
{tilde over ( P )}( C   i   →w   j )=(weight c     i     →w     i   )(activation C     i   ),
 
and wherein
 
{tilde over ( P )}( w   j )= O 1( w   j )×(# words).
 
This formula indicates that the guess of C i  is the order one probability of C i  multiplied by a product of conditional probability contributions from active child nodes w j  of C i . The numerator of this contribution, {tilde over (P)}(C i →w j ), is the weight of the link from C i  to w j  multiplied by a guess at the activation of C i . Recall that the activation of C i  is an indicator of the number of active links out of node C i . The denominator of this contribution, {tilde over (P)}(w j ), is the order one probability of w j  multiplied by the number of words in the set of words.
 
     For a cluster node, C i , that points to other cluster nodes, the formula is slightly different,
 
Guess( C   i )= O 1( C   i )·Score( C   i ),
 
wherein
 
               Score   ⁡     (     C   i     )       =       ∏   k     ⁢           ⁢       Contribution   ⁡     (       C   k     ,     C   i       )       ⁢       ∏   j     ⁢           ⁢       Contribution   ⁡     (       w   j     ,     C   i       )       .                 
As in the case of a cluster node that only points to terminals, the guess of C i  is the order one probability of C i  multiplied by a product of conditional probability contributions. However, these conditional probability contributions come from other cluster nodes C k  as well as from child nodes w j .
 
     The contribution from child nodes is the same as in the case where the cluster node only points to terminals: 
     
       
         
           
             
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     The contribution from other cluster nodes is more complicated: 
                 Contribution   ⁡     (       C   k     ,     C   i       )       =           P   ⁡     (       C   k     |     C   i       )       ·     Score   ⁡     (     C   k     )         +   1   -     P   ⁡     (       C   k     |     C   i       )               P   ⁡     (     C   k     )       ·     Score   ⁡     (     C   k     )         +   1   -     P   ⁡     (     C   k     )             ,         
wherein P(C k |C i ) is the conditional probability of C k  given C i , P(C k ) is the order one probability of C k , and Score(C k ) is the previously calculated score of C k . Note that since the evidence tree is constructed from terminals up, the score of the child node C k  will have been computed before the score of the parent node C i  is computed.
 
     In one embodiment of the present invention, the system marks terminal nodes during the estimation process for a given cluster node to ensure that terminal nodes are not factored into the estimation more than once. 
     Finally, the system selects parent nodes to be candidate cluster nodes based on these estimated likelihoods (step  906 ). At the end of this “parent picking” process, the system has a set of candidate clusters to consider along with their activations. 
       FIG. 10  presents a flow chart of the process of approximating probabilities for candidate clusters in accordance with an embodiment of the present invention. The system first selects states for the probabilistic model that are likely to have generated the set of words (step  1002 ). 
     Next, the system constructs the vector, wherein the vector includes components for candidate clusters. Each of these components indicates a likelihood that a corresponding candidate cluster is active in generating the set of words. In order to estimate a component, the system considers only selected states in approximating the probability that an associated candidate cluster is active in generating the set of words (step  1004 ). 
     More specifically, in one embodiment of the present invention, the system calculates a given component V i  of the vector associated with a cluster node C i  to be:
 
 V   i =Activation( C   i )× P ( C   i ),
 
wherein the Activation(C i ) is an indicator of the number of links that will fire if node C i  fires, and wherein P(C i ) is the probability that C i  is active in generating the set of words in the document.
 
     P(C i ) can be calculated a: 
               P   ⁡     (     C   i     )       =         ∑       P   network     ⁡     (       C   i     ⁢           ⁢   is   ⁢           ⁢   on     )           ∑       P   network     ⁡     (   explored   )           .           
This formula indicates that P(C i ) is the sum of the network probabilities for networks in which C i  is discovered to be active divided by the sum of all network probabilities for networks that have been explored.
 
     The probability of a given network state occurring can be calculated as: 
               P   network     =       ∏       nodes   ⁢           ⁢   j       that   ⁢           ⁢   are   ⁢           ⁢   on         ⁢           ⁢       (     1   -       ∏       nodes   ⁢           ⁢   i   ⁢           ⁢   that   ⁢           ⁢   are       on   ⁢           ⁢   and   ⁢           ⁢   po   ⁢           ⁢   int   ⁢           ⁢   to   ⁢           ⁢   j                 ⁢           ⁢     (     1   -     w     i   →   j         )         )     ⁢       ∏       nodes   ⁢           ⁢   k       that   ⁢           ⁢   are   ⁢           ⁢   off         ⁢       (       ∏       nodes   ⁢           ⁢   i   ⁢           ⁢   that   ⁢           ⁢   are       on   ⁢           ⁢   and   ⁢           ⁢   po   ⁢           ⁢   int   ⁢           ⁢   to   ⁢           ⁢   k         ⁢     (     1   -     w     i   →   k         )       )     .                 
This probability includes contributions from nodes that are “on”. More specifically, for each node j that is on in a given network, the system computes the probability that at least one link into j (from an active parent node i) fires. This is one minus the probability that no link into j from an active parent node i fires, wherein the probability that a link from an active node does not fire is one minus the link weight.
 
     The probability also includes contributions from nodes k that are “off”. For a given node k that is off, the contribution is the probability that no link points to k from active node i, which is simply the product of one minus the link weights. 
       FIG. 11  illustrates how states for the probabilistic model are selected in accordance with an embodiment of the present invention. This flow chart describes in more detail the operations involved in performing step  1002  in  FIG. 10 . In order to limit the amount of computational work involved in selecting states, one embodiment of the present invention considers only candidate cluster nodes and terminal nodes associated with the set of words in the document. All other terminals are assumed to be off and are summarized in a simple term which is used to reduce the probability of the parent being on. 
     The system starts by randomly selecting a starting state for the probabilistic model (step  1102 ). Each starting state indicates which nodes in the probabilistic model are active and which ones are not. Note that any starting state is possible because the universal node can trigger any subset of the candidate nodes to fire. 
     Also note that link weights in the probabilistic model tend to make some states more likely than others in generating the set of words in the document. Hence, it is unlikely that a random starting state would have generated the set of words in the document. In order to find a more likely state, the system performs “hill-climbing” operations to reach a state that is likely to have generated the set of words in the document (step  1104 ). Note that a large number of well-known hill-climbing techniques can be used for this purpose. A hill-climbing operation typically changes the state of the system in a manner that increases the value of a specific objective function. In this case, the objective function is the probability of a given network state occurring, P network , which is described above. 
     In one embodiment of the present invention, the system periodically changes the state of an individual candidate cluster between hill-climbing operations without regard to the objective function. In doing so, the system fixes the changed state so it does not change during subsequent hill-climbing operations. This produces a local optimum for the objective function, which includes the changed state, which enables the system to explore states of the probabilistic model that are otherwise unreachable through hill-climbing operations alone. 
     Learning Process 
       FIG. 12  presents a flow chart summarizing the learning process in accordance with an embodiment of the present invention. During the learning process, the system first receives a current model (step  1202 ). Note that if no current model exists, an initial current model can be created from a set of words by: (1) generating a universal node that is always active; (2) generating terminal nodes representing words in the set of words; (3) generating cluster nodes by selecting training instances; and (4) directly linking the universal node with all the nodes. 
     Next, the system receives a set of training documents (step  1204 ). Note that in one embodiment of the present invention, the system starts with a small set of training documents for an initial iteration, and doubles the number of training documents in each subsequent iteration until all available training documents are used. This allows the system to learn larger concepts, which require fewer training documents to learn, during the earlier iterations. 
     Next the system applies the set of training documents to links defined in the current model to produce weights for corresponding links in the new model. During this process, the system determines expected counts for the number of times the links and prospective links are activated during the training process (step  1206 ), where the expectation is over the probability that the links are activated given the training data. Next, the system applies expectation maximization (EM) to the expected counts to produce weights for links in the new model (step  1208 ). 
     The system then selectively deletes clusters from the new model (step  1210 ). This process is described in more detail below with reference to  FIG. 13 . The system then considers the new model to be the current model (step  1212 ) and repeats the process for a number of iterations to produce a generative model which explains the set of training documents. 
     Selectively Deleting Cluster Nodes 
       FIG. 13  presents a flow chart of the process of selectively deleting cluster nodes in accordance with an embodiment of the present invention. This flow chart illustrates in more detail what takes place during step  1210  in the flow chart illustrated in  FIG. 12 . During this selective-deletion process, for each cluster node in the new model, the system determines the number of outgoing links from the cluster node to other nodes (step  1302 ). These other nodes can be terminal nodes associated with words or other cluster nodes. Using the expected counts collected over the training data, the system also determines the frequency with which the cluster node is activated (step  1304 ). If the number of outgoing links is less than a minimum value, or if the determined frequency is less than a minimum frequency, the system deletes the cluster node (step  1306 ). 
     If a cluster node has very few outgoing links, it is not useful for generalizing. Hence, deleting the cluster node reduces memory usage, improves the computational efficiency of the model, and improves the quality of clusters returned by the model without adversely affecting the usefulness of the model. Similarly, if a cluster node is rarely activated, deleting the cluster node has similar benefits. 
     Note that the process of deleting a cluster node from the model involves: (1) deleting outgoing links from the cluster node; (2) deleting incoming links into the cluster node; and (3) deleting the cluster node itself. 
     Merging Cluster Nodes 
       FIG. 14  presents a flow chart illustrating the process of identifying and merging similar cluster nodes in accordance with an embodiment of the present invention. In one embodiment of the present invention, this merging process takes place during a separate iteration of the training process illustrated in  FIG. 13 . Note that this merging iteration can be interspersed with the training iterations illustrated in  FIG. 13 . Referring to  FIG. 14 , during the merging process the system first receives the current model (step  1402 ). Next, the system determines whether cluster nodes in the current model “explain” other cluster nodes in the current model (step  1404 ). (This process is described in more detail below with reference to  FIG. 15 .) Finally, if two cluster nodes explain each other, the system merges the two cluster nodes to form a combined cluster node (step  1406 ). (This process is described in more detail below with reference to  FIG. 16 .) 
     Determining which Cluster Nodes Explain a Cluster Node 
       FIG. 15  presents a flow chart illustrating the process of determining whether cluster nodes explain each other in accordance with an embodiment of the present invention. During this process, the system iteratively analyzes each given cluster node to determine which other cluster nodes explain the given cluster node. 
     More specifically, for each cluster node, the system forms a query which includes a set of “top words” associated with the cluster node (step  1502 ). This set of top words can include words whose nodes are most likely to fire if the cluster node fires. Next, the system runs the query against the current model minus the given cluster node to produce a set of resulting cluster nodes (step  1504 ). More specifically, the given cluster node is temporarily removed from the current model and the query is run against this temporarily modified model. The query produces a set of resulting cluster nodes. 
     Finally, if the activation strength of a resulting cluster node exceeds a threshold, the system determines that the resulting cluster node explains the given cluster node (step  1506 ). 
     Merging Two Cluster Nodes to Form a Combined Cluster Node 
       FIG. 16  presents a flow chart illustrating the process of merging two cluster nodes to form a combined cluster node in accordance with an embodiment of the present invention. During this process, the system merges the parents of the two cluster nodes to produce a set of parents for the combined cluster node (step  1602 ). The system also merges the children of the two cluster nodes to produce a set of children for the combined cluster node (step  1604 ). 
     In the special case where a given cluster node is a parent of one cluster node and a child of the other cluster node, the system makes the given cluster node a child but not a parent of the combined cluster node (step  1606 ). This makes sense because in our model parent nodes occur more frequently than their child nodes. Because the combined cluster node will by definition be more frequent than the given cluster node, the given cluster node should be a child and not a parent of the combined cluster node. 
     Finally, if merging the two cluster nodes causes two weighted links to exist from a given parent node to the combined cluster node, or from the combined cluster node to a given child node, the system combines the two weighted links into a single combined weighted link (step  1608 ). The weight on this combined weighted link can be calculated by exponentially combining (or even adding) the weights of the two weighted links. Note that any reasonable approximation for the combined weight can be used because subsequent iterations of the training process will further refine the weight on this combined weighted link. 
     Selecting Links 
       FIG. 17  presents a flow chart illustrating the process of selecting links in accordance with an embodiment of the present invention. This flow chart illustrates in more detail the sequence of operations which take place in steps  1206  and  1208  of the flow chart which appears in  FIG. 12 . 
     First, the system applies training documents to links and prospective links in the current model to determine expected counts for the links and prospective links (step  1702 ). For a given document, the system activates terminals associated with words that occur in the given document. The system then determines a model structure which is consistent with the activated terminals. During this process, the system keeps track of an expected count for each link, which indicates the expected number times the link fired. 
     In one embodiment of the present invention, the system also multiplies expected counts for prospective links by a factor, such as 0.25. This reduces expected counts for the prospective links and compensates for an overly optimistic assumption made while counting prospective link activations. The assumption is that whenever a cluster and an associated terminal are both activated, the prospective link between the cluster and the terminal caused the terminal to be activated. This assumption is overly optimistic because it is possible that the terminal was not activated by the link, but was instead activated by another link from another cluster. The reduction of the expected count by 0.25 helps to compensate for this overly optimistic assumption. 
     Next, the system filters links based on “source diversity” (step  1704 ). This involves only considering links which are associated with inputs from multiple sources. A source indicates where the training document came from, e.g., a URL, of a web document, a user id, and so on. (Note that every session originates from some source.) It has been observed that links associated with inputs from only one or two sources are likely to be less reliable in generating a model for queries from a large number of people. Hence, in one embodiment of the present invention, the system only considers links which are associated with inputs from three or more sources. 
     In yet another embodiment, the system automatically considers links with five or more sources and does not consider links with only two or fewer sources. In this embodiment, the system selectively considers links with three or four sources, but only after reducing their expected count by limiting the contribution from the most significant source. This prevents situations in which a single source provides the dominant contribution for a link. 
     The result of all these steps is an adjusted expected count for the existing links and for some prospective links. 
     The system then determines link-ratings for links and prospective links based on the expected counts (step  1706 ). Referring to  FIG. 18 , this involves calculating a “significance” for the given link by dividing the probability of the child given the parents by the probability of the child, significance=p(child|parents)/p(child) (step  1802 ). (Note that the parent is always a cluster node while the child can be either a terminal node or a cluster node.) The significance is derived by calculating the number of times the child arises in the context of a parent divided by the expected number of times the child would arise if the child and the parent were independent. This can be calculated as follows: 
     
       
         
           
             
               
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     Note that the significance is essentially the weight of the link divided by the probability of the child associated with the link. Hence, if the child is exceedingly rare, the fact that it shows up in a cluster is significant. Conversely, if the child is extremely common, the fact that it shows up in a cluster is insignificant. 
     Finally, the system calculates the link-rating for the given link as a function of the significance and the expected count for the given link (step  1804 ). 
     In one embodiment of the present invention, the function for the link-rating is significance 2 ×expected count. Note that this function gives more weight to significance than count, which discounts the value of commonly occurring terminals that have a low significance. Furthermore, note that as the amount of training data that is considered increases, the expected count increases, but significance does not. This is because significance is a function of probabilities of occurrence, whereas the expected count is associated with an actual expected number of occurrences. The fact that expected counts increase over time is desirable, because as more training data is considered expected counts become more reliable and can hence be given more weight. 
     Referring back to  FIG. 17 , after the link-ratings are computed, the system ranks the links based on the link-ratings (step  1708 ). For example, this can involve sorting the links based on their link-ratings. 
     Finally, the system selects the top N links to include in the new model (step  1710 ) and disregards the other links. By including only the top N links, the system can limit the number of links which occur in the model, which helps to limit the memory requirements for the model. 
     In one embodiment of the present invention, the system selects the top N links for a number of iterations, and during the last iteration selects fewer links to include in the new model. For example, the system can select N links for all but the last iteration and can select M links for the final iteration, where M&lt;N. This technique allows a larger number of links to be considered during the training iterations, which gives more links the opportunity to iteratively attain a sufficiently high link-rating to be included in the ultimate model. 
     Uses of the Model 
     This section outlines some of the possible uses of our model.
         (1) Guessing at the concepts behind a piece of text. The concepts can then be displayed to a user allowing the user to better understand the meaning behind the text.   (2) Comparing the words and concepts between a document and a query. This can be the information retrieval scoring function that is required in any document search engine, including the special case where the documents are web pages.   (3) A different way of using our model for web searches is to assume that the distribution of clusters extends the query. For example, a query for the word “jaguar” is ambiguous. It could mean either the animal or the car. Our model will identify clusters that relate to both meanings in response to this search. In this case, we can consider that the user typed in one of either two queries, the jaguar (CAR) query or the jaguar (ANIMAL) query. We can then retrieve documents for both of these queries taking into account the ratio of their respective clusters&#39; probabilities. By carefully balancing how many results we return for each meaning, we assure a certain diversity of results for a search.   (4) Comparing the words and concepts between a document and an advertisement. This can be used as a proxy for how well an advertisement will perform if attached to a certain piece of content. A specialization of this is attaching advertisements to web pages.   (5) Comparing the words and concepts between a query and an advertisement (or targeting criteria for an advertisement). In search engines, advertisers often select a set of “targeting criteria”, that trigger an ad to be served. The text of these criteria (and the ad copy itself) can be compared to a query via the use of clusters in our model. This comparison can be a proxy for how well the ad will perform if served on a search page resulting from the query.   (6) Comparing the words and concepts between two documents. This can be used as a distance metric for conceptual clustering of documents, where similar documents are grouped together.   (7) Projecting text into the space of clusters. The probabilities of clusters in the text can be used as features for an arbitrary classification task. For example, a pornography filter can be produced by projecting the text of a page onto clusters, and then building a classifier that uses the clusters and the words as its input.   (8) Generalizing a web query to retrieve more results, using the bit cost or probability of a set of words or terminals given their parent clusters.   (9) Guessing at whether a particular word is a misspelling of another word by looking at the concepts induced by the two words.       

     The foregoing descriptions of embodiments have been presented for purposes of illustration and description only. They are not intended to be exhaustive or to limit the present description to the forms disclosed. Accordingly, many modifications and variations will be apparent to practitioners skilled in the art. Additionally, the above disclosure is not intended to limit the present description. The scope of the present description is defined by the appended claims.