Patent Publication Number: US-2019197013-A1

Title: Parallelized block coordinate descent for machine learned models

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 62/610,076, filed Dec. 22, 2017, entitled “GENERALIZED ADDITIVE MIXED EFFECT MACHINE-LEARNED MODELS FOR COMPUTERIZED PREDICTIONS,” which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure generally relates to technical problems encountered in providing personalized predictions on computer networks. More specifically, the present disclosure relates to the use of parallel block coordinate descent for machine learned models. 
     BACKGROUND 
     The rise of the Internet has occasioned two disparate yet related phenomena: the increase in the presence of social networking services, with their corresponding member profiles visible to large numbers of people, and the increase in the use of these social networking services to perform searches or obtain information. An example of a common search or recommendation provided on a social networking service is the search for jobs that have been posted on, or linked to by, the social networks. 
     A technical problem encountered by social networking services in managing online job searches is that determining how to serve the most appropriate and relevant job results with minimal delay becomes significantly challenging as the number of sources and volumes of job opportunities via the social networking services grows at an unprecedented pace 
     Personalization of job search and other results is also preferential. For example, when user&#39;s search for a query like “software engineer”, depending on the skills, background, experience, location, and other factors about the users, the odds that the users will interact with the results (such as by applying to an underlying job) can be drastically different. For example, a person skilled in user interfaces would see a very different set of job results compared to someone specializing in hardware. Indeed, even people having the same skill sets and current job could have different odds of interacting with the same results. 
     Results may also be presented without an explicit search performed by a user, specifically in the form of recommendations. Recommender systems are automated computer programs that match items to users in different contexts. In order to achieve accurate recommendations on a large scale, machine learned models are used to estimate user preferences from user feedback data. Such models are constructed using large amounts of high-frequency data obtained from past user interactions with objects or results. 
     Historically, models to rank job search results in response to a query or perform other recommendations have heavily utilized text and entity-based features extracted from the query and job postings to derive a global ranking or recommendation. An example of such models is a Generalized Linear Model (GLM) A GLM is a generalization of linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. 
     GLMs may utilize the following prediction formula: g(E[y ij ])=x′ ij   w , where this formula predicts the response of user i to item j, and x ij  is a feature vector, w is a coefficient vector, E[y ij ] an expectation of response, and g( ) is a link function. 
     However, in scenarios where data is abundant having a more fine-grained model at the user or item level would potentially lead to more accurate prediction, as the user&#39;s personal preferences on items and the item&#39;s specific attraction for users could be better captured. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Some embodiments of the technology are illustrated, by way of example and not limitation, in the figures of the accompanying drawings 
         FIG. 1  is a block diagram illustrating a client-server system, in accordance with an example embodiment. 
         FIG. 2  is a block diagram showing the functional components of a social networking service, including a data processing module referred to herein as a search engine, for use in generating and providing search results for a search query, consistent with some embodiments of the present disclosure. 
         FIG. 3  is a block diagram illustrating an application server module of  FIG. 2  in more detail, in accordance with an example embodiment. 
         FIG. 4  is a block diagram illustrating the job posting result ranking engine of  FIG. 3  in more detail, in accordance with an example embodiment. 
         FIG. 5  is a block diagram illustrating the kth iteration of a parallelized block coordinate descent under a Bulk Synchronous Parallel (BSP) paradigm, in accordance with an example embodiment. 
         FIG. 6  is a flow diagram illustrating a method for training a generalized additive mixed effect model in accordance with an example embodiment. 
         FIG. 7  is a flow diagram illustrating a method for using a generalized additive mixed effect model in accordance with an example embodiment. 
         FIG 8  is a flow diagram illustrating a method for parallelized block coordinate descent in accordance with an example embodiment. 
         FIG. 9  is a block diagram illustrating a software architecture, in accordance with an example embodiment. 
         FIG. 10  illustrates a diagrammatic representation of a machine in the form of a computer system within which a set of instructions may be executed for causing the machine to perform any one or more of the methodologies discussed herein, according to an example embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     The present disclosure describes, among other things, methods, systems, and computer program products that individually provide various functionality. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the various aspects of different embodiments of the present disclosure It will be evident, however, to one skilled in the art, that the present disclosure may be practiced without all of the specific details. 
     One approach for better capturing a user&#39;s personal preference for items and an item&#39;s specific attraction for users in prediction/recommender systems would be to introduce ID-level regression coefficients in addition to the global regression coefficients in a GLM setting. Such a solution is known as a generalized linear mixed model (GLMix). However, for large data sets with a large number of ID-level coefficients, fitting a GLMix model can be computationally challenging, especially as the solution scales 
     In an example embodiment, the scalability bottleneck is overcome by applying parallelized block coordinate descent under a Bulk Synchronous Parallel (BSP) paradigm. This will be described in more detail below. 
     Additionally, in an example embodiment, predictions/recommendations are made even more accurate by using three models instead of a single GLMix model. Specifically, rather than having a single GLMix model with different coefficients for users and items, three separate models are used and then combined. Each of these models has different granularities and dimensions. A global model may model the similarity between user attributes (e.g., from the member profile or activity history) and item attributes. A per-user model may model user attributes and activity history. A per-item model may model item attributes and activity history. Such a model may be termed a Generalized Additive Mixed Effect (GAME) model. 
     In the context of a job search result ranking or recommendation, this results in the following components:
     a global model that captures the general behavior of how members apply for jobs   a member-specific model with parameters (to be learned from data) specific to the given member to capture member&#39;s personal behavior that deviates from the general behavior, and   a job-specific model with parameters (to be learned from data) specific to the given job to capture the job&#39;s unique behavior that deviates from the general behavior.   

     The following is a description of bow a GAME model enables such a level of personalization. Let y mjt  denote the binary response of whether user m would apply for job j in context t, where the context usually includes the time and location where the job is shown q m  is used to denote the feature vector of user m, which includes the features extracted from the user&#39;s public profile, e.g., the member&#39;s title, job function, education history, industry, etc. s j  is used to denote the feature vector of job j, which includes features extracted from the job post, e.g. the job title, desired skills and experiences, etc. Let x mjt  represent the overall feature vector for the (m, j, t) triple, which can include q m  and s j  for feature-level main effects, the outer product between q m  and s j  interactions among member and job features, and features of the context. It may be assumed that x mjt  does not contain member IDs or item IDs as features, because IDs will be treated differently from regular features. The GAME model for predicting the probability of user m applying for job j using logistic regression is: 
         g ( E[y   mjt ])= x′   mjt   b+s′   j α m   +q′   m β j  
 
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     the link function, b is the global coefficient vector (also called fixed effect coefficients: and α m  and β j  are the coefficient vectors specific to user m and job j, respectively. α m  and β j  are called random effect coefficients, which capture user m&#39;s personal preference on different item features and job j&#39;s attraction for different member features. For a user m with many responses to different items in the past, this is able to accurately estimate her personal coefficient vector α m  and provide personalized predictions. On the other hand, if user m does not have much past response data, the posterior mean of α m  will be close to zero, and the model for user m will fall back to the global fixed effect component x′ mjt b. The same behavior applies to the per-job coefficient vector β j . 
       FIG. 1  is a block diagram illustrating a client-server system  100 , in accordance with an example embodiment. A networked system  102  provides server-side functionality via a network  104  (e.g., the Internet or a wide area network (WAN)) to one or more clients.  FIG. 1  illustrates, for example, a web client  106  (e.g., a browser) and a programmatic client  108  executing on respective client machines  110  and  112   
     An application program interface (API) server  114  and a web server  116  are coupled to, and provide programmatic and web interfaces respectively to, one or more application servers  118 . The application server(s)  118  host one or more applications  120 . The application server(s)  118  are, in turn, shown to be coupled to one or more database servers  124  that facilitate access to one or more databases  126 . While the application(s)  120  are shown in  FIG. 1  to form part of the networked system  102 , it will be appreciated that, in alternative embodiments, the application(s)  120  may form part of a service that is separate and distinct from the networked system  102 . 
     Further, while the client-server system  100  shown in  FIG. 1  employs a client-server architecture, the present disclosure is, of course, not limited to such an architecture, and could equally well find application in a distributed, or peer-to-peer, architecture system, for example. The various applications  120  could also be implemented as standalone software programs, which do not necessarily have networking capabilities. 
     The web client  106  accesses the various applications  120  via the web interface supported by the web server  116 . Similarly, the programmatic client  108  accesses the various services and functions provided by the application(s)  120  via the programmatic interface provided by the API server  114 . 
       FIG. 1  also illustrates a third-party application  128 , executing on a third-party server  130 , as having programmatic access to the networked system  102  via the programmatic interface provided by the API server  114 . For example, the third-party application  128  may, utilizing information retrieved from the networked system  102 , support one or more features or functions on a website hosted by a third party. The third-party website may, for example, provide one or more functions that are supported by the relevant applications  120  of the networked system  102   
     In some embodiments, any website referred to herein may comprise online content that may be rendered on a variety of devices including, but not limited to, a desktop personal computer (PC), a laptop, and a mobile device (e.g., a tablet computer, smartphone, etc.). In this respect, any of these devices may be employed by a user to use the features of the present disclosure. In some embodiments, a user can use a mobile app on a mobile device (any of the machines  110 ,  112  and the third-party server  130  may be a mobile device) to access and browse online content, such as any of the online content disclosed herein. A mobile server (e.g., API server  114 ) may communicate with the mobile app and the application server(s)  118  in order to make the features of the present disclosure available on the mobile device. 
     In some embodiments, the networked system  102  may comprise functional components of a social networking service.  FIG. 2  is a block diagram showing the functional components of a social networking service, including a data processing module referred to herein as a search engine  216 , for use in generating and providing search results for a search query, consistent with some embodiments of the present disclosure, in some embodiments, the search engine  216  may reside on the application server(s)  118  in  FIG. 1 . However, it is contemplated that other configurations are also within the scope of the present disclosure. 
     As shown in  FIG. 2 , a front end may comprise a user interface module (e.g., a web server  116 )  212 , which receives requests from various client computing devices, and communicates appropriate responses to the requesting client devices. For example, the user interface module(s)  212  may receive requests in the form of Hypertext Transfer Protocol (HTTP) requests or other web-based API requests. In addition, a user interaction detection module  213  may be provided to detect various interactions that members have with different applications  120 , services, and content presented. As shown in  FIG. 2 , upon detecting a particular interaction, the member interaction detection module  213  logs the interaction, including the type of interaction and any metadata relating to the interaction, in a member activity and behavior database  222 . 
     An application logic layer may include one or more various application server modules  214 , which, in conjunction with the user interface module(s)  212 , generate various user interfaces (e.g., web pages) with data retrieved from various data sources in a data layer. In some embodiments, individual application server modules  214  are used to implement the functionality associated with various applications  120  and/or services provided by the social networking service. 
     As shown in  FIG. 2 , the data layer may include several databases  126 , such as a profile database  218  for storing profile data, including both user profile data and profile data for various organizations (e.g., companies, schools, etc.). Consistent with some embodiments, when a person initially registers to become a user of the social networking service, the person will be prompted to provide some personal information, such as his or her name, age (e.g., birthdate), gender, interests, contact information, home town, address, spouse&#39;s and/or family members&#39; names, educational background (e.g., schools, majors, matriculation and/or graduation dates, etc.), employment history, skills, professional organizations, and so on. This information is stored, for example, in the profile database  218 . Similarly, when a representative of an organization initially register&#39;s the organization with the social networking service, the representative may be prompted to provide certain information about the organization. This information may be stored, for example, in the profile database  218 , or another database (not shown). In some embodiments, the profile data may be processed (e.g., in the background or offline) to generate various derived profile data. For example, if a member has provided information about various job titles that the member has held with the same organization or different organizations, and for how long, this information can be used to infer or derive a member profile attribute indicating the member&#39;s overall seniority level, or seniority level within a particular organization. In some embodiments, importing or otherwise accessing data from one or more externally hosted data sources may enrich profile data for both members and organizations, for instance, with organizations in particular, financial data may be imported from one or more external data sources and made part of an organization&#39;s profile. This importation of organization data and enrichment of the data will be described in more detail later in this document. 
     Once registered, a user may invite other members, or be invited by other members, to connect via the social networking service. A “connection” may constitute a bilateral agreement by the users, such that both users acknowledge the establishment of the connection. Similarly, in some embodiments, a user may elect to “follow” another user. In contrast to establishing a connection, the concept of “following” another user typically is a unilateral operation and, at least in some embodiments, does not require acknowledgement or approval by the user that is being followed. When one user follows another, the user who is following may receive status updates (e.g., in an activity or content stream) or other messages published by the user being followed, relating to various activities undertaken by the user being followed. Similarly, when a user follows an organization, the user becomes eligible to receive messages or status updates published on behalf of the organization. For instance, messages or status updates published on behalf of an organization that a user is following will appear in the user&#39;s personalized data feed, commonly referred to as an activity stream or content stream. In any case, the various associations and relationships that the users establish with other users, or with other entities and objects, are stored and maintained within a social graph in a social graph database  220 . 
     As users interact with the various applications  120 , services, and content made available via the social networking service, the users+ interactions and behavior (e.g., content viewed, links or buttons selected, messages responded to, etc.) may be tracked, and information concerning the users&#39; activities and behavior may be logged or stored, for example, as indicated in  FIG. 2 , by the user activity and behavior database  222 . This logged activity information may then be used by die search engine  216  to determine search results for a search query 
     In some embodiments, the databases  218 ,  220 , and  222  may be incorporated into the database(s)  126  in  FIG. 1 . However, other configurations are also within the scope of the present disclosure. 
     Although not shown, in some embodiments, the social networking system  210  provides an API module via which applications  120  and services can access various data and services provided or maintained by the social networking service. For example, using an API, an application may be able to request and/or receive one or more recommendations. Such applications  120  may be browser-based applications  120 , or may be operating system-specific. In particular, some applications  120  may reside and execute (at least partially) on one or more mobile devices (e.g., phone or tablet computing devices) with a mobile operating system. Furthermore, while in many cases the applications  120  or services that leverage the API may be applications  120  and services that are developed and maintained by the entity operating the social networking service, nothing other than data privacy concerns prevents the API from being provided to the public or to certain third parties under special arrangements, thereby making the navigation recommendations available to third-party applications  128  and services. 
     Although the search engine  216  is referred to herein as being used in the context of a social networking service, it is contemplated that it may also be employed in the context of any website or online services. Additionally, although features of the present disclosure are referred to herein as being used or presented in the context of a web page, it is contemplated that any user interface view (e.g., a user interface on a mobile device or on desktop software) is within the scope of the present disclosure. 
     In an example embodiment, when user profiles are indexed, forward search indexes are created and stored. The search engine  216  facilitates the indexing and searching for content within the social networking service, such as the indexing and searching for data or information contained in the data layer, such as profile data (stored, e.g., in the profile database  218 ), social graph data (stored, e.g., in the social graph database  220 ), and member activity and behavior data (stored, e.g., in the member activity and behavior database  222 ), as well as job postings. The search engine  216  may collect, parse, and/or store data in an index or other similar structure to facilitate the identification and retrieval of information in response to received queries for information. This may include, but is not limited to, forward search indexes, inverted indexes, N-gram indexes, and so on. 
       FIG 3  is a block diagram illustrating application server module  214  of  FIG. 2  in more detail, in accordance with an example embodiment. While in many embodiments the application server module  214  will contain many subcomponents used to perform various different actions within the social networking system, in  FIG. 3  only those components that are relevant to the present disclosure are depicted. A job posting query processor  300  comprises a query ingestion component  302 , which receives a user input “query” related to a job posting search via a user interface (not pictured). Notably, this user input may take many forms. In some example embodiments, the user may explicitly describe a job posting search query, such as by entering one or more keywords or terms into one or more fields of a user interface screen. In other example embodiments, the job posting query may be inferred based on one or more user actions, such as selection of one or more filters, other job posting searches by the user, searches for other users or entities, etc. 
     This “query” may be sent to a job posting database query formulation component  304 , which formulates an actual job posting database query, which will be sent via a job posting database interface  306  to job posting database  308 . Job posting results responsive to this job posting database query may then be sent to the job posting result ranking engine  310 , again via the job posting database interface  306 . The job posting result ranking engine  310  then ranks the job posting results and sends the ranked job posting results back to the user interlace for display to the user. 
       FIG. 4  is a block diagram illustrating job posting result ranking engine  310  of  FIG. 3  in more detail, in accordance with an example embodiment. The job posting result ranking engine  310  may use machine learning techniques to learn a job posting result ranking model  400 , which can then be used to rank actual job posting results from the job posting database  308 . 
     The job posting result ranking engine  310  may comprise a training component  402  and a job posting result processing component  404 . The training component  402  feeds sample job postings results  406  and sample member data  407  into a feature extractor  408  that extracts one or more features  410  for the sample job postings results  406  and sample member data  407 . The sample job postings results  406  may each include job postings results produced in response to a particular query as well as one or more labels, such as a job posting application likelihood score, which is a score indicating a probability that a user with a corresponding sample user data  407  will apply for the job associated with the corresponding sample job postings result  406 . 
     Sample user data  407  may include, for example, a history of job searches and resulting expressions of interest (such as clicking on job posting results or applications to corresponding jobs) in particular job posting results for particular users. In some example embodiments, sample user data  407  can also include other data relevant for personalization of the query results to the particular user, such as a user profile for the member or a history of other user activity. 
     A machine learning algorithm  412  produces the job posting result ranking model  400  using the extracted features  410  along with the one or more labels. In the job posting result processing component  404 , candidate job postings results  414  resulting from a particular query are fed to a feature extractor  416  along with a candidate user data  415 . The feature extractor  416  extracts one or more features  418  from the candidate job postings results  414  and candidate user data  415 . These features  418  are then fed to the job posting result ranking model  400 , which outputs a job posting application likelihood score for each candidate job postings result for the particular query. 
     This job posting application likelihood score for each candidate job posting result may then be passed to a job posting result sorter  420 , which may sort the candidate job postings results  414  based on their respective job posting application likelihood scores. 
     It should be noted that the job posting result ranking model  400  may be periodically updated via additional training and/or user feedback. The user feedback may be either feedback from members performing searches, or from companies corresponding to the job postings. The feedback may include an indication about how successful the job posting result ranking model  400  is in predicting member interest in the job posting results presented. 
     The machine learning algorithm  412  may be selected from among many different potential supervised or unsupervised machine learning algorithms  412 . Examples of supervised learning algorithms include artificial neural networks, Bayesian networks, instance-based learning, support vector machines, random forests, linear classifiers, quadratic classifiers, k-nearest neighbor, decision trees, and hidden Markov models. Examples of unsupervised learning algorithms include expectation-maximization algorithms, vector quantization, and information bottleneck method. In an example embodiment, a multi-class logistical regression model is used. 
     In an example embodiment, the machine learning algorithm  412  may actually comprise one or more machine learning algorithms that train three separate models that may be combined in order to form the job posting result ranking model  400 . 
     Of course, the above techniques can be extended to other types of models than ranking models, such as job posting result ranking model  400 . For example, rather than use the predictions to rank job results in response to a query, a system could use the predictions to recommend one or more job postings to a user without the user expressly requesting a job search. Furthermore, the techniques can be extended to other type of predictions for items other than job postings or job results, such as feed objects. 
     As described briefly above, in some example embodiments the scalability bottleneck is overcome by applying parallelized block coordinate descent under a Bulk Synchronous Parallel (BSP) paradigm. Traditionally, the fitting algorithms for random effect models required random effect coefficients Γ to be integrated out either analytically or numerically, which becomes infeasible when facing industry-scale large data sets. Similarity, both deterministic and MCMC sampling that operate on Γ as a whole become cumbersome. 
     In an example embodiment, a parallel block-wise coordinate descent-based iterative conditional mode process may be used, where the posterior mode of the random effect coefficients Γ r , for each random effect r, is treated as a block-wise coordinate to be optimized in the space of unknown parameters Given the scores, the optimization problems for updating the fixed effects b and the random effects Γ, are as follows: 
     
       
         
           
             
                 
             
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     |Ω| is used to denote the size of Ω, i.e., the total number of training samples Additionally,   is the number of types of random effects, and M is the number of computing nodes in the cluster. These numbers can be used to compute the network Input/Output cost of the disclosed techniques, with this network Input/Output cost typically being one of the major technical challenges in scaling up in a distributed computing environment. 
     The process involves preparing the training data for fixed effect model training with scores, updating the fixed effect coefficients (b), and updating the score s. Then the training data for random effects model training is prepared with scores and the random effect coefficients and scores are updated. The random effects model training and updating can then continue for each additional random effects model. 
       FIG. 5  is a block diagram illustrating the kth iteration of a parallelized block coordinate descent under a Bulk Synchronous Parallel (BSP) paradigm, in accordance with an example embodiment. As can be seen, there is the fixed effects training  500 , the random effects training  502 , and any additional effects training  504 . The process begins with addressing the details of updating the fixed effect b at iteration k. Here, at  506 , the training data is prepared with both the feature set x n  and the latest score s n   k , and they are partitioned into M nodes. Given the training data, numerous types of distributed algorithms can be applied to learn b. For example, the gradient of b at each sample n can be computed and aggregated from each node to the master node. The gradient may be aggregated, in a parallel reduce operation, performed by one or more executor nodes, with the final product being known to the master node. The master node updates b. This Is depicted at  508  in  FIG. 5 . The new coefficients b new  are then broadcast back to each node together with b old  to update the score s as in s n   new =s n   old −x′ n b old +x′ n b new , in order to prepare for the next effect&#39;s update. This is depicted at  510  in  FIG. 5 . Since the main network communication here is the transmission of b from the master node to the worker nodes, the overall network communication cost for one iteration of updating the fixed effects is  (MP). In some cases, convergence can be improved by updating b multiple times before updating the random effects, for each iteration. 
     The main technical challenge in designing a scalable architecture for GLMix on data sets with a large number of random effects is that the dimension of the random effect coefficient space can potentially be as large as N r P r . Therefore, if the same approach as the one used in updating fixed effects is used, the network communication cost for updating the random effects for r becomes MN r P r . Given some data of moderate size, for example, if N r =10 6 , P r 32 10 5  and a cluster with M=100, the network Input/Output cost amounts to 10 13 . As a result, one key to making the process scalable is to avoid communicating or broadcasting the random effect coefficient across the computing nodes in the cluster. 
     Before the random effect updating phase and as a pre-processing step, for each random effect r and ID l, the feature vectors z   rn  are combined to form a feature matrix Z rl , which comprises all of the z   rn  that satisfy i(r,n)=1. At iteration k and for random effect r, the current values of s={s n   k } n∈Ω  may be shuffled using the same strategy, i.e., or ID l, s n   k  may be grouped to form a vector S l   k , which comprises all of the s n   k  that satisfy  i(r, n)=1. With the right partitioning strategies, S l   k  can be made to collocate with the corresponding feature matrix Z rl , to prepare the training data for updating the random effects r using 
     
       
         
           
             
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     This is depicted at  512  in  FIG. 5 . 
     With the training data ready for each ID l, an optimizer can be applied again to solve the optimization problem locally, such that the random effects γ rl  can be learned in parallel without any additional network communication cost. 
     It should be noted that because both the coefficients and data collocate in the same node, the scores can be updated locally within the same step, as depicted at  514  in  FIG. 5 . It should also be noted that during the whole process, the random effect coefficients γ rl  live with the data and would never get communicated through the network, only s i  would get shuffled around the nodes. As a result, the overall network communication cost for one iteration of updating one random effect is  (|Ω|), and  (| ||Ψ|) for | | random effects. 
     Since the optimization problem can be solved locally, it is possible to further reduce the memory complexity C. Although the overall feature space size is P r  for random effect r, sometimes the underlying dimension of the feature matrix Z rl  could be smaller than P r , due to the lack of support for certain features. For example, a member who is a software engineer is unlikely to be served jobs with the required skill “medicine”. Hence there will not be any data for the feature/job skill=medicine for this user&#39;s random effects, and in such a scenario, Z rl  would end up with an empty column. As a result, for each random effect r and ID l, Z rl  can be condensed by removing ail the empty columns and reindexing the features to form a more compact feature matrix, which would also reduce the size of random effect coefficients γ rl  and potentially improve the overall efficiency of solving the local optimization problem. 
     The result is that the fixed effects training  500  trains the fixed effects model and produces some residuals. These residuals are then used in the random effects training  502  to train the random effects model, which also produces some residuals. These residuals are then used in an additional effects training  504 . This process iterates, passing the residuals from the additional effects training  504  back to the fixed effects training  500 . These iterations continue until convergence occurs 
     The residuals at each stage are the errors produced by whatever model is used by each stage This allows any type of model to be used at any stage. Thus, the fixed effects model can be a completely different type of model than the random effects model. The residuals are the difference between the values produced by the model and a target. 
     It should be noted that the training process described above with respect to  FIG. 5  can be applied to linear or non-linear models, or any combination thereof. 
       FIG. 6  is a flow diagram illustrating a method  600  for training a generalized additive mixed effect model in accordance with an example embodiment. At operation  602 , a first set of training features is extracted from attributes of sample users in a social networking service. In some example embodiments, these training features may be extracted by retrieving relevant information from fields of user profiles or other user-specific information maintained by the social networking service. At operation  604 , a second set of training features is extracted of attributes of items m the social networking service. Items may include, for example, job postings, articles, videos, announcements, or any other object m the social networking service that can be interacted with (e.g., applied for, shared, linked, commented on) by a user. In some example embodiments, these training features may be obtained by parsing the item itself and/or metadata about the item. For example, a job posting may include text portions from which various training features, such as term frequency-inverse document frequency, can be obtained, as well as metadata such as category and geographic region, from which various training features may be extracted. 
     At operation  606 , a third set of training features is extracted from activity of the users, with respect to the items, in the social networking service. These training features may be extracted from information about which items the users interacted with, and/or how frequently they interact with them. 
     At operation  608 , a fourth set of training features is extracted from activity of the users, with respect to the items, in the social networking service. The fourth set of training features is extracted from similar if not the same underlying social networking data as the third set of training features, but is from the inverse perspective. Whereas the third set of training features is relevant to determining which users interacted with which items, the fourth set of training features is relevant to determining which items were interacted with by which users. 
     At operation  610 , a first machine learning algorithm is used to train a machine-learned global model to produce a first computer-based numerical estimate of similarity between the attributes of user&#39;s and the attributes of items, based on the first and second set of training features. 
     At operation  612 , a second machine learning algorithm is used to train a machine learned per-user model to produce a second computer-based numerical estimate of likelihood that the various users will engage in an activity with an item in the social networking service, based on the first and third set of training features. 
     At operation  614 , a third machine learning algorithm is used to train a machine learned per-item model to produce a third computer-based numerical estimate of likelihood that a user in the social networking service will engage in an activity with various items, based on the second and fourth set of training features. 
     In some example embodiments, operations  610 - 614  may be continually iterated until some convergence criteria is met. Additionally, in some example embodiments, residuals from operation  610  may be used in operation  612  and residuals from operation  612  may be used in operation  614 . For embodiments where iteration is used, residuals from operation  614  in one iteration may be used in operation  610  in the following iteration. 
       FIG. 7  is a flow diagram illustrating a method  700  for using a generalized additive mixed effect model in accordance with, an example embodiment. 
     At operation  702 , a first set of features derived from attributes of a first user in a social networking service is obtained. At operation  704 , a second set of features derived from attributes of a first item in the social networking service is obtained. At operation  706 , a third set of features derived from activity of the first user, with respect to a plurality of items, including the first item, in the social networking service is obtained. At operation  708 , a fourth set of features derived from activity of a plurality of users, including the first user, with respect to the items in the social networking service is obtained. 
     At operation  710 , the first and second set of features are fed into a machine-learned global model, producing a first computer-based numerical estimate of similarity between the attributes of users and the attributes of items. At operation  712 , the first and third set of features are fed into a machine-learned per-user model, producing a second computer-based numerical estimate of likelihood that the first user will engage in an activity with an item in the social networking service. At operation  714 , the second and fourth set of features are fed into a machine-learned per-item model, producing a third computer-based numerical estimate of likelihood that a user in the social networking service will engage in an activity with the first item. At operation  716 , the first, second, and third computer-based numerical estimates are combined to produce an estimate of likelihood that the first user will engage in an activity with the first item in the social networking service. 
       FIG. 8  is a flow diagram illustrating a method  800  for parallelized block coordinate descent in accordance with an example embodiment. One or more iterations of a machine learned model training process are performed. At operation  802 , a fixed effects machine learned model is trained using a first machine learning algorithm. At operation  804 , residuals of the training of the fixed effects machine learned model are determined by comparing results of the trained fixed effects machine learned model to a first set of target results. At operation  806 , a first random effects machine learned model is trained, using a second machine learning algorithm and the residuals of the training of the fixed effects machine learned model. At operation  808 , residuals of the training of the first random effect machine learned model are determined by comparing results of the trained first random effects machine learned model to a second set of target results. 
     At operation  810 , a second random effects machine learned model is trained using a third machine learning algorithm and the residuals of the training of the first random effects machine learned model. At operation  812 , residuals of the training of the second random effect machine learned model are determined by comparing results of the trained second random effects machine learned model to a third set of target results. At operation  814 , a convergence test is performed. If this test is met, then the training is complete. If not, then the method  800  returns to operation  802  for the next iteration, with each subsequent iteration using the residuals of the training of the second random effect machine learned model from the previous model in the training of the fixed effects machine learned model. 
       FIG. 9  is a block diagram  900  illustrating a software architecture  902 , which can be installed on any one or more of the devices described above  FIG. 9  is merely a non-limiting example of a software architecture, and it will be appreciated that many other architectures can be implemented to facilitate the functionality described herein. In various embodiments, the software architecture  902  is implemented by hardware such as a machine  1000  of  FIG. 10  that includes processors  1010 , memory  1030 , and input/output (I/O) components  1050 . In this example architecture, the software architecture  902  cars be conceptualized as a stack of layers where each layer may provide a particular functionality. For example, the software architecture  902  includes layers such as an operating system  904 , libraries  906 , frameworks  908 , and applications  910 . Operationally, the applications  910  invoke API calls  912  through the software stack and receive messages  914  in response to the API calls  912 , consistent with some embodiments. 
     In various implementations, the operating system  904  manages hardware resources and provides common services. The operating system  904  includes, for example, a kernel  920 , services  922 , and drivers  924 . The kernel  920  acts as an abstraction layer between the hardware and the other software layers, consistent with some embodiments. For example, the kernel  920  provides memory management, processor management (e.g., scheduling), component management, networking, and security settings, among other functionality. The services  922  can provide other common services for the other software layers. The drivers  924  are responsible for controlling or interfacing with the underlying hardware, according to some embodiments. For instance, the drivers  924  can include display drivers, camera drivers, BLUETOOTH® or BLUETOOTH® Low Energy drivers, flash memory drivers, serial communication drivers (e.g., Universal Serial Bus (USB) drivers), Wi-Fi® drivers, audio drivers, power management drivers, and so forth. 
     In some embodiments, the libraries  906  provide a low-level common infrastructure utilized by the applications  910 . The libraries  906  can include system libraries  930  (e.g., C standard library) that can provide functions such as memory allocation functions, string manipulation functions, mathematic functions, and the like. In addition, the libraries  906  can include API libraries  932  such as media libraries (e.g., libraries to support presentation and manipulation of various media formats such as Moving Picture Experts Group-4 (MPEG4), Advanced Video Coding (H.264 or AVC), Moving Picture Experts Group Layer-3 (MP3), Advanced Audio Coding (AAC), Adaptive Multi-Rate (AMR) audio codec, Joint Photographic Experts Group (JPEG or IPG), or Portable Network Graphics (PNG)), graphics libraries (e.g., an OpenGL framework used to render in two dimensions (2D) and three dimensions (3D) in a graphic context on a display), database libraries (e.g., SQLite to provide various relational database functions), web libraries (e.g., WebKit to provide web browsing functionality), and the like. The libraries  906  can also include a wide variety of other libraries  934  to provide many other APIs to the applications  910 . 
     The frameworks  908  provide a high-level common infrastructure that can be utilized by the applications  910 , according to some embodiments. For example, the frameworks  908  provide various graphic user interface (GUI) functions, high-level resource management, high-level location services, and so forth. The frameworks  908  can provide a broad spectrum of other APIs that can be utilized, by the applications  910 , some of which may be specific to a particular operating system  904  or platform. 
     In an example embodiment, the applications  910  include a home application  950 , a contacts application  952 , a browser application  954 , a book reader application  956 , a location application  958 , a media application  960 , a messaging application  962 , a game application  964 , and a broad assortment of other applications, such as a third-party application  966 . According to some embodiments, the applications  910  are programs that execute functions defined in the programs. Various programming languages can be employed to create one or more of the applications  910 , structured in a variety of manners, such as object-oriented programming languages (e.g., Objective-C, Java, or C++) or procedural programming languages (e.g., C or assembly language). In a specific example, the third-party application  966  (e.g., an application developed using the ANDROD™ or IDS™ software development kit (SDK) by an entity other than the vendor of the particular platform) may be mobile software running on a mobile operating system such as IDS™, ANDROID™, WINDOWS® Phone, or another mobile operating system. In this example, the third-party application  966  can invoke the API calls  912  provided by the operating system  904  to facilitate functionality described herein. 
       FIG. 10  illustrates a diagrammatic representation of a machine  1000  in the form of a computer system within which a set of instructions may be executed for causing the machine to perform any one or more of the methodologies discussed herein, according to an example embodiment. Specifically,  FIG. 10  shows a diagrammatic representation of the machine  1000  in the example form of a computer system, within which Instructions  1016  (e.g., software, a program, an application  910 , an applet, an app, or other executable code) for causing the machine  1000  to perform any one or more of the methodologies discussed herein may be executed. For example, the instructions  1016  may cause the machine  1000  to execute the method  600  of  FIG. 6 . Additionally, or alternatively, the instructions  1016  may implement  FIGS. 1-7 , and so forth. The instructions  1016  transform the general, non-programmed machine  1000  into a particular machine  1000  programmed to carry out the described and illustrated functions in the manner described. In alternative embodiments, the machine  1000  operates as a standalone device or may be coupled (e.g., networked) to other machines. In a networked deployment, the machine  1000  may operate in the capacity of a server machine or a client machine in a server-client network environment, or as a peer machine in a peer-to-peer (or distributed) network environment. The machine  1000  may comprise, but not be limited to, a server computer, a client computer, a PC, a tablet computer, a laptop computer, a netbook, a set-top box (STB), a portable digital assistant (PDA), an entertainment media system, a cellular telephone, a smartphone, a mobile device, a wearable device (e.g., a smart watch), a smart home device (e.g., a smart appliance), other smart devices, a web appliance, a network router, a network switch, a network bridge, or any machine capable of executing the instructions  1016 , sequentially or otherwise, that specify actions to be taken by the machine  1000 . Further, while only a single machine  1000  is illustrated, the term “machine” shall also be taken to include a collection of machines  1000  that individually or jointly execute the instructions  1016  to perform any one or more of the methodologies discussed herein. 
     The machine  1000  may include processors  1010 , memory  1030 , and I/O components  1050 , which may be configured to communicate with each other such as via a bus  1002  In an example embodiment, the processors  1010  (e.g., a central processing unit (CPU), a reduced instruction set computing (RISC) processor, a complex instruction set computing (CISC) processor, a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a radio-frequency integrated circuit (RFIC), another processor, or any suitable combination thereof) may include, for example, a processor  1012  and a processor  1014  that may execute the instructions  1016 . The term “processor” is intended to include multi-core processors that may comprise two or more independent processors (sometimes referred to as “cores”) that may execute instructions  1016  contemporaneously. Although  FIG. 10  shows multiple processors  1010 , the machine  1000  may include a single processor with a single core, a single processor with multiple cores (e.g., a multi-core processor), multiple processors with a single core, multiple processors with multiple cores, or any combination thereof. 
     The memory  1030  may include a main memory  1032 , a static memory  1034 , and a storage unit  1036 , all accessible to the processors  1010  such as via the bus  1002 . The main memory  1032 , the static memory  1034 , and the storage unit  1036  store the instructions  1016  embodying any one or more of the methodologies or functions described herein. The instructions  1016  may also reside, completely or partially, within the main memory  1032 , within the static memory  1034 , within the storage unit  1036 , within at least one of the processors  1010  (e.g., within the processor&#39;s cache memory), or any suitable combination thereof, during execution thereof by the machine  1000 . 
     The I/O components  1050  may include a wide variety of components to receive input, provide output, produce output, transmit information, exchange information, capture measurements, and so on. The specific I/O components  1050  that are included in a particular machine  1000  will depend on the type of machine  1000 . For example, portable machines such as mobile phones will likely include a touch input device or other such input mechanisms, while a headless server machine will likely not include such a touch input device. It will be appreciated that the I/O components  1050  may include many other components that are not shown in  FIG. 10 . The I/O components  1050  are grouped according to functionality merely for simplifying the following discussion, and the grouping is in no way limiting. In various example embodiments, the I/O components  1050  may include output components  1052  and input components  1054 . The output components  1052  may include visual components (e.g., a display such as a plasma display panel (PDF), a light-emitting diode (LED) display, a liquid crystal display (LCD), a projector, or a cathode ray tube (CRT)), acoustic components (e.g., speakers), haptic components (e.g., a vibratory motor, resistance mechanisms), other signal generators, and so forth. The input components  1054  may include alphanumeric input components (e.g., a keyboard, a touch screen configured to receive alphanumeric input, a photo-optical keyboard, or other alphanumeric input components), point-based input components (e.g., a mouse, a touchpad, a trackball, a joystick, a motion sensor; or another pointing instrument), tactile input components (e.g., a physical button, a touch screen that provides location and/or force of touches or touch gestures, or other tactile input components), audio input components (e.g., a microphone), and the like. 
     In further example embodiments, the I/O components  1050  may include biometric components  1056 , motion components  1058 , environmental components  1060 , or position components  1062 , among a wide array of other components. For example, the biometric components  1056  may include components to detect expressions (e.g., hand expressions, facial expressions, vocal expressions, body gestures, or eye tracking), measure biosignals (e.g., blood pressure, heart rate, body temperature, perspiration, or brain waves), identify a person (e.g., voice identification, retinal identification, facial identification, fingerprint identification, or electroencephalogram-based identification), and the like. The motion components  1058  may include acceleration sensor components (e.g., accelerometer), gravitation sensor components, rotation sensor components (e.g., gyroscope), and so forth. The environmental components  1060  may include, for example, illumination sensor components (e.g., photometer), temperature sensor components (e.g., one or more thermometers that detect ambient temperature), humidity sensor components, pressure sensor components (e.g., barometer), acoustic sensor components (e.g., one or more microphones that detect background noise), proximity sensor components (e.g., infrared sensors that detect nearby objects), gas sensors (e g., gas detection sensors to detect concentrations of hazardous gases for safety or to measure pollutants in the atmosphere), or other components that may provide indications, measurements, or signals corresponding to a surrounding physical environment. The position components  1062  may include location sensor components (e.g., a Global Positioning System (GPS) receiver component), altitude sensor components (e.g., altimeters or barometers that detect air pressure from which altitude may be derived), orientation sensor components (e.g., magnetometers), and the like. 
     Communication may be implemented using a wide variety of technologies The I/O components  1050  may include communication components  1064  operable to couple the machine  1000  to a network  1080  or devices  1070  via a coupling  1082  and a coupling  1072 , respectively. For example, the communication components  1064  may include a network interlace component or another suitable device to interface with the network  1080 . In further examples, the communication components  1064  may include wired communication components, wireless communication components, cellular communication components, near field communication (NFC) components, Bluetooth® components (e.g., Bluetooth® Low Energy), Wi-Fi® components, and other communication components to provide communication via other modalities. The devices  1070  may be another machine or any of a wide variety of peripheral devices (e.g., a peripheral device coupled via a USB). 
     Moreover, the communication components  1064  may detect identifiers or include components operable to detect identifiers. For example, the communication components  1064  may include radio frequency identification (RFID) tag reader components, NFC smart tag detection components, optical reader components (e.g., an optical sensor to detect one-dimensional bar codes such as Universal Product Code (UPC) bar code, multi-dimensional bar codes such as Quick Response (QR) code, Aztec code, Data Matrix, Dataglyph, MaxiCocie, PDF417, Ultra Code, UCC RSS-2D bar code, and other optical codes), or acoustic detection components (e.g., microphones to identify tagged audio signals). In addition, a variety of information may be derived via the communication components  1064 , such as location via Internet Protocol (IP) geolocation, location via Wi-Fi® signal triangulation, location via detecting an NFC beacon signal that may indicate a particular location, and so forth. 
     Executable Instructions and Machine Storage Medium 
     The various memories (i.e.,  1030 ,  1032 ,  1034 , and/or memory of the processor(s)  1010 ) and/or the storage unit  1036  may store one or more sets of instructions  1016  and data structures (e.g., software) embodying or utilized by any one or more of the methodologies or functions described herein. These instructions (e.g., the instructions  1016 ), when executed by the processor(s)  1010 , cause various operations to implement the disclosed embodiments. 
     As used herein, the terms “machine-storage medium,” “device-storage medium,” and “computer-storage medium” mean the same thing and may be used interchangeably. The terms refer to a single or multiple storage devices and/or media (e.g., a centralized or distributed database, and/or associated caches and servers) that store executable instructions  1016  and/or data. The terms shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media, including memory internal or external to the processors  1010 . Specific examples of machine-storage media, computer-storage media, and/or device-storage media include non-volatile memory, including by way of example semiconductor memory devices, e.g., erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), field-programmable gate array (FPGA), and flash memory devices; magnetic disks such as internal hard disks and removable disks, magneto-optical disks; and CD-ROM and DVD-ROM disks. The terms “machine-storage media,” “computer-storage media,” and “device-storage media” specifically exclude carrier waves, modulated data signals, and other such media, at least some of which are covered under die term “signal medium” discussed below. 
     Transmission Medium 
     In various example embodiments, one or more portions of the network  1080  may be an ad hoc network, an intranet, an extranet, a VPN, a LAN, a WLAN, a WAN, a WWAN, a MAN, the Internet, a portion of the Internet, a portion of the PSTN, a plain old telephone service (POTS) network, a cellular telephone network, a wireless network, a Wi-Fi® network, another type of network, or a combination of two or more such networks. For example, the network  1080  or a portion of the network  1080  may include a wireless or cellular network, and the coupling  1082  may be a Code Division Multiple Access (CDMA) connection, a Global System for Mobile communications (GSM) connection, or another type of cellular or wireless coupling. In this example, the coupling  1082  may implement any of a variety of types of data transfer technology, such as Single Carrier Radio Transmission Technology (1×RTT), Evolution-Data Optimized (EVDO) technology, General Packet Radio Service (GPRS) technology. Enhanced Data rates for GSM Evolution (EDGE) technology, third Generation Partnership Project (3GPP) including 3G, fourth generation wireless (4G) networks, Universal Mobile Telecommunications System (UMTS), High-Speed Packet Access (HSPA), Worldwide Interoperability for Microwave Access (WiMAX), Long-Term Evolution (LTE) standard, others defined by various standard-setting organizations, other long-range protocols, or other data-transfer technology. 
     The instructions  1016  may be transmitted or received over the network  1080  using a transmission medium via a network interface device (e.g., a network interface component included in the communication components  1064 ) and utilizing any one of a number of well-known transfer protocols (e.g., HTTP). Similarly, the instructions  1016  may be transmitted or received using a transmission medium via the coupling  1072  (e.g., a peer-to-peer coupling) to the devices  1070 . The terms “transmission medium” and “signal medium” mean the same thing and may be used, interchangeably in this disclosure. The terms “transmission medium” and “signal medium” shall be taken to include any intangible medium that is capable of storing, encoding, or carrying the instructions  1016  for execution by the machine  1000 , and include digital or analog communications signals or other intangible media to facilitate communication of such software. Hence, the terms “transmission medium” and “signal medium” shall be taken to include any form of modulated data signal, carrier wave, and so forth. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. 
     Computer-Readable Medium 
     The terms “machine-readable medium,” “computer-readable medium,” and “device-readable medium” mean the same thing and may be used interchangeably in this disclosure. The terms are defined to include both machine-storage media and transmission media. Thus, the terms include both storage devices/media and earner waves/modulated data signals.