Patent Publication Number: US-11023910-B2

Title: Recommending a budget for an online job posting utilizing machine learning forecasting

Description:
BACKGROUND 
     Field 
     The disclosed embodiments relate to forecasting models. More specifically, the disclosed embodiments relate to techniques for forecasting job applications. 
     Related Art 
     Online networks may include nodes representing individuals and/or organizations, along with links between pairs of nodes that represent different types and/or levels of social familiarity between the entities represented by the nodes. For example, two nodes in an online network may be connected as friends, acquaintances, family members, classmates, and/or professional contacts. Online networks may further be tracked and/or maintained on web-based networking services, such as online networks that allow the individuals and/or organizations to establish and maintain professional connections, list work and community experience, endorse and/or recommend one another, promote products and/or services, and/or search and apply for jobs. 
     In turn, online networks may facilitate activities related to business, recruiting, networking, professional growth, and/or career development. For example, professionals may use an online network to locate prospects, maintain a professional image, establish and maintain relationships, and/or engage with other individuals and organizations. Similarly, recruiters may use the online network to search for candidates for job opportunities and/or open positions. At the same time, job seekers may use the online network to enhance their professional reputations, conduct job searches, reach out to connections for job opportunities, and apply to job listings. Consequently, use of online networks may be increased by improving the data and features that can be accessed through the online networks. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  shows a schematic of a system in accordance with the disclosed embodiments. 
         FIG. 2  shows a system for forecasting job applications in accordance with the disclosed embodiments. 
         FIG. 3  shows a flowchart illustrating a process of forecasting job applications in accordance with the disclosed embodiments. 
         FIG. 4  shows a flowchart illustrating a process of creating a machine learning model to forecast quality applicants in accordance with the disclosed embodiments. 
         FIG. 5  shows a computer system in accordance with the disclosed embodiments. 
     
    
    
     In the figures, like reference numerals refer to the same figure elements. 
     DETAILED DESCRIPTION 
     The following description is presented to enable any person skilled in the art to make and use the embodiments, 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 disclosure. Thus, the present invention is not limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein. 
     Overview 
     The disclosed embodiments provide a method, apparatus, and system for forecasting job applications for a given job post. The jobs are posted within an online system such as an online professional network and/or online marketplace. Each job is associated with a daily and/or other budget that is spent as users view, click on, apply to, and/or perform other actions related to the job. As a result, the rate at which users perform these actions may be affected by the budget set by the job&#39;s poster. 
     More specifically, the disclosed embodiments predict the number of applications (or applicants) for a job, given a budget for the job. The budget and/or other features of the job are inputted into one or more machine learning models to predict the number of impressions of the job (e.g., created by potential applicants of the job within the online system), as well as an application rate for the job. The number of impressions and the application rate are then combined in a Bayesian Poisson-Gamma state space model to produce a distribution of applications to the job, given the job&#39;s budget. For example, a Gamma distribution for the application rate may be approximated based on a mean and variance of the application rate. The distribution of applications to the job may then be generated as a negative binomial distribution that is parameterized using one or more parameters of the Gamma distribution and a Poisson rate for the number of impressions of the job. 
     One or more values from the distribution are then outputted as guidance for setting the job&#39;s budget. For example, an average value from the distribution may be displayed to a poster of the job as the forecasted number of applications to the job for a given value of the job&#39;s budget. In another example, values associated with the 10 th  and 90 th  percentiles in the distribution may be displayed to the job poster as lower and upper bounds for the number of applications to the job, given the job&#39;s budget. 
     By predicting numbers and/or rates of job applications based on budgets for the jobs and generating budgeting guidance based on the predictions, the disclosed embodiments may improve setting and/or utilization of the jobs&#39; budgets. In contrast, conventional techniques may involve workflows for posting advertisements, jobs, and/or other types of content that lack such guidance and/or use heuristics to estimate applications or other actions based on the corresponding budgets. In turn, job posters may fail to set budgets that provide for adequate exposure of applicants to jobs, which may result in a failure to hire for the jobs and/or an inability to hire the best applicants for the jobs. The job posters may also, or instead, fail to post jobs due to lack of guidance on how to set budgets for the jobs. Consequently, the disclosed embodiments may provide improvements in computer systems, applications, user experiences, tools, and/or technologies related to delivering online content and/or carrying out activities within online systems. 
     Forecasting Job Applications 
       FIG. 1  shows a schematic of a system in accordance with the disclosed embodiments. As shown in  FIG. 1 , the system may include an online network  118  and/or other user community. For example, online network  118  may include an online professional network that is used by a set of entities (e.g., entity 1  104 , entity x  106 ) to interact with one another in a professional and/or business context. 
     The entities may include users that use online network  118  to establish and maintain professional connections, list work and community experience, endorse and/or recommend one another, search and apply for jobs, and/or perform other actions. The entities may also include companies, employers, and/or recruiters that use online network  118  to list jobs, search for potential candidates, provide business-related updates to users, advertise, and/or take other action. 
     Online network  118  includes a profile module  126  that allows the entities to create and edit profiles containing information related to the entities&#39; professional and/or industry backgrounds, experiences, summaries, job titles, projects, skills, and so on. Profile module  126  may also allow the entities to view the profiles of other entities in online network  118 . 
     Profile module  126  may also include mechanisms for assisting the entities with profile completion. For example, profile module  126  may suggest industries, skills, companies, schools, publications, patents, certifications, and/or other types of attributes to the entities as potential additions to the entities&#39; profiles. The suggestions may be based on predictions of missing fields, such as predicting an entity&#39;s industry based on other information in the entity&#39;s profile. The suggestions may also be used to correct existing fields, such as correcting the spelling of a company name in the profile. The suggestions may further be used to clarify existing attributes, such as changing the entity&#39;s title of “manager” to “engineering manager” based on the entity&#39;s work experience. 
     Online network  118  also includes a search module  128  that allows the entities to search online network  118  for people, companies, jobs, and/or other job- or business-related information. For example, the entities may input one or more keywords into a search bar to find profiles, job postings, job candidates, articles, and/or other information that includes and/or otherwise matches the keyword(s). The entities may additionally use an “Advanced Search” feature in online network  118  to search for profiles, jobs, and/or information by categories such as first name, last name, title, company, school, location, interests, relationship, skills, industry, groups, salary, experience level, etc. 
     Online network  118  further includes an interaction module  130  that allows the entities to interact with one another on online network  118 . For example, interaction module  130  may allow an entity to add other entities as connections, follow other entities, send and receive emails or messages with other entities, join groups, and/or interact with (e.g., create, share, re-share, like, and/or comment on) posts from other entities. 
     Those skilled in the art will appreciate that online network  118  may include other components and/or modules. For example, online network  118  may include a homepage, landing page, and/or content feed that delivers, to the entities, the latest posts, articles, and/or updates from the entities&#39; connections and/or groups. Similarly, online network  118  may include features or mechanisms for recommending connections, job postings, articles, and/or groups to the entities. 
     In one or more embodiments, data (e.g., data 1  122 , data x  124 ) related to the entities&#39; profiles and activities on online network  118  is aggregated into a data repository  134  for subsequent retrieval and use. For example, each profile update, profile view, connection, follow, post, comment, like, share, search, click, message, interaction with a group, address book interaction, response to a recommendation, purchase, and/or other action performed by an entity in online network  118  may be tracked and stored in a database, data warehouse, cloud storage, and/or other data-storage mechanism providing data repository  134 . 
     In one or more embodiments, data repository  134  stores data that represents standardized, organized, and/or classified attributes for the users or entities. For example, skills in data repository  134  may be organized into a hierarchical taxonomy. The taxonomy may model relationships between skills and/or sets of related skills (e.g., “Java programming” is related to or a subset of “software engineering”) and/or standardize identical or highly related skills (e.g., “Java programming,” “Java development,” “Android development,” and “Java programming language” are standardized to “Java”). In another example, locations in data repository  134  may include cities, metropolitan areas, states, countries, continents, and/or other standardized geographical regions. In a third example, data repository  134  includes standardized company names for a set of known and/or verified companies associated with the members and/or jobs. In a fourth example, data repository  134  includes standardized titles, seniorities, and/or industries for various jobs, members, and/or companies in the online network. In a fifth example, data repository  134  includes standardized job functions such as “accounting,” “consulting,” “education,” “engineering,” “finance,” “healthcare services,” “information technology,” “legal,” “operations,” “real estate,” “research,” and/or “sales.” In a sixth example, data repository  134  includes standardized time periods (e.g., daily, weekly, monthly, quarterly, yearly, etc.) that can be used to retrieve other data that is represented by the time periods (e.g., starting a job in a given month or year, graduating from university within a five-year span, job listings posted within a two-week period, etc.). 
     Data in data repository  134  may be used to generate recommendations and/or other insights related to listings of jobs or opportunities within online network  118 . For example, one or more components of online network  118  may track searches, clicks, views, text input, applications, conversions, and/or other feedback during the entities&#39; interaction with a job search tool in online network  118 . The feedback may be stored in data repository  134  and used as training data for one or more machine learning models, and the output of the machine learning model(s) may be used to display and/or otherwise recommend a number of job listings to current or potential job seekers in online network  118 . 
     More specifically, data in data repository  134  and one or more machine learning models are used to produce rankings related to candidates for jobs or opportunities listed within or outside online network  118 . The candidates may include users who have viewed, searched for, or applied to jobs, positions, roles, and/or opportunities, within or outside online network  118 . The candidates may also, or instead, include users and/or members of online network  118  with skills, work experience, and/or other attributes or qualifications that match the corresponding jobs, positions, roles, and/or opportunities. 
     After the candidates are identified, profile and/or activity data of the candidates may be inputted into the machine learning model(s), along with features and/or characteristics of the corresponding opportunities (e.g., required or desired skills, education, experience, industry, title, etc.). The machine learning model(s) may output scores representing the strengths of the candidates with respect to the opportunities and/or qualifications related to the opportunities (e.g., skills, current position, previous positions, overall qualifications, etc.). For example, the machine learning model(s) may generate scores based on similarities between the candidates&#39; profile data with online network  118  and descriptions of the opportunities. The model(s) may further adjust the scores based on social and/or other validation of the candidates&#39; profile data (e.g., endorsements of skills, recommendations, accomplishments, awards, etc.). 
     In turn, ranking or thresholding based on the scores and/or associated insights may improve the quality of the candidates and/or recommendations of opportunities to the candidates, increase user activity with online network  118 , and/or guide the decisions of the candidates and/or moderators involved in screening for or placing the opportunities (e.g., hiring managers, recruiters, human resources professionals, etc.). For example, one or more components of online network  118  may display and/or otherwise output a member&#39;s position (e.g., top 10%, top 20 out of 138, etc.) in a ranking of candidates for a job to encourage the member to apply for jobs in which the member is highly ranked. In a second example, the component(s) may account for a candidate&#39;s relative position in rankings for a set of jobs during ordering of the jobs as search results in response to a job search by the candidate. In a third example, the component(s) may recommend highly ranked candidates for a position to recruiters and/or other moderators as potential applicants and/or interview candidates for the position. In a fourth example, the component(s) may recommend jobs to a candidate based on the predicted relevance or attractiveness of the jobs to the candidate and/or the candidate&#39;s likelihood of applying to the jobs. 
     Jobs, advertisements, and/or other types of content displayed or delivered within online network  118  may also be associated with budgetary constraints. For example, posters of jobs may pay per view, click, application, and/or other action taken with respect to the jobs by members of online network  118 . The posters may set daily budgets for the jobs, from which costs are deducted as the members take the corresponding actions with the jobs. After a job&#39;s daily budget is depleted, the job&#39;s position in search results, rankings, and/or recommendations may be decreased for the remainder of the day. As a result, the visibility of the job, the level of interaction between candidates and the job, and/or the ability to effectively hire for the job may be influenced by the budget set for the job. 
     In one or more embodiments, online network  118  includes functionality to improve budgeting of jobs by forecasting the number of applications to a job based on the job&#39;s budget and generating guidance to job posters based on the forecasted number of applications. As shown in  FIG. 2 , data repository  134  and/or another primary data store may be queried for data  202  that includes profile data  216  for members of an online system (e.g., online network  118  of  FIG. 1 ), as well as jobs data  218  for jobs that are listed or described within or outside the online system. 
     Profile data  216  includes data associated with member profiles in the online system. For example, profile data  216  for an online professional network may include a set of attributes for each user, such as demographic (e.g., gender, age range, nationality, location, language), professional (e.g., job title, professional summary, employer, industry, experience, skills, seniority level, professional endorsements), social (e.g., organizations of which the user is a member, geographic area of residence), and/or educational (e.g., degree, university attended, certifications, publications) attributes. Profile data  216  may also include a set of groups to which the user belongs, the user&#39;s contacts and/or connections, and/or other data related to the user&#39;s interaction with the online system. 
     Attributes of the members from profile data  216  may be matched to a number of member segments, with each member segment containing a group of members that share one or more common attributes. For example, member segments in the online system may be defined to include members with the same industry, title, location, and/or language. 
     Connection information in profile data  216  may additionally be combined into a graph, with nodes in the graph representing entities (e.g., users, schools, companies, locations, etc.) in the online system. Edges between the nodes in the graph may represent relationships between the corresponding entities, such as connections between pairs of members, education of members at schools, employment of members at companies, following of a member or company by another member, business relationships and/or partnerships between organizations, and/or residence of members at locations. 
     Jobs data  218  includes structured and/or unstructured data for job listings and/or job descriptions that are posted and/or provided by members of the online system and/or external entities. For example, jobs data  218  for a given job or job listing may include a declared or inferred title, company, required or desired skills, responsibilities, qualifications, role, location, industry, seniority, salary range, benefits, and/or member segment. 
     Data  202  in data repository  134  may further be updated using records of recent activity received over one or more event streams  200 . For example, event streams  200  may be generated and/or maintained using a distributed streaming platform such as Apache Kafka (Kafka™ is a registered trademark of the Apache Software Foundation). One or more event streams  200  may also, or instead, be provided by a change data capture (CDC) pipeline that propagates changes to data  202  from a source of truth for data  202 . For example, an event containing a record of a recent profile update, job search, job view, job application, response to a job application, connection invitation, post, like, comment, share, and/or other recent member activity within or outside the community may be generated in response to the activity. The record may then be propagated to components subscribing to event streams  200  on a nearline basis. 
     An analysis apparatus  204  uses data in data repository  134  to estimate a distribution of applications  220  for a job, given a budget  238  for the job. In particular, analysis apparatus  204  applies a first machine learning model  208  to a value of budget  238  and/or other features related to the job from data repository  134  to predict a number of impressions  212  of the job. Analysis apparatus  204  also applies a second machine learning model  210  to a different set of features to predict an application rate  214  for the job. Analysis apparatus  204  then combines number of impressions  212  and application rate  214  into a distribution of applications  220  for the job, given the value of budget  238 . 
     For example, machine learning model  208  may include a Poisson regression model that estimates a Poisson rate for number of impressions  212 . As a result, machine learning model  208  may have the following representation:
 
 i   jt   ˜Poi (λ jt ),log(λ jt )= X   jt β
 
In the above representation, i jt  represents number of impressions  212  for a job j at time t, which has a Poisson distribution with rate parameter λ jt . The Poisson regression model estimates the rate parameter as a function of regression covariates X jt  and coefficients β. The covariates may include the day of the week on which the job was posted and/or a number of days since the job was posted. The covariates may also, or instead, include features related to the job, such as the job&#39;s location, company, function, industry, and/or minimum or maximum level of experience. The covariates may also, or instead, include a source of applications for the job (e.g., a jobs module or other onsite source within the online system or a company website or another offsite source that is external to the online system) and/or a payment model for the job (e.g., pay per click (PPC) or a prepaid fixed price throughout the job&#39;s lifetime).
 
     Continuing with the example, machine learning model  210  may include a log-linear regression model that estimates application rate  214  based on features related to the job. As a result, machine learning model  210  may include the following representation:
 
log({tilde over (γ)} jt )= x   jt   T β j +ε jt ,
 
{tilde over (γ)} jt   :=a   jt /{circumflex over (λ)} jt  
 
In the above representation, {tilde over (γ)} jt  represents an estimate of application rate  214  for job j at time t, which is calculated as the number of applications a jt  divided by an estimated number of impressions  212  {circumflex over (λ)} jt . The log-linear regression model estimates the logarithm of application rate  214  based on covariates x jt   T , coefficients β j , and measurement errors ε jt . The covariates may include, but are not limited to, the job&#39;s function, industry, and/or level of experience.
 
     A Bayesian Poisson-Gamma state space model may then be used to generate distribution of applications  220  based on the estimated number of impressions  212  and application rate  214 :
 
 a   jt |λ jt ,γ j   ˜Poi (γ j λ jt )
 
γ j ˜Gamma( c   j   ,d   j )
 
In other words, the number of applications to the job, given number of impressions  212  and application rate  214 , may have a Poisson distribution and a Gamma-distributed prior γ j .
 
     The mean and variance of the logarithm of application rate  214  may be calculated as:
 
 f   j   =E (logγ j )=ϕ 0 ( c   j )−logd j  
 
 q   j   =V (logγ j )=ϕ 1 ( c   j ),
 
where f j  is the mean of the logarithm of application rate  214 , q 1  is the variance of the logarithm of application rate  214 , ϕ 0  is the digamma function, and ϕ 1  is the trigamma function.
 
     The Newton-Raphson method may be used with the expressions above to approximate c 1  and d 1  in an iterative fashion: 
               c     j   ,     n   +   1         =       c     j   ,   n       -           ϕ   1     ⁢     (     c     j   ,   n       )       -     q   j           ϕ   2     ⁡     (     c     j   ,   n       )                           d   j     =     exp   ⁢     {         ϕ   0     ⁡     (     c   j     )       -     f   j       }         ,         
where ϕ 2  is the polygamma function of order 2.
 
     Finally, the Gamma-distributed application rate  214  γ j  may be marginalized out to obtain the marginal distribution of applications  220  as a negative binomial distribution with the following form: 
     
       
         
           
             
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     A model-training apparatus  246  uses historical data  202  from data repository  134  as training data  224  for updating parameters  226  of one or both machine learning models  208 - 210 . For example, model-training apparatus  246  may input budgets, impression counts, and job features for previously posted jobs into machine learning model  208  and update parameters  226  of machine learning model  208  so that machine learning model  208  predicts the impression counts based on the corresponding budgets and job features. In another example, model-training apparatus  246  may input application rates and job features for previously posted jobs into machine learning model  210  and update parameters  226  of machine learning model  210  so that machine learning model  210  predicts the application rates based on the corresponding job features. 
     In one or more embodiments, model-training apparatus  246  generates and/or filters training data  224  used to update parameters  226  of one or both machine learning models  208 - 210  based on quality scores  222  associated with the corresponding job applicants. Quality scores  222  may represent a measure of “quality” for a set of applicants with respect to a corresponding set of jobs, with a higher quality score indicating a more desirable or suitable applicant for a job and a lower quality score indicating a less desirable or suitable applicant for a job. In some embodiments, desirable is defined as desirable to the job poster. 
     Model-training apparatus  246  calculates quality scores  222  for historical applicants of jobs based on attributes of the applicants and jobs. For example, model-training apparatus  246  may calculate match scores between a set of attributes for each applicant and a corresponding set of attributes for a job (e.g., a job viewed by the applicant and/or for which an application from the applicant was received). The match scores may characterize the degree to which the applicant&#39;s educational background, function, location, level of experience, industry, and/or set of skills matches those of the job. The match scores may then be combined with a set of weights to produce a quality score for the applicant with respect to the job. 
     Model-training apparatus  246  then applies a threshold and/or rank ordering to the quality scores  222  to identify a subset of applicants as “quality” applicants for the corresponding jobs and inputs training data  224  for the identified applicants into one or both machine learning models  208 - 210 . Model-training apparatus  246  may thus train machine learning model  208  to predict numbers of impressions for quality applicants of jobs and/or train machine learning model  208  to predict application rates of quality applicants of jobs. In turn, subsequent use of machine learning models  208 - 210  by analysis apparatus  204  may result in estimates of number of impressions  212 , application rate  214 , and/or distribution of applications  220  associated with quality applicants for a given job instead of all applicants for the job. 
     Model-training apparatus  246  may also, or instead, omit the use of quality scores  222  in generating and/or selecting training data  224  for one or both machine learning models  208 - 210 . Consequently, machine learning models  208 - 210  may be trained to predict a number of impressions  212  and/or application rate  214  for all applicants of a given job, and distribution of applications  220  may also be predicted for all applicants of the job. 
     A management apparatus  206  uses output of analysis apparatus  204  to guide the selection and/or updating of budget  238 . First, management apparatus  206  may output one or more values  240  from distribution of applications  220  as guidance for selecting budget  238 . For example, management apparatus  206  may provide a user interface that guides a job poster through a workflow for posting a job and/or for managing a previously posted job. Within the user interface, management apparatus  206  may display the value of budget  238  used to generate a given distribution of applications  220  for a job, as well as the mean of the distribution as the forecasted number of applications to the job given the displayed value of budget  238 . Management apparatus  206  may also, or instead, display values  240  for the 10 th  percentile and 90 th  percentile of distribution of applications  220  (or some other quantiles) as lower and upper bounds for the forecasted number of applications. 
     Management apparatus  206  may also provide user-interface elements within the user interface for adjusting budget  238 . When a new value of budget  238  is specified through the user interface, management apparatus  206  may transmit the value to analysis apparatus  204 , and analysis apparatus  204  may generate new estimates of number of impressions  212 , application rate  214 , and distribution of applications  220  based on the value. In turn, management apparatus  206  may update values  240  representing the forecasted number of applications for the job to reflect the change in budget  238 . A poster of the job may thus interact with the user interface to identify and/or set a value of budget  238  that produces the desired number or range of applications to the job. 
     Second, management apparatus  206  may output recommendations  242  related to values  240  and/or budget  238 . For example, management apparatus  206  may display a “likelihood of hire” associated with the forecasted number of applications to the job. When the likelihood is low, management apparatus  206  may suggest an amount by which budget  238  should be increased to improve the chances of hiring an employee for the job. 
     By predicting numbers and/or rates of job applications based on budgets for the jobs and generating budgeting guidance based on the predictions, the disclosed embodiments may improve setting and/or utilization of the jobs&#39; budgets. In contrast, conventional techniques may involve workflows for posting advertisements, jobs, and/or other types of content that lack such guidance and/or use heuristics to estimate applications or other actions based on the corresponding budgets. Consequently, the disclosed embodiments may provide improvements in computer systems, applications, user experiences, tools, and/or technologies related to delivering online content and/or carrying out activities within online systems. 
     Those skilled in the art will appreciate that the system of  FIG. 2  may be implemented in a variety of ways. First, analysis apparatus  204 , management apparatus  206 , model-training apparatus  246 , and data repository  134  may be provided by a single physical machine, multiple computer systems, one or more virtual machines, a grid, one or more databases, one or more filesystems, and/or a cloud computing system. Analysis apparatus  204 , management apparatus  206 , and model-training apparatus  246  may additionally be implemented together and/or separately by one or more hardware and/or software components and/or layers. 
     Second, a number of techniques may be used to estimate number of impressions  212 , application rate  214 , and/or distribution of applications  220 . For example, the functionality of analysis apparatus  204  and/or machine learning models  208 - 210  may be provided by one or more regression models, artificial neural networks, support vector machines, decision trees, naïve Bayes classifiers, Bayesian networks, random forests, gradient boosted trees, deep learning models, hierarchical models, and/or ensemble models. 
     Third, the functionality of the system may be adapted to various types of content and/or pricing. For example, the system may be used to predict actions related to advertisements, posts, images, audio, video, and/or other types of online content based on budgets for the content. 
       FIG. 3  shows a flowchart illustrating a process of forecasting job applications in accordance with the disclosed embodiments. In one or more embodiments, one or more of the steps may be omitted, repeated, and/or performed in a different order. Accordingly, the specific arrangement of steps shown in  FIG. 3  should not be construed as limiting the scope of the embodiments. 
     Initially, a first machine learning model is applied to features that include a budget for a job to predict a number of impressions of the job (operation  302 ). For example, the first machine learning model may include a Poisson regression model that estimates the Poisson rate for the number of impressions based on the budget of the job, the day of the week on which the job was originally posted, a number of days since the job was posted, features related to the job (e.g., the job&#39;s location, company, function, industry, level of experience), a source of applications for the job, a payment model for the job, and/or a cross product of two other features (e.g., a cross product of the job&#39;s function and industry). 
     Next, a second machine learning model is applied to additional features for the job to estimate an application rate for the job (operation  304 ). For example, the second machine learning model may include a log-linear regression model that estimates the application rate for the job based on the job&#39;s function, industry, and/or level of experience. 
     A distribution of applications to the job is then determined based on the number of impressions and the application rate (operation  306 ). 
     For example, a Gamma distribution for the application rate may be approximated based on a mean and a variance of the application rate, and the distribution of applications to the job may be generated as a negative binomial distribution based on one or more parameters of the Gamma distribution and a Poisson rate for the number of impressions. 
     Finally, one or more values from the distribution of applications to the job are outputted as guidance for setting the budget of the job (operation  308 ). For example, an average value from the distribution may be displayed to a poster of the job as the forecasted number of applications to the job for a given value of the job&#39;s budget. In another example, values associated with the 10 th  and 90 th  percentiles in the distribution (and/or other quantiles in the distribution) may be displayed to the job poster as lower and upper bounds for the number of applications to the job, given the job&#39;s budget. In a third example, a visual representation of the distribution of applications (e.g., a plot of the distribution&#39;s probability mass function) may be displayed to the job&#39;s poster. The visual representation may be updated as the poster interacts with a slider, dial, text field, and/or other user-interface element for specifying the job&#39;s budget. 
       FIG. 4  shows a flowchart illustrating a process of creating a machine learning model in accordance with the disclosed embodiments. In one or more embodiments, one or more of the steps may be omitted, repeated, and/or performed in a different order. Accordingly, the specific arrangement of steps shown in  FIG. 4  should not be construed as limiting the scope of the embodiments. 
     First, historical data containing attributes of applicants to jobs is obtained (operation  402 ). For example, the attributes may include an educational background, function, location, level of experience, industry, and/or a set of skills for each applicant. Next, quality scores for the applicants are calculated based on the attributes and additional attributes of the jobs (operation  404 ). For example, match scores between the attributes of the applicants and corresponding attributes of the jobs may be calculated and combined with a set of weights to produce the quality scores. As a result, each quality score may reflect the extent to which qualifications and/or requirements for a job are met by a corresponding applicant. 
     A threshold or rank order is applied to the quality scores to identify a subset of the applicants as quality applicants for the jobs (operation  406 ). For example, the threshold may represent a percentile associated with the quality scores (e.g., the top 20% of quality scores using rank order or applicants that match to 80% of the job post) and/or a numeric quality score value, and applicants with quality scores that exceed the threshold may be identified as quality applicants. 
     Finally, application rates and/or impressions associated with the quality applicants and jobs are inputted as training data for a machine learning model (operation  408 ). In turn, the machine learning model may learn to predict application rates and/or impressions of jobs by quality applicants. 
       FIG. 5  shows a computer system  500  in accordance with the disclosed embodiments. Computer system  500  includes a processor  502 , memory  504 , storage  506 , and/or other components found in electronic computing devices. Processor  502  may support parallel processing and/or multi-threaded operation with other processors in computer system  500 . Computer system  500  may also include input/output (I/O) devices such as a keyboard  508 , a mouse  510 , and a display  512 . 
     Computer system  500  may include functionality to execute various components of the present embodiments. In particular, computer system  500  may include an operating system (not shown) that coordinates the use of hardware and software resources on computer system  500 , as well as one or more applications that perform specialized tasks for the user. To perform tasks for the user, applications may obtain the use of hardware resources on computer system  500  from the operating system, as well as interact with the user through a hardware and/or software framework provided by the operating system. 
     In one or more embodiments, computer system  500  provides a system for forecasting job applications. The system includes an analysis apparatus and a management apparatus, one or more of which may alternatively be termed or implemented as a module, mechanism, or other type of system component. The analysis apparatus applies a first machine learning model to features that include a budget for a job to predict a number of impressions of the job. Next, the analysis apparatus applies a second machine learning model to additional features for the job to estimate an application rate for the job. The analysis apparatus then determines a distribution of applications to the job based on the number of impressions and the application rate. Finally, the management apparatus outputs one or more values from the distribution of applications to the job as guidance for setting the budget for the job. 
     In addition, one or more components of computer system  500  may be remotely located and connected to the other components over a network. Portions of the present embodiments (e.g., analysis apparatus, management apparatus, model-training apparatus, data repository, online network, etc.) may also be located on different nodes of a distributed system that implements the embodiments. For example, the present embodiments may be implemented using a cloud computing system that predicts applications to jobs by a set of remote users based on budgets for the jobs. 
     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. The computer-readable storage medium 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 code and/or data now known or later developed. 
     The methods and processes described in the detailed description section can be embodied as code and/or data, which can be stored in a computer-readable storage medium as described above. When a computer system reads and executes the code and/or data stored on the computer-readable storage medium, the computer system performs the methods and processes embodied as data structures and code and stored within the computer-readable storage medium. 
     Furthermore, methods and processes described herein can be included in hardware modules or apparatus. These modules or apparatus may include, but are not limited to, an application-specific integrated circuit (ASIC) chip, a field-programmable gate array (FPGA), a dedicated or shared processor (including a dedicated or shared processor core) that executes a particular software module or a piece of code at a particular time, and/or other programmable-logic devices now known or later developed. When the hardware modules or apparatus are activated, they perform the methods and processes included within them. 
     The foregoing descriptions of various embodiments have been presented only for purposes of illustration and description. They are not intended to be exhaustive or to limit the present invention 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 invention.