Prospecting the Career Development of Talents: A Survival Analysis Perspective

Transcription

1 Prospectng the Career Development of Talents: A Survval Analyss Perspectve Huayu L,2, Yong Ge 3, Hengshu Zhu 2, Hu Xong 4, and Hongke Zhao 5 UNC Charlotte, 2 Badu Talent Intellgence Center, 3 Unversty of Arzona, 4 Rutgers Unversty, 5 Unversty of Sc. & Tech. of Chna, zhhk@mal.ustc.edu.cn hl38@uncc.edu,yongge@emal.arzona.edu,zhuhengshu@badu.com,hxong@rutgers.edu ABSTRACT The study of career development has become more mportant durng a tme of rsng competton. Even wth the help of newly avalable bg data n the feld of human resources, t s challengng to prospect the career development of talents n an effectve manner, snce the nature and structure of talent careers can change quckly. To ths end, n ths paper, we propose a novel survval analyss approach to model the talent career paths, wth a focus on two crtcal ssues n talent management, namely turnover and career progresson. Specfcally, for modelng the talent turnover behavors, we formulate the predcton of survval status at a sequence of tme ntervals as a mult-task learnng problem by consderng the predcton at each tme nterval as a task. Also, we mpose the rankng constrants to model both censored and uncensored data, and capture the ntrnsc propertes exhbted n general lfetme modelng wth non-recurrent and recurrent events. Smlarly, for modelng the talent career progresson, each task concerns the predcton of a relatve occupatonal level at each tme nterval. The rankng constrants mposed on dfferent occupatonal levels can help to reduce the predcton error. Fnally, we evaluate our approach wth several state-of-the-art baselne methods on realworld talent data. The expermental results clearly demonstrate the effectveness of the proposed models for predctng the turnover and career progresson of talents. KEYWORDS Mult-task Learnng; Rankng; Career Path Modelng; Career Development; Survval Analyss INTRODUCTION Due to the ntensve competton for talents globally, many companes strve not only to attract the rght talents, but also provde sound career development gudance for retanng ther sklled and competent employees. Thus, the study of career development has been ganng more mportance n strategc human resource management [2,, 3, 8, 24, 27, 3]. Hu Xong and Hengshu Zhu are correspondng authors. Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. Copyrghts for components of ths work owned by others than ACM must be honored. Abstractng wth credt s permtted. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. Request permssons from permssons@acm.org ACM. ISBN /7/08...$5.00 DOI: Recently, the newly avalable bg talent data provde unparalleled opportuntes for busness leaders to understand talent behavors and gan tangble knowledge about career paths for assstng talents to plan ther future career development. For example, the management team can provde more tmely decsons to promote ther employees whenever there s a need. To ths end, n ths paper, we provde a data-drven soluton for modelng talent career paths, and thus help talents better plan ther career development. However, the complex and dynamc nature of talent career data, and the presence of large censored and recurrent events can mpose sgnfcant challenges to model the talent career paths n an effectve manner. Frst, the event of nterests, e.g., turnover or promoton, may not be observed durng the study perod due to the lmted observaton tme. In real-world scenaros, more than 65% career data exhbts ths censorng phenomenon. Ths ndcates that smple regresson approaches [, 20] may not be sutable for career path modelng. Second, wth the hgh moblty of talents between organzatons, an ndvdual s career path may comprse a sequence of changng events, whch can no longer be regarded as non-recurrent. Fnally, the change of talent s career path s hghly affected by a varety of dynamc factors, such as tme-varyng performance ratngs and superor-and-subordnate relatonshps. Therefore, how to ncorporate these dynamc factors nto the modelng process presents another crucal challenge. In the lterature, some survval models can be adapted to career path modelng by predctng employee s survval tme at an event of nterest [3, 0]. For example, the Cox proportonal hazards model [3] calculates the hazard n a multplcatve manner, whch s assocated wth a baselne hazard functon and the observed covarates. However, ts assumpton that the survval curves of all nstances share a smlar shape s not always true for all applcaton scenaros [0]. Parametrc survval model [6] s another popular technque n survval analyss, whch assumes that the survval tmes of all nstances share a partcular dstrbuton, such as log-logstc, log-normal, webull, and exponental dstrbuton. However, ths hgh dependence on the choce of the dstrbuton leads to a more crtcal weakness. Recently, a mult-task learnng based method s developed to predct survval tme by modelng the non-ncreasng lst structure [0]. However, ths approach only works on non-recurrent events, and thus s not sutable for modelng talent career paths. To address the aforementoned ssues, n ths paper, we propose a novel survval analyss approach for modelng talent career paths, whch s based on mult-task learnng wth rankng constrant formulaton. In partcular, we focus our study on two crtcal ssues n talent management, namely turnover and career progresson. 97

2 Specfcally, for modelng the talent turnover behavors, we formulate the predcton of survval status at a sequence of tme ntervals as a mult-task learnng problem. The rankng constrant wth dfferent margns mposed on each par of dfferent survval status labels s used to dstngush censored and uncensored data, and smultaneously captures the unque characterstc n general survval analyss wth both non-recurrent and recurrent events. Smlarly, for career progresson modelng, each task only focuses on the predcton of a relatve level at a sngle tme nterval. Also, we mpose rankng constrants between dfferent levels, effectvely ensurng that dfferent levels are well separated, and thus, levels are estmated n a more relable fashon. In addton, the observed tme-varyng factors are embedded nto dynamc feature space and then ncorporated nto these two models. Fnally, we evaluate our approach wth several state-of-the-art baselne methods and dfferent valdaton metrcs on real-world talent data. The expermental results frmly demonstrate the effectveness of the proposed models for predctng the turnover and career progresson of employees. The major contrbutons of ths paper can be summarzed as follows. We study the problem of wthn-frm career path modelng for talents, wth a focus on two ssues n talent management, namely, turnover and career progresson. We propose a novel survval analyss approach for modelng the career paths of employees, whch s based on mult-task learnng wth rankng constrant formulaton. We conduct extensve evaluatons wth real-world talent data to demonstrate the effectveness of our survval models n terms of predctng turnover and career progresson of employees. 2 DATA DESCRIPTION We collected a set of anonymzed employee career records from a hgh tech company across a tmespan of 48 months from January st, 20 to December 3st, 204. Specfcally, each employee has a date of jonng the company, and a tme duraton (or tenure) untl leavng the company or reachng the end of the tmespan. The career progresson of employees wthn a company s reflected by a seres of observed occupatonal levels and ther correspondng tme duratons. Each level s denoted by an nteger and the change of level ndcates whether an employee gets promoted or demoted. For example, Fgure (a) shows an employee s career path wthn a company. Specfcally, she stayed at level 6 for sx months, and spent twelve months gettng promoton from level 7 to level 8. Fnally she left ths company sx months later after the last promoton. In addton, our dataset contans both statc profle (e.g., gender and age) and other dynamc nformaton of each employee. The dynamc nformaton of each employee ncludes a numerc performance ratng, rangng from one star to fve stars, and a tree structurelke report chan, recordng employee s superor and subordnate relatonshp, at dfferent tme stamps. Fgure (b) s an example of report chan. Dfferent from statc profle, the dynamc nformaton changes over tme. To guarantee the effectveness of our model, n ths paper we only study the employees who joned the company on or after January st, 20. Level Month (a) An example of career path Employee Employee 2 Employee 3 Employee 4 Employee 5 Employee 6 (b) An example of report chan Fgure : (a) An example of employee s career path wthn a company, where the end marker ndcates that she leaves the company. (b) An example of report chan, where employee s the superor of 2 and 3; Employee 4 and 5, and employee 6 are the subordnates of 2 and 3, respectvely. 3 METHOD In ths secton, we frst state the problem of wthn-frm career path modelng for talents and two essental predcton tasks, namely, turnover and career progresson. We then present our methods for each task n detals. Fnally, we dscuss the feature space representaton for our models and the optmzaton algorthm. 3. Problem Formulaton We focus on the analyss of employee s wthn-frm career path, whch s manly reflected by the status of employment and occupatonal level. Suppose E (r ) = (or E (p) = ) ndcates a turnover (or level changng) event of the -th employee, and E (r ) = 0 (or E (p) = 0) denotes stayng at current company (or level). Gven a tme duraton t from the date of jonng the company, the jont probablty of the -th employee s employment status and level status can be denoted as, { P(E (r ) P(E (r ), E (p) = t) t) = P(E (r ) = 0 t) P(E (p) E (r ) () = 0, t), where the equaton holds due to that an employee s level wll never change after she leaves the company,.e., P(E (p) = E (r ) =, t) = 0 and P(E (p) = 0 E (r ) =, t) =. The essental task for modelng an employee s career path wthn a company s to predct two crtcal events,.e., when she wll leave ths company and when her occupatonal level wll get changed. In other words, gven a tme nterval t, the task s to nfer employee s turnover probablty P(E (r ) and level changng probablty P(E (p) = E (r ) = t), = 0, t) f she s stayng at ths company 2. In the followng, we wll ntroduce turnover behavor predcton n 3.2 and career progresson modelng n 3.3 after gvng all notatons used n ths paper. Notatons. Scalars, vectors and matrces are denoted by lower case letters, bold face lower case letters and bold face captal letters, respectvely. Sets and lsts are represented by callgraphc captal letters, where the -th element of lst S s denoted by S[]. b (b,. ) denotes the -th column (row) of matrx B. Eucldean and Frobenus norms are denoted by and F. N n s defned as the set {,, n}. A predcted value s denoted wth aˆ(hat) over t. 2 Note that due to P(E (r ) = 0 t) + P(E (r ) = t) =, once one of them s estmated, the other one wll be known. The same goes for P(E (p) E (r ) = 0, t). 98

3 3.2 Turnover Behavor Modelng Boomerang employees who leave a company and return n the future have recently receved attentons n human resource research [9]. Such turnover behavor may even occur more than once for an employee n a company. We propose to model employee s turnover behavor as a general survval problem whch s applcable for both non-recurrent and recurrent events, and ntroduce a mult-task learnng model wth rankng based constrants to solve ths problem. Suppose we have n employees, each of who has ether a career lfetme o for stayng at a company or a censorng tme c, not both. For each employee n our data, we observe t = mn(o,c ), the mnmum of the censorng and lfetme. A censorng ndcator δ s ntroduced to descrbe whether observaton s termnated by turnover event or censorng,.e., δ = for an uncensored nstance, and δ = 0 for a censored nstance. The observed tme t s then defned as: { o f δ =, t = (2) c f δ = 0. We transform turnover behavor modelng nto a mult-task learnng problem by decomposng the classfcaton problem nto a seres of related tasks by the reason of ts popularty [0, 3]. Employee s observed tme t s consdered as countable tme ntervals wth granularty as day, week or month. Let m = max{t }, =,, n, be the maxmum observaton tme of all employees. All employee s observaton tme s translated nto a lfetme matrx R R n m. Each element n the matrx s a bnary value, where r, j = f employee stays at tme nterval j and r, j = 0 otherwse. Suppose we have a feature tensor X n p m, where each feature matrx X j R n p s observed at the start of the j-th tme nterval (whch wll be ntroduced n detals n Secton 3.4). The target vector r j s approxmated usng coeffcents B R p m as: ˆr j = X j b j. (3) As we do not know whether turnover wll occur or not for censored nstance, an ndcator matrx W r R n m s ntroduced to denote the mssng values, where w r, j = 0 f r, j s unknown and w r, j = otherwse. The sum-of-squared error based loss functon then can be acheved by only modelng those observed values as: m mn l r (B, X) = mn w r j (r j X j b j ) 2 + θ r (B, X), (4) j= where denotes the element-wse multplcaton. The left part of Fgure 2 shows an example of transformaton from orgnal data nto lfetme matrx R and ndcator matrx W r, where the tme unt of duraton s month. θ r (B, X) ncorporates regularzaton term that avods overfttng and addtonal constrants. Dfferent from [0], we capture the followng two unque propertes n general turnover modelng desgned for θ r (B, X): Rankng Relatonshp. Three types of rankng relatonshps are observed n lfetme matrx as follows: () The values durng career lfetme are larger than those after turnover event, (2) and are probably larger than those uncensored data; (3) All values are larger than or equal to zero. Temporal Smoothness. Due to the temporal consecutveness, most adjacent tasks are smlar. There are two advantages to relax non-ncreasng property proposed n [0] nto parwse rankng. Frst, the rankng constrants can be used to handle both non-recurrent and recurrent events n lfetme modelng. Second, t places more strct constrants on modelng censored data and uncensored data. Specfcally for censored nstance, unknown data s actually a mxture of survvng and turnover data. In other words, the observed values should be larger than or equal to unknown values,.e., ˆr, j ˆr,k, j M r,, k M r,, and Mr s defned as Eq.(5). For uncensored nstance, the values durng career lfetme are strctly larger than those after turnover,.e., ˆr, j ˆr,k + ξ r, j M r,, k Mr,0. ξ r (0, ] s a margn label used for uncensored data [4]. {j r, j = } M,h r = {j r, j = 0} {j r, j =? } f h = (before observed turnover), f h = 0 (after observed turnover), f h = (for unknown value). Therefore, the rankng relatonshp can be formulated as follows: (5) ˆr, j ˆr,k + r, (, j, k) Ur, (6) ˆr, j 0, N n, j N m, (7) where U r = {, j, k N n, j M, r, k Mr } denotes all,δ comparson tuples, and r s the margn label used to dstngush censored data and uncensored data as follows: { r ξ r f δ =, = (8) 0 f δ = 0. Consequently, θ r (B, X) s obtaned by penalzng those volated constrants shown n Eq.(6) and Eq.(7) as, θ r (B, X) = λ r (, j,k) U r (ˆr,k + r ˆr ), j + + λ r ( 2 ˆr, j )+ + λr 3 2 B 2 F + λr 4 B 2,,, j (9) where (x) + = max{x, 0} s the plus functon. λ r are regularzaton parameters. Frobenus norm s used to avod overfttng, and l 2, - norm s used to capture temporal smoothness property by selectng a set of common features across all tasks. Once the probablty that employee stays at the company at tme nterval j,.e., P(E (r ) = 0 t j ) ˆr, j, s estmated, the correspondng turnover probablty can be easly derved. 3.3 Career Progresson Modelng Gven feature tensor X and hstorcal career data, our goal s to predct the career progresson measured by the occupatonal level. Durng the career lfetme, an employee s level possbly changes over tme. Let AS be a lst of levels that employee has stayed at, where AS [x] s the x-th element n the lst and t,l denotes the duraton that she stays at level AS [l] wth t = l t,l. Therefore, the observed career progresson of the -th employee can be represented as follows: {< t,, AS [] >, < t,2, AS [2] >,, < t, AS, AS [ AS ] > }, 99

4 ID T T2 T3 T4 T5 T6 T ? 3???? 4 ID T T2 T3 T4 T5 T6 T Employee s Career Lfetme ID Duraton Status Employee s Level Lfetme ID Duraton Level ID T T2 T3 T4 T5 T6 T ?? 2? 3???? ID T T2 T3 T4 T5 T6 T Fgure 2: An example of transformaton from orgnal career path data nto mult-task learnng settngs. where AS s the length of lst AS. In the example of Fgure 2, the career progresson of employee wth ID = 4 can be descrbed as {< 2, 2 >, < 3, 3 >, < 2, 4 >}. As the observed tme t s consdered as countable tme ntervals ( 3.2), the observed level of employee at j-th tme nterval s denoted as l, j. The career progresson s then converted to mult-task learnng settng and rewrtten as, { M p,h, AS [h] h R AS }, (0) where M p denotes a set of contnuous tme ntervals for level,h AS [h]. In the example of Fgure 2, for employee wth ID = 4, we have M p, = {T,T 2 }, M p,2 = {T 3,T 4,T 5 }, and M p,3 = {T 6,T 7 }. To model employee s career progresson, we transform the orgnal level lfetme data nto an n-by-m relatve level matrx P. Each element p, j of matrx P s the relatve dfference between level l, j observed at j-th tme nterval and the frst level observed when employee enters the company, p, j = l, j l, +, () where we add as an offset. The purpose of addng ths offset s to guarantee the relatve levels n our data to be non-negatve for better model learnng. Please note that each employee s frst observed level l, wll stll be ncorporated to X as a statc feature because t s very mportant for career progresson. The reason that we choose to model the relatve level s to decrease the matrx bas because most employees levels get changed often less than fve tmes durng ther career lfetmes. As the level changng only occurs durng an employee s career lfetme, we only model the observed level data 3. To do ths, we use another ndcator matrx W p R n m to ndcate the observed data, where w p, j = f employee s stayng at a level at the j-th tme nterval, and w p, j = 0 otherwse. The rght part of Fgure 2 shows an example of generatng a relatve level matrx P and ts correspondng ndcator matrx W p. For example, an employee wth ID = has labels as for two ntervals (T, T 2 ) and as 2 for three ntervals (T 3, T 4, T 5 ) n the correspondng row of relatve level matrx P, where the remanng unobserved values are labeled as?. Accordngly, the values n the correspondng row of ndcator matrx W p are durng the observed career lfetme (T T 5 ) and 0 n the remanng tme ntervals (T 6, T 7 ). The relatve levels for all employees at tme nterval j can be approxmated usng feature matrx X j as, ˆp j = X j a j, (2) 3 Please note that we do not fuse R and P together due to () We want to enable our method to handle demoton scenaro. If fusng them together, t cannot dstngush zero from demoton event and turnover event. (2) They have dfferent propertes. where a j s the j-th column of coeffcent matrx A R p m. Thus, the loss functon n terms of squared error can be acheved as, m mn l p (A, X) = mn w p j (p j X j a j ) 2 + θ p (A, X), (3) j= where θ p (A, X) s the regularzer ncorporatng the regularzaton term and addtonal constrants. The proposed two propertes n Secton 3.2,.e., rankng relatonshp and temporal smoothness, also can be ncorporated nto career progresson modelng. Dstnct from turnover predcton, the rankng constrant desgned for career progresson s revsed as follows 4 : Suppose S s a lst of relatve levels for employee,.e., S = {p, j j M p,h,h R AS }. The parwse rankng holds for each par of adjacent levels, shown as, ˆp, j ˆp,k + ξ p, (j, k) U p (4) where ξ p [0, ], and U p ncludes all possble adjacent comparson pars and are defned as follows: U p = {, j, k R n, j M p,h l, k M p,h s, (h s,h l ) = mn max(h,h +, S ),h R S }, (5) mn max(h,h +, S ) = { (h,h + ) f S [h] < S [h + ], (h +,h) f S [h + ] < S [h]. Non-negatve property,.e., ˆp, j 0, R n, j R m. We have ths constrant because the relatve levels n our data are always larger than or equal to zero. Fnally θ p (A, X) n Eq.(3) s obtaned by penalzng those volated rankng constrants and placng Frobenum norm and l 2, -norm on A as follows: θ p (A, X) = λ p ( ˆp,k + ξ p ) ˆp, j + + (, j,k) U p λ p 2, j ( ˆp, j )+ + λp 3 2 A 2 F + λp 4 A 2,, (6) Gven the relatve level p,s observed at tme nterval s, once the relatve level ˆp, j of employee at tme nterval j s estmated, the probablty that her level wll get changed can be calculated and proportonal to the dfference between values at tme nterval j and s,.e., P(E (p) = E (r ) = 0, t j ) ˆp, j p,s. Dscusson about Two Models. Here we would further clarfy the relatonshp between turnover behavor modelng and career progresson modelng. Indeed, the career status of an employee 4 If only promoton or demoton s consdered, censored data can be modeled lke

5 Tasks Eq.(4) and Eq.(3) as follows: l = mn βl r (B, X) + ( β)l p (A, X) + θ x (X), (8) Features Statc Features Dynamc Features Fgure 3: Left s mappng an observed feature value o,z to a vector through a lookup table Q z, where dx(o,z ) = 3. Rght s the vsualzaton of both statc and dynamc features. s determned by her employment status and occupaton level status together. Thus, modelng the career path of an employee s essentally to model her turnover behavor and career progresson, whch are nterconnected from the followng two aspects. From problem formulaton perspectve, both can be treated as the general survval problem wth recurrent events, amng at estmatng the career lfetme and level lfetme, respectvely. From techncal soluton perspectve, both are solved by a mult-task learnng wth rankng constrants, where dfferent partcular rankng constrants and predcton targets are nvolved. 3.4 Feature Space Representaton In ths secton, we wll dscuss the feature representaton X. As employee s career path s affected by the tme-varyng factors ncludng performance ratng and report chan, we ncorporate them as dynamc features. Specfcally, we transform employee s tme-varyng report chan nto features by countng the number of changed superors and subordnates. Fgure 6 n Appendx provdes some statstcs about the mpact of these dynamc features on career development. As we also have statc nformaton about employee, we totally have two types of features,.e., statc and dynamc features, as shown n Fgure 3. Suppose we observe a set of features {o,z } z=0 d at the j-th tme nterval for employee, ncludng both statc and dynamc features, where o,0 = s used for bas term. To address the low feature dmenson ssue of our data, we map orgnal feature space nto a hgher dmensonal space where data s more separable. Thus, each observed-and-quantzed feature o,z s embedded nto a p z -dmensonal vector q dx(o,z ) through the lookup matrx Q z R p z r anдe z. The -th row x j,. of feature matrx X j R n p at j-th tme nterval s represented as, x j,. = (qt dx(o,0 ), qt dx(o, ),, qt dx(o,d )), (7) where z p z = p, dx( ) s the correspondng ndex. An example s provded n Fgure 3. We wll study two commonly used embeddng representatons n ths paper [23]: one s usng one-hot vector (.e., a bnary vector wth all 0s and only a for the correspondng ndex), denoted as sparse embeddng; the other one s dense embeddng by mappng each feature o,z nto a p z -dmensonal latent vector whch then can be optmzed under an approprate loss functon. 3.5 Optmzaton Algorthm The models for turnover behavor and career progresson predcton can be traned both separately and jontly. For the convenence of presentaton, we provde ther jont objectve functon based on where β [0, ] s a controllng parameter, and θ x (X) = λ x 2 j X j 2 F s the regularzaton term desgned for feature learnng wth dense embeddng. In Eq.(9) and Eq.(6), plus functon (x) + s not twce dfferentable and can be smoothly approxmated usng the ntegral to a smooth approxmaton of the sgmod functon [7, 9]: (x) + σ(x) = x + log( + exp( αx)), (9) α where α > 0 s a constant parameter. θ r (B, X) and θ p (A, X) then can be refned as follows: θ r (B, X) = λ r σ (ˆr,k + r (, j,k) U r ˆr, j ) + λ2 r σ ( ˆr, j ) + λr 3 2 B 2 F + λr 4 B 2,,, j θ p (A, X) = λ p σ ( ˆp,k + ξ p ˆp, j ) + λ p (, j,k) U p 2 σ ( ˆp, j ) + λp 3 2 A 2 F + λp 4 A 2,., j Based on Eq.(8), the optmal soluton of B, A and X (for dense embeddng) are gven as follows: m B t + = argmn w r j (r j X j b j ) 2 + θ r (B, X), (20) B j= m A t + = argmn w p j (p j X j a j ) 2 + θ p (A, X), (2) A j= X t + = argmn β l r (B, X) + ( β)l p (A, X) + θ x (X). (22) X The optmzaton problems assocated wth B and A can be regarded as the followng l 2, -norm regularzaton problem: mn B loss(b) + λ B 2,. (23) As loss(b) and loss(a) are convex, B and A then can be solved by Nesterov s method wth effcent Eucldean projecton [2]. The proposed optmzaton algorthm s summarzed n Algorthm, where X wll be optmzed by gradent descent method f dense embeddng s used and not optmzed otherwse. Algorthm : Optmzaton of the Proposed Method Input: Job lfetme matrx R, Relatve level matrx P, Indcator matrces W r, W p, and parameters λ r, λ p, λ x, ξ r, ξ p, α, β Output: B, A, X Randomly ntalze B and A, X, t 2 whle t maxiter and not convergence do 3 Compute B t + by solvng Eq.(20); 4 Compute A t + by solvng Eq.(2); 5 Update X t + by usng the gradent of Eq.(22) wth respect to X; 6 t t +. 7 end 8 return B, A, X Complexty Analyss. In each teraton, the worst case s to model all values n the matrx for the emprcal loss, so tme complexty s O(nmp). For the parwse rankng constrants, the runnng tme s O(m 2 p) for each nstance. Samplng technque can be also used to reduce the comparson number [8, 7], such as samplng mk comparson pars for each nstance. It leads to the tme complexty as O(mkp), whch approxmates to O(mp) because of the small value k m. Suppose #ter s the number of teratons, the 92

6 Table : The statstcs of datasets. Dataset #Employees #Censored #Tasks Tranng 7,343 5,323 Data 47 Testng 6,564 5,688 Data 2 Type Statc Feature Dynamc Feature Tranng 6,986 4,56 47 Testng,746,27 Table 2: The descrpton of features. Descrpton gender, age, year of start date, month of start date, ntal level, and ntal subordnate number performance ratng, number of changed superors, and number of changed subordnates total runnng tme s O(nm 2 p#ter), and reduces to O(nmp#ter) when samplng method s appled to optmzaton. 4 EXPERIMENTS In ths secton, we evaluate the proposed model wth the baselne methods on the real-world dataset. 4. Expermental Setup Datasets. In ths paper, we use a real-world dataset collected from a hgh tech company (more detals can be found n Secton 2) to evaluate the performance of the proposed models. Before fttng our models wth the data, we conduct the followng preprocessng on our data: ) removng employees who do not have profles and performance ratngs, 2) flterng out employees whose levels have changed more than fve tmes, 3) removng those employees who have stayed at the company (or level) less than four (or three) months. After preprocessng, we totally have 8, 732 employees. Then we splt the data nto two parts (.e., tranng and testng sets) n two dfferent ways. The frst way s to splt data n chronologcal order and denote as Data, where the earler data rangng from January 20 to May 204 s used as tranng and the remanng half-year data s used as testng. The second way follows standard survval analyss evaluaton method,.e., splttng the data randomly, whch s denoted as Data 2, where we randomly select 80% employees as tranng and use the rest as testng. The statstcs of two datasets are shown n Table, and ther hstograms about the duratons of stayng at a company and a level are shown n Fgure 4. We dvde the data wth month-based granularty, and regard each month as a learnng task. In addton, we totally have seven statc features and three dynamc features, whch are summarzed n Table 2. Parameters. In the experments, the parameters λ r and λp are set as 2/#Tasks. Parameters λ 2, λ 3 λ 4, λ x, ξ r, ξ p, and α are set as 0., 0.0, 0.0, 0.0, 0.4, 0., and 5, respectvely. 4.2 Evaluaton Metrcs Due to the presence of censored data, we adopt wdely-used evaluaton metrc,.e., the concordance ndex (C-ndex), to measure the performance of predcton models n survval analyss [5, 0]. Suppose there are N test employees n testng data, r s the groundtruth career (or level) lfetme tme of the -th employee, and ˆr s the correspondng predcted lfetme. C-ndex s defned as, C ndex = Ω I [ˆr j > ˆr ], (24) R N t est &δ = r j >r (a) Data (b) Data (c) Data 2 (d) Data 2 Fgure 4: Hstograms of the career lfetme (left) and level lfetme (rght) for dfferent tranng and testng data. where I[x] s an ndcator functon that equals to f x s true, and equals to 0 otherwse. Ω s the total comparson number,.e., Ω = {, j R Nt est, δ =, r j > r }. In addton, we also evaluate model s performance n terms of weghted average AUC (WAUC), ndcatng whether an employee survves at a company (or a level) at each tme nterval [0]. WAUC s defned as follows, W AU C = k AU C () n () c k= n (), (25) c where k s the total task number, AUC () s the AUC value of the -th task, and n () c s the number of nstances n the testng data whch have an observed survval status n the -th tme nterval. Table 3: Settngs of the proposed models and varous baselne methods. Y ndcates the presence of censorshp, statc features ( StatFea ) or dynamc features ( DynFea ) n the model. N ndcates the absence. Method Censorng StatFea DynFea COX COX Y Y N Log-Logstc Y Y N Parametrc Log-gaussan Y Y N Webull Y Y N Exponental Y Y N M-LASSO N Y N M-L2, N Y N MTLSAV2 Y Y N MTLSA Y Y N Mult-task M-LASSO+DF N Y Y M-L2,+DF N Y Y MTLSAV2+DF Y Y Y MTLSA+DF Y Y Y CDT+SE Y Y Y CDT+DE Y Y Y 4.3 Baselne Methods To comprehensvely demonstrate the effectveness of our model, we compare t wth the followng models: COX [3], whch models the hazard functon n exp proportonal fashon and relates to a baselne hazard functon; Log-Logstc, Log-gaussan,Webull, and Exponental [6]: whch are popular parametrc survval models wth logstc, gaussan, webull, and exponental dstrbutons, respectvely; 922

7 Table 4: Performance comparson for turnover predcton based on two datasets. Method Data Data 2 C-ndex WAUC C-ndex WAUC COX Log-logstc Log-gaussan Webull Exponental M-LASSO M-L2, MTLSA.V MTLSA M-LASSO+DF M-L2,+DF MTLSAV2+DF MTLSA+DF CDT+SE CDT+DE M-LASSO [2], whch s a standard mult-task learnng model wth LASSO penalty, and only models uncensored data. M-L2, [2], whch s a standard mult-task learnng model wth l 2, -norm penalty, and only models uncensored data. MTLSAV2 [0], whch uses l 2, -norm mult-task learnng to model both censored and uncensored data. MTLSA [0], whch s desgned for survval analyss and places non-ncreasng constrant on MTLSAV2 model. All above baselne methods use statc features to tran model. Also, M-LASSO, M-L2,, MTLSAV2, and MTLSA are extended to ncorporate dynamc features as well and denoted as M-LASSO+DF, M-L2,+DF, MTLSAV2+DF, and MTLSA+DF, respectvely. The features for all baselne methods are represented by sparse embeddng. In the experments, our methods wth two feature representatons are denoted as CDT+SE for sparse embeddng, and CDT+DE for dense embeddng wth hdden dmenson sze as 0. The proposed methods and varous baselne methods are summarzed n Table Performance Comparson We frst evaluate the proposed methods for turnover behavor modelng and career progresson modelng. Then, we dscuss the nfluence of dfferent dynamc features on the above tasks Performance of Turnover Behavor Modelng. The performance of our models and varous baselne methods for predctng employee s turnover n terms of C-ndex and WAUC over two dfferent datasets are reported n Table 4. As mult-task learnng based methods can predct whether an employee wll survve at each tme nterval, they can be used to predct the lfetme and evaluated from C-ndex. From the results, we conclude the followng observatons. Frst, our models CDT+SE and CDT+DE outperform all baselne methods. For example, our method ncreases 5.6% and 4.9% over the best of all baselne methods n terms of C-ndex and WAUC on data, respectvely. The sgnfcant mprovement s due to the rankng constrants, whch help more accurately optmze the sum-of-squared error loss functon. The superor performance of our method over MTLSA+DF also demonstrates that Table 5: Performance comparson for career progresson predcton based on two datasets. Method Data Data 2 C-ndex WAUC C-ndex WAUC COX Log-logstc Log-gaussan Webull Exponental M-LASSO M-L2, MTLSAV MTLSA M-LASSO+DF M-L2,+DF MTLSAV2+DF MTLSA+DF CDT+SE CDT+DE the relaxed rankng constrant s better than drectly modelng the non-ncreasng property for survval analyss based on mult-task learnng formulaton. We also observe that CDT+DE s slghtly better than CDT+SE. Although optmzng X brngs a lttle mprovement, we observe that t easly overftts and ts result s not very stable n the experments because a large number of data are used to ft only a lmted number of features. Second, the performance of methods wth dynamc features are much better than the ones wthout dynamc features. Thrd, modelng censored data results n more accurate turnover behavor predcton, whch reflects on the performance comparson of M-LASSO*, M-L2,* and other multtask learnng based methods. Fourth, mult-task learnng based methods perform slghtly better than most parametrc survval models. Parametrc survval models are qute data-senstve, where the dstrbuton assumpton s specfcally desgned based on the emprcal data. Dfferent from them, mult-task models can convert the global censored classfcaton problem to a seres of local classfcaton problem, and thus acheve a comparatvely better result. Ffth, the results on data are totally better than the ones on data 2. The possble reason s that most employees n data have hstorcal observatons n the tranng set, whch helps generate more accurate predcton on ther career path observed n the testng set Performance of Career Progresson Modelng. In ths secton, we compare the model s performance on career progresson predcton wth focus on predctng when employee s level wll get changed next tme. As employee s level changes over tme, conventonal survval models (COX, Log-logstc, Log-gaussan, Webull, Exponental, MTLSA, and MTLSA+DF) cannot be drectly used to predct career progresson. To do ths, we utlze these methods to model each level changng event for each employee, and then use the traned model to predct testng data. For example, n employee s level lfetme records of Fgure 2, each level changng record s regarded as an nstance and the correspondng level wll be used as one statc feature. Smlar to our model, other multtask learnng based baselne methods (M-LASSO*, M-L2,*, and MTLSAV2*) can be used to ft the relatve level lfetme matrx P. 923

8 The performance of the proposed models and baselne methods for modelng employee s level changng s shown n Table 5. Based on the results, we can obtan the followng observatons. () Our models outperform all baselne models. Ths result clearly valdates the effectveness of our models n two aspects. Frst, t demonstrates the usefulness of mult-task learnng formulaton by predctng a relatve level at each tme nterval, whch s further justfed by the better results of M-LASSO*, M-L2,*, and MTLSAV2* over other conventonal survval baselne methods. Second, the rankng constrant does help to mprove the performance, whch reflects on the superor result of our model over MTLSAV2+DF method. (2) MTLSA* methods perform even worse than other multtask learnng based models for the sake of ts lmtaton of nonncreasng property whch s only sutable for non-recurrent events (a) C-ndex on Data for Turnover (b) WAUC on Data for Turnover Study of Dynamc Features. In ths secton, we study the nfluence of dfferent dynamc features on employee s career path modelng. We frst tran CDT+DE model wth all dynamc features, and then tran the model by removng each of them and check the performance change n terms of C-ndex and WAUC wth both datasets. The performance of the proposed method wth dfferent dynamc features s shown n Fgure 5. From the results, we can observe that model s performance decreases dramatcally wthout the feature of performance ratng. It ndcates that an employee s performance ratng plays an mportant role n her career path, and to some extend s able to affect the career status. Compared wth the mpact of an employee s performance ratng, the nfluence of report chan on her career path s a lttle weaker. There are two possble reasons for ths. Frst, n our data, there are only a small number of employees whose superors wll change more than one tmes, and the change of superors sometmes s caused by the decson of company s strategy rather than the personal reason of employees themselves. Thus, the superor changng has relatvely small mpact on employee s career path. Second, although the change of subordnates has sgnfcant nfluence on employee s career path as reflected on the observaton of Fgure 6 n Appendx, most employees do not have subordnates. Therefore, t s reasonable that modelng ths type of feature does not brng very sgnfcant mprovement. 5 RELATED WORK The related works about ths paper can be grouped nto two categores. The frst category s about mult-task learnng (MTL), whch learns multple related tasks smultaneously to mprove generalzaton performance [29, 32]. Early research work proposes LASSO regresson method to shrnk some coeffcents and requre others to be zero n order to retan some good features [6, 2]. MTL wth LASSO can be used to select some mportant features n each sngle task, but t gnores the relatedness of dfferent tasks. To capture the task relatedness, group lasso regularzaton based on l 2, -norm penalty for feature selecton s used to select features across all data ponts wth jont sparsty [2, 5, 30]. Totally, dfferent assumptons about how tasks are related lead to dfferent regularzaton terms. The second category throws lght on survval analyss [22, 25, 26, 28]. Cox proportonal hazards model [3, 4] s a popular technque n survval analyss due to ts smplcty and assumpton-free about 0.5 (c) C-ndex on Data 2 for Turnover 5 5 (e) C-ndex on Data for CP (g) C-ndex on Data 2 for CP (d) WAUC on Data 2 for Turnover (f) WAUC on Data for CP (h) WAUC on Data 2 for CP Fgure 5: The nfluence of dynamc features on turnover and career progresson predctons, where the results are obtaned usng CDT+DE model. ndcates all three types of dynamc features. 2, 3, and 4 ndcate all dynamc features other than performance ratng, the changed number of superors, and the changed number of subordnates, respectvely. CP represents career progresson. the survval tme. It determnes the hazard n a multplcatve manner assocated wth baselne hazard and some observed covarates. In addton to cox based survval model, another research lne for survval modelng s the parametrc survval model. It assumes that the survval tmes of all nstances n the dataset follow a partcular dstrbuton, such as log-logstc, log-normal, webull, and exponental dstrbutons [6]. There s a hypothess for above models,.e., the survval curve of all nstances shares a smlar shape. To overcome ths lmtaton, MTL based survval model [0] s developed to convert orgnal non-recurrent survval problem nto a seres of related bnary classfcaton problems, where the non-negatve and non-ncreasng lst constrants are mposed on the modelng process at the same tme. In ths paper, we propose a novel survval analyss approach for modelng the career paths of employees, wth a focus on two 924

9 crtcal ssues,.e., turnover and career progresson. Dfferent from the aforementoned methods, we formulate survval analyss nto a MTL problem wth rankng constrants, whch s sutable for general survval problem wth non-recurrent and recurrent events. Specfcally, based on the proposed framework, each task n turnover behavor modelng concerns the predcton of employment status at each tme nterval, and each task n career progresson predcton focuses on the predcton of a relatve level at each tme nterval. 6 CONCLUSION In ths paper, we proposed a novel survval analyss approach for modelng the career paths of employees, whch s based on multtask learnng wth rankng constrant formulaton. Wth dfferent rankng constrants and predcton targets, t s capable of modelng two crtcal ssues n talent management,.e., turnover and career progresson. Specfcally, for modelng the turnover behavors of employees, we formulated the predcton of survval status at a sequence of tme ntervals as a mult-task learnng problem by consderng the predcton at each tme nterval as a task. To model both censored and uncensored data, and capture the ntrnsc propertes exhbted n general lfetme modelng wth non-recurrent and recurrent events, we mposed the rankng constrants on each par of dfferent survval status labels. For modelng career progresson, we formulated the predcton of the relatve occupatonal level at each tme nterval as a task, where the rankng constrants mposed on dfferent levels are used to mprove the performance accuracy. Fnally, extensve expermental results on real-world talent data clearly valdated the effectveness of our models compared wth several state-of-the-art baselne methods n terms of varous evaluaton metrcs. ACKNOWLEDGMENTS Ths work s partally supported by the NIH (R2AA ) and NSFC ( , , , ). REFERENCES [] Jonathan Buckley and Ian James Lnear Regresson wth Censored Data. Bometrka 66, 3 (979), [2] Kenneth Burdett, Ncholas M. Kefer, and Sunl Sharma Layoffs and duraton dependence n a model of turnover. Journal of Econometrcs (985). [3] D. R. Cox Regresson Models and Lfe-Tables. Royal Statstcal Socety 34, 2 (972), [4] Komal Kapoor, Mngxuan Sun, Jadeep Srvastava, and Tao Ye A Hazard Based Approach to User Return Tme Predcton. In SIGKDD [5] Fasal M. Khan and Valentna Bayer Zubek Support Vector Regresson for Censored Data (SVRc): A Novel Tool for Survval Analyss. In ICDM. [6] Elsa T. Lee and John Wenyu Wang Statstcal Methods for Survval Data Analyss. Wley.com. [7] YUH-JYE Lee and O. L. Mangasaran SSVM: A Smooth Support Vector Machne for Classfcaton. Computatonal Optmzaton and Applcatons (200). [8] Huayu L, Yong Ge, Rchang Hong, and Hengshu Zhu Pont-of-Interest Recommendatons: Learnng Potental Check-ns from Frends. In KDD [9] Huayu L, Rchang Hong, Defu Lan, Zhang Wu, Meng Wang, and Yong Ge A Relaxed Rankng-Based Factor Model for Recommender System from Implct Feedback. In IJCAI [0] Yan L, Je Wang, Jepng Ye, and Chandan K. Reddy A Mult-Task Learnng Formulaton for Survval Analyss. In SIGKDD [] Hao Ln, Hengshu Zhu, Yuan Zuo, Chen Zhu, Hu Xong, and Junje Wu Collaboratve Company Proflng: Insghts from an Employee s Perspectve. In AAAI [2] Jun Lu, Shuwang J, and Jepng Ye Mult-Task Feature Learnng Va Effcent l2,-norm Mnmzaton. CoRR abs/ (202). [3] Ye Lu, Lumng Zhang, Lqang Ne, Yan Yan, and Davd S. Rosenblum Fortune Teller: Predctng Your Career Path. In AAAI [4] Taesup Moon, Alex Smola, Y Chang, and Zhaohu Zheng IntervalRank: Isotonc Regresson wth Lstwse and Parwse Constrants. In WSDM [5] Fepng Ne, Heng Huang, Xao Ca, and Chrs Dng Effcent and Robust Feature Selecton va Jont ℓ2,-norms Mnmzaton. In NIPS [6] Gullaume Oboznsk, Ben Taskar, and Mchael Jordan Mult-task feature selecton. In Techncal Report. [7] Steffen Rendle, Chrstoph Freudenthaler, Zeno Gantner, and Lars Schmdt- Theme BPR: Bayesan personalzed rankng from mplct feedback. In UAI [8] James E. Rosenbaum Tournament Moblty: Career Patterns n a Corporaton. Admnstratve Scence Quarterly 24, 2 (979), [9] Abbe J. Shpp, Stace Furst-Holloway, T. Brad Harrs, and Benson Rosen Gone today but here tomorrow: Extendng the unfoldng model of turnover to consder boomerang employees. PERSONNEL PSYCHOLOGY 67 (204), [20] Pannagadatta K. Shvaswamy, We Chu, and Martn Jansche A Support Vector Approach to Censored Targets. In ICDM [2] Robert Tbshran Regresson Shrnkage and Selecton Va the Lasso. Journal of the Royal Statstcal Socety 58 (994), [22] Wllam Trouleau, Azn Ashkan, Wecong Dng, and Bran Erksson Just One More: Modelng Bnge Watchng Behavor. In SIGKDD [23] Joseph Turan, Lev Ratnov, and Yoshua Bengo Word Representatons: A Smple and General Method for Sem-supervsed Learnng. In ACL [24] Kush R. Varshney, Vjl Chenthamarakshan, Scott W. Fancher, Jun Wang, Dongpng Fang, and Aleksandra Mojslovć Predctng Employee Expertse for Talent Management n the Enterprse. In SIGKDD [25] Jan Wang, Y Zhang, Chrstan Posse, and Anmol Bhasn Is It Tme for a Career Swtch?. In WSDM [26] Shu-Chen Wu A sem-markov model for survval data wth covarates. Mathematcal Boscences 60, 2 (982), [27] Huang Xu, Zhwen Yu, Jngyuan Yang, Hu Xong, and Zhu Hengshu Talent Crcle Detecton n Job Transton Networks. In SIGKDD [28] Janfe Zhang, Lfe Chen, Alan Vanasse, Josane Courteau, and Shengru Wang Survval Predcton by an Integrated Learnng Crteron on Intermttently Varyng Healthcare Data. In AAAI [29] Lang Zhao, Qan Sun, Jepng Ye, Feng Chen, Chang-Ten Lu, and Naren Ramakrshnan Mult-Task Learnng for Spato-Temporal Event Forecastng. In SIGKDD [30] Jayu Zhou, Le Yuan, Jun Lu, and Jepng Ye. 20. A Mult-task Learnng Formulaton for Predctng Dsease Progresson. In SIGKDD [3] Chen Zhu, Hengshu Zhu, Hu Xong, Penglang Dng, and Fang Xe Recrutment Market Trend Analyss wth Sequental Latent Varable Models. In SIGKDD [32] Hengshu Zhu, Hu Xong, Fangshuang Tang, Q Lu, Yong Ge, Enhong Chen, and Yanje Fu Days on Market: Measurng Lqudty n Real Estate Markets. In SIGKDD A Probablty IMPACT OF DYNAMIC FEATURES ON CAREER PATHS OF EMPLOYEES Turnover Prob. Level Changng Prob. 0 5 Performance Ratng (a) Probablty Probablty Turnover Prob. Level Changng Prob Number of Changed Superors Turnover Prob. Level Changng Prob. 0 <= >=4 Number of Changed Subordnates (c) Fgure 6: Probablty of turnover and level changng as a functon of performance ratng (a), number of changed subordnates (b) and number of changed superors (c). (b) 925