CostSensitive Learning by CostProportionate Example Weighting


 Nicholas Franklin
 1 years ago
 Views:
Transcription
1 CosSensiive Learning by CosProporionae Example Weighing Bianca Zadrozny, John Langford, Naoki Abe Mahemaical Sciences Deparmen IBM T. J. Wason Research Cener Yorkown Heighs, NY 0598 Absrac We propose and evaluae a family of mehods for convering classifier learning algorihms and classificaion heory ino cossensiive algorihms and heory. The proposed conversion is based on cosproporionae weighing of he raining examples, which can be realized eiher by feeding he weighs o he classificaion algorihm (as ofen done in boosing), or by careful subsampling. We give some heoreical performance guaranees on he proposed mehods, as well as empirical evidence ha hey are pracical alernaives o exising approaches. In paricular, we propose cosing, a mehod based on cosproporionae rejecion sampling and ensemble aggregaion, which achieves excellen predicive performance on wo publicly available daases, while drasically reducing he compuaion required by oher mehods. Inroducion Highly nonuniform misclassificaion coss are very common in a variey of challenging realworld daa mining problems, such as fraud deecion, medical diagnosis and various problems in business decisionmaking. In many cases, one class is rare bu he cos of no recognizing some of he examples belonging o his class is high. In hese domains, classifier learning mehods ha do no ake misclassificaion coss ino accoun do no perform well. In exreme cases, ignoring coss may produce a model ha is useless because i classifies every example as belonging o he mos frequen class even hough misclassificaions of he leas frequen class resul in a very large cos. Recenly a body of work has aemped o address his issue, wih echniques known as cossensiive learning in he machine learning and daa mining communiies. Curren cossensiive learning research falls ino hree caegories. The firs is concerned wih making paricular classifier learners cossensiive [3, 7]. The second uses Bayes risk heory o assign each example o is lowes risk This auhor s presen address: Toyoa Technological Insiue a Chicago, 47 Eas 60h Sree, Second Floor  Press Building, Chicago, IL class [, 9, 4]. This requires esimaing class membership probabiliies and, in he case where coss are nondeerminisic, also requires esimaing expeced coss [9]. The hird caegory concerns mehods for convering arbirary classificaion learning algorihms ino cossensiive ones []. The work described here belongs o he las caegory. In paricular, he approach here is akin o he pioneering work of Domingos on MeaCos [], which also is a general mehod for convering cossensiive learning problems o cosinsensiive learning problems. However, he mehod here is disinguished by he following properies: () i is even simpler; () i has some heoreical performance guaranees; and (3) i does no involve any probabiliy densiy esimaion in is process: MeaCos esimaes condiional probabiliy disribuions via bagging wih a classifier in is procedure, and as such i also belongs o he second caegory (Bayes risk minimizaion) menioned above. The family of proposed mehods is moivaed by a folk heorem ha is formalized and proved in secion.. This heorem saes ha alering he original example disribuion D o anoher ˆD, by muliplying i by a facor proporional o he relaive cos of each example, makes any errorminimizing classifier learner accomplish expeced cos minimizaion on he original disribuion. Represening samples drawn from ˆD, however, is more challenging han i may seem. There are wo basic mehods for doing his: (i) Transparen Box: Supply he coss of he raining daa as example weighs o he classifier learning algorihm. (ii) Black Box: resample according o hese same weighs. While he ransparen box approach canno be applied o arbirary classifier learners, i can be applied o many, including any classifier which only uses he daa o calculae expecaions. We show empirically ha his mehod gives good resuls. The black box approach has he advanage ha i can be applied o any classifier learner. I urns ou, however, ha sraighforward samplingwihreplacemen can resul in severe overfiing relaed o duplicae examples. We propose, insead, o employ cosproporionae rejecion sampling o realize he laer approach, which allows us o independenly draw examples according o ˆD. This mehod comes wih a heoreical guaranee: In he wors case i produces a classifier ha achieves a leas as good
2 approximae cos minimizaion as applying he base classifier learning algorihm on he enire sample. This is a remarkable propery for a subsampling scheme: in general, we expec any echnique using only a subse of he examples o compromise predicive performance. The runime savings made possible by his sampling echnique enable us o run he classificaion algorihm on muliple draws of subsamples and average over he resuling classifiers. This las mehod is wha we call cosing (cosproporionae rejecion sampling wih aggregaion). Cosing allows us o use an arbirary cosinsensiive learning algorihm as a black box in order o accomplish cossensiive learning, achieves excellen predicive performance and can achieve drasic savings of compuaional resources. Moivaing Theory and Mehods. A Folk Theorem We assume ha examples are drawn independenly from a disribuion D wih domain X Y C where X is he inpu space o a classifier, Y is a (binary) oupu space and C 0 is he imporance (exra cos) associaed wih mislabeling ha example. The goal is o learn a classifier h : X Y which minimizes he expeced cos, E x y c D ci h x given raining daa of he form: x y c, where I is he indicaor funcion ha has value in case is argumen is rue and 0 oherwise. This model does no explicily allow using cos informaion a predicion ime alhough X migh include a cos feaure if ha is available. This formulaion of cossensiive learning in erms of one number per example is more general han cos marix formulaions which are more ypical in cossensiive learning [6, ], when he oupu space is binary. In he cos marix formulaion, coss are associaed wih false negaive, false posiive, rue negaive, and rue posiive predicions. Given he cos marix and an example, only wo enries (false posiive, rue negaive) or (false negaive, rue posiive) are relevan for ha example. These wo numbers can be furher reduced o one: (false posiive  rue negaive) or (false negaive  rue posiive), because i is he difference in cos beween classifying an example correcly or incorrecly which conrols he imporance of correc classificaion. This difference is he imporance c we use here. This seing is more general in he sense ha he imporance may vary on a examplebyexample basis. A basic folk heorem saes ha if we have examples drawn from he disribuion: c ˆD x y c D x y c E x y c D c How o formulae he problem in his way when he oupu space is no binary is nonrivial and is beyond he scope of his paper. We say folk heorem here because he resul appears o be known by some and i is sraighforward o derive i from resuls in decision heory, alhough we have no found i published. y hen opimal error rae classifiers for ˆD are opimal cos minimizers for daa drawn from D. Theorem.. (Translaion Theorem) For all disribuions, D, here exiss a consan N E x y c D c such ha for all classifiers, h: Proof. E x y c ˆD I h x y N E x y c D ci h x E x y c D ci h x y y D x y c ci h x y x y c N x y c NE x y c ˆD I h x y where ˆD x y c c D x y c N ˆD x y c I h x y Despie is simpliciy, his heorem is useful o us because he righhand side expresses he expecaion we wan o conrol (via he choice of h) and he lefhand side is he probabiliy ha h errs under anoher disribuion. Choosing h o minimize he rae of errors under ˆD is equivalen o choosing h o minimize he expeced cos under D. Similarly, εapproximae error minimizaion under ˆD is equivalen o Nεapproximae cos minimizaion under D. The prescripion for coping wih cossensiive problems is sraighforward: reweigh he disribuion in your raining se according o he imporances so ha he raining se is effecively drawn from ˆD. Doing his in a correc and general manner is more challenging han i may seem and is he opic of he res of he paper.. Transparen Box: Using Weighs Direcly.. General conversion Here we examine how imporance weighs can be used wihin differen learning algorihms o accomplish cossensiive classificaion. We call his he ransparen box approach because i requires knowledge of he paricular learning algorihm (as opposed o he black box approach ha we develop laer). The mechanisms for realizing he ransparen box approach have been described elsewhere for a number of weak learners used in boosing, bu we will describe hem here for compleeness. The classifier learning algorihm mus use he weighs so ha i effecively learns from daa drawn according o ˆD. This requiremen is easy o apply for all learning algorihms which fi he saisical query model [3]. As shown in figure, many learning algorihms can be divided ino wo componens: a porion which calculaes he (approximae) expeced value of some funcion (or query) f and a porion which forms hese queries and uses heir oupu o consruc a classifier. For example, neural neworks, decision rees, and Naive Bayes classifiers can be
3 Learning Algorihm Query/Reply Pairs Query Oracle Figure. The saisical query model. consruced in his manner. Suppor vecor machines are no easily consrucible in his way, because he individual classifier is explicily dependen upon individual examples raher han on saisics derived from he enire sample. Wih finie daa we canno precisely calculae he expecaion E x y D f x y. Wih high probabiliy, however, we can approximae he expecaion given a se of examples drawn independenly from he underlying disribuion D. Whenever we have a learning algorihm ha can be decomposed as in figure, here is a simple recipe for using he weighs direcly. Insead of simulaing he expecaion wih S x y S f x y, we use x y c S c x y c S c f x y. This mehod is equivalen o imporance sampling for ˆD using he disribuion D, and so he modified expecaion is an unbiased Mone Carlo esimae of he expecaion w.r.. ˆD. Even when a learning algorihm does no fi his model, i may be possible o incorporae imporance weighs direcly. We now discuss how o incorporae imporance weighs ino some specific learning algorihms... Naive Bayes and boosing Naive Bayes learns by calculaing empirical probabiliies for each oupu y using Bayes rule and assuming ha each feaure is independen given he oupu: P y x P x y P y P x i P x i y P y i P x i Each probabiliy esimae in he above expression can be hough of as a funcion of empirical expecaions according o D, and hus i can be formulaed in he saisical query model. For example, P x i y is jus he expecaion of I x i x i I y y divided by he expecaion of I y y. More specifically, o compue he empirical esimae of P x i y wih respec o D, we need o coun he number of raining examples ha have y as oupu, and hose having x i as he ih inpu dimension among hose. When we compue hese empirical esimaes wih respec o ˆD, we simply have o sum he weigh of each example, insead of couning he examples. (This propery is used in he implemenaion of boosed Naive Bayes [5].) To incorporae imporance weighs ino AdaBoos [8], we give he imporance weighs o he weak learner in he firs ieraion, hus effecively drawing examples from ˆD. In he subsequen ieraions, we use he sandard AdaBoos rule o updae he weighs. Therefore, he weighs are adjused according o he accuracy on ˆD, which corresponds o he expeced cos on D...3 C4.5 C4.5 [6] is a widely used decision ree learner. There is a sandard way of incorporaing example weighs o i, which in he original algorihm was inended o handle missing aribues (examples wih missing aribues were divided ino fracional examples, each wih a smaller weigh, during he growh of he ree). This same faciliy was laer used by Quinlan in he implemenaion of boosed C4.5 [5]...4 Suppor Vecor Machine The SVM algorihm [] learns he parameers a and b describing a linear decision rule h x sign a x b, so ha he smalles disance beween each raining example and he decision boundary (he margin) is maximized. I works by solving he following opimizaion problem: a a C n i ξ i subjec o: i : y i a x i b ξ i ξ i 0 minimize: V a b ξ The consrains require ha all examples in he raining se are classified correcly up o some slack ξ i. If a raining example lies on he wrong side of he decision boundary, he corresponding ξ i is greaer han. Therefore, n i ξ i is an upper bound on he number of raining errors. The facor C is a parameer ha allows one o rade off raining error and model complexiy. The algorihm can be generalized o nonlinear decision rules by replacing inner producs wih a kernel funcion in he formulas above. The SVM algorihm does no fi he saisical query model. Despie his, i is possible o incorporae imporance weighs in a naural way. Firs, we noe ha n i c iξ i, where c i is he imporance of example i, is an upper bound on he oal cos. Therefore, we can modify V a b ξ o V a b ξ a a C n i c iξ i Now C conrols model complexiy versus oal cos. The SVMLigh package [0] allows users o inpu weighs c i and works wih he modified V a b ξ as above, alhough his feaure has no ye been documened..3 Black Box: Sampling mehods Suppose we do no have ransparen box access o he learner. In his case, sampling is he obvious mehod o conver from one disribuion of examples o anoher o obain a cossensiive learner using he ranslaion heorem (Theorem.). As i urns ou, sraighforward sampling does no work well in his case, moivaing us o propose an alernaive mehod based on rejecion sampling.
4 .3. Samplingwihreplacemen Samplingwihreplacemen is a sampling scheme where each example x y c is drawn according o he disribuion p x y c c x y c S c. Many examples are drawn o creae a new daase S. This mehod, a firs pass, appears useful because every example is effecively drawn from he disribuion ˆD. In fac, very poor performance can resul when using his echnique, which is essenially due o overfiing because of he fac ha he examples in S are no drawn independenly from ˆD, as we will elaborae in he secion on experimenal resuls (Secion 3). Samplingwihoureplacemen is also no a soluion o his problem. In samplingwihoureplacemen, an example x y c is drawn from he disribuion p x y c c x y c S c and he nex example is drawn from he se S x y c. This process is repeaed, drawing from a smaller and smaller se according o he weighs of he examples remaining in he se. To see how his mehod fails, noe ha samplingwihoureplacemen m imes from a se of size m resuls in he original se, which (by assumpion) is drawn from he disribuion D, and no ˆD as desired..3. Cosproporionae rejecion sampling There is anoher sampling scheme called rejecion sampling [8] which allows us o draw examples independenly from he disribuion ˆD, given examples drawn independenly from D. In rejecion sampling, examples from ˆD are obained by firs drawing examples from D, and hen keeping (or acceping) he sample wih probabiliy proporional o ˆD D. Here, we have ˆD D c, so we accep an example wih probabiliy c Z, where Z is some consan chosen so ha max x y c S c Z, 3 leading o he name cosproporionae rejecion sampling. Rejecion sampling resuls in a se S which is generally smaller han S. Furhermore, because inclusion of an example in S is independen of oher examples, and he examples in S are drawn independenly, we know ha he examples in S are disribued independenly according o ˆD. Using cosproporionae rejecion sampling o creae a se S and hen using a learning algorihm A S is guaraneed o produce an approximaely cosminimizing classifier, as long as he learning algorihm A achieves approximae minimizaion of classificaion error. Theorem.. (Correcness) For all cossensiive sample ses S, if cosproporionae rejecion sampling produces a sample se S and A S achieves ε classificaion error: E x y c ˆD I h x y ε 3 In pracice, we choose Z max x y w S c so as o maximize he size of he se S. A daadependen choice of Z is no formally allowed for rejecion sampling. However, he inroduced bias appears small when S. A precise measuremen of small is an ineresing heoreical problem. hen h A S approximaely minimizes cos: E x y c D ci h x y εn where N E x y c D c. Proof. Rejecion sampling produces a sample se S drawn independenly from ˆD. By assumpion A S oupus a classifier h such ha E x y c ˆD I h x y ε By he ranslaion heorem (Theorem.), we know ha E x y c ˆD I h x y N E x y c D ci h x y Thus, E x y c D ci h x y εn.3.3 Sample complexiy of cosproporionae rejecion sampling The accuracy of a learned classifier generally improves monoonically wih he number of examples in he raining se. Since cosproporionae rejecion sampling produces a smaller raining se (by a facor of abou N Z), one would expec worse performance han using he enire raining se. This urns ou o no be he case, in he agnosic PAClearning model [7, ], which formalizes he noion of probably approximaely opimal learning from arbirary disribuions D. Definiion.. A learning algorihm A is said o be an agnosic PAClearner for hypohesis class H, wih sample complexiy m ε δ if for all ε 0 and δ 0, m m ε δ is he leas sample size such ha for all disribuions D (over X Y), he classificaion error rae of is oupu h is a mos ε more han he bes achievable by any member of H wih probabiliy a leas δ, whenever he sample size exceeds m. By analogy, we can formalize he noion of cossensiive agnosic PAClearning. Definiion.. A learning algorihm A is said o be a cossensiive agnosic PAClearner for hypohesis class H, wih cossensiive sample complexiy m ε δ, if for all ε 0 and δ 0, m m ε δ is he leas sample size such ha for all disribuions D (over X Y C), he expeced cos of is oupu h is a mos ε more han he bes achievable by any member of H wih probabiliy a leas δ, whenever he sample size exceeds m. We will now use his formalizaion o compare he cossensiive PAClearning sample complexiy of wo mehods: applying a given base classifier learning algorihm o a sample obained hrough cosproporionae rejecion sampling, and applying he same algorihm on he original raining se. We show ha he cossensiive sample complexiy of he laer mehod is lowerbounded by ha of he former.
5 Theorem.3. (Sample Complexiy Comparison) Fix an arbirary base classifier learning algorihm A, and suppose ha m orig ε δ and m rej ε δ, respecively, are cossensiive sample complexiy of applying A on he original raining se, and ha of applying A wih cosproporionae rejecion sampling. Then, we have m orig ε δ Ω m rej ε δ Proof. Le m ε δ be he (cosinsensiive) sample complexiy of he base classifier learning algorihm A. (If no such funcion exiss, hen neiher m orig ε δ nor m rej ε δ exiss, and he heorem holds vacuously.) Since Z is an upper bound on he cos of misclassifying an example, we have ha he cossensiive sample complexiy of using he original raining se saisfies m orig ε δ Θ m Z ε δ This is because given a disribuion ha forces ε more classificaion error han opimal, anoher disribuion can be consruced, ha forces εz more cos han opimal, by assigning cos Z o all examples on which A errs. Now from Theorem. and noing ha he cenral limi heorem implies ha cosproporionae rejecion sampling reduces he sample size by a facor of Θ N Z, he cossensiive sample complexiy for rejecion sampling is: m rej ε δ () δ Z Θ m N ε N A fundamenal heorem from PAClearning heory saes ha m ε δ Ω ε ln δ [4]. When m ε δ Θ ε ln δ δ, Equaion Θ () implies: δ m rej ε δ Z N Θ ln m orig ε N ε Finally, noe ha when m ε δ grows faser han linear in ε, we have m rej ε δ o m orig ε δ, which finishes he proof. Noe ha he linear dependence of sample size on ε is only achievable by an ideal learning algorihm, and in pracice superlinear dependence is expeced, especially in he presence of noise. Thus, he above heorem implies ha cosproporionae rejecion sampling minimizes cos beer han no sampling for wors case disribuions. This is a remarkable propery abou any sampling scheme, since one generally expecs ha predicive performance is compromised by using a smaller sample. Cosproporionae rejecion sampling seems o disill he original sample and obains a sample of smaller size, which is a leas as informaive as he original..3.4 Cosproporionae rejecion sampling wih aggregaion (cosing) From he same original raining sample, differen runs of cosproporionae rejecion sampling will produce differen raining samples. Furhermore, he fac ha rejecion sampling produces very small samples means ha he ime required for learning a classifier is generally much smaller. We can ake advanage of hese properies o devise an ensemble learning algorihm based on repeaedly performing rejecion sampling from S o produce muliple sample ses S S m, and hen learning a classifier for each se. The oupu classifier is he average over all learned classifiers. We call his echnique cosing: Cosing(Learner A, Sample Se S, coun ). For i o do (a) S rejecion sample from S wih accepance probabiliy c Z. (b) Le h i A S. Oupu h x sign i h i x The goal in averaging is o improve performance. There is boh empirical and heoreical evidence suggesing ha averaging can be useful. On he empirical side, many people have observed good performance from bagging despie hrowing away a e fracion of he samples. On he heoreical side, here has been considerable work which proves ha he abiliy o overfi of an average of classifiers migh be smaller han naively expeced when a large margin exiss. The preponderance of learning algorihms producing averaging classifiers provides significan evidence ha averaging is useful. Noe ha despie he exra compuaional cos of averaging, he overall compuaional ime of cosing is generally much smaller han ha of a learning algorihm using sample se S (wih or wihou weighs). This is he case because mos learning algorihms have running imes ha are superlinear in he number of examples. 3 Empirical evaluaion We show empirical resuls using wo realworld daases. We seleced daases ha are publicly available and for which cos informaion is available on a per example basis. Boh daases are from he direc markeing domain. Alhough here are many oher daa mining domains ha are cossensiive, such as credi card fraud deecion and medical diagnosis, publicly available daa are lacking. 3. The daases used 3.. KDD98 daase This is he wellknown and challenging daase from he KDD98 compeiion, now available a he UCI KDD reposiory [9]. The daase conains informaion abou persons who have made donaions in he pas o a paricular chariy. The decisionmaking ask is o choose which donors o mail a reques for a new donaion. The measure of success is he oal profi obained in he mailing campaign.
6 The daase is divided in a fixed way ino a raining se and a es se. Each se consiss of approximaely records for which i is known wheher or no he person made a donaion and how much he person donaed, if a donaion was made. The overall percenage of donors is abou 5%. Mailing a soliciaion o an individual coss he chariy $0 68. The donaion amoun for persons who respond varies from $ o $00. The profi obained by soliciing every individual in he es se is $0560, while he profi aained by he winner of he KDD98 compeiion was $47. The imporance of each example is he absolue difference in profi beween mailing and no mailing an individual. Mailing resuls in he donaion amoun minus he cos of mailing. No mailing resuls in zero profi. Thus, for posiive examples (respondens), he imporance varies from $0 3 o $99 3. For negaive examples (nonrespondens), i is fixed a $ DMEF daase This daase can be obained from he DMEF daase library [] for a nominal fee. I conains cusomer buying hisory for 9655 cusomers of a naionally known caalog. The decisionmaking ask is o choose which cusomers should receive a new caalog so as o maximize he oal profi on he caalog mailing campaign. Informaion on he cos of mailing a caalog is no available, so we fixed i a $. The overall percenage of respondens is abou.5%. The purchase amoun for cusomers who respond varies from $3 o $647. As is he case for he KDD98 daase, he imporance of each example is he absolue difference in profi beween mailing and no mailing a cusomer. Therefore, for posiive examples (respondens), he imporance varies from $ o $645. For negaive examples (nonrespondens), i is fixed a $. We divided he daase in half o creae a raining se and a es se. As a baseline for comparison, he profi obained by mailing a caalog o every individual on he raining se is $6474 and on he es se is $ Experimenal resuls 3.. Transparen box resuls Table (op) shows he resuls for Naive Bayes, boosed Naive Bayes (00 ieraions) C4.5 and SVMLigh on he KDD98 and DMEF daases, wih and wihou he imporance weighs. Wihou he imporance weighs, he classifiers label very few of he examples posiive, resuling in small (and even negaive) profis. Wih he coss given as weighs o he learners, he resuls improve significanly for all learners, excep C4.5. Cossensiive boosed Naive Bayes gives resuls comparable o he bes so far wih his daase [9] using more complicaed mehods. We opimized he parameers of he SVM by crossvalidaion on he raining se. Wihou weighs, no seing of he parameers prevened he algorihm of labeling all examples as negaives. Wih weighs, he bes parameers were KDD98: Mehod Wihou Weighs Wih Weighs Naive Bayes Boosed NB C SVMLigh DMEF: Mehod Wihou Weighs Wih Weighs Naive Bayes Boosed NB 3638 C SVMLigh Table. Tes se profis wih ransparen box. a polynomial kernel wih degree 3 and C for KDD98 and a linear kernel wih C for DMEF. However, even wih his parameer seing, he resuls are no so impressive. This may be a hard problem for marginbased classifiers because he daa is very noisy. Noe also ha running SVMLigh on his daase akes abou 3 orders of magniude longer han AdaBoos wih 00 ieraions. The failure of C4.5 o achieve good profis wih imporance weighs is probably relaed o he fac ha he faciliy for incorporaing weighs provided in he algorihm is heurisic. So far, i has been used only in siuaions where he weighs are fairly uniform (such as is he case for fracional insances due o missing daa). These resuls indicae ha i migh no be suiable for siuaions wih highly nonuniform coss. The fac ha i is nonrivial o incorporae coss direcly ino exising learning algorihms is he moivaion for he black box approaches ha we presen here. 3.. Black box resuls Table shows he resuls of applying he same learning algorihms o he KDD98 and DMEF daa using raining ses of differen sizes obained by samplingwihreplacemen. For each size, we repea he experimens 0 imes wih differen sampled ses o ge mean and sandard error (in parenheses). The raining se profis are on he original raining se from which we draw he sampled ses. The resuls confirm ha applicaion of samplingwihreplacemen o implemen he black box approach can resul in very poor performance due o overfiing. When here are large differences in he magniude of imporance weighs, i is ypical for an example o be picked wice (or more). In able, we see ha as we increase he sampled raining se size and, as a consequence, he number of duplicae examples in he raining se, he raining profi becomes larger while he es profi becomes smaller for C4.5. Examples which appear muliple imes in he raining se of a learning algorihm can defea complexiy conrol mechanisms buil ino learning algorihms For example, suppose ha we have a decision ree algorihm which divides he raining daa ino a growing se (used o consruc a ree)
7 KDD98: Training Tes Training Tes Training Tes NB 5 (330) 0850 (35) 8 (55) 993 (85) 53 (4) 06 (56) BNB 658 (3) 76 (383) 3838 (65) 886 () 407 (5) 335 (59) C4.5 4 (55) 9548 (33) 083 (7) 7599 (30) (5) 59 (07) SVM 030 (37) 03 (8) 8 (8) 05 (6) 3565 (9) 808 (0) DMEF: Training Tes Training Tes Training Tes NB 3398 (495) 3464 (49) 374 (793) (798) 335 (475) (405) BNB 3390 (558) (660) 3480 (806) 334 (77) (8) 3889 (733) C (467) 40 (93) (763) 988 (458) 7574 (05) 349 (59) SVM 8837 (09) 3077 (96) 363 () 3585 (89) (79) (600) Table. Profis using samplingwihreplacemen. and a pruning se (used o prune he ree for complexiy conrol purposes). If he pruning se conains examples which appear in he growing se, he complexiy conrol mechanism is defeaed. Alhough no as markedly as for C4.5, we see he same phenomenon for he oher learning algorihms. In general, as he size of he resampled size grows, he larger is he difference beween raining se profi and es se profi. And, even wih examples, we do no obain he same es se resuls as giving he weighs direcly o Boosed Naive Bayes and SVM. The fundamenal difficuly here is ha he samples in S are no drawn independenly from ˆD. In paricular, if ˆD is a densiy, he probabiliy of observing he same example wice given independen draws is 0, while he probabiliy using samplingwihreplacemen is greaer han 0. Thus samplingwihreplacemen fails because he sampled se S is no consruced independenly. Figure shows he resuls of cosing on he KDD98 and DMEF daases, wih he base learners and Z 00 or Z 647, respecively. We repeaed he experimen 0 imes for each and calculaed he mean and sandard error of he profi. The resuls for, 00 and 00 are also given in able 3. In he KDD98 case, each resampled se has only abou 600 examples, because he imporance of he examples varies from 0.68 o 99.3 and here are few imporan examples. Abou 55% of he examples in each se are posiive, even hough on he original daase he percenage of posiives is only 5%. Wih 00, he C4.5 version yields profis around $5000, which is excepional performance for his daase. In he DMEF case, each se has only abou 35 examples, because he imporances vary even more widely (from o 646) and here are even fewer examples wih a large imporance han in he KDD98 case. The percenage of posiive examples in each se is abou 50%, even hough on he original daase i was only.5%. For learning he SVMs, we used he same kernels as we did in secion. and he defaul seing for C. In ha KDD98: NB 667 (9) 3 (0) 363 (68) BNB 377 (63) 489 (9) 474 (6) C (5) 4935 (0) 506 (6) SVM 004 (393) 3075 (4) 35 (56) DMEF: NB 687 (3444) 3767 (335) 3769 (39) BNB 440 (839) (393) 3789 (364) C (345) 3699 (374) (307) SVM 7 (3487) (5) 3590 (849) Table 3. Tes se profis using cosing. secion, we saw ha by feeding he weighs direcly o he SVM, we obain a profi of $3683 on he KDD98 daase and of $36443 on he DMEF daase. Here, we obain profis around $300 and $35000, respecively. However, his did no require parameer opimizaion and, even wih 00, was much faser o rain. The reason for he speedup is ha he ime complexiy of SVM learning is generally superlinear in he number of raining examples. 4 Discussion Cosing is a echnique which produces a cossensiive classificaion from a cosinsensiive classifier using only black box access. This simple mehod is fas, resuls in excellen performance and ofen achieves drasic savings in compuaional resources, paricularly wih respec o space requiremens. This las propery is especially desirable in applicaions of cossensiive learning o domains ha involve massive amoun of daa, such as fraud deecion, argeed markeing, and inrusion deecion. Anoher desirable propery of any reducion is ha i applies o he heory as well as o concree algorihms. Thus, he reducion presened in he presen paper allows us o auomaically apply any fuure resuls in cosinsensiive classificaion o cossensiive classificaion. For example, a
8 KDD98: x 0 4 Cosing NB: KDD 98 Daase x 0 4 Cosing BNB: KDD 98 Daase x 0 4 Cosing C45: KDD 98 Daase x 0 4 Cosing SVM: KDD 98 Daase Profi. Profi. Profi. Profi x Cosing NB: DMEF Daase DMEF: 4 x Cosing BNB: DMEF Daase 04 4 x Cosing C4.5: DMEF Daase x Cosing SVM: DMEF Daase Profi 3.8 Profi 3.8 Profi 3.8 Profi Figure. Cosing: es se profi vs. number of sampled ses. bound on he fuure error rae of A S implies a bound on he expeced cos wih respec o he disribuion D. This addiional propery of a reducion is especially imporan because cossensiive learning heory is sill young and relaively unexplored. One direcion for fuure work is muliclass cossensiive learning. If here are K classes, he minimal represenaion of coss is K weighs. A reducion o cosinsensiive classificaion using hese weighs is an open problem. References [] Anifanis, S. The DMEF Daa Se Library. The Direc Markeing Associaion, New York, NY, 00. [hp://www.hedma.org/dmef/dmefdse.shml] [] Domingos, P. MeaCos: A general mehod for making classifiers cos sensiive. Proceedings of he 5h Inernaional Conference on Knowledge Discovery and Daa Mining, 5564, 999. [3] Drummond, C. & Hole, R. Exploiing he cos (in)sensiiviy of decision ree spliing crieria. Proceedings of he 7h Inernaional Conference on Machine Learning, 3946, 000. [4] Ehrenfeuch, A., Haussler, D., Kearns, M. & Valian. A general lower bound on he number of examples needed for learning. Informaion and Compuaion, 8:3, 476, 989. [5] Elkan, C. Boosing and naive bayesian learning (Technical Repor). Universiy of California, San Diego, 997. [6] Elkan, C. The foundaions of cossensiive learning. Proceedings of he 7h Inernaional Join Conference on Arificial Inelligence, , 00. [7] Fan, W., Solfo, S., Zhang, J. & Chan, P. AdaCos: Misclassificaion cossensiive boosing. Proceedings of he 6h Inernaional Conference on Machine Learning, 9705, 999. [8] Freund, Y. & Schapire, R. E. A decisionheoreic generalizaion of online learning and an applicaion o boosing. Journal of Compuer and Sysem Sciences, 55:, 939, 997. [9] Heich, S. & Bay, S. D. The UCI KDD Archive. Universiy of California, Irvine. [hp://kdd.ics.uci.edu/]. [0] Joachims, T. Making largescale SVM learning pracical. In Advances in Kernel Mehods  Suppor Vecor Learning. MIT Press, 999. [] Joachims, T. Esimaing he generalizaion performance of a SVM efficienly. Proceedings of he 7h Inernaional Conference on Machine Learning, , 000. [] Kearns, M., Schapire, R., & Sellie, L. Toward Efficien Agnosic Learning. Machine Learning, 7, 54, 998. [3] Kearns, M. Efficien noiseoleran learning from saisical queries. Journal of he ACM, 45:6, , 998. [4] Margineanu, D. Class probabiliy esimaion and cossensiive classificaion decisions. Proceedings of he 3h European Conference on Machine Learning, 708, 00. [5] Quinlan, J. R. Boosing, Bagging, and C4.5. Proceedings of he Thireenh Naional Conference on Arificial Inelligence, , 996. [6] Quinlan, J. R. C4.5: Programs for Machine Learning. San Maeo, CA: Morgan Kaufmann, 993. [7] Valian, L. A heory of he learnable. Communicaions of he ACM, 7:, 344, 984. [8] von Neumann, J. Various echniques used in connecion wih random digis, Naional Bureau of Sandards, Applied Mahemaics Series,, 3638, 95. [9] Zadrozny, B. and Elkan, C. Learning and making decisions when coss and probabiliies are boh unknown. Proceedings of he 7h Inernaional Conference on Knowledge Discovery and Daa Mining, 033, 00.
PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationPrice elasticity of demand for crude oil: estimates for 23 countries
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationTask is a schedulable entity, i.e., a thread
RealTime Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T:  s: saring poin  e: processing ime of T  d: deadline of T  p: period of T Periodic ask T
More informationMultiprocessor SystemsonChips
Par of: Muliprocessor SysemsonChips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationRealtime Particle Filters
Realime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationA Short Introduction to Boosting
Journal of Japanese Sociey for Arificial Inelligence,14(5):771780, Sepember, 1999. (In Japanese, ranslaion by Naoki Abe.) A Shor Inroducion o Boosing Yoav Freund Rober E. Schapire AT&T Labs Research Shannon
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationDistributing Human Resources among Software Development Projects 1
Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationUSE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES
USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were
More informationSPEC model selection algorithm for ARCH models: an options pricing evaluation framework
Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationPredicting Stock Market Index Trading Signals Using Neural Networks
Predicing Sock Marke Index Trading Using Neural Neworks C. D. Tilakarane, S. A. Morris, M. A. Mammadov, C. P. Hurs Cenre for Informaics and Applied Opimizaion School of Informaion Technology and Mahemaical
More informationMaking a Faster Cryptanalytic TimeMemory TradeOff
Making a Faser Crypanalyic TimeMemory TradeOff Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationSupplementary Appendix for Depression Babies: Do Macroeconomic Experiences Affect RiskTaking?
Supplemenary Appendix for Depression Babies: Do Macroeconomic Experiences Affec RiskTaking? Ulrike Malmendier UC Berkeley and NBER Sefan Nagel Sanford Universiy and NBER Sepember 2009 A. Deails on SCF
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationA Reexamination of the Joint Mortality Functions
Norh merican cuarial Journal Volume 6, Number 1, p.166170 (2002) Reeaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationAn Online Learningbased Framework for Tracking
An Online Learningbased Framework for Tracking Kamalika Chaudhuri Compuer Science and Engineering Universiy of California, San Diego La Jolla, CA 9293 Yoav Freund Compuer Science and Engineering Universiy
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationMarket Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand
36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,
More informationTowards IncentiveCompatible Reputation Management
Towards InceniveCompaible Repuaion Managemen Radu Jurca, Boi Falings Arificial Inelligence Laboraory Swiss Federal Insiue of Technology (EPFL) INEcublens, 115 Lausanne, Swizerland radu.jurca@epfl.ch,
More informationOption PutCall Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 22523 Opion Puall Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationStock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783
Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic
More informationOn the degrees of irreducible factors of higher order Bernoulli polynomials
ACTA ARITHMETICA LXII.4 (1992 On he degrees of irreducible facors of higher order Bernoulli polynomials by Arnold Adelberg (Grinnell, Ia. 1. Inroducion. In his paper, we generalize he curren resuls on
More informationWorking Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits
Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion
More informationAnalysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer
Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationInformation Theoretic Evaluation of Change Prediction Models for LargeScale Software
Informaion Theoreic Evaluaion of Change Predicion Models for LargeScale Sofware Mina Askari School of Compuer Science Universiy of Waerloo Waerloo, Canada maskari@uwaerloo.ca Ric Hol School of Compuer
More informationSampling TimeBased Sliding Windows in Bounded Space
Sampling TimeBased Sliding Windows in Bounded Space Rainer Gemulla Technische Universiä Dresden 01062 Dresden, Germany gemulla@inf.udresden.de Wolfgang Lehner Technische Universiä Dresden 01062 Dresden,
More informationPATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM
PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationAppendix D Flexibility Factor/Margin of Choice Desktop Research
Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\22348900\4
More informationPerformance Center Overview. Performance Center Overview 1
Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationThe Kinetics of the Stock Markets
Asia Pacific Managemen Review (00) 7(1), 14 The Kineics of he Sock Markes Hsinan Hsu * and BinJuin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he
More informationSELFEVALUATION FOR VIDEO TRACKING SYSTEMS
SELFEVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD20742 {wh2003, qinfen}@cfar.umd.edu
More informationCaring for trees and your service
Caring for rees and your service Line clearing helps preven ouages FPL is commied o delivering safe, reliable elecric service o our cusomers. Trees, especially palm rees, can inerfere wih power lines and
More informationEfficient Onetime Signature Schemes for Stream Authentication *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, 61164 (006) Efficien Oneime Signaure Schemes for Sream Auhenicaion * YONGSU PARK AND YOOKUN CHO + College of Informaion and Communicaions Hanyang Universiy
More informationCointegration: The Engle and Granger approach
Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be nonsaionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationMTH6121 Introduction to Mathematical Finance Lesson 5
26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random
More informationEntropy: From the Boltzmann equation to the Maxwell Boltzmann distribution
Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are
More informationChapter 4: Exponential and Logarithmic Functions
Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion
More informationINTRODUCTION TO FORECASTING
INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationSinglemachine Scheduling with Periodic Maintenance and both Preemptive and. Nonpreemptive jobs in Remanufacturing System 1
Absrac number: 050407 Singlemachine Scheduling wih Periodic Mainenance and boh Preempive and Nonpreempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationHedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buyside of a forward/fuures
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationVector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101115. Macroeconomericians
More informationGOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA
Journal of Applied Economics, Vol. IV, No. (Nov 001), 31337 GOOD NEWS, BAD NEWS AND GARCH EFFECTS 313 GOOD NEWS, BAD NEWS AND GARCH EFFECTS IN STOCK RETURN DATA CRAIG A. DEPKEN II * The Universiy of Texas
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 073807 Ifeachor
More informationTime Series Analysis Using SAS R Part I The Augmented DickeyFuller (ADF) Test
ABSTRACT Time Series Analysis Using SAS R Par I The Augmened DickeyFuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationReal Time Bid Optimization with Smooth Budget Delivery in Online Advertising
Real Time Bid Opimizaion wih Smooh Budge Delivery in Online Adverising KuangChih Lee Ali Jalali Ali Dasdan Turn Inc. 835 Main Sree, Redwood Ciy, CA 94063 {klee,ajalali,adasdan}@urn.com ABSTRACT Today,
More informationForecasting Sales: A Model and Some Evidence from the Retail Industry. Russell Lundholm Sarah McVay Taylor Randall
Forecasing Sales: A odel and Some Evidence from he eail Indusry ussell Lundholm Sarah cvay aylor andall Why forecas financial saemens? Seems obvious, bu wo common criicisms: Who cares, can we can look
More informationInformation Theoretic Approaches for Predictive Models: Results and Analysis
Informaion Theoreic Approaches for Predicive Models: Resuls and Analysis Monica Dinculescu Supervised by Doina Precup Absrac Learning he inernal represenaion of parially observable environmens has proven
More informationII.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal
Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationIssues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d
These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?
More informationFactors Affecting Initial Enrollment Intensity: PartTime versus FullTime Enrollment
acors Affecing Iniial Enrollmen Inensiy: artime versus ulltime Enrollmen By Leslie S. Sraon Associae rofessor Dennis M. O Toole Associae rofessor James N. Wezel rofessor Deparmen of Economics Virginia
More informationLEASING VERSUSBUYING
LEASNG VERSUSBUYNG Conribued by James D. Blum and LeRoy D. Brooks Assisan Professors of Business Adminisraion Deparmen of Business Adminisraion Universiy of Delaware Newark, Delaware The auhors discuss
More informationDDoS Attacks Detection Model and its Application
DDoS Aacks Deecion Model and is Applicaion 1, MUHAI LI, 1 MING LI, XIUYING JIANG 1 School of Informaion Science & Technology Eas China Normal Universiy No. 500, DongChuan Road, Shanghai 0041, PR. China
More informationNikkei Stock Average Volatility Index Realtime Version Index Guidebook
Nikkei Sock Average Volailiy Index Realime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
More informationBidask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation
Bidask Spread and Order Size in he Foreign Exchange Marke: An Empirical Invesigaion Liang Ding* Deparmen of Economics, Macaleser College, 1600 Grand Avenue, S. Paul, MN55105, U.S.A. Shor Tile: Bidask
More informationPremium Income of Indian Life Insurance Industry
Premium Income of Indian Life Insurance Indusry A Toal Facor Produciviy Approach Ram Praap Sinha* Subsequen o he passage of he Insurance Regulaory and Developmen Auhoriy (IRDA) Ac, 1999, he life insurance
More informationKeldysh Formalism: Nonequilibrium Green s Function
Keldysh Formalism: Nonequilibrium Green s Funcion Jinshan Wu Deparmen of Physics & Asronomy, Universiy of Briish Columbia, Vancouver, B.C. Canada, V6T 1Z1 (Daed: November 28, 2005) A review of Nonequilibrium
More informationOptimal Stock Selling/Buying Strategy with reference to the Ultimate Average
Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July
More informationInventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds
OPERATIONS RESEARCH Vol. 54, No. 6, November December 2006, pp. 1079 1097 issn 0030364X eissn 15265463 06 5406 1079 informs doi 10.1287/opre.1060.0338 2006 INFORMS Invenory Planning wih Forecas Updaes:
More informationBayesian Filtering with Online Gaussian Process Latent Variable Models
Bayesian Filering wih Online Gaussian Process Laen Variable Models Yali Wang Laval Universiy yali.wang.1@ulaval.ca Marcus A. Brubaker TTI Chicago mbrubake@cs.orono.edu Brahim Chaibdraa Laval Universiy
More informationModeling a distribution of mortgage credit losses Petr Gapko 1, Martin Šmíd 2
Modeling a disribuion of morgage credi losses Per Gapko 1, Marin Šmíd 2 1 Inroducion Absrac. One of he bigges risks arising from financial operaions is he risk of counerpary defaul, commonly known as a
More informationUNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert
UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of ErlangenNuremberg Lange Gasse
More informationRelationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith**
Relaionships beween Sock Prices and Accouning Informaion: A Review of he Residual Income and Ohlson Models Sco Pirie* and Malcolm Smih** * Inernaional Graduae School of Managemen, Universiy of Souh Ausralia
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationA Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities *
A Universal Pricing Framework for Guaraneed Minimum Benefis in Variable Annuiies * Daniel Bauer Deparmen of Risk Managemen and Insurance, Georgia Sae Universiy 35 Broad Sree, Alana, GA 333, USA Phone:
More informationTSGRAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999
TSGRAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macrodiversiy for he PRACH Discussion/Decision
More informationStochastic Recruitment: A LimitedFeedback Control Policy for Large Ensemble Systems
Sochasic Recruimen: A LimiedFeedback Conrol Policy for Large Ensemble Sysems Lael Odhner and Harry Asada Absrac This paper is abou sochasic recruimen, a conrol archiecure for cenrally conrolling he ensemble
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationResearch on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment
Vol. 7, No. 6 (04), pp. 365374 hp://dx.doi.org/0.457/ijhi.04.7.6.3 Research on Invenory Sharing and Pricing Sraegy of Mulichannel Reailer wih Channel Preference in Inerne Environmen Hanzong Li College
More informationMeasuring the Effects of Monetary Policy: A FactorAugmented Vector Autoregressive (FAVAR) Approach * Ben S. Bernanke, Federal Reserve Board
Measuring he Effecs of Moneary Policy: A acoraugmened Vecor Auoregressive (AVAR) Approach * Ben S. Bernanke, ederal Reserve Board Jean Boivin, Columbia Universiy and NBER Pior Eliasz, Princeon Universiy
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationAutomatic measurement and detection of GSM interferences
Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde
More informationNetwork Discovery: An Estimation Based Approach
Nework Discovery: An Esimaion Based Approach Girish Chowdhary, Magnus Egersed, and Eric N. Johnson Absrac We consider he unaddressed problem of nework discovery, in which, an agen aemps o formulae an esimae
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 20080530 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
More informationHotel Room Demand Forecasting via Observed Reservation Information
Proceedings of he Asia Pacific Indusrial Engineering & Managemen Sysems Conference 0 V. Kachivichyanuul, H.T. Luong, and R. Piaaso Eds. Hoel Room Demand Forecasing via Observed Reservaion Informaion aragain
More informationDYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
More information1.2 Goals for Animation Control
A Direc Manipulaion Inerface for 3D Compuer Animaion Sco Sona Snibbe y Brown Universiy Deparmen of Compuer Science Providence, RI 02912, USA Absrac We presen a new se of inerface echniques for visualizing
More informationStrategic Optimization of a Transportation Distribution Network
Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,
More information