Information Theoretic Approaches for Predictive Models: Results and Analysis


 Poppy Johnson
 2 years ago
 Views:
Transcription
1 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 o be a dicul problem. Sae represenaions which rely on prior models, such as parially observable Markov decision processes (POMDPs) are compuaion expensive and sensiive o he accuracy of he underlying model dynamics. Recen work by Sill and Bialek oers an informaion heoreic approach ha compresses he available hisory ino an inernal represenaion and maximizes is predicive power. We propose an alernaive algorihm ha ensures a more accurae inernal represenaion, and faser opimal policy convergence imes. In addiion, in order o validae he asympoic naure of he heoreical algorihm, we presen he rs empirical resuls in he eld, comparing he inernal represenaions reurned by boh approaches, heir accuracy, and heir predicive powers. 1 Inroducion Increasing aenion has been given o modelling parially observable sysems, where he agen is no allowed o observe he sae direcly; insead, observaions are received which allow he agen o infer informaion abou he sae. Consider he problem of an agen who ineracs wih a dynamical sysem. In his paper, we focus on an acive scenario, in which he agen has he capaciy o ac on he world, and inuence he observaions produced. Acive scenarios can be compared o passive ones, where he agen simply observes he daa produced by he world and consrucs an inernal represenaion of he sysem. Thus, in he acive scenario, he challenge becomes 1) deriving he inernal represenaion, given he available daa as well as 2) deciding on an acion sraegy. Having he abiliy o predic he oucome of an acion is cenral o all asks ha a human or aricial agen may encouner. Thus, raher han rying o solve he learning problem, in which he agen ries o discover he sysem srucure by updaing model parameers from observaion daa, we are ineresed in consrucing an inernal represenaion ha has maximal predicive power. 1
2 Tha is, he inernal represenaion of he sysem should be able o make good predicions abou fuure observaions, based on available daa. There have been wo predominan approaches in predicing a sequence of observaions: parially observable Markov decision processes (POMDPs), and he recenly proposed predicive sae represenaions (PSRs)[Liman e al., 22]. We discuss he advanages and disadvanages of each of he mehods, and propose an informaion heoreic approach based on ha developed by [Sill and Bialek,24]. Our approach is dieren from he above in ha he inernal represenaion considers he informaion ha boh he inernal sae, as well as he acion performed by he agen have abou he fuure. Finally, o demonsrae he eeciveness of our approach we consider he example of he oarese problem, creaed by [Liman e al., 22], and compare he predicive powers of he wo algorihms. 2 Background Before discussing he specic deails of each of he above approaches, we inroduce he basic erminology used in he paper. We dene a hisory, x pas as a  nie lengh sequence of acionobservaion pairs, x pas = [a k o k,..., a 1 o 1 ], where k is he lengh of he hisory and a i o i he acionobservaion pair observed a ime sep i in ha hisory. Similarly, a es is an ordered sequence of acionobservaion pairs = [a o o o,..., a 1 o 1 ], from he curren ime sep, ino he fuure. Finally, a fuure y fu is an observaion o ha will be observed afer aking acion a a ime sep. POMDPs A parially observable Markov decision process (POMDP) is a general framework for decision making under uncerainy. Formally, a POMDP is dened as a uplem = (S, A, O, b o, T, O) where he sae se S is he se of saes ha he sysem can be in, A is he discree se of acions, and O is he discree se of observaions. The se T consiss of (n n) ransiion marices T a, where Tij a is he probabiliy of reaching sae j, by aking acion a in sae i. The se O consiss of diagonal (n n) observaion marices O a,o, where O a,o ii is he probabiliy of an observaion o, given ha acion a was seleced in sae i. Finally, he (1 n) vecor b o is an iniial probabiliy disribuion over he sysem saes [Singh e al., 24]. Inuiively, he ransiion funcion T deermines he disribuion over nex saes, given ha a cerain acion was seleced in a sae, while he observaion funcion O reecs he parially observable naure of he sysem (he agen canno deermine, wih cerainy, he rue sae of he sysem). The sae represenaion in a POMDP is a (1 n) belief vecor b(h), where b i (h) is probabiliy of he sysem being in he hidden sae i, given ha he hisory h has been observed. The belief sae is updaed by compuing: 2
3 b(h, a, o) = b(h)t a O a,o b(h)t a O a,o e T, n where e T n is he 1 n vecor of all 1's. Thus, predicions are given by P ( h) = P (a 1 o 1...a k o k h) = b(h)t a1 O a1,o1...t a k O a k,o k e T n The main disadvanage of he POMDP approach is ha, as seen above, esimaing he sae assumes perfec knowledge of he underlying model. Algorihms ha ry o learn he dynamics require, a minimum, an assumpion abou he opology of he model. In addiion, belief sae mainenance has, in he wors case, complexiy equal o he size of he sae space, and exponenial in he number of variables. Taken ogeher wih he fac ha here exis dynamic sysems wih a nie sae space ha canno be modeled by any nie POMDPs [Jaeger, 1998], his shows ha he capabiliies of he POMDP framework are raher limied. PSRs Predicive sae represenaions are a recen approach ha ry o represen he sae of a sysem as a se of predicions of observable oucomes of experimens ha he agen can perform on he sysem. A se of ess Q = {q 1...q m } is called a linear Predicive Sae Represenaion (PSR) if, for all hisories h, he probabiliy of any es occurring can be compued as a linear combinaion of he predicions for he ess in Q. More generally, Q is a linear PSR if, for every es, here exiss a 1 q projecion vecor m, such ha, for all hisories h, P ( h) = P (h)m T. We call he ess q 1...q m in Q, he core ess of he PSR [Liman e al., 22]. In addiion, [Singh e al., 24] dene a Sysem Dynamics Marix D as an ordering over all possible ess and hisories, of all lenghs, where each of D's enries is he probabiliy of a es given a hisory, P ( h). The niely many linearly independen columns of D are he core ess of he PSR. The marix is generaed by compuing he weigh vecors m from he model parameers, for each es. A reason for ineres in PSRs is ha he sae represenaion is consruced only from acions and observaions seen, hus resuling in a less resricive model. However, empirical resuls show ha learning he PSR weigh vecors requires signican amouns of daa, making learning algorihms boh daa and compuaionally expensive [Singh, Liman e. al]. Acive Learning and Opimal Predicions [Sill and Bialek,24] recenly proposed a soluion o he specifed problem. Using principles from informaion heory, hey propose a sae represenaion wih he objecive of exracing predicive informaion from a ime series. 3
4 The sae represenaion is consruced as a nie se of saes s ha should 1) compress he informaion conained by he pas ime series and 2) reain maximal predicive powers. Inuiively, he beer he sae represenaion, he closer is fuure predicions should be o hose given by he available daa alone. s, such he s is a lossy compression of he pas hisories wih maximal predicive power. Using informaion heory, his can be formalized as he opimizaion principle : We wan o nd a mapping from x pas F = max p(s x pas )[I(s y fu ) λi(s, x pas )] where I(X, Y )is he muual informaion of X relaive o Y, given byi(x, Y ) = p(x,y) p(x, y) log x,y p(x)p(y). Taken ogeher wih a Markovian assumpion, he soluion o he above principle is he opimal x pas s mapping. This is he Gibbs probabiliy disribuion: p(s x pas ) p(s )e 1 λ D KL[p(y fu x pas ) p(y fu s )], where in place of he energy, we nd he KullbachLeibler disance: D KL [p(y fu x pas ) p(y fu s )] = p(y fu x pas ) log p(yfu x pas ) p(y fu s ) I has been proven ha, in he limi as λ, he assignmen becomes deerminisic. Thus, he opimal inernal sae ha a specic hisory is mapped o is he one ha gives a fuure predicion closes o ha given by he hisory alone (i.e. minimizes he D KL disance beween p(y fu x pas )and p(y fu s ) ): s (x pas ) = argmin s D KL [p(y fu x pas ) p(y fu s )] The bane of he above represenaion is ha he acions aken by he agen are independen of he inernal sae. Since fuure observaions are he resul of an acion being aken, he inuiion is ha he inernal sae aken ogeher wih he acion should in fac be predicive. 3 Proposed Soluion The fundamenal idea behind our approach is ha acions, aken ogeher wih he inernal sae are predicive, raher han jus he sae iself. The moivaion behind his approach is ha he fuure produced is solely caused by he acion choice; herefore, i is reasonable o expec ha predicions ha accoun for he acion sraegy should be more accurae han hose ha depend on he sae alone. Thus, he above opimizaion principle can be modied o incorporae he informaion ha he sae and acion joinly hold abou he fuure. Formally, 4
5 F = max p(s x pas )[I({s, a } y fu ) λi(s, x pas )] The rs erm in he equaion ensures ha he inernal represenaion maximizes he informaion held abou he fuure, while he second represens he compression of hisories ino saes. The x pas s assignmen in his case becomes sochasic. Since he acion choices are probabilisic and depend on he opimal acion policy (given by p(a x pas )), he saehisory mapping will be as well, and depend on he aforemenioned policy. By solving he opimizaion principle, we obain anoher Gibbs disribuion: p(s x pas ) e 1 λ where p(y fu a, s ) a p(a x pas x pas p(y fu x pas x pas ) D KL [p(y fu x pas, a )p(a x pas )p(s x pas p(a x pas )p(s x pas, a ) p(y fu s, a )], )p(x pas ) )p(x pas ) Thus, he opimal inernal sae ha a specic hisory is mapped o is: s (x pas ) = argmin s p(a x pas ) D KL [p(y fu x pas, a ) p(y fu s, a ) Algorihmic Implemenaion a Based on he heoreical analysis presened above, we have consruced an ieraive algorihm ha performs well in any parially observable seing. The algorihm is composed of hree pars. Firs, we simulae he iniial esimaes of p(y fu x pas, a ) and p(x pas ), by aking random acions and creaing a nie lengh iniial rajecory. Secondly, we ieraively solve he above wo equaions, unil p(s x pas ) converges. This resul is he opimal x pas s assignmen ha maps he specic hisory being observed o an inernal sae. Finally, an acion is aken according o an acion policy, producing a new hisory and observaion, which are used o updae he p(y fu x pas, a ) and p(x pas ) disribuions. The ieraive algorihm converges o a local opimum afer every ieraion, according o he same argumens ha were previously used by [Sill and Bialek,24]. 4 Example: Ineracively learning a oarese sysem Descripion We describe a very simple parially observable sysem, creaed by [Liman e al., 22]. The sysem is composed of 5 hidden saes, 2 acions and 2 observaions. The. 5
6 oa acion moves o he sae on he lef/righ wih uniform probabiliy, and always produces an observaion of. The rese acion moves o he sae on he far righ. If he sysem was already in ha sae, he observaion produced is a 1; oherwise, a is observed. Each observed hisory is of lengh 3 (i.e. exends 3 ime seps ino he pas). Figure 1. Floarese problem We have evaluaed boh he iniial algorihm proposed by Sill and Bialek, as well as our proposed algorihm, in 4 dieren scenarios: The agen has sucien knowledge of he pas (i.e. he iniial disribuions are sucien o capure all he srucure in he environmen), and he inernal represenaion is an uncompressed mapping of he available hisories (he number of inernal saes s is equal o ha of hidden saes in he sysem, namely s = 5). The agen has sucien knowledge of he pas, and he inernal represenaion is a compression of he available hisories (he number of inernal saes s is smaller han ha of hidden saes in he sysem, namely s = 3). The agen has insucien knowledge of he pas (i.e. he iniial disribuions are oo sparse and do no capure all he srucure in he environmen), and he inernal represenaion is an uncompressed mapping of he available hisories (s = 5). The agen has insucien knowledge of he pas and he inernal represenaion is an compression of he available hisories (s = 3). Empirical resuls Due o space consrains, we will only presen he resuls for he fourh scenario, where he agen has insucien knowledge of he pas, and he inernal represenaion is a compression of he available hisories. The resuls for he oher hree scenarios are consisen wih he presened one. We are concerned wih deermining which algorihm produces he inernal represenaion wih he greaes predicive power, and ha bes compresses he available daa. Opimizaion Funcion To begin, we compare he values of each of he opimizaion funcions over ime. This ensures ha he rade o beween he predicive power and he compression capaciies of he inernal represenaion is mainained. 6
7 F Graph of he Opimizaion Funcion F Time Graph of P(y s) vs. P(y x) y, Fuure observaion F Graph of he Opimizaion Funcion F Time Graph of P(y s) vs. P(y x) y, Fuure observaion Proposed algorihm Acive Learning algorihm Figure 2 : Opimizaion funcion F. The horizonal axis in each plo is he number of ieraions of he algorihm. Noice ha he value of he opimizaion funcion in our approach increases wih he number of ieraions. This implies ha he accuracy of he inernal represenaion increases as well. Conversely, he inernal represenaion as consruced by he original Acive Learning algorihm does no vary much. In oher words, is predicive powers improves very lile pas he iniial ones. This is problemaic, as a noisy iniial disribuion will resul in a very inaccurae saehisory mapping. Lossy Compression The inernal represenaion has o be a lossy compression of he pas hisories. In oher words, he predicions given by a sae should be very similar o hose given by he hisories ha become assigned o i. Proposed algorihm Acive Learning algorihm P(y s) and P(y x) P(y s) and P(y x) Figure 3 : Hisorysae mapping. The horizonal axis in each plo conains he possible fuure observaions, namely y fu. The verical axes are p(y fu x pas ), in black, and p(y fu s ), in red. Noice ha he number of saes used in he inernal represenaion diers beween algorihms. This is because, while he original Acive Learning algorihm is deerminisic, and hus employs all 3 available inernal saes, our 7
8 Graph of P(y= s*,a), where s* is he opimal sae assignmen for pas 16 = [ffr], and P(y= x=,a) Time a = in P(y= s*,a) a = 1 in P(y= s*,a) a = in P(y= x,a) a = 1 in P(y= x,a) Graph of P(y= s*) and P(y= x), where s* is he opimal sae assignmen for pas 16 = [ffr] Time P(y= s*) P(y= x,a) proposed algorihm is probabilisic. Since here are wo possible observaions, here are wo dieren possible predicions, and hus only 2 inernal saes are needed o represen he sysem. If he inernal represenaion is o be a compression of he available hisories, hen he fuure predicions as given by i (he red lines) should bes approximae he fuure predicions given by he enire daa (he black lines). The fuure informaion conained in he available hisory is beer approximaed by he 2 inernal saes as consruced by he proposed algorihm, han he 3 saes used in he Acive Learning algorihm, as can be seen from he above graph. Predicive Powers From he problem deniion, we know wih cerainy ha a oa acion will produce an observaion of. Consequenly, a good inernal represenaion should make he same predicion regardless of previous observaions. On he oher hand, he observaion produced by a rese acion depends on he acion aken on he previous ime sep. Specically, if he previous acion was a rese, we know wih cerainy ha he sysem is in he end sae. Thus, aking anoher rese acion is expeced o produce an observaion of. If he previous acion was a oa, hen he probabiliy of observing a 1 is idenical o he probabiliy of he sysem being in he end sae. Wih his in mind, we begin by considering he case when he las acion aken is a rese. Proposed algorihm Acive Learning algorihm P(y= s*,a) and P(y= x,a) P(y= s*) and P(y= x) Figure 4 : Fuure predicions. The horizonal axis in each plo is he number of ieraions of he algorihm. The verical axis diers beween he plos. In he case of he proposed algorihm, i is p(y fu = x pas = [ffr], a = floa), in red, vs. p(y fu = s, a = floa), in blue, and p(y fu = x pas = [ffr], a = rese), in purple, vs. p(y fu = s, a = rese), in green. In he case of he original Acive Learning algorihm he verical axis is p(y fu = x pas = [ffr]), in red vs. p(y fu = s ), in blue. Here, s is he opimal sae o which he hisory is mapped. In he case of he original Acive Learning algorihm, he inernal represenaion is independen of he acion choice, and hus he fuure observaions 8
9 Graph of P(y= s*,a), where s* is he opimal sae assignmen for pas 4 = [frf], and P(y= x=,a) a = in P(y= s*,a) a = 1 in P(y= s*,a) a = in P(y= x,a) a = 1 in P(y= x,a) Time Graph of P(y= s*) and P(y= x), where s* is he opimal sae assignmen for pas 4 = [frf] Time P(y= s*) P(y= x,a) depend on he sae alone. Noice ha he predicions given by he proposed inernal represenaion converge very quickly o he value of he predicions given by he hisory alone, hus proving is accuracy. This convergence is faser han ha of he original algorihm. Proposed algorihm Acive Learning algorihm P(y= s*,a) and P(y= x,a) P(y= s*) and P(y= x) Figure 5: Fuure predicions. The horizonal axis in each plo is he number of ieraions of he algorihm. The verical axis diers for boh plos. In he case of he proposed algorihm, i is p(y fu = x pas = [frf], a = floa), in red, vs. p(y fu = s, a = floa), in blue, and p(y fu = x pas = [frf], a = rese), in purple, vs. p(y fu = s, a = rese, in green. In he case of he original Acive Learning algorihm he verical axis is p(y fu = x pas = [frf]), in red vs. p(y fu = s ), in blue. Here, s is he opimal sae ha he hisory ges mapped o. Since he previous acion was a oa, he sysem can be found in eiher he end sae, or he one o he lef of i, each wih a probabiliy of.5. Thus, he probabiliy of seeing an observaion of afer aking anoher rese acion is also.5. Again, he inernal represenaion consruced by he proposed algorihm predics fuure observaions ha are closer o hose prediced from all he available daa alone. Clusering Finally, we are ineresed in wheher he predicions given by he inernal represenaion are consisen. In oher words, wheher he same ype of hisories consisenly ge mapped ogeher, over ime. 9
10 Proposed algorihm Acive Learning algorihm Graph of similar clusers o pas 16=[ffr] vs.ime xpas xpas Graph of similar clusers o pas 16=[ffr] vs.ime Time Time Figure 6 : Hisory clusers. The horizonal axis in each plo is he number of ieraions of he algorihm. The verical axis represens all he hisories of lengh 3 ha ge mapped o he same sae as xpas = [f f r]. Proposed algorihm Acive Learning algorihm Graph of similar clusers o pas =[fff] vs.ime xpas xpas Graph of similar clusers o pas =[fff] vs.ime Time Time Figure 7 : Hisory clusers. The horizonal axis in each plo is he number of ieraions of he algorihm. The verical axis represens all he hisories of lengh 3 ha ge mapped o he same sae as xpas = [f rf ]. Using he same argumen used in he lossy compression case, we expec o see wo di eren clusers being formed by he proposed algorihm. All he hisories ha are mapped o he same sae as xpas = [f f r] are, in fac, hisories ha end in eiher an r or r1 acionobservaion pair. This is because he fuure predicion based on each of hese hisories is known wih cerainy. Consequenly, he remaining hisories will be mapped o he second sae, as he fuure predicion in each of hese cases is probabilisic. If hese hisories were o be mapped o wo di eren saes, raher han one, i may be possible o ell small probabiliy di erences in he case of he rese acion. However, i is unrealisic o assume ha his could happen, as he agen is learning from noisy and insu cien daa. This however, is no he case when considering he original Acive Learning algorihm. Since he saehisory mapping is deerminisic, in order o reain good predicive powers, he saes need o be more spread ou among he possible hisories. 1
11 5 Conclusion We have presened an informaion heoreic approach o he problem of predicing fuure observaions from limied available daa, by proposing ha he inernal represenaion, ogeher wih he acion sraegy employed by he agen, should reain maximal predicive powers, and compress he pas hisories seen by an agen. We have compared our proposed algorihm o ha of [Sill and Bialek,24] in four dieren asks. The experimenal resuls illusrae an increase in he predicive power of he inernal represenaion, as well as a faser convergence o he opimal saehisory mapping. These experimens sugges ha our approach of considering acions in creaing he inernal sae represenaions is a viable soluion for predicing parially observable sysems, using a limied amoun of daa. Fuure work will analyze furher problems ha can be addressed by our approach, as well as compare our inernal represenaion of he world o ha consruced by a PSR. References [Sill and Bialek,24] Susanne Sill and William Bialek. Acive Learning and opimal predicions. 24. [Liman e al., 22] [Singh e al., 24] [Jaeger, 1998] Michael Liman, Richard S. Suon and Sainder Singh. Predicive represenaions of sae. In NIPS 14, pages , 22. Sainder Singh, Michael R. James, and Mahew R. Ruddary. Predicive sae represenaions: A new heory for modelling dynamical sysems. In Proceedings of UAI, pages , 24. Herber Jaeger. Discreeime, discreevalued observable operaor models: a uorial. In GMD Repor 42, [Singh, Liman e. al] Sainder Singh, Michael L. Liman, Nicholas K. Jong, David Pardoe, Peer Sone. Learning Predicive Sae Represenaions. In The Twenieh Inernaional Conference on Machine Learning (ICML23), 23. [Lovejoy, 1991] [Tishby e al., 1999] William S. Lovejoy. A survey of algorihmic mehods for parially observable Markov decision processes. In Annals of Operaions Research, 28, pages 4765, Nafali Tishby, Fernando Pereira, William Bialek. The informaion boleneck mehod. In Proceedings of he 37h Annual Alleron Conference, pages ,
Chapter 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 informationPROFIT 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 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 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 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 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 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 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 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 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 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 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 informationMultiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States
Deparmen of Economics Discussion Paper 0007 Muliple Srucural Breaks in he Nominal Ineres Rae and Inflaion in Canada and he Unied Saes Frank J. Akins, Universiy of Calgary Preliminary Draf February, 00
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationDynamic programming models and algorithms for the mutual fund cash balance problem
Submied o Managemen Science manuscrip Dynamic programming models and algorihms for he muual fund cash balance problem Juliana Nascimeno Deparmen of Operaions Research and Financial Engineering, Princeon
More informationGene Regulatory Network Discovery from TimeSeries Gene Expression Data A Computational Intelligence Approach
Gene Regulaory Nework Discovery from TimeSeries Gene Expression Daa A Compuaional Inelligence Approach Nikola K. Kasabov 1, Zeke S. H. Chan 1, Vishal Jain 1, Igor Sidorov 2 and Dimier S. Dimirov 2 1 Knowledge
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 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 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 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 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 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 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 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 informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
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 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 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 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 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 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 informationThe Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closelyheld, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
More informationThe Belief Roadmap: Efficient Planning in Belief Space by Factoring the Covariance
1 The Belief Roadmap: Efficien Planning in Belief Space by Facoring he Covariance Samuel Prenice and Nicholas Roy Absrac When a mobile agen does no known is posiion perfecly, incorporaing he prediced uncerainy
More informationMachine Learning in Pairs Trading Strategies
Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu
More informationCan Individual Investors Use Technical Trading Rules to Beat the Asian Markets?
Can Individual Invesors Use Technical Trading Rules o Bea he Asian Markes? INTRODUCTION In radiional ess of he weakform of he Efficien Markes Hypohesis, price reurn differences are found o be insufficien
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 informationMulticamera scheduling for video production
Mulicamera scheduling for video producion Fahad Daniyal and Andrea Cavallaro Queen Mary Universiy of London Mile End Road, E 4S London, Unied Kingdom Email: {fahad.daniyal, andrea.cavallaro}@eecs.qmul.ac.uk
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 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 information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
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 informationEvolutionary building of stock trading experts in realtime systems
Evoluionary building of sock rading expers in realime sysems Jerzy J. Korczak Universié Louis Paseur Srasbourg, France Email: jjk@dpinfo.usrasbg.fr Absrac: This paper addresses he problem of consrucing
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 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 informationThe Roos of Lisp paul graham Draf, January 18, 2002. In 1960, John McCarhy published a remarkable paper in which he did for programming somehing like wha Euclid did for geomery. 1 He showed how, given
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 informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationStatistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by SongHee Kim and Ward Whitt
Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by SongHee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 1799
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 informationOptimal Investment and Consumption Decision of Family with Life Insurance
Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker
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 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 informationWe addressed the problem of developing a model to simulate at a high level of detail the movements of over
Published online ahead of prin Augus 15, 28 Aricles in Advance, pp. 1 2 issn 411655 eissn 15265447 informs doi 1.1287/rsc.18.238 28 INFORMS An Approximae Dynamic Programming Algorihm for LargeScale
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
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 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 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 informationLoad Prediction Using Hybrid Model for Computational Grid
Load Predicion Using Hybrid Model for Compuaional Grid Yongwei Wu, Yulai Yuan, Guangwen Yang 3, Weimin Zheng 4 Deparmen of Compuer Science and Technology, Tsinghua Universiy, Beijing 00084, China, 3, 4
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 informationA Distributed MultipleTarget Identity Management Algorithm in Sensor Networks
A Disribued MulipleTarge Ideniy Managemen Algorihm in Sensor Neworks Inseok Hwang, Kaushik Roy, Hamsa Balakrishnan, and Claire Tomlin Dep. of Aeronauics and Asronauics, Sanford Universiy, CA 94305 Elecrical
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 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 informationDoes Option Trading Have a Pervasive Impact on Underlying Stock Prices? *
Does Opion Trading Have a Pervasive Impac on Underlying Sock Prices? * Neil D. Pearson Universiy of Illinois a UrbanaChampaign Allen M. Poeshman Universiy of Illinois a UrbanaChampaign Joshua Whie Universiy
More informationLearning Patterns in Noise: Environmental Statistics Explain the Sequential Effect
Learning Paerns in Noise: Environmenal Saisics Explain he Sequenial Effec Friederike Schüür (fs62@nyu.edu), Brian Tam (bp218@nyu.edu), Laurence T. Maloney (lm1@nyu.edu) Deparmen of Psychology, 6 Washingon
More informationA Bayesian framework with auxiliary particle filter for GMTI based ground vehicle tracking aided by domain knowledge
A Bayesian framework wih auxiliary paricle filer for GMTI based ground vehicle racking aided by domain knowledge Miao Yu a, Cunjia Liu a, Wenhua Chen a and Jonahon Chambers b a Deparmen of Aeronauical
More informationTimeExpanded Sampling (TES) For Ensemblebased Data Assimilation Applied To Conventional And Satellite Observations
27 h WAF/23 rd NWP, 29 June 3 July 2015, Chicago IL. 1 TimeExpanded Sampling (TES) For Ensemblebased Daa Assimilaion Applied To Convenional And Saellie Observaions Allen Zhao 1, Qin Xu 2, Yi Jin 1, Jusin
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUNSHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 67 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUNSHAN WU Deparmen of Bussines Adminisraion
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 informationCALCULATION OF OMX TALLINN
CALCULATION OF OMX TALLINN CALCULATION OF OMX TALLINN 1. OMX Tallinn index...3 2. Terms in use...3 3. Comuaion rules of OMX Tallinn...3 3.1. Oening, realime and closing value of he Index...3 3.2. Index
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 informationSmooth Priorities for MultiProduct Inventory Control
Smooh rioriies for Muliroduc Invenory Conrol Francisco José.A.V. Mendonça*. Carlos F. Bispo** *Insiuo Superior Técnico  Universidade Técnica de Lisboa (email:favm@mega.is.ul.p) ** Insiuo de Sisemas e
More informationConstant Data Length Retrieval for Video Servers with Variable Bit Rate Streams
IEEE Inernaional Conference on Mulimedia Compuing & Sysems, June 173, 1996, in Hiroshima, Japan, p. 151155 Consan Lengh Rerieval for Video Servers wih Variable Bi Rae Sreams Erns Biersack, Frédéric Thiesse,
More informationEfficient Risk Sharing with Limited Commitment and Hidden Storage
Efficien Risk Sharing wih Limied Commimen and Hidden Sorage Árpád Ábrahám and Sarola Laczó March 30, 2012 Absrac We exend he model of risk sharing wih limied commimen e.g. Kocherlakoa, 1996) by inroducing
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 informationTrading on ShortTerm Information
428 Trading on ShorTerm Informaion by ALEXANDER GÜMBEL This paper shows ha invesors may wan fund managers o acquire and rade on shorerm insead of more profiable longerm informaion. This improves learning
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 informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationDOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR
Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios
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 informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
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 informationSURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES
Inernaional Journal of Accouning Research Vol., No. 7, 4 SURVEYING THE RELATIONSHIP BETWEEN STOCK MARKET MAKER AND LIQUIDITY IN TEHRAN STOCK EXCHANGE COMPANIES Mohammad Ebrahimi Erdi, Dr. Azim Aslani,
More informationSPECULATION AND THE TERM STRUCTURE OF INTEREST RATES. Abstract
SPECULATION AND THE TERM STRUCTURE OF INTEREST RATES KRISTOFFER P. NIMARK Absrac A racable equilibrium erm srucure model populaed wih raional bu heerogeneously informed raders is developed and esimaed.
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 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 informationDistributed and Secure Computation of Convex Programs over a Network of Connected Processors
DCDIS CONFERENCE GUELPH, ONTARIO, CANADA, JULY 2005 1 Disribued and Secure Compuaion of Convex Programs over a Newor of Conneced Processors Michael J. Neely Universiy of Souhern California hp://wwwrcf.usc.edu/
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 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 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 informationMaintaining MultiModality through Mixture Tracking
Mainaining MuliModaliy hrough Mixure Tracking Jaco Vermaak, Arnaud Douce Cambridge Universiy Engineering Deparmen Cambridge, CB2 1PZ, UK Parick Pérez Microsof Research Cambridge, CB3 0FB, UK Absrac In
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 informationAnnuity Decisions with Systematic Longevity Risk
Annuiy Decisions wih Sysemaic Longeviy Risk Ralph Sevens This draf: November, 2009 ABSTRACT In his paper we invesigae he effec of sysemaic longeviy risk, i.e., he risk arising from uncerain fuure survival
More informationImpact of scripless trading on business practices of Subbrokers.
Impac of scripless rading on business pracices of Subbrokers. For furher deails, please conac: Mr. T. Koshy Vice Presiden Naional Securiies Deposiory Ld. Tradeworld, 5 h Floor, Kamala Mills Compound,
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 informationMSCI Index Calculation Methodology
Index Mehodology MSCI Index Calculaion Mehodology Index Calculaion Mehodology for he MSCI Equiy Indices Index Mehodology MSCI Index Calculaion Mehodology Conens Conens... 2 Inroducion... 5 MSCI Equiy Indices...
More informationA PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES *
CUADERNOS DE ECONOMÍA, VOL. 43 (NOVIEMBRE), PP. 285299, 2006 A PROPOSAL TO OBTAIN A LONG QUARTERLY CHILEAN GDP SERIES * JUAN DE DIOS TENA Universidad de Concepción y Universidad Carlos III, España MIGUEL
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 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 information