Xin Li Department of Information Systems, College of Business, City University of Hong Kong, Hong Kong, CHINA
|
|
- Clara Arnold
- 6 years ago
- Views:
Transcription
1 RESEARCH ARTICLE MOELING FIXE OS BETTING FOR FUTURE EVENT PREICTION Weyun Chen eartment of Educatona Informaton Technoogy, Facuty of Educaton, East Chna Norma Unversty, Shangha, CHINA Xn L eartment of Informaton Systems, Coege of Busness, Cty Unversty of Hong Kong, Hong Kong, CHINA {xn..hd@gma.com} ane Zeng eartment of Management Informaton Systems, Unversty of Arzona, Tucson, AZ 8572 U.S.A., and State Key Laboratory of Management and Contro for Comex Systems, Insttute of Automaton, Chnese Academy of Scences, Beng, CHINA {zeng@ema.arzona.edu} Aendx Theorem : If α ()= β (-), then f(x;,θ) = f(-x;-,θ). Proof: λ f( x;, θ ) = Beta x;, = λ = = ( α β ) λ = Beta x = λ ( - ; β, α ) λ = Beta ( - x; α, ) ( ;, ) β = f x θ = λ = # Theorem 2: E[Beta(x; α (),β ())] s strcty ncreasng wth. Proof: α E[Beta(x; α (),β ())] = = α + β β + α Snce s wthn (0, ), both α () and β () are ostve. MIS Quartery Vo. 4 No. 2 Aendx/June 207 A
2 Chen et a./modeng Fxed Odds Bettng β β α α Z Z h h α ( A) β α u uh β u + uh A = h= 2 h= 2 = α α β Ceary, α and the equa sgn hods ony f a u h =0 when s wthn range (0, ). 0 If a u h =0, both α () and β () equa 0, whch s n confct wth our assumtons. β () α Thus s strcty decreasng n, and s strcty ncreasng wth. # α() α + β Theorem 3: If arameters q,, ρ, γ, τ, o A, o B are a ostve, there exsts and ony exsts one beef vaue c 0 (0,), caed baance beef hereafter, satsfyng U(c, o A ) = U( c, o B ). Proof: When q,, ρ, γ, τ are ostve, both w + ( ) and w - ( ) are strcty ncreasng functons. Accordngy, the utty functon U(x, o) s a strcty ncreasng functon and U( x,o) s a strcty decreasng functon n beef x. Gven o A > 0 and o B > 0, [U(x, o A ) U(-x, o B )] s strcty ncreasng. It s easy to verfy that U(x = 0, o A ) < 0 < U(x =, o B ) and U(x =, o A ) > 0 > U(x = 0, o B ). Thus, [U(x, o A ) U(-x, o B )] < 0 for x = 0 and [U(x, o A ) U( x, o B )] > 0 for x =. As such, there must exst one and ony one baance beef x = c, satsfyng U(c, o A ) = U( c, o B ). # Theorem 4: For suffcenty arge m, maxmzng equaton 7 reduces to sovng PA(,θ) = s A. Proof: Lc(,θ) n equaton (7) s contnuous and dfferentabe. Snce 0 < <, the vaue of that maxmzes Lc(,θ), f t exsts, must satsfy the Lc(, θ) frst-order condton = 0. Lc(, θ ) PA(, θ) PA(, θ) = ms A + m( sa) + R + ( R) PA(, θ) PA(, θ) ( s ) ( R ) PA(, θ ) s A A R = m PA(, θ) PA(, θ) ( θ ) θ ( θ ) PA(, ) (, ) - (, ) θ sa PA sa PA θ R R = m + PA(, ) PA(, ) PA(, θ) sa- PA(, θ) R = m + PA(, θ) PA(, ) Namey: [ PA θ s ] ( θ ) =0 ( θ )( ) ( ) PA(, ) (, ) (, ) θ PA θ PA R (, )- A = m A2 MIS Quartery Vo. 4 No. 2/June 207
3 Chen et a./modeng Fxed Odds Bettng ( θ )( ) ( ) PA(, ) (, ) (, ) θ PA θ PA R m [ PA(, θ )- sa] = m =0 + m + m m PA(, θ) Accordng to Theorem 4, >0, we obtan m [ PA(, θ )- sa] =0. # m + Theorem 5: I c (α (),β ()) s strcty decreasng n, where I c (α (),β ()) s the reguarzed ncomete Beta functon 0 c B eta ( x; α, β ) dx. Ic( α, β ) Ic( α, β ) α Ic( α, β) β Proof: Based on the chan rue of mutvarabe cacuus, = +. α β k I c ( α, β ) Γ( α) Γ ( α + β ) α ( α) k( α) k( β ) kc = [og( c) ϕ ( α) + ϕ ( α + β )] Ic ( α, β ) c α Γ( β ) k! Γ ( k + + α ) Γ ( k + + β ) where ( ) k s the Pochhammer symbo secfed as (x) 0 = ; (x) n = x(x + )(x + 2) (x + n-). Snce ϕ( α) = ( ) r, ϕ ( α + β) ϕ ( α) = ( ) < 0 when α > 0 and β > 0. k = k k + α k = k + α + β k + α Snce c<, og (c) < 0 and [og(c) φ(α) + φ(α + β)] < 0. Snce I c (α,β) > 0 f 0 < c <, we have [og(c) φ(α) + φ(α + β)]i c (α, β) < 0. k = 0 Snce Γ(x)>0 f x>0, we have k Γ( α) Γ ( α + β) α ( α) k( α) k( β) kc c > 0 Γ( β) k! Γ ( k + + α) Γ ( k + + β) k = 0 I Thus, ( c α, β ) < 0 when 0 < c<. α I Smary, we can rove ( c α, β ) > 0 when 0 < c <. β α β It s cear > 0 and < 0 when 0 < <. Ic( α, β ) Thus, < 0,.e., I c (α(),β()) s strcty decreasng n. # Formua for AIC The vaue of AIC crtera s comuted as AICc = 2t + 2 t( t + )/( N t ) 2Lc θ where N denotes the number of data nstances and t denotes the number of arameters, whch s ( + Z) > t = Z = accordng to equatons () and (2). MIS Quartery Vo. 4 No. 2 Aendx/June 207 A3
4 Chen et a./modeng Fxed Odds Bettng Inut: {o A, o B, R, s A, o B,}, 0 {,, H}, k max, ε. Outut: estmated otma arameter θ*.. Comute baance beef c, c 2,, c H for each bettng game accordng to (9), usng a root fndng agorthm. 2. Intaze a smex SX whch conssts of J + sets of arameters θ n the arameter sace Θ, where J s the dmenson of the arameter sace. 3. Whe: 4. For each θ : 5. Sove A from each bettng accordng to (0) usng a root fndng agorthm. 6. Comute the Lc( ) accordng to (2). ( max( Lc ) mn( ) ) * θ Lc * θ ε 7. If or IteratonCount < k max : 8. Udate vertces n SX usng Refect, Exand, Outsde contracton, Insde contracton, or Shrnk oeratons. 9. If oeraton <> Shrnk : IteratonCount = IteratonCount + 0. Ese: *. Return the arameter set corresondng to max( Lc ( θ )) as θ*. Fgure A. Maxmum Lkehood Estmaton Usng a Neder Mead Method etaed Beef strbuton Estmaton Procedure Sna 2008 Oymc Games ataset For each settng of and Z, varyng from to 3, resectvey, we numercay obtaned the otma arameters θ* 0 Θ. Tabe A reorts the og kehood and AIC vaues for these modes. Generay, the mode s kehood converges when and Z are arger than 2. The mode wth = 2 and Z = 2 s the mode wth the maxmum kehood. The estmated beef dstrbuton functon s gven as: f( x; ) = 0.74* Beta( x;3.76* +0.*,3.76*( )+0.*( ) ) * Beta( x;0.* *,0.*( ) *( ) ) For the AIC crtera, we combned the three comonents wth smaest AICc ( =, Z = ; =, Z = 2; and =, Z = 3). The estmated beef dstrbuton functon s gven as f ( x; ) = 0.67* Beta( x;5.98*,5.98*( )) * Beta( x;5.95* *,5.95*( ) *( ) ) 0.24* Beta( x;5.69* 2 0.6*,5.69* 0.6*( 2 ) ) 3 3 Tabe A. Log Lkehood and AIC Vaues (Sna 2008 Oymc Games) Z = Z = 2 Z = 3 Log kehood AIC Log kehood AIC Log kehood AIC A4 MIS Quartery Vo. 4 No. 2/June 207
5 Chen et a./modeng Fxed Odds Bettng Sohu Entertanment ataset Tabe A2 shows the resuts on the Sohu entertanment event dataset, varyng and Z from to 3. The mode ( = 3 and Z = 3) s the mode wth the maxmum kehood. The estmated beef dstrbuton functon s as foows: f x Beta x ( ; ) = 0.84* ( ;0.* +0.* + 000*,0.*( )+0.*( ) + 000*( ) ) * Beta( x;7.54* 0.* 0.*,7.54* 0.* 0.* ) For the AIC crtera, we combned the three comonents wth smaest AIC ( =, Z = and =, Z = 2 and =, Z = 3). The estmated beef dstrbuton functon s gven as f ( x; ) = 0.62* Beta( x;2.28*, 2.28*( )) * Beta( x;.29* + 3.3*,.29*( ) + 3.3*( ) ) * Beta( x; + 2.6* +,( ) + 2.6*( ) + ( ) ) Tabe A2. Lkehood and AIC Vaues (Sohu Entertanment) Z = Z = 2 Z = 3 Log kehood AIC Log kehood AIC Log kehood AIC Sohu 204 FIFA ataset Tabe A3 shows the resuts on the Sohu 204 FIFA dataset, varyng and Z from to 3. The mode ( = and Z = ) s the mode wth the maxmum kehood. The estmated beef dstrbuton s gven as ( ; ) = ; 428., 428. ( ) f x Beta x For the AIC crtera, we combne the three comonents wth smaest AIC ( =, Z = ; =, Z = 2; and =, Z = 3). The estmated beef dstrbuton functon s gven as f ( x; ) = 0.67* Beta( x;42.8*, 42.8*( )) * Beta( x;4.88*, 4.88*( )) * Beta( x;4.98*,4.98*( )) Tabe A-3: Lkehood and AIC Vaues (Sohu 204 FIFA) Z = Z = 2 Z = 3 Log kehood AIC Log kehood AIC Log kehood AIC MIS Quartery Vo. 4 No. 2 Aendx/June 207 A5
6 Chen et a./modeng Fxed Odds Bettng Wth the estmated beef dstrbuton functon, we can cacuate the ercentage of eoe who consder the event may haen f there are no odds (or equa odds on both sdes) n the redcton market, as ustrated n Fgure A2. In a three datasets, the bettors beefs are more extreme than the actua event robabty. If the event robabty s ess than 0.5, the fna bet rato w be ower than the event robabty. If the event robabty s hgher than 0.5, the fna bet rato s hgher than event robabty. Peoe wth a Beef >.5 Sna 2008 Oymc Games Sohu Entertanment Sohu 204 FIFA Fgure A2. Bettor Beef Wthout Odds Infuence A6 MIS Quartery Vo. 4 No. 2/June 207
we have E Y x t ( ( xl)) 1 ( xl), e a in I( Λ ) are as follows:
APPENDICES Aendx : the roof of Equaton (6 For j m n we have Smary from Equaton ( note that j '( ( ( j E Y x t ( ( x ( x a V ( ( x a ( ( x ( x b V ( ( x b V x e d ( abx ( ( x e a a bx ( x xe b a bx By usng
More informationResearch on Complex Networks Control Based on Fuzzy Integral Sliding Theory
Advanced Scence and Technoogy Letters Vo.83 (ISA 205), pp.60-65 http://dx.do.org/0.4257/ast.205.83.2 Research on Compex etworks Contro Based on Fuzzy Integra Sdng Theory Dongsheng Yang, Bngqng L, 2, He
More informationAppendix for An Efficient Ascending-Bid Auction for Multiple Objects: Comment For Online Publication
Appendx for An Effcent Ascendng-Bd Aucton for Mutpe Objects: Comment For Onne Pubcaton Norak Okamoto The foowng counterexampe shows that sncere bddng by a bdders s not aways an ex post perfect equbrum
More informationNeural network-based athletics performance prediction optimization model applied research
Avaabe onne www.jocpr.com Journa of Chemca and Pharmaceutca Research, 04, 6(6):8-5 Research Artce ISSN : 0975-784 CODEN(USA) : JCPRC5 Neura networ-based athetcs performance predcton optmzaton mode apped
More informationA finite difference method for heat equation in the unbounded domain
Internatona Conerence on Advanced ectronc Scence and Technoogy (AST 6) A nte derence method or heat equaton n the unbounded doman a Quan Zheng and Xn Zhao Coege o Scence North Chna nversty o Technoogy
More informationManaging Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration
Managng Caacty Through eward Programs on-lne comanon age Byung-Do Km Seoul Natonal Unversty College of Busness Admnstraton Mengze Sh Unversty of Toronto otman School of Management Toronto ON M5S E6 Canada
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More informationCOXREG. Estimation (1)
COXREG Cox (972) frst suggested the modes n whch factors reated to fetme have a mutpcatve effect on the hazard functon. These modes are caed proportona hazards (PH) modes. Under the proportona hazards
More informationSupplementary material: Margin based PU Learning. Matrix Concentration Inequalities
Supplementary materal: Margn based PU Learnng We gve the complete proofs of Theorem and n Secton We frst ntroduce the well-known concentraton nequalty, so the covarance estmator can be bounded Then we
More informationMARKOV CHAIN AND HIDDEN MARKOV MODEL
MARKOV CHAIN AND HIDDEN MARKOV MODEL JIAN ZHANG JIANZHAN@STAT.PURDUE.EDU Markov chan and hdden Markov mode are probaby the smpest modes whch can be used to mode sequenta data,.e. data sampes whch are not
More informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More informationSupplementary Material: Learning Structured Weight Uncertainty in Bayesian Neural Networks
Shengyang Sun, Changyou Chen, Lawrence Carn Suppementary Matera: Learnng Structured Weght Uncertanty n Bayesan Neura Networks Shengyang Sun Changyou Chen Lawrence Carn Tsnghua Unversty Duke Unversty Duke
More informationOn the Power Function of the Likelihood Ratio Test for MANOVA
Journa of Mutvarate Anayss 8, 416 41 (00) do:10.1006/jmva.001.036 On the Power Functon of the Lkehood Rato Test for MANOVA Dua Kumar Bhaumk Unversty of South Aabama and Unversty of Inos at Chcago and Sanat
More informationThe line method combined with spectral chebyshev for space-time fractional diffusion equation
Apped and Computatona Mathematcs 014; 3(6): 330-336 Pubshed onne December 31, 014 (http://www.scencepubshnggroup.com/j/acm) do: 10.1164/j.acm.0140306.17 ISS: 3-5605 (Prnt); ISS: 3-5613 (Onne) The ne method
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationMachine learning: Density estimation
CS 70 Foundatons of AI Lecture 3 Machne learnng: ensty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 539 Sennott Square ata: ensty estmaton {.. n} x a vector of attrbute values Objectve: estmate the model of
More informationPredicting Model of Traffic Volume Based on Grey-Markov
Vo. No. Modern Apped Scence Predctng Mode of Traffc Voume Based on Grey-Marov Ynpeng Zhang Zhengzhou Muncpa Engneerng Desgn & Research Insttute Zhengzhou 5005 Chna Abstract Grey-marov forecastng mode of
More informationMATH 5707 HOMEWORK 4 SOLUTIONS 2. 2 i 2p i E(X i ) + E(Xi 2 ) ä i=1. i=1
MATH 5707 HOMEWORK 4 SOLUTIONS CİHAN BAHRAN 1. Let v 1,..., v n R m, all lengths v are not larger than 1. Let p 1,..., p n [0, 1] be arbtrary and set w = p 1 v 1 + + p n v n. Then there exst ε 1,..., ε
More informationUnified Subspace Analysis for Face Recognition
Unfed Subspace Analyss for Face Recognton Xaogang Wang and Xaoou Tang Department of Informaton Engneerng The Chnese Unversty of Hong Kong Shatn, Hong Kong {xgwang, xtang}@e.cuhk.edu.hk Abstract PCA, LDA
More informationNot-for-Publication Appendix to Optimal Asymptotic Least Aquares Estimation in a Singular Set-up
Not-for-Publcaton Aendx to Otmal Asymtotc Least Aquares Estmaton n a Sngular Set-u Antono Dez de los Ros Bank of Canada dezbankofcanada.ca December 214 A Proof of Proostons A.1 Proof of Prooston 1 Ts roof
More informationNested case-control and case-cohort studies
Outne: Nested case-contro and case-cohort studes Ørnuf Borgan Department of Mathematcs Unversty of Oso NORBIS course Unversty of Oso 4-8 December 217 1 Radaton and breast cancer data Nested case contro
More informationA Local Variational Problem of Second Order for a Class of Optimal Control Problems with Nonsmooth Objective Function
A Local Varatonal Problem of Second Order for a Class of Optmal Control Problems wth Nonsmooth Objectve Functon Alexander P. Afanasev Insttute for Informaton Transmsson Problems, Russan Academy of Scences,
More information2E Pattern Recognition Solutions to Introduction to Pattern Recognition, Chapter 2: Bayesian pattern classification
E395 - Pattern Recognton Solutons to Introducton to Pattern Recognton, Chapter : Bayesan pattern classfcaton Preface Ths document s a soluton manual for selected exercses from Introducton to Pattern Recognton
More informationStanford University CS359G: Graph Partitioning and Expanders Handout 4 Luca Trevisan January 13, 2011
Stanford Unversty CS359G: Graph Parttonng and Expanders Handout 4 Luca Trevsan January 3, 0 Lecture 4 In whch we prove the dffcult drecton of Cheeger s nequalty. As n the past lectures, consder an undrected
More informationDelay tomography for large scale networks
Deay tomography for arge scae networks MENG-FU SHIH ALFRED O. HERO III Communcatons and Sgna Processng Laboratory Eectrca Engneerng and Computer Scence Department Unversty of Mchgan, 30 Bea. Ave., Ann
More informationQuality-of-Service Routing in Heterogeneous Networks with Optimal Buffer and Bandwidth Allocation
Purdue Unversty Purdue e-pubs ECE Technca Reorts Eectrca and Comuter Engneerng -6-007 Quaty-of-Servce Routng n Heterogeneous Networs wth Otma Buffer and Bandwdth Aocaton Waseem Sheh Purdue Unversty, waseem@urdue.edu
More information8/25/17. Data Modeling. Data Modeling. Data Modeling. Patrice Koehl Department of Biological Sciences National University of Singapore
8/5/17 Data Modelng Patrce Koehl Department of Bologcal Scences atonal Unversty of Sngapore http://www.cs.ucdavs.edu/~koehl/teachng/bl59 koehl@cs.ucdavs.edu Data Modelng Ø Data Modelng: least squares Ø
More informationCS 2750 Machine Learning. Lecture 5. Density estimation. CS 2750 Machine Learning. Announcements
CS 750 Machne Learnng Lecture 5 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 539 Sennott Square CS 750 Machne Learnng Announcements Homework Due on Wednesday before the class Reports: hand n before
More informationAssortment Optimization under MNL
Assortment Optmzaton under MNL Haotan Song Aprl 30, 2017 1 Introducton The assortment optmzaton problem ams to fnd the revenue-maxmzng assortment of products to offer when the prces of products are fxed.
More informationCase Study of Markov Chains Ray-Knight Compactification
Internatonal Journal of Contemporary Mathematcal Scences Vol. 9, 24, no. 6, 753-76 HIKAI Ltd, www.m-har.com http://dx.do.org/.2988/cms.24.46 Case Study of Marov Chans ay-knght Compactfcaton HaXa Du and
More informationRegulation No. 117 (Tyres rolling noise and wet grip adhesion) Proposal for amendments to ECE/TRANS/WP.29/GRB/2010/3
Transmtted by the expert from France Informal Document No. GRB-51-14 (67 th GRB, 15 17 February 2010, agenda tem 7) Regulaton No. 117 (Tyres rollng nose and wet grp adheson) Proposal for amendments to
More informationThe Minimum Universal Cost Flow in an Infeasible Flow Network
Journal of Scences, Islamc Republc of Iran 17(2): 175-180 (2006) Unversty of Tehran, ISSN 1016-1104 http://jscencesutacr The Mnmum Unversal Cost Flow n an Infeasble Flow Network H Saleh Fathabad * M Bagheran
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationCollege of Computer & Information Science Fall 2009 Northeastern University 20 October 2009
College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:
More informationAssignment 5. Simulation for Logistics. Monti, N.E. Yunita, T.
Assgnment 5 Smulaton for Logstcs Mont, N.E. Yunta, T. November 26, 2007 1. Smulaton Desgn The frst objectve of ths assgnment s to derve a 90% two-sded Confdence Interval (CI) for the average watng tme
More informationDeriving the Dual. Prof. Bennett Math of Data Science 1/13/06
Dervng the Dua Prof. Bennett Math of Data Scence /3/06 Outne Ntty Grtty for SVM Revew Rdge Regresson LS-SVM=KRR Dua Dervaton Bas Issue Summary Ntty Grtty Need Dua of w, b, z w 2 2 mn st. ( x w ) = C z
More informationp(z) = 1 a e z/a 1(z 0) yi a i x (1/a) exp y i a i x a i=1 n i=1 (y i a i x) inf 1 (y Ax) inf Ax y (1 ν) y if A (1 ν) = 0 otherwise
Dustn Lennon Math 582 Convex Optmzaton Problems from Boy, Chapter 7 Problem 7.1 Solve the MLE problem when the nose s exponentally strbute wth ensty p(z = 1 a e z/a 1(z 0 The MLE s gven by the followng:
More informationHidden Markov Model Cheat Sheet
Hdden Markov Model Cheat Sheet (GIT ID: dc2f391536d67ed5847290d5250d4baae103487e) Ths document s a cheat sheet on Hdden Markov Models (HMMs). It resembles lecture notes, excet that t cuts to the chase
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationThe lower and upper bounds on Perron root of nonnegative irreducible matrices
Journal of Computatonal Appled Mathematcs 217 (2008) 259 267 wwwelsevercom/locate/cam The lower upper bounds on Perron root of nonnegatve rreducble matrces Guang-Xn Huang a,, Feng Yn b,keguo a a College
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationPROBLEM SET 7 GENERAL EQUILIBRIUM
PROBLEM SET 7 GENERAL EQUILIBRIUM Queston a Defnton: An Arrow-Debreu Compettve Equlbrum s a vector of prces {p t } and allocatons {c t, c 2 t } whch satsfes ( Gven {p t }, c t maxmzes βt ln c t subject
More informationPricing and Resource Allocation Game Theoretic Models
Prcng and Resource Allocaton Game Theoretc Models Zhy Huang Changbn Lu Q Zhang Computer and Informaton Scence December 8, 2009 Z. Huang, C. Lu, and Q. Zhang (CIS) Game Theoretc Models December 8, 2009
More informationLecture 4. Instructor: Haipeng Luo
Lecture 4 Instructor: Hapeng Luo In the followng lectures, we focus on the expert problem and study more adaptve algorthms. Although Hedge s proven to be worst-case optmal, one may wonder how well t would
More informationGreyworld White Balancing with Low Computation Cost for On- Board Video Capturing
reyword Whte aancng wth Low Computaton Cost for On- oard Vdeo Capturng Peng Wu Yuxn Zoe) Lu Hewett-Packard Laboratores Hewett-Packard Co. Pao Ato CA 94304 USA Abstract Whte baancng s a process commony
More informationMaximizing the number of nonnegative subsets
Maxmzng the number of nonnegatve subsets Noga Alon Hao Huang December 1, 213 Abstract Gven a set of n real numbers, f the sum of elements of every subset of sze larger than k s negatve, what s the maxmum
More informationModelli Clamfim Equazione del Calore Lezione ottobre 2014
CLAMFIM Bologna Modell 1 @ Clamfm Equazone del Calore Lezone 17 15 ottobre 2014 professor Danele Rtell danele.rtell@unbo.t 1/24? Convoluton The convoluton of two functons g(t) and f(t) s the functon (g
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationChapter 12. Ordinary Differential Equation Boundary Value (BV) Problems
Chapter. Ordnar Dfferental Equaton Boundar Value (BV) Problems In ths chapter we wll learn how to solve ODE boundar value problem. BV ODE s usuall gven wth x beng the ndependent space varable. p( x) q(
More informationApproximate merging of a pair of BeÂzier curves
COMPUTER-AIDED DESIGN Computer-Aded Desgn 33 (1) 15±136 www.esever.com/ocate/cad Approxmate mergng of a par of BeÂzer curves Sh-Mn Hu a,b, *, Rou-Feng Tong c, Tao Ju a,b, Ja-Guang Sun a,b a Natona CAD
More informationNonextensibility of energy in Tsallis statistics and the zeroth law of
Nonextensbty of energy n Tsas statstcs and the zeroth a of thermodynamcs onge Ou and Jncan hen* T Word Laboratory, P. O. 870, eng 00080, Peoe s Reubc of hna and Deartment of Physcs, Xamen nversty, Xamen
More informationReconstruction History. Image Reconstruction. Radon Transform. Central Slice Theorem (I)
Reconstructon Hstory wth Bomedca Acatons EEG-475/675 Prof. Barner Reconstructon methods based on Radon s wor 97 cassc mage reconstructon from roectons aer 97 Hounsfed deveo the frst commerca x-ray CT scanner
More informationSOME NOISELESS CODING THEOREM CONNECTED WITH HAVRDA AND CHARVAT AND TSALLIS S ENTROPY. 1. Introduction
Kragujevac Journal of Mathematcs Volume 35 Number (20, Pages 7 SOME NOISELESS COING THEOREM CONNECTE WITH HAVRA AN CHARVAT AN TSALLIS S ENTROPY SATISH KUMAR AN RAJESH KUMAR 2 Abstract A new measure L,
More informationChapter 4: Root Finding
Chapter 4: Root Fndng Startng values Closed nterval methods (roots are search wthn an nterval o Bsecton Open methods (no nterval o Fxed Pont o Newton-Raphson o Secant Method Repeated roots Zeros of Hgher-Dmensonal
More informationA generalization of Picard-Lindelof theorem/ the method of characteristics to systems of PDE
A generazaton of Pcard-Lndeof theorem/ the method of characterstcs to systems of PDE Erfan Shachan b,a,1 a Department of Physcs, Unversty of Toronto, 60 St. George St., Toronto ON M5S 1A7, Canada b Department
More informationFirst day August 1, Problems and Solutions
FOURTH INTERNATIONAL COMPETITION FOR UNIVERSITY STUDENTS IN MATHEMATICS July 30 August 4, 997, Plovdv, BULGARIA Frst day August, 997 Problems and Solutons Problem. Let {ε n } n= be a sequence of postve
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationAssociative Memories
Assocatve Memores We consder now modes for unsupervsed earnng probems, caed auto-assocaton probems. Assocaton s the task of mappng patterns to patterns. In an assocatve memory the stmuus of an ncompete
More informationAn Upper Bound on SINR Threshold for Call Admission Control in Multiple-Class CDMA Systems with Imperfect Power-Control
An Upper Bound on SINR Threshold for Call Admsson Control n Multple-Class CDMA Systems wth Imperfect ower-control Mahmoud El-Sayes MacDonald, Dettwler and Assocates td. (MDA) Toronto, Canada melsayes@hotmal.com
More informationY. Guo. A. Liu, T. Liu, Q. Ma UDC
UDC 517. 9 OSCILLATION OF A CLASS OF NONLINEAR PARTIAL DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLES* ОСЦИЛЯЦIЯ КЛАСУ НЕЛIНIЙНИХ ЧАСТКОВО РIЗНИЦЕВИХ РIВНЯНЬ З НЕПЕРЕРВНИМИ ЗМIННИМИ Y. Guo Graduate School
More informationFirst Year Examination Department of Statistics, University of Florida
Frst Year Examnaton Department of Statstcs, Unversty of Florda May 7, 010, 8:00 am - 1:00 noon Instructons: 1. You have four hours to answer questons n ths examnaton.. You must show your work to receve
More informationAn LSB Data Hiding Technique Using Prime Numbers
An LSB Data Hdng Technque Usng Prme Numbers Sandan Dey (), Aj Abraham (), Sugata Sanya (3) Anshn Software Prvate Lmted, Kokata 79 Centre for Quantfabe Quaty of Servce n Communcaton Systems Norwegan Unversty
More informationPHY688, Statistical Mechanics
Department of Physcs & Astronomy 449 ESS Bldg. Stony Brook Unversty January 31, 2017 Nuclear Astrophyscs James.Lattmer@Stonybrook.edu Thermodynamcs Internal Energy Densty and Frst Law: ε = E V = Ts P +
More informationA A Non-Constructible Equilibrium 1
A A Non-Contructbe Equbrum 1 The eampe depct a eparabe contet wth three payer and one prze of common vaue 1 (o v ( ) =1 c ( )). I contruct an equbrum (C, G, G) of the contet, n whch payer 1 bet-repone
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More information2-Adic Complexity of a Sequence Obtained from a Periodic Binary Sequence by Either Inserting or Deleting k Symbols within One Period
-Adc Comlexty of a Seuence Obtaned from a Perodc Bnary Seuence by Ether Insertng or Deletng Symbols wthn One Perod ZHAO Lu, WEN Qao-yan (State Key Laboratory of Networng and Swtchng echnology, Bejng Unversty
More informationModelli Clamfim Equazioni differenziali 7 ottobre 2013
CLAMFIM Bologna Modell 1 @ Clamfm Equazon dfferenzal 7 ottobre 2013 professor Danele Rtell danele.rtell@unbo.t 1/18? Ordnary Dfferental Equatons A dfferental equaton s an equaton that defnes a relatonshp
More informationLOW-DENSITY Parity-Check (LDPC) codes have received
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 59, NO. 7, JULY 2011 1807 Successve Maxmzaton for Systematc Desgn of Unversay Capacty Approachng Rate-Compatbe Sequences of LDPC Code Ensembes over Bnary-Input
More informationRandić Energy and Randić Estrada Index of a Graph
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 5, No., 202, 88-96 ISSN 307-5543 www.ejpam.com SPECIAL ISSUE FOR THE INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND ALGEBRA 29 JUNE -02JULY 20, ISTANBUL
More informationREAL ANALYSIS I HOMEWORK 1
REAL ANALYSIS I HOMEWORK CİHAN BAHRAN The questons are from Tao s text. Exercse 0.0.. If (x α ) α A s a collecton of numbers x α [0, + ] such that x α
More informationComputation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models
Computaton of Hgher Order Moments from Two Multnomal Overdsperson Lkelhood Models BY J. T. NEWCOMER, N. K. NEERCHAL Department of Mathematcs and Statstcs, Unversty of Maryland, Baltmore County, Baltmore,
More informationon the improved Partial Least Squares regression
Internatonal Conference on Manufacturng Scence and Engneerng (ICMSE 05) Identfcaton of the multvarable outlers usng T eclpse chart based on the mproved Partal Least Squares regresson Lu Yunlan,a X Yanhu,b
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationOptimal Guaranteed Cost Control of Linear Uncertain Systems with Input Constraints
Internatona Journa Optma of Contro, Guaranteed Automaton, Cost Contro and Systems, of Lnear vo Uncertan 3, no Systems 3, pp 397-4, wth Input September Constrants 5 397 Optma Guaranteed Cost Contro of Lnear
More informationMATH 281A: Homework #6
MATH 28A: Homework #6 Jongha Ryu Due date: November 8, 206 Problem. (Problem 2..2. Soluton. If X,..., X n Bern(p, then T = X s a complete suffcent statstc. Our target s g(p = p, and the nave guess suggested
More information3 Basic boundary value problems for analytic function in the upper half plane
3 Basc boundary value problems for analytc functon n the upper half plane 3. Posson representaton formulas for the half plane Let f be an analytc functon of z throughout the half plane Imz > 0, contnuous
More informationOptimum Selection Combining for M-QAM on Fading Channels
Optmum Seecton Combnng for M-QAM on Fadng Channes M. Surendra Raju, Ramesh Annavajjaa and A. Chockangam Insca Semconductors Inda Pvt. Ltd, Bangaore-56000, Inda Department of ECE, Unversty of Caforna, San
More informationPerron Vectors of an Irreducible Nonnegative Interval Matrix
Perron Vectors of an Irreducble Nonnegatve Interval Matrx Jr Rohn August 4 2005 Abstract As s well known an rreducble nonnegatve matrx possesses a unquely determned Perron vector. As the man result of
More informationGENERATIVE AND DISCRIMINATIVE CLASSIFIERS: NAIVE BAYES AND LOGISTIC REGRESSION. Machine Learning
CHAPTER 3 GENERATIVE AND DISCRIMINATIVE CLASSIFIERS: NAIVE BAYES AND LOGISTIC REGRESSION Machne Learnng Copyrght c 205. Tom M. Mtche. A rghts reserved. *DRAFT OF September 23, 207* *PLEASE DO NOT DISTRIBUTE
More informationCHAPTER III Neural Networks as Associative Memory
CHAPTER III Neural Networs as Assocatve Memory Introducton One of the prmary functons of the bran s assocatve memory. We assocate the faces wth names, letters wth sounds, or we can recognze the people
More informationProblem Set 9 Solutions
Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem
More informationModelli Clamfim Equazioni differenziali 22 settembre 2016
CLAMFIM Bologna Modell 1 @ Clamfm Equazon dfferenzal 22 settembre 2016 professor Danele Rtell danele.rtell@unbo.t 1/22? Ordnary Dfferental Equatons A dfferental equaton s an equaton that defnes a relatonshp
More informationSTAT 405 BIOSTATISTICS (Fall 2016) Handout 15 Introduction to Logistic Regression
STAT 45 BIOSTATISTICS (Fall 26) Handout 5 Introducton to Logstc Regresson Ths handout covers materal found n Secton 3.7 of your text. You may also want to revew regresson technques n Chapter. In ths handout,
More informationCounting Solutions to Discrete Non-Algebraic Equations Modulo Prime Powers
Rose-Hulman Insttute of Technology Rose-Hulman Scholar Mathematcal Scences Techncal Reorts (MSTR) Mathematcs 5-20-2016 Countng Solutons to Dscrete Non-Algebrac Equatons Modulo Prme Powers Abgal Mann Rose-Hulman
More informationOutline. EM Algorithm and its Applications. K-Means Classifier. K-Means Classifier (Cont.) Introduction of EM K-Means EM EM Applications.
EM Algorthm and ts Alcatons Y L Deartment of omuter Scence and Engneerng Unversty of Washngton utlne Introducton of EM K-Means EM EM Alcatons Image Segmentaton usng EM bect lass Recognton n BIR olor lusterng
More informationHila Etzion. Min-Seok Pang
RESERCH RTICLE COPLEENTRY ONLINE SERVICES IN COPETITIVE RKETS: INTINING PROFITILITY IN THE PRESENCE OF NETWORK EFFECTS Hla Etzon Department of Technology and Operatons, Stephen. Ross School of usness,
More informationImage Classification Using EM And JE algorithms
Machne earnng project report Fa, 2 Xaojn Sh, jennfer@soe Image Cassfcaton Usng EM And JE agorthms Xaojn Sh Department of Computer Engneerng, Unversty of Caforna, Santa Cruz, CA, 9564 jennfer@soe.ucsc.edu
More informationAsymptotics of the Solution of a Boundary Value. Problem for One-Characteristic Differential. Equation Degenerating into a Parabolic Equation
Nonl. Analyss and Dfferental Equatons, ol., 4, no., 5 - HIKARI Ltd, www.m-har.com http://dx.do.org/.988/nade.4.456 Asymptotcs of the Soluton of a Boundary alue Problem for One-Characterstc Dfferental Equaton
More informationGoodness of fit and Wilks theorem
DRAFT 0.0 Glen Cowan 3 June, 2013 Goodness of ft and Wlks theorem Suppose we model data y wth a lkelhood L(µ) that depends on a set of N parameters µ = (µ 1,...,µ N ). Defne the statstc t µ ln L(µ) L(ˆµ),
More informationMachine Learning. Classification. Theory of Classification and Nonparametric Classifier. Representing data: Hypothesis (classifier) Eric Xing
Machne Learnng 0-70/5 70/5-78, 78, Fall 008 Theory of Classfcaton and Nonarametrc Classfer Erc ng Lecture, Setember 0, 008 Readng: Cha.,5 CB and handouts Classfcaton Reresentng data: M K Hyothess classfer
More informationBézier curves. Michael S. Floater. September 10, These notes provide an introduction to Bézier curves. i=0
Bézer curves Mchael S. Floater September 1, 215 These notes provde an ntroducton to Bézer curves. 1 Bernsten polynomals Recall that a real polynomal of a real varable x R, wth degree n, s a functon of
More informationHMMT February 2016 February 20, 2016
HMMT February 016 February 0, 016 Combnatorcs 1. For postve ntegers n, let S n be the set of ntegers x such that n dstnct lnes, no three concurrent, can dvde a plane nto x regons (for example, S = {3,
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationMalaya J. Mat. 2(1)(2014) 49 60
Malaya J. Mat. 2(1)(2014) 49 60 Functonal equaton orgnatng from sum of hgher owers of arthmetc rogresson usng dfference oerator s stable n Banach sace: drect and fxed ont methods M. Arunumar a, and G.
More informationChapter 7 Channel Capacity and Coding
Wreless Informaton Transmsson System Lab. Chapter 7 Channel Capacty and Codng Insttute of Communcatons Engneerng atonal Sun Yat-sen Unversty Contents 7. Channel models and channel capacty 7.. Channel models
More informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationMultispectral Remote Sensing Image Classification Algorithm Based on Rough Set Theory
Proceedngs of the 2009 IEEE Internatona Conference on Systems Man and Cybernetcs San Antono TX USA - October 2009 Mutspectra Remote Sensng Image Cassfcaton Agorthm Based on Rough Set Theory Yng Wang Xaoyun
More informationDETERMINATION OF UNCERTAINTY ASSOCIATED WITH QUANTIZATION ERRORS USING THE BAYESIAN APPROACH
Proceedngs, XVII IMEKO World Congress, June 7, 3, Dubrovn, Croata Proceedngs, XVII IMEKO World Congress, June 7, 3, Dubrovn, Croata TC XVII IMEKO World Congress Metrology n the 3rd Mllennum June 7, 3,
More informationSELECTED SOLUTIONS, SECTION (Weak duality) Prove that the primal and dual values p and d defined by equations (4.3.2) and (4.3.3) satisfy p d.
SELECTED SOLUTIONS, SECTION 4.3 1. Weak dualty Prove that the prmal and dual values p and d defned by equatons 4.3. and 4.3.3 satsfy p d. We consder an optmzaton problem of the form The Lagrangan for ths
More information