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Machine Learning and Big Data for Economics and Finance

创建日期：2024-07-23 18:12:14

所属分类：计算机computer science

标签： Machine

Machine Learning and Big Data for Economics and Finance

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Machine Learning and Big Data for Economics and Finance

Consider the two variables in the dataset Assign3.csv. We are interested in predicting the second variable Y given the first variable X.

Fit a linear regression model to the data. Show the data scatter plot on the samefigure with the values predicted by the linear
Fit a quadratic regression model to the data. Show the data scatter plot on the same figure with the values predicted by the quadratic.

3.We are interested in constructing a step function learner asfollows:

First draw a random number U uniformly on the interval spanned by the minimum and maximum values of the inputs (x1; :::; xn) and then use it to construct the following function whose purpose is to give the prediction of Y given X = x:

f(x) = a1I(U 6 x) + a2I(U > x);

where a1 and a2. are just unknown constants to be learned. It goes without saying that I(some statement) is the indicator function that equals 1 when the statement is true and 0 otherwise.

a.Usetwo different methods to compute the estimate f^(x) = a^1I(U 6x)+a^2I(U > x). Is f^ a strong learner?

b.Use one of the previous two methods to write an Rfunction that takes as input x and the data (x1; :::; xn; y1; :::; yn) and gives as output f^(x).

Make sure the function is capable of dealing with the case where

x conatains more than one number.

c.Usingthree different runs of the previous function, create three dif- ferent plots where, on each, f^ is shown together with the scatter plot of the

4.Write an R function that applies boosting to the previous step function learner.

That R function should take as inputs: the data, B the number of boosting iterations, L the learning rate and an optional argument indicating thesize of the test subsample in case a validation set approach is

As output the function should give: f^boost the boosted learner evaluated

at the training data and the training mean squared error evaluated for each iteration b = 1; :::; B of the boosting algorithm. Also, in case the size of the test subsample is greater than zero, the function should output: f^boost evaluated

at the test sample and the test MSE evaluated for each iteration b = 1; :::; B.

a.Use that function to plot f^boost on top of the data scatter plot for

L = 0.01 and for B = 10000. Show the same with different values of B.

b.Plot the training MSE vs. the number of iterations

c.Was there overfitting when B =10000?

Note: Even though the algorithm is described in detail in both the slides and textbook, for the sake of making the implementation easier, its special case per- taining to the questions in the assignment is presented here.

Boosting algorithm:

Inputs:

A sample of covariates (i.e. inputs) x1; :::; xn and responses (i.e. out- puts) y1; :::; yn.

A (weak) learnerf^.
A learning rate L >0.

Initialize:

Set f^boost(x) 0.
Compute the first learner f^0(x) = a^1I(U 6 x) + a^2I(U > x) on the original data.
Setri yi ¡ Lf^0(xi) for i = 1; :::; n.

Do the following for b = 1; :::;B:

a.Givenx1; :::; xn as covariates and r1; :::; rn as responses, fit a learner f^b by first sampling U and then estimating f^b(x) = a^1I(U 6 x) + a^2I(U > x).

b.Set f^boost(x) f^boost(x) + Lf^b(x).

c.Setri ri ¡ Lf^b(xi).

4.Output: f^boost(x).

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BCPM0008 ECN 620 QBUS6830 ECSE-415 ECON5102 MGMT20005 MAT 653 ECO 480 COMP 5/600 CSSE 5600 ME 571 7CCMMS61 CS 550 COMP2865 MATH3075 STATS 506 QTM 220 ISYS2120 FIT5106 STAT 153 MKTG3112 ECON2102 ELE2018 COMP3031 MSIN0010 SCC461 MATH237 CS246 CSC3065 CSE 101 ICTWEB411 COMP9313 ECOS 2025 FN620 MATH11111 MATH 3018 KE1068 FINA 6112 C++ MISM 6202 MSIN0105 CSC8631 MECO6935 COMP4121 ACCT2011 DPBS1150 EEL 3701C F19PL OPM 661 CSE 310 CS918 BIOL30001 ACCT3563 BANK3600 MET CS622 MATH367 ACCT5907 Continuing COMP5048 COMP61021 CS3334 GSOE9210 CSCI-570 COMP 5322 HW 2 ALY-6020 IEOR 4706 DATA 200 EBUS504 CGE12412 COMP4108 7SSMM800 ECMM171P MATE50002 CS225 RS 6003 BH2274 ELEC3111 MAT6669 ECON-UA 227 PHIL 1012 7SSMM603 TB028A P6 ECS708 CSC 427 CS6476 CSE 250A A1A2 ITS61504 EECS 376 model HW6 UV0010 ECON 6074 MG4F7 CMP-7030Y INFO3008 BFIP013 ECON 5068 MATH6002 CS3483 PSTAT 131 C31FM CSOR W4246 AAEC 5307 DATA ELEC362 COMSM0047 ECN6006 MA20224 BST351 MATH 323 MATH323 AA2021 COMP3811 COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 MAS316/414 ACCT2522 MSIN0181 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