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EECE5644 Assignment
创建日期：2024-05-02 09:04:02
标签： EECE5644
Assignment

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EECE5644  Assignment 

Please submit in Canvas a single PDF file showing all results, and include code as appendix
or as an external repository link in the PDF file. Cite all appropriate sources you benefit from.
Directly exchanging writing/code/results between classmates are not acceptable, but you may talk
to each other in classes, office periods, benefit from each others’ questions and answers for those.
Question 1 (60%)
In this exercise, you will train many multilayer perceptrons (MLP) to approximate the class
label posteriors, using maximum likelihood parameter estimation (equivalently, with minimum
average cross-entropy loss) to train the MLP. Then, you will use the trained models to approximate
a MAP classification rule in an attempt to achieve minimum probability of error (i.e. to minimize
expected loss with 0-1 loss assignments to correct-incorrect decisions).
Data Distribution: ForC= 4 classes with uniform priors, specify Gaussian class-conditional
pdfs for a 3-dimensional real-valued random vector x (pick your own mean vectors and covariance
matrices for each class). Try to adjust the parameters of the data distribution so that the MAP
classifier that uses the true data pdf achieves between 10%−20% probability of error.
MLP Structure: Use a 2-layer MLP (one hidden layer of perceptrons) that has P perceptrons
in the first (hidden) layer with smooth-ramp style activation functions (e.g., ISRU, Smooth-ReLU,
ELU, etc). At the second/output layer use a softmax function to ensure all outputs are positive
and add up to 1. The best number of perceptrons for your custom problem will be selected using
cross-validation.
Generate Data: Using your specified data distribution, generate multiple datasets: Training
datasets with 100,200,500,1000,2000,5000 samples and a test dataset with 100000 samples. You
will use the test dataset only for performance evaluation.
Theoretically Optimal Classifier: Using the knowledge of your true data pdf, construct the
minimum-probability-of-error classification rule, apply it on the test dataset, and empirically esti-
mate the probability of error for this theoretically optimal classifier. This provides the aspirational
performance level for the MLP classfier.
Model Order Selection: For each of the training sets with different number of samples,
perform 10-fold cross-validation, using minimum classification error probability as the objective
function, to select the best number of perceptrons (that is justified by available training data).
Model Training: For each training set, having identified the best number of perceptrons using
cross-validation, using maximum likelihood parameter estimation (minimum cross-entropy loss)
train an MLP using each training set with as many perceptrons as you have identified as optimal
for that training set. These are your final trained MLP models for class posteriors (possibly each
with different number of perceptrons and different weights). Make sure to mitigate the chances
of getting stuck at a local optimum by randomly reinitializing each MLP training routine multiple
times and getting the highest training-data log-likelihood solution you encounter.
Performance Assessment: Using each trained MLP as a model for class posteriors, and using
the MAP decision rule (aiming to minimize the probability of error) classify the samples in the test
set and for each trained MLP empirically estimate the probability of error.
Report Process and Results: Describe your process of developing the solution; numerically
and visually report the test set empirical probability of error estimates for the theoretically opti-
mal and multiple trained MLP classifiers. For instance show a plot of the empirically estimated
1
test P(error) for each trained MLP versus number of training samples used in optimizing it (with
semilog-x axis), as well as a horizontal line that runs across the plot indicating the empirically
estimated test P(error) for the theoretically optimal classifier.
Note: You may use software packages for all aspects of your implementation. Make sure you
use tools correctly. Explain in your report how you ensured the software tools do exactly what you
need them to do.
Question 2 (40%)
Conduct the following model order selection exercise using 10-fold cross-validation procedure
and report your procedure and results in a comprehensive, convincing, and rigorous fashion:
1. Select a Gaussian Mixture Model as the true probability density function for 2-dimensional
real-valued data synthesis. This GMM will have 4 components with different mean vectors,
different covariance matrices, and different probability for each Gaussian to be selected as
the generator for each sample. Specify the true GMM that generates data.
2. Generate multiple data sets with independent identically distributed samples using this true
GMM; these datasets will have respectively 10, 100, 1000, 10000 samples.
3. For each data set, using maximum likelihood parameter estimation principle (e.g. with the
EM algorithm), within the framework of K-fold (e.g., 10-fold) cross-validation, evaluate
GMMs with different model orders; specifically evaluate candidate GMMs with 1, 2, 3,
4, 5, 6 Gaussian components. Note that both model parameter estimation and validation
performance measures to be used is log-likelihood of data.
4. Repeat the experiment multiple times (e.g., at least 30 times) and report your results, indi-
cating the rate at which each of the the six GMM orders get selected for each of the datasets
you produced. Develop a good way to describe and summarize your experiment results in
the form of tables/figures.
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 MAS8383 ECO 512 STAT 8310 CMN3102 MA577 CMPT 225 COMP0045 Methods Equations MATH 113 Math 3283W ICS-33 EN4302/ENT603 BIA B350F MA318 MTHM506 MECH 5315M ECONOMICS MAS8382 COM 2004 PX3142 XJEL 3662 STAT 231 MGT B399F PX4131 COM2108 30AM MSCI521 ECONM1015 ACFI304 GR5241 MATH10101 ECON 2070 COMS31900 EFIM20011 CSE 250B ACSE-5 STAT4207 SOFT2412 ELEC 331 AY2020 MSIN0209 FIT2094 CS 241L ST404 CS 411 3D CA3 INF4002 COMP3506 SIT718 CS 188 CS 170 MATH 138 CSE 251A CMT118 DATA5207 CMPT307 CMPT459 T1 PGEE11108 COSC 3P32 ME 163 MATH96007 7QQMM203 EE6227 BA 574 STA 4234 ECO206Y1Y ECO2008 MT2300 MATH 11158 CS 527 MACM 316 CSE474 2DI70 ISE 525 COMP3411 EMAT30007 7CCSMBDT MFIN704 MFIN704W21 MfIB ECE 438 CS 436 F36 CS5344 FE 621A FE621 TBA 612 ECM3151 ECMM422 MF1 MSIN0107 ESSMENT CS 5854 MFIT 5008 MIPS R4000 ENG5274 BU52018 ENG2079 BIOA02 STA2570 F0 INF553 STAT 440 STAT3008 COMP9417 COMP6451 6COM1042 BU52006 ST303 HW-1 CISC-235 CS 510 MATH3161 ECN 140 ECE391 Comp 3613 CVEN 9625 PRG455 UESTION 1 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