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S6140: Machine Learning

创建日期：2024-08-06 15:20:50

所属分类：数学mathematics

标签： S6140

Machine Learning

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S6140: Machine Learning

Homework Assignment

Problem 1. (40 points) Consider two classification concepts given in Figure 1, where x ∈ X = [?6, 6] ×

[?4, 4], y ∈ Y = {?1,+1} and p(y|x) ∈ {0, 1} is defined in the drawing.

Figure 1: Two concepts where examples that fall within any of the three 3 × 3 (panel A) or 1 × 1 (panel

B) squares are labeled positive and the remaining examples (outside each of the squares but within X ) are

labeled negative. The position of the point x = (x1, x2) in the upper left-hand corner for each square is

shown in the picture. Consider horizontal axis to be x1 and vertical axis as x2.

Your experiments in this question will rely on generating a data set of size n ∈ {250, 1000, 10000} drawn from

a uniform distribution in X and labeled according to the rules from Figure 1; e.g., P (Y = 1|x) = 0.97 if x

that was randomly drawn is inside any of the three squares in either of the two panels, and P (Y = 1|x) = 0.01

otherwise (notice that this introduces a certain amount of asymmetric noise in the data). The goal of the

following two problems will be to train and evaluate classifiers created from the data generated in this way.

You can use any library you want in this assignment and do programming in Python, MATLAB, or R. Your

code should be easy to run for each question and sub-question below so that we can replicate your results

to the maximum extent possible.

Consider single-output feed-forward neural networks with one or two hidden layers such that the number of

hidden neurons in each layer is h1 ∈ {1, 4, 12} and h2 ∈ {0, 3}, respectively, with h2 = 0 meaning that there

is no second hidden layer. Consider one of the standard objective functions as your optimization criterion

and use early stopping and regularization as needed. Consider a hyperbolic tangent activation function in

each neuron and the output but you are free to experiment with others if you’d like to. For each of the

architectures, defined by a parameter combination (h1, h2), evaluate the performance of each model using

classification accuracy, balanced accuracy, and area under the ROC curve as your two performance criteria.

To evaluate the performance of your models use cross-validation. However, to evaluate the performance of

performance evaluation, generate another very large data set on a fine grid in X . Then use the predictions

2 Homework Assignment # 4

from your trained model on all these points to determine the “true” performance. You can threshold your

predictions in the middle of your prediction range (i.e., at 0.5 if you are predicting between 0 and 1) to

determine binary predictions of your models and to then compare those with true class labels you generated

on the fine grid.

Provide meaningful comments about all aspects of this exercise (performance results for different network

architectures, accuracy in and of cross-validation, true accuracy when you disregard class-label noise, run

time, etc.). The comments should not just re-state the results but rather capture trends and give reasoning

as to why certain behavior was observed.

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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 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