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cpts350 Symbolic graph project
创建日期：2024-06-25 18:09:37
标签： cpts350
Symbolic graph project

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cpts350 Symbolic graph project

Problem 1: Two-class classification with neural networks (40 points)

Use a multi-layer fully connected neural network architecture to perform nonlinear classification on the provided dataset (eggs.csv). Here, we choose the network to have four hidden layers with ten units in each layer, and the tanh activation. We then tune the parameters of this model by minimizing an associated twoclass Softmax cost via gradient descent.

Provided below is a sample visualizing of the nonlinear decision boundary learned in the top row of Figure along with the dataset itself. You need to produce a scattered plot like the one on the right panel of Figure 1,but it is optional to plot the (black) decision boundary. In addition, produce a cost history plot and an accuracy history plot like the example given in Lecture Slide 54.

Use the Python code in Lecture Slides to create and initialize neural network architecture, and use autograd to compute the gradients.

Problem 2: Number of weights to learn in a neural network (20 points)

(a) Find the total number Q of tunable parameters in a general L-hidden-layer neural network, in terms of variables expressed in the layer sizes below

(b) Based on your answer in part (a), explain how the input dimension N and number of data points P each contributes to Q. How is this different from what you saw with kernel methods in the previous chapter?

Problem 3: Early stopping cross-validation (40 points)

Experiment:

This experiment illustrates the early stopping procedure using a simple non-linear regression dataset (split into 2/3 training and 1/3 validation), and a three-hidden-layer neural network with ten units per layer, and with tanh activation. Three different steps from a single run of gradient descent (for a total of 10, 000 steps) is illustrated in Figure 2, one per each column, with the resulting fit at each step shown over the original (first row), training (second row), and validation data (third row). Stopping the gradient descent early after taking

(around) 2000 steps provides, for this training-validation split of the original data, a fine nonlinear model for the entire dataset.

Problem:

Implement the above experiment with the above a) training-validation split b) network architecture and c) training configuration on the provided dataset (noisy_sin_sample.csv). You need only to produce the top and bottom plots in the last column, i.e., the top right (on original data) and the bottom right (the error curve till the last step).

Bonus question (10 pts):

If you also produce the top and bottom plots in the middle column correctly, you will gain 10 bonus points. In other words, the full marks of this homework become 110 points if you choose to do so.


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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 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