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ECE4179 - Deep Learning and Neural Networks

创建日期：2024-04-15 16:56:35

所属分类：计算机computer science

标签： ECE4179

Deep Learning and Neural Networks

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ECE4179 - Deep Learning and Neural Networks

Assignment 1
? Please submit your report along with the code (Jupyter notebook is preferred) as a single zip file.
? Include your name and student number in the filename for both the zip file and PDF. Do not send
doc/docx files.
? Include your name and email address on the report and use a single column format when you prepare
your report.
? Please ensure all of your results are included in your report. Marking is based on what is in the report.
This includes plots, tables, code screen-shots etc.
? Make sure you answer questions in full and support any discussions with relevant additional informa-
tion/experiments if necessary.
Late submission. Late submission of the assignment will incur a penalty of 10% for each day late. That
is with one day delay, the maximum mark you can get from the assignment is 90 out of 100, so if you score
99, we will (sadly) give you 90. Assignments submitted with more than a week delay will not be assessed.
Please apply for special consideration for late submission as soon as possible (, documented serious illness).
Note from ECE4179/5179 Team. The nature of assignments in ECE4179/5179 is different from many
other courses. Here, we may not have a single solution to a problem. Be creative in your work and feel free
to explore beyond questions. Creativity will be awarded by bonus points.
Good Luck
Question: 1 2 3 4 Total
Points: 10 35 40 15 100
Score:
ECE4179 Assignment1, Page 3 of 4 Due: 18:00, 20/08/2021
1. [10 points] Would it be possible to train a perceptron using a variant of the perceptron training algorithm
in which the bias weight is left unchanged, and only the other weights are modified?
2. Recall that for the logistic regression, the cross entropy loss is defined as:
LCE(w) = ? 1
m
m∑
i=1
{
yi log
(
σ(w>xi)
)
+ (1? yi) log
(
1? σ(w>xi)
)}
. (1)
Here, σ(z) = 1/
(
1 + exp(?z)) denotes the sigmoid function, and (x1, y1), (x2, y2), · · · , (xm, ym) with
xi ∈ Rn, yi ∈ {0, 1} showing m training samples. The gradient of the cross entropy loss wrt w can be
written as
?wLCE = 1
m
m∑
i=1
(
σ(w>xi)? yi
)
xi . (2)
Use the starter code provided as a Jupyter notebook and implement the following functions. Pay
attention to the comments and guidelines in the starter code
2.1. [5 points] a function to compute the sigmoid.
2.2. [15 points] a function to compute gradient and cost of the logistic regression
2.3. [10 points] complete the for loop that performs the gradient descent algorithm
2.4. [5 points] function that predicts the class of its inputs according to the parameters of the logistic
model
3. Load the data file called “toy data.npz” and use the training data (X train, y train) to train your logistic
model. Note that each sample xi is a point in R2 and each label is yi ∈ {0, 1}. Also note that samples
are bounded in xi ∈ [?5, 5]× [?5, 5] (meaning that each feature is within the range [-5,5]).
In your report,
3.1. [10 points] discuss the effect of the learning rate parameter in your model. Be specific here and
discuss in what range, the model performance is acceptable, whether your model becomes unstable
when changing the learning rate, or if you have observed slow convergence. In your report, provide
the loss curves and learning rates for the following cases;
1. if your model becomes unstable
2. if your model converges very slowly
3. if your model converges nicely.
3.2. [10 points] report the accuracy of your model on the test data (X test, y test). Here you need to
use the predict function and see what fraction of the test samples your model predicts correctly.
3.3. [10 points] compare the solution with and without the bias term in your model. Recall that to have
a bias, you need to augment your samples with “1”.
3.4. [10 points] plot the decision boundary of your model for points [?5, 5]× [?5, 5]. Here you need to
scan all the points (with a reasonable gap) in the region [?5, 5] × [?5, 5] and check the prediction
of your model. Then you can plot the results to visualize how your model predicts points in the
input region.
Hint: You can use the “meshgrid” function from Numpy to create a grid of points. Also, the function
“contourf” from Matplotlib will come handy for plotting the decision boundary.
ECE4179 Assignment1, Page 4 of 4 Due: 18:00, 20/08/2021
4. Load the data file called “toy data two circles.npz” and use the training data (X train, y train) to train
a logistic model. Note that each sample xi is a point in R2 and each label is yi ∈ {0, 1}.
In your report,
4.1. [5 points] report the accuracy of your model on the test data (X test, y test).
4.2. [10 points] Your friend suggests that to better classify this data, we need to use nonlinear features.
In particular, (s)he suggests to map a sample R2 3 x = (x1, x2)> to R5 3 x? = (x1, x2, x21, x22, x1x2)>.
Use the above mapping and then train a new logistic model. Compute the accuracy of the resulting
model and compare it with the model from part 4.1. Plot the decision boundaries and compare it
with the model in part 4.1.

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1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A PHIL2617 PHYS3116 MIE250 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