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Deep Learning
Creation date：2024-07-03 15:12:27
Belonging category：计算机computer science
Tag Python
Deep Learning
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Deep Learning 
1. Prove that the softmax and sigmoid functions are equivalent when the number of possible
labels is two (for binary classification problem).
2. According to what you have learned about BP algorithm including feed forward
propagation and backward propagation processes of Neural Network, answer Question 1
in the slide below to prove whether the 6 equations hold or do not hold:
3. Answer Question 2 in the slide “Homework” above to “implement an NN …”. Using the
3-layer NN codes I gave you as a reference example
Requirements: Implement the NN algorithm by using Python (submit the codes and
make sure that your codes can be tested by our TAs or instructors through a simple
“click”. You can submit a readme file if needed). Note: that the architecture (2 – 3 – 2)
used in the given code is different from the one (2 – 2 – 2) in this Question 2 of
Homework Assignment 2. Also, note that the activation functions are different as well.
4. Given the network architecture as shown in the slide “Homework” above in Question 2
(assumed that the loss function is: ?(?, ŷ) =
1
2
∑ (? − ŷ)
?
?=1
2
, learning rate, α =0.5,
answer the questions below (provide the details step by step):
a. According to the forward propagation process, calculate the output: ŷ = ?
b. Calculate the loss (errors): L (?, ŷ)= ?
c. According to the BP algorithm: calculate the updated values of the weights W1
after 1 iteration.
5. Given the same dataset as Qn5 in HA1:
• “on the street” 50 times;
• “on the table” 1000 times;
• “on the computer” 2000 times;
• “standing on the street” 40 times;
• “standing on the computer” 1 time;
• “standing on the table” 100 times;
• “on the sky” 5 times;
• “on the water” 10 times;
• “on the cloud” 2 times;
• “it is magic that the guy smiles standing on the sky” 1 time;
• “it is magic that the guy smiles standing on the water” 2 times;
• “it is magic that the guy smiles standing on the cloud” 3 times;
a. Leverage RNN to perform the same task (build the language model) to guess the
next word: I notice three guys standing on the ( ).
b. Compare this with the results obtained by probabilistic language model in HA1.
c. Leverage the feedforward neural network for the same task, compare the result
with that of RNN.
d. If we use the corpus plus (shown in “HA1-Question 5 corpus plus.xlsx”), compare
the results obtained by language model, feedforward neural network, and RNN.
Explain what you find.
6. According to what you have learned about RNN algorithm, do the homework in the slide
below. Compare the results obtained by a feedforward neural network and RNN for this
task. Explain what you find. (You can leverage a large dataset, such as “shakespeare.txt”
to further explain your findings or explain why RNN is better (or worse) than feedforward
NN for sequence analysis.)
7. (Optional question) For a three-layer feedforward neural network, how do you
determine the number of nodes/neurons in the hidden layer? For the given dataset below,
how many neurons in the hidden layer is the best choice? (Hint: general, the following 3
equations can be used:
∑??ℎ
?
?
?=0
> ? (1)
where k is the number of samples, ?ℎ is number of nodes/neurons in the hidden layer; ? is
the number of inputs; ? ∈ [0, ?].
?ℎ = √? + ? + ? (2)
where ?ℎ is number of nodes/neurons in the hidden layer; ? is the number of input units,
? is the number of output units; ? ∈ [1, 10].
?ℎ = log2 ? (3)
where ?ℎ is number of nodes/neurons in the hidden layer; ? is the number of input units.
Table 1: Training dataset:
No. x1 x2 x3 x4 x5 x6 x7 x8 y
1 -1.7817 -0.2786 -0.2954 -0.2394 -0.1842 -0.1572 -0.1584 -0.1998 1
2 -1.8710 -0.2957 -0.3494 -0.2904 -0.1460 -0.1387 -0.1492 -0.2228 1
3 -1.8347 -0.2817 -0.3566 -0.3476 -0.1820 -0.1435 -0.1778 -0.1849 1
4 -1.8807 -0.2467 -0.2316 -0.2419 -0.1938 -0.2103 -0.2010 -0.2533 1
5 -1.4151 -0.2282 -0.2124 -0.2147 -0.1271 -0.0680 -0.0872 -0.1684 2
6 -1.2879 -0.2252 -0.2012 -0.1298 -0.0245 -0.0390 -0.0762 -0.1672 2
7 -1.5239 -0.1979 -0.1094 -0.1402 -0.0094 -0.1394 -0.1673 -0.2810 2
8 -1.6781 -0.2047 -0.1180 -0.1532 -0.1732 -0.1716 -0.1851 -0.2006 2
9 0.1605 -0.0920 -0.0160 0.1246 0.1802 0.2087 0.2234 0.1003 3
10 0.2045 0.1078 0.2246 0.203I 0.2428 0.2050 0.0704 0.0403 3
11 -1.0242 -0.1461 -0.1018 -0.0778 -0.0363 -0.0476 -0.0160 -0.0253 3
12 -0.7915 -0.1018 -0.0737 -0.0945 -0.0955 0.0044 0.0467 0.0719 3
Table 2: Test dataset:
13 -1.4736 -0.2845 -3.0724 -0.2108 -0. 190 4 -0.1467 -0.1696 -0.2001 1
14 -1.6002 -0.2011 -0.1021 -0.1394 -0.1001 -0.1572 -0.1584 -0.2790 2
15 -1.0314 -0.1521 -0.1101 -0.0801 -0.0347 -0.0482 -0.0158 -0.0301 3
Part 2: Sequence Labelling and POS
Application of POS Tagging to Sentiment Analysis
POS tagging is a necessary step for performing sentiment analysis, as the part of speech has
a great impact on a word’s sentiment polarity. Design an algorithm in which different parts of
speech are assigned different sentiment weights. For example, we assume that adjectives
convey the stronger sentiment information than verbs and nouns. So we assign larger sentiment
weights to the adjectives. Verbs and nouns may also convey sentiment information from time
to time. For example, the verb love and the noun congratulations are often associated with
positive sentiment. However, to express the sentiment, we believe adjectives play a much more
dominant role than verbs and nouns. Therefore, we will assign smaller sentiment weights to
verbs and nouns than adjectives. Similarly, we should assign smaller or zero sentiment weights
to determiner and preposition, ….
A small dataset “amazon_cells_labelled.csv” can be used as a case study for your homework.
1. Based on what we learnt from our class and what is described above, improve the Naïve
Bayes method for sentiment classification and implement it (Python codes are
preferred)—(application of POS Tagging to improve Naïve Bayes method for sentiment
classificationn).
Case category
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CMP7000A CMP-7038B Math 263 LAW3016 CS371 STAT 334 FIN0008 ACC3004 STAT 371 ​COMP1921 MTH201 ACCT2000 UN3412 CIV6000 MATHS 3021 MATE7014 ECON1 CIBC6035 LAW121G COMM 321 CSC8204R TTM2033 CSCI 2600 MAE 115 LNG302 CENV6175W1 ECON30019 CPS2015 BST969 DDES9015 AMATH242 CS 1151 N1592 ACCT600 EG503G SMM519 EC318 Ecstatistics EEE 471 MARK2051 Topology COM00037H ACCT3000 MTHM501 EG501V COM00055H BUSN9085 GGR273 MATH 2B ITD102 MA214 ECON0060 ECE3114 ECMM447 Mechanics CCT361H5S BSAN3210 WELF2001 Fin3001 RESP5001 STA 137 Linguistics 101 CSCI368 CMPSC497 LUBS3655 OMBA 5355 BUSM2562 ​BFF5902 CYBR7001 CULT2005 ECON 7720 MTRX3760 FSE598 ​LUE1001 MGSC 7100 CS3240 COSC7500 ACCT3091 INFOGR TRAN 2080 DESIGN CIVE215001 CIVE2360 CPSC 8430 FNCE2003 Stoichiometry INFS6023 Quantitative Method Math 21D ECE5179 Design ​ECON8022 Chemical DMS 213 ADM1370 BFF5902 BFF2701 AGRI10051 AMN400 ECON7322 ​FINC5090 ​MATH1052 ​SciComp Elec4622 ​FINS5516 ENG 101 MMM143 CS431CA2 BSAN2201 EBSC7070 ES9v9-10 PLIN0009 DATA 8 MATH 101 BCPM0097 ​MAT 237 BISM2201 EEE8099 Physics 11 ECE2238B Biostat 234 ​ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 ​MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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