R语言机器学习代写: Latent Variables and Neural Networks

Assessment 2

Latent Variables and Neural Networks

Objectives

This assignment consists of three parts (A,B,C), which cover latent variables models and neural networks (Modules 4 and 5). The total marks of this assessment is 100.

Part A. Document Clustering
In this part, you solve a document clustering problem using unsupervised learning algorithms

(i.e., soft and hard Expectation Maximization for document clustering. Question 1 [EM for Document Clustering, 40 Marks]

1. Derive Expectation and Maximisation steps of the hard-EM algorithm for Document Clustering, show your work in your submitted report. In particular, include all model parameters that should be learnt and the exact expression (using the same math convention that we saw in the Module 4) that should be used to update these parameters during the learning process (ie., E step, M step and assignments).
2. Implement the hard-EM (you derived above) and soft-EM (derived in Chapter 5 of Module 4). Please provide enough comments in your submitted code.
   Hint. If it helps, feel free to base your code on the provided code for EM algorithm

   for GMM in Activity 4.1 or the codebase provided in the Moodle).

3. Load Task3A.text file and necessary libraries (if needed, perform text preprocessing similar to what we did in Activity 4.2), set the number of clusters K=4, and run both

   the soft-EM and hard-EM algorithms on the provided data.

4. Perform a PCA on the clusterings that you get based on the hard-EM and soft-EM in

   the same way we did in Activity 4.2. Then, visualise the obtained clusters with different colors where x and y axes are the first two principal components (similar to Activity 4.2). Save your visualizations as plots in your Notebook file.

Part B. Neural Network vs. Perceptron

In this part, you apply a 3-layer Neural Network on a synthetically generated data to compare its performance with Perceptron. Here, we are looking for your explanation about the differences between perceptron and NN that leads to different results.

Question 2 [Neural Network’s Decision Boundary, 30 Marks]

1. Load Task3B_train.csv and Task3B_test.csv sets, plot the training data with classes are marked with different colors, and attach the plot to your report.
2. Run the implementations of Perceptron given to you in Activity 3.1, calculate the test error, and plot the test data while the points are colored with their estimated class labels; attach the pdf to your report.
   Hint. Note that you must remove NA records from the datasets (using “complete.cases()’ function). You may also choose to change the labels from [0, 1] to [-1, +1] for your convenience. If you decided to use the code from Activity 3.1, you may need to change some initial settings (e.g., epsilon and tau.max). Finally, remember that perceptron is sensitive to initial weights. Therefore, we recommend to run your code a few times with different initial weights.
3. Run the 3-layer Neural Network given to you in Activity 5.1 with different values of K (i.e, number of units in the hidden layer) and record testing error for each of them; plot the error vs K and attach it to your report. Based on this plot, find the best K and the corresponding model, then plot the test data while the points are colored with their estimated class labels using the best model that you have selected; attach the plot to your report.

   Hint. In case you choose to use the provided examples in Activity 5.1, you may need to transpose the dataset ()using “t()” function) and use different values for parameter settings (e.g., lambda). We also recommend to change K to 2, 4, 6, .., 100 (i.e. from 2 to 100 with the step size of 2).

4. In a table, report the error rates obtained by the perceptron and all variants of NN. Then bold the best model (with minimum error). Save this table to your Notebook file.
5. In your Notebookfile, explain the reason(s) responsible for such difference between perceptron and a 3-layer NN.

   Hint: Look at the plots and think about the model assumptions.

Part C. Self-Taught Learning
In this part, you implement self-taught learning for Neural Network using the Autoencoder

that provided in Activity 5.2 and a 3-layer NN (from Activity 5.1 or H2O package) Question 3 [Self Taught Neural Network Learning, 30 Marks]

1. Load Task3C_labeled.csv, Task3C_unlabeled.csv and Task3C_test.csv data sets and required libraries (e.g., H2O). Note that we are going to use Task3C_labeled.csv and Task3C_unlabeled.csv for training the autoencoder. We are going to use Task3C_labeled.csv for training the classifier. Finally, we evaluate the trained classifier on the test Task3C_test.csv.
2. Train an autoencoder (similar to Activity 5.2) with only one hidden layer and change the number of its neurons to: 20, 40, 60, 80, .., 500 (i.e. from 20 to 500 with a step size of 20).
3. For each model in Step II, calculate and record the reconstruction error which is simply the average (over all data points while the model is fixed) of Euclidian distances between the input and output of the autoencoder (you can simply use “h2o.anomaly()” function). Plot these values where the x-axis is the number of units in the middle layer and the y-axis is the reconstruction error. Then, save and attach the plot to your Notebook file, and explain your findings based on the plot.
4. Use the 3-layer NN from Activity 3.1 or “h2o.deeplearning” function (make sure you set “ autoencoder = FALSE”) to build a model with 100 units in the hidden layer using all the original attributes from the training set. Then, calculate and record the test error.
5. Build augmented self-taught networks using the models learnt in Step II. For each model:

A. Add the output of the middle layer as extra features to the original feature set, B. Train a 3-layer NN (similar to Step IV) using all features (original + extra).

Then calculate and record the test error.

6. Plot the error rates for the 3-layer neural networks from Step IV and V while the

   x-axis is the number of features and y-axis is the classification error. Save the plot

   in your Notebook file.

7. Report the optimum number(s) of units in the middle layer of the autoencoder in

   terms of the reconstruction and misclassification errors.

8. Comparing the plot from Step III and VI, do you observe any relation between

the reconstruction error and misclassification error? Explain your finding in your Notebook file.

Hint. Since the dataset for this task is large and high-dimensional, running the whole experiments several times is very time consuming. Therefore, it is recommended to only use a small portion of your data when you develop or debug your code.

Hint. If you can combine Step II and V (so learn each autoencoder only once), you may save a great portion of the execution time.

Hint. If you don’t see the expected behaviour in your plots, you may need to check that the data is clean, i.e. it doesn’t have NA entries, it’s normalised etc. Moreover, you may need to check that your implementation of the model and training/decoding algorithms are correct.

Submission & Due Date:

The files that you need to submit are:
1. Jupyter Notebook files containing the code for questions {1,2,3} with the extension

“.ipynb”. The file names should be in the following format:

STUDNETID_assessment_2_qX.ipynb

where ‘X=1,2,3’ is the question number. For example, the Notebook for Question 3 Should be named STUDNETID_assessment_2_q3.ipynb

2. You must add enough comments to your code to make it readable and understandable by the tutor. Furthermore, you may be asked to meet (online) with your tutor when your assessment is marked to complete your interview.

3. A PDF file that contains your answer to Q1.I (it is the only pen & paper question in this assignment, all the other questions are answered in Notebook files.The file name should be in the following format: STUDNETID_assessment_2_report.pdf

4. All the above files must be zipped in one zip file named “STUDNETID_assessment_2.zip”, and be submitted via Moodle before the deadline.

You should replace STUDENTID with your own student ID.

Assessment Criteria:

The following outlines the criteria which you will be assessed against:

• ●  Ability to understand the fundamentals of neural networks and latent variable models.
• ●  Working code: The code executes without errors and produces correct results.
• ●  Quality of explanations: You should show your understanding of the latent variable

  models and neural networks by answering the explanation questions.

  Penalties:

• ●  Late submission (-20% of awarded marks for between 1-3 days late pro-rata, -50% for between 4-6 days late pro-rata. 0 marks awards after 6 days)
• ●  Jupyter Notebook file is not properly named (-5%)
• ●  The PDF file is not properly named (-5%)