Generate a time-series plot similar to the one on the right above. What could be the

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Please show your work for each problem, even if it does not completely solve the problem.

Problem 1 [50 points] - Missing Data

No programming is needed for this problem. Justify your response for all the answers you provide.

Let's say you're given a signal with some missing data, as shown in the figure above, and your goal is to fill in the blanks.

1. Would you say that this is a supervised learning, or an unsupervised learning problem?

2. Which of the following models do you think fits the data above?

3. Describe how you would proceed to solve it if you were given such a problem.

Problem 2 [50 points] - Decision boundaries

No programming is needed for this problem. Justify your response for all the answers you provide.

Let's say you're given four different datasets, (labelled A, B, C and D in the figures below), each with two-dimensional points, labelled either as members of a "Red Class" or a "Green Class". For each dataset, you'd like to come up with a decision boundary that splits the two classes. 

You express the decision boundary as the set of points   such that  , and let's call   the decision function.

For example, let's say you determine whether a point   is Red or Green by adopting the following rule:

then, you'd select a decision function  .

Question:

For each of the 4 datasets given above, which of the following decision functions would you use?

Hint: You might find Desmos Graphing Calculator helpful for this problem, to give you an idea of what   looks like for each of these cases. 

BONUS [25 points] - Choosing a Retail Electricity Provider

Knowing your experience in retail electricity markets, your friend, who resides in ZIP code 77002 in Houston, seeks your help in choosing the best electric plan for them. Using

powertochoose.com, select the top three plans to present to them, and justify why they should consider those. Consider the following priorities:

1. Estimated consumption of 500 kWh per month.

2. Not willing to pay more than 10 cents per kWh.

3. A preference of at least 15% of their energy to be from renewables.

You are given in some 7-day time-series data for real photovoltaic (PV) power output

at 3 different locations in Texas. The three locations are labelled in the file as 'east red', 'east green' and 'west blue' to match the map and plot above.

1. Reading files:

Extract The 3 time-series measurements, and store them as three different variables in 

Python, say x_red ,

2. Plotting Time-series: 

and x_blue . 

Generate a time-series plot similar to the one on the right above. What could be the reasons why the blue signal looks quite different from the other two?

3. Cross-correlation:

Using np.correlate , compute the cross-correlation between all pairs of time-series (i.e. red- green, red-blue, green-blue). Finally, what conclusions can you draw?

Problem 2 [50 points] - Dimensionality Reduction

You are a power systems engineer, and your manager seeks your help to interpret a dataset of voltage magnitude measurements which are collected at 240 different buses in a transmission network. Each row of measurement (one per bus) contains 5 minutes of time-series data at 60 samples per second. To perform PCA on the given dataset, you first construct the measurement matrix, .

1. What is the dimension of . That is, how many rows and columns does it contain?

2. Do you expect the covariance of to be a diagonal matrix? (Yes/No, and why) 

3. Say you perform PCA, and obtain the transformed measurement matrix, . What can you say about the covariance of ?

BONUS [25 points] - Power Systems Data

1. Download a publicly available power systems time-series dataset, other than the ones shown in class. Make sure to provide a link in your solution.

2. Analyze portions of the data using any of the methods we learned in class, and present some interesting findings.

3. Use Python for the step above, and share your code along with any files you used (e.g. the dataset).

Attachments:

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