WEEK 10 HOMEWORK – SAMPLE SOLUTIONS IMPORTANT NOTE, Questions with accurate answers, 100% Accurate.

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WEEK 10 HOMEWORK – SAMPLE SOLUTIONS IMPORTANT NOTE These homework solutions show multiple approaches and some optional extensions for most of the questions in the assignment. You don’t need to ... submit all this in your assignments; they’re included here just to help you learn more – because remember, the main goal of the homework assignments, and of the entire course, is to help you learn as much as you can, and develop your analytics skills as much as possible! Question 14.1 The breast cancer data set breast-cancer-wisconsin.data.txt from http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/ (description at http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Original%29 ) has missing values. 1. Use the mean/mode imputation method to impute values for the missing data. 2. Use regression to impute values for the missing data. 3. Use regression with perturbation to impute values for the missing data. 4. (Optional) Compare the results and quality of classification models (e.g., SVM, KNN) build using (1) the data sets from questions 1,2,3; (2) the data that remains after data points with missing values are removed; and (3) the data set when a binary variable is introduced to indicate missing values. Here’s one possible solution. Please note that a good solution doesn’t have to try all of the possibilities in the code; they’re shown to help you learn, but they’re not necessary. The file solution 14.1.R shows one possible solution. In it, missing data is identified (only variable V7 has any, and it is only a small amount). Five different data sets are created to deal with the missing data: (1) Replacing missing values with the mode. This could have gone either way (mode or mean). The data is categorical, but it takes integer values from 1 to 10, and as we’ll see later the values seem to have some relative meaning, so they’re also somewhat continuous. (2) Using regression to estimate missing values. Here too could have gone either way (see above)… but since we didn’t cover multinomial logistic regression in this course, the solutions treat the data as continuous for this part. Once the missing values are estimated, the estimates are rounded (because the original values are all integer) and values larger or smaller than the extremes are shrunk to the extremes. (3) Using regression plus perturbation. (4) Removing rows with missing data.(5) Adding a binary variables to indicate when data is missing, and adding the necessary interaction variables also. Once the data sets have been created, we use KNN (for k=1,2,3,4,5) and SVM (C=0.0001,0.001,0.01,0.1,1,10) to create classification models, and measure their quality. The table below shows the results. Method for dealing with missing data Model Impute using mode Impute using regression Impute using regression, then perturb Remove rows with missing data Add binary variable for missing data KNN (k=1) 0.952 0.948 0.948 0.952 0.952 KNN (k=2) 0.952 0.948 0.948 0.952 0.952 KNN (k=3) 0.924 0.919 0.919 0.923 0.924 KNN (k=4) 0.924 0.919 0.919 0.923 0.924 KNN (k=5) 0.919 0.914 0.914 0.913 0.919 SVM (C=0.0001) 0.662 0.662 0.662 0.659 0.662 SVM (C=0.001) 0.943 0.943 0.943 0.942 0.943 SVM (C=0.01) 0.957 0.957 0.957 0.957 0.957 SVM (C=0.1) 0.962 0.962 0.962 0.962 0.962 SVM (C=1) 0.967 0.962 0.967 0.966 0.967 SVM (C=10) 0.967 0.962 0.967 0.966 0.967 It turns out that there isn’t much difference in model performance across the five ways of dealing with missing data. The best SVM models are a little better than the best KNN models, but SVM is harder to calibrate; the worst SVM models tested are much worse than the worst KNN models. Question 15.1 Describe a situation or problem from your job, everyday life, current events, etc., for which optimization would be appropriate. What data would you need? Some (perhaps overzealous!) baseball fans have tried to drive around the country to see a baseball game at each of the 30 Major League stadiums, and then return home, in the shortest number of days. This can be modeled using optimization: minimize the number of days it takes, subject to the constraints that a game is seen at each stadium, and the planned sequence of games is possible given the driving times and game schedules. The necessary data would include the Major League schedule (which stadiums have games scheduled on each day, and what time they’re scheduled for), and how long it takes to drive between each pair of stadiums. Question 15.2 In the videos, we saw the “diet problem”. (The diet problem is one of the first large-scale optimizationproblems to be studied in practice. Back in the 1930’s and 40’s, the Army wanted to meet the nutritional requirements of its soldiers while minimizing the cost.) In this homework you get to solve a diet problem with real data. The data is given in the file diet.xls. Here’s one possible solution. Please note that a good solution doesn’t have to try all of the possibilities in the code; they’re shown to help you learn, but they’re not necessary. 1. Formulate an optimization model (a linear program) to find the cheapest diet that satisfies the maximum and minimum daily nutrition constraints, and solve it using PuLP. Turn in your code and the solution. (The optimal solution should be a diet of air-popped popcorn, poached eggs, oranges, raw iceberg lettuce, raw celery, and frozen broccoli. UGH!) Algebraically, here’s what the model looks like: Data ???? = cost per unit of food ?? ?????? = amount of nutrient ?? per unit of food ?? ???? = minimum amount of nutrient ?? required ???? = maximum amount of nutrient ?? required Variables ???? = amount of food ?? eaten Objective Minimize ∑?? ???????? (minimize total cost) Constraints ∑?? ?????????? ≥ ???? for each nutrient ?? (take in at least minimum amount of each nutrient) ∑?? ?????????? ≤ ???? for each nutrient ?? (take in no more than max amount of each nutrient) ???? ≥ 0 for each food ?? (can’t eat negative amounts) The file solution 15.2-1-separate.py shows one way to solve the problem. This file deals with each nutrient separately, to show what the problem looks like. However, an easier way to do it is shown in file solution 15.2-1-simpler.py, where data is read and constraints are written in a loop, so individual nutrients don’t need to each be written out. This will come in handy when there are more constraints (like the optional part below). However you set up the problem, here’s the optimal solution: ## ---------The solution to the diet problem is---------- ## 52.64371 units of Celery,_Raw ## 0.25960653 units of Frozen_Broccoli ## 63.988506 units of Lettuce,Iceberg,Raw ## 2.2929389 units of Oranges ## 0.14184397 units of Poached_Eggs ## 13.869322 units of Popcorn,Air_Popped ## ## Total cost of food = $4.34 [Show More]

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