Question

Given a list of predicted values and a list of their corresponding observed values, complete the function FilterOutliers that computes the error of the data, removes outliers, and re-computes the error. The input arguments: • predicted: A double precision 10 array of size n containing the predicted values. . observed: A double precision 1D array of size n containing the observed values • threshold: A double precision positive scalar that determines if an observation is an outlier. The output arguments: • oldError: A double precision scalar representing the error before the removal of outliers. . numOutliers: An integer precision scalar representing the number of outliers in the original data • newError: A double precision scalar representing the error after the removal of outliers.. Here, error is defined as the mean-squared-error (MSE). MSE = 0,- E1 is the number of data points . O represents observed values Prepresents predicted values Therefore, to compute the error, take the difference between each predicted-observed value, square the difference, sum all the differences, and divide the sum by the number of data points. An observed value is considered an outlier it. OP > threshold To determine if an observed value is an outlier, take the absolute value of the difference between the observed value and its corresponding predicted value and check if the difference is greater than the positive threshold value. The function FilterOutliers performs the following: • Compute the MSE using the original input values, and store the result in oldError. • Find the outliers, and store the number of outliers in the output nunOutliers. • Remove the outliers (the observed values and their corresponding predicted values), and re-compute the MSE, storing the result in newError Restrictions. Do not use loops or if else statements. Use array indexing. logical indexing and Matlab functions that operate on arrays. For example predicted = [ 8 259 2283] observed = [ 35 15 5 7 95] threshold = 4 [oldError, nunoutliers, newError] = FilterOutliers (predicted, observed, threshold) This results in the output: oldError = 23 numOutliers = 3 newError = 6.8000 The old error is computed by summing the square of differences and dividing by the number of data pairs, i.e ( 3 – 87+(5-2)2 + (15-512+(5-92+ (7-2)2 + 0-2)2+ (9-8)2+(5-3)2) = 8 = 23. The function found 3 outliers. These occur at positions 1, 3, and 5. At these positions, the absolute value of the differences 3–8). 15-5 and 7-2 are all greater than the threshold value of 4. With these value-pairs removed, the new error is computed as 6.8000. Function A Save e Reset MATLAB Documentation function (oldError, numOutliers, newError] = FilterOutliers(predicted, observed, threshold) X insert your code here

Answer 1

function [] = FilterOutliers(predicted, observed, threshold)
    
    % finding difference between elements and squaring and 
    % finding mean of them
    oldErr = mean(abs(predicted-observed).^2);
    
    % counting outliers if difference between predicted &
    % observed is greater than threshold
    nOutliers = sum(abs(predicted-observed) > threshold(:)==1);
    
    % difference between predicted & observed
    % is less than or equal to threshold
    error = (abs(predicted-observed) <= threshold);
    
    % squaring the error
    error = (predicted(error)-observed(error)).^2;
    % calculating mean of error
    newErr = mean(error);
    % display the oldError, Number of outliers, new Error
    fprintf("oldError    = %d\n",oldErr);
    fprintf("numOutliers = %d\n",nOutliers);
    fprintf("newError    = %.4f\n",newErr);
    
    
end

Code :

Filter Outliers.m X + function [] = FilterOutliers (predicted, observed, threshold) 로 4 о со но си со ме 1 finding difference between elements and squaring and finding mean of them oldErr = mean (abs (predicted-observed). ^2); counting outliers if difference between predicted & s observed is greater than threshold noutliers = sum (abs (predicted-observed) > threshold (:)==1); 9 - 10 11 12 13 & difference between predicted & observed less than or equal to eshold error = (abs (predicted-observed) <= threshold); 14 15 16 - 17 18 - 19 20 squaring the error error = (predicted (error) -observed (error)).^2; calculating mean of error newErr = mean (error); display the oldError, Number of outliers, new Error fprintf("oldError = %d\n", oldErr); fprintf("numoutliers = %d\n", noutliers); fprintf("newError = $.4f\n", newErr); - 21 22 - 23 24 25 end

Output :

Command Window >> predicted = [8, 2, 5, 9, 2, 2, 8, 3]; >> observed = [3, 5, 15, 5, 7, 0, 9, 5]; >> threshold = 4; >> FilterOutliers (predicted, observed, threshold) oldError = 23 numOutliers = 3 newError = 6.8000 fx >>|