ISYE 6501 – original set Mid term 2 A+ Pass Revised 2023//2024

ISYE 6501 – original set Mid term 2 A+ Pass Revised 2023//2024 when might overfitting occur when the # of factors is close to or larger than the # of data points causing the model to potentially fit too closely to random effects Why are simple models better than complex ones less data is required; less chance of insignificant factors and easier to interpret what is forward selection we select the best new factor and see if it's good enough (R^2, AIC, or p-value) add it to our model and fit the model with the current set of factors. Then at the end we remove factors that are lower than a certain threshold what is backward elimination we start with all factors and find the worst on a supplied threshold (p = 0.15). If it is worse we remove it and start the process over. We do that until we have the number of factors that we want and then we move the factors lower than a second threshold (p = .05) and fit the model with all set of factors what is stepwise regression it is a combination of forward selection and backward elimination. We can either start with all factors or no factors and at each step we remove or add a factor. As we go through the procedure after adding each new factor and at the end we eliminate right away factors that no longer appear. what type of algorithms are stepwise selection? Greedy algorithms - at each step they take one thing that looks best what is LASSO a variable selection method where the coefficients are determined by both minimizing the squared error and the sum of their absolute value not being over a certain threshold t How do you choose t in LASSO use the lasso approach with different values of t and see which gives the best trade off why do we have to scale the data for LASSO if we don't, the measure of the data will artificially affect how big the coefficients need to be What is elastic net? A variable selection method that works by minimizing the squared error and constraining the combination of absolute values of coefficients and their squares what is a key difference between stepwise regresson and lasso regression *** If the data is not scaled, the coefficients can have artificially different orders of magnitude, which means they'll have unbalanced effects on the lasso constraint. Why doesn't Ridge Regression perform variable selection? The coefficients values are squared so they go closer to zero or regularizes them, but the coefficient values are never equal to zero What are the pros and cons of Greedy Algorithms (Forward selection, stepwise elimination, stepwise regression) Good for initial analysis but often don't perform as well on other data because they fit more to random effects than you'd like and appear to have a better fit What are the pros and cons of LASSO, Ridge and Elastic Net They are slower but help make models that make better predictions Which two methods does elastic net look like it combines and what are the downsides from it? Ridge Regression and LASSO