You are working on a two-class {A,B} prediction problem using two features {X1, X2}. You want to use QDA. You’ve estimat
Posted: Mon Nov 15, 2021 9:51 am
You are working on a two-class {A,B} prediction problem using
two features {X1, X2}. You want to use QDA.
You’ve estimated mean vectors
and find that they are the same.
(For simplicity, since you
centered the data their means are the origin.)
HA 0 AB 00
When you estimate the covariance matrices, you find they are both diagonal matrices, În = [1 1 Σ 2n = [4 2 4 0 4 - Lastly, the number of samples for class A and B are the same, so în = 3 = îs. (a). What is the equation for the QDA decision boundary for this problem? Simplify it as much as possible. (b). Sketch a plot by hand showing the boundary. Indicate for what region(s) Ỹ = A and for what region(s) Y = B (c). What would the prediction be for the mean value of both conditional distributions, 3 ? What would the prediction be for the point ? 02 -3 (d). Would your answers to the above questions have differed if you had used naive Bayes with a Gaussian assumption instead of QDA? Briefly explain why or why not. (e). Suppose we had a third class C, also centered at the origin and with a diagonal covariance matrix, MC Σς [ ] 09 and that all classes had equal priors, TT A = TTB = TTC Sketch a plot, similar to (b)., of the decision regions for this problem with three classes (eg make it clear on the plot what region has Y = A, what region has Y = B, and what region has Ỹ =C). You do not need to do calculations, but extrapolate from what you just observed for the two class problem.
two features {X1, X2}. You want to use QDA.
You’ve estimated mean vectors
and find that they are the same.
(For simplicity, since you
centered the data their means are the origin.)
- You Are Working On A Two Class A B Prediction Problem Using Two Features X1 X2 You Want To Use Qda You Ve Estimat 1 (2.01 KiB) Viewed 120 times
- You Are Working On A Two Class A B Prediction Problem Using Two Features X1 X2 You Want To Use Qda You Ve Estimat 2 (86.96 KiB) Viewed 120 times
When you estimate the covariance matrices, you find they are both diagonal matrices, În = [1 1 Σ 2n = [4 2 4 0 4 - Lastly, the number of samples for class A and B are the same, so în = 3 = îs. (a). What is the equation for the QDA decision boundary for this problem? Simplify it as much as possible. (b). Sketch a plot by hand showing the boundary. Indicate for what region(s) Ỹ = A and for what region(s) Y = B (c). What would the prediction be for the mean value of both conditional distributions, 3 ? What would the prediction be for the point ? 02 -3 (d). Would your answers to the above questions have differed if you had used naive Bayes with a Gaussian assumption instead of QDA? Briefly explain why or why not. (e). Suppose we had a third class C, also centered at the origin and with a diagonal covariance matrix, MC Σς [ ] 09 and that all classes had equal priors, TT A = TTB = TTC Sketch a plot, similar to (b)., of the decision regions for this problem with three classes (eg make it clear on the plot what region has Y = A, what region has Y = B, and what region has Ỹ =C). You do not need to do calculations, but extrapolate from what you just observed for the two class problem.