AI and ML for Finance Practitioners

Quiz LO 2.1.3

Test your knowledge of LO 2.1.3

 8%

Question 1 of 13

1. Is it true or false that this is the equation for the mean squared error?

\boxed{M S E=\frac{1}{n} \sum_{i=1}^{n}\left(y_{i}-\widehat{f}\left(x_{i}\right)\right)^{2}}

Question 1 of 13

Question 2 of 13

2. Is it true or false that the training MSE indicates the prediction accuracy of the learning method on the training data?

Question 2 of 13

Question 3 of 13

3. Is it true or false that the test MSE indicates the prediction accuracy of the learning method on the test data?

Question 3 of 13

Question 4 of 13

4. Is it true or false that Cross-validation is a method for estimating test MSE values using the training dataset?

Question 4 of 13

Question 5 of 13

5. Is it true or false that the expected test MSE \boxed{E\left[y_{0}-\hat{f}\left(x_{0}\right)\right]^{2}} can be split into three fundamental quantities:

1) \boxed{\operatorname{Var}\left(\hat{f}\left(x_{0}\right)\right)^{2}}

2) \boxed{\left[\operatorname{Bias}\left(\hat{f}\left(x_{0}\right)\right)\right]^{2}}

3) \boxed{\operatorname{Var}(\varepsilon)}

Question 5 of 13

Question 6 of 13

6. Is the following statement true or false?

Statement:
Good test performance of a statistical learning method requires both a low variance and a low squared bias. This is called a trade-off, because it is easy to obtain a method with extremely low bias but high variance (for example, drawing a curve that passes through every single training observation) or a method with very low variance but high bias (fitting a horizontal line to the data). The challenge lies in finding a method for which both the variance and the squared bias are low.

Question 6 of 13

Question 7 of 13

7. With regard to the true function (black curve), the three fitting curves (orange, blue, and green), and the MSE plots depicted in the figure below, which fitting curve is the best predictive learning model?

213B pictureSource: Assigned reading

Question 7 of 13

Question 8 of 13

8. With regard to the true function (black curve), the three fitting curves (orange, blue, and green), and the MSE plots depicted in the figure below, which fitting curve is the best predictive learning model?

213B2 pictureSource: Assigned reading

Question 8 of 13

Question 9 of 13

9. Which plot is illustrating a typical trade-off Bias-Variance?

Legend: Red curve = test MSE; Green curve = bias; Orange curve = variance.
213D2 pictureSource: Assigned reading

Question 9 of 13

Question 10 of 13

10. Is the following statement true or false?

Statement:
In a two-class problem where there are only two possible response values, say class 1 or class 2, the Bayes classifier predicts class 1 if \boxed{Pr\left(Y=1 \mid X=x_{0}\right)>0.5} and class 2 otherwise;

Question 10 of 13

Question 11 of 13

11. Are the following statements true or false?

Statement I:
The Bayes classifier produces the lowest possible test error rate, called the Bayes error rate. Since the Bayes classifier will always choose the class for which P(Y = yi| X = x0 ) is largest, the error rate at X = x0 will be \boxed{1-\max _{i} P\left(Y=y_{i} \mid X=x_{0}\right)}


Statement II:
In general, the overall Bayes error rate is given by \boxed{1-E\left[\max _{i} P\left(Y=y_{i} \mid X=x_{0}\right)\right]} where the expectation averages the probability over all possible values of X.

Question 11 of 13

Question 12 of 13

12. With reference to the figure below, which of the following statements is correct?


213FSource: Assigned reading


Statement I: the Baysian decision boundary (purple line), the gold standard, is fixed.

Statement II: The decision boundary associated with K = 1 is the closest to the theoretical Baysian decision boundary.

Statement III: When K is very high, the decision boundary approaches a linear-like boundary.

Question 12 of 13

Question 13 of 13

13. With reference to the figure below, which of the following statements is correct?


213F2Source: Assigned reading


Statement I: KNN approaches a less flexible learning model as K increases (i.e. 1/ K decreases).

Statement II: With K = 1, the KNN training error rate approaches 0, but the test error rate may be quite high. In general, as we use more flexible classification methods (lower K values), the training error rate will decline but the test error rate may not.

Statement III: The test error exhibits a characteristic U-shape, declining at first (with a minimum at approximately K = 10) before increasing again when the method becomes excessively flexible and overfits.

Statement IV: The test error rate is greater than the Bayesian Error rate (dot line).

Question 13 of 13


 

x Powerful Protection for WordPress, from Shield Security
This Site Is Protected By
Shield Security →