0 0 votes Your manager hypothesizes that for a given novice player with $x$ practice hours, their scrimmage performance is $g(x)$, where $g$ is some unknown function you are trying to model. However, the observed performance is a random variable $Y=g(x)+\epsilon$, where $\epsilon$ is the player's random, zero-mean performance error on scrimmage day. A model's prediction $\hat{Y}(x)$ is also a random variable because the parameter estimates depend on the training set (which your manager assumes is a random sample of past novices' scrimmage performances).Match the following expressions to the appropriate terms: Column 1Column 2(i) $\operatorname{Var}(\hat{Y}(x))$a. $\text{(Model Bias)^2}$(ii)$(\mathbb{E}[\hat{Y}(x)]-g(x))^2$b. $\text{Model Variance}$(iii) $\mathbb{E}\left[(\hat{Y}(x)-\mathbb{E}[\hat{Y}(x)])^2\right]$c. $\text{Model Risk}$(i)-b, (ii)-a, (iii)-b(i)-c, (ii)-a, (iii)-b(i)-b, (ii)-c, (iii)-a(i)-c, (ii)-a, (iii)-b Machine Learning goclasses goclasses-da-course machine-learning bias-variance-tradeoff + – GO Classes 163 views answer comment Share Follow Print 0 reply Please log in or register to add a comment.
0 0 votes (i) Model variance is defined as the variance of the predictions $\hat{Y}(x)$ (ii) Model bias is the expected difference between the predictions $\hat{Y}(x)$ and the ground truth $g(x)$ (iii) The variance of an arbitrary random variable $Z$ is $\mathbb{E}\left[(Z-\mathbb{E}[Z])^2\right]$. Substituting the predictions $\hat{Y}(x)$, we find that this statement is equivalent to the model variance $\operatorname{Var}(\hat{Y}(x))$ GO Classes answered Mar 29, 2025 GO Classes comment Share Follow 0 reply Please log in or register to add a comment.
