# Loss for univariate regression ```toc ``` - Predict a single scalar output $y \in \mathbb{R}$ - Use univariate [Normal Distribution](Normal%20Distribution.md) -  -  -  - Find parameters $\hat \phi$ that minimize $L[\phi]$\ - [Least squares loss](Least%20squares%20loss.md) ## Inference - Predict the mean $\mu = f[x, \phi]$ of the [Normal Distribution](Normal%20Distribution.md) over y - We find the single best point estimate $\hat y$ and we take max of the predicted distribution $\hat y = \underset{y}{argmax}[Pr(y|f|x, \hat \phi, \sigma^{2})] = f[x, \hat \phi]$ ### Estimating if variance constant everywhere - [Homoscedatic](Homoscedatic.md) - Since the equation does not depend on variance, we pretend $\sigma^{2}$ is a learned parameter and minimize it wrt $\phi, \sigma^{2}$ -  -  ### Estimating if variance is not constant - [Heteroscedatic](Heteroscedatic.md) - Train a network that computes both mean and variance - Variance should be positive, but the result of composing networks might not be. To make it, pass it through the squaring function -  ### [Homoscedatic](Homoscedatic.md) vs [Heteroscedatic](Heteroscedatic.md) Regression -