04 Perceptron Regressor

We can also use perceptron as linear regressor. By just removing the $sgn$ function. So, the equation would become

$$\hat{y}=b+\sum _i^D{w}_i{x}_i$$

Perceptron Regressor - 1D input

• Predict commute time to University
  • Input variables (features):
    • Distance to University (km)
    • Day of the week (1 for weekday, 0 for weekend)
  • Output/tagert ?
    • Commute time (min)
  • Solution:
    • Perceptron without sign-function
    • Equal to standard linear regression

Summary

• Perceptron without sign function is linear regressor
• Output is linear function of inputs
  • $\mathbf{w}$ and $b$ define function
    • Weight vector $\mathbf{w}$ determines slope in each direction
    • Bias $b$ shifts function up and down
  • Don’t mix up with hyperplane in classifier!