Deep Learning: Difference between revisions
No edit summary |
|||
| Line 16: | Line 16: | ||
<math>l(f_W(x), y) = \frac{1}{2}\Vert f_W(x)-y \Vert^2</math> | <math>l(f_W(x), y) = \frac{1}{2}\Vert f_W(x)-y \Vert^2</math> | ||
For classification, can use hinge-loss: | For 2-way classification, can use hinge-loss: | ||
<math>l(f_W(x), y) = \max(0, 1-yf_W(x))</math> | <math>l(f_W(x), y) = \max(0, 1-yf_W(x))</math> | ||
For multi-way classification, can use cross-entropy loss: | |||
<math>g(z)=\frac{1}{1+e^{-z}}</math> | |||
<math>-\sum_{i=1}^{N}\left[y_i\log(y(f_W(x)) + (1-y_i)\log(1-g(f_W(x))\right]</math> | |||
==Misc== | ==Misc== | ||
Revision as of 15:45, 1 September 2020
Notes for CMSC 828W: Foundations of Deep Learning (Fall 2020) taught by Soheil Feizi
My notes are intended to be a concise reference for myself, not a comprehensive replacement for lecture.
Basics
A refresher of Machine Learning and Supervised Learning.
Empirical risk minimization (ERM)
Minimize loss function over your data: \(\displaystyle \min_{W} \frac{1}{N} \sum_{i=1}^{N} l(f_{W}(x_i), y_i))\)
Loss functions
For regression, can use quadratic loss: \(\displaystyle l(f_W(x), y) = \frac{1}{2}\Vert f_W(x)-y \Vert^2\)
For 2-way classification, can use hinge-loss: \(\displaystyle l(f_W(x), y) = \max(0, 1-yf_W(x))\)
For multi-way classification, can use cross-entropy loss:
\(\displaystyle g(z)=\frac{1}{1+e^{-z}}\)
\(\displaystyle -\sum_{i=1}^{N}\left[y_i\log(y(f_W(x)) + (1-y_i)\log(1-g(f_W(x))\right]\)