#!/usr/bin/env python
# coding: utf-8

# # Targets and Deltas Summary

# 
# <table>
#    <tr>
#         <td style='text-align:center, width=10%'> </td>
#         <td style=width=30%, align="center"> <strong style="font-size: 15px;">Terms </strong> </td>
#         <td width=30% align="center"> <strong style="font-size: 15px;">Error </strong> </td>
#         <td width=30% align="center"> <strong style="font-size: 15px;">Output Layer Delta </strong></td>
#     </tr>
#     <tr>
#         <td width=10%> <strong style="font-size: 15px;">Regression </strong> </td>
#         <td width=30%> $$T = \mathbb{R}^{N\times K}$$ </td>
#         <td width=30%> $$\frac{1}{NK} \sum_{n=1}^N \sum_{k=1}^K (T_{n,k} - Y_{n,k})^2$$ </td>
#         <td width=30% > $$\frac{-2}{NK} (T_{n,k} - Y_{n,k}) \\
#         \text{ for each } n \text{ and } k \text{ or, }\\  \frac{-2}{NK} (T - Y)$$ </td> 
#     </tr>
#     <tr>
#         <td width=10%> <strong style="font-size: 15px;">Classification </strong> </td>
#         <td width=30%> $$\begin{align*}
#             T &= \mathbb{C}^{N\times 1}\\
#             \mathit{Tiv}^{N\times K} &= \text{indvars}(T)\\
#             \mathit{Ysm}^{N\times K} &= \frac{e^Y}{\sum_{k=1}^K e^{Y_{*,k}}}
#             \end{align*}$$ </td>
#         <td width=30%> $$\begin{align*}
#             -\log \left( (\prod_{n=1}^N \prod_{k=1}^K \mathit{Ysm}_{n,k}^{\mathit{Tiv}_{n,k}})^{\frac{1}{NK}} \right )\\
#             = -\frac{1}{NK} \sum_{n=1}^N \sum_{k=1}^K \mathit{Tiv}_{n,k} \log(\mathit{Ysm}_{n,k})
#             \end{align*}$$  </td>
#         <td width=30%> $$-\frac{1}{NK} (\mathit{Tiv}_{n,k} - \mathit{Ysm}_{n,k}) \\ \text{ for each } n \text{ and } k \text{ or, }\\  -\frac{1}{NK} (\mathit{Tiv} - \mathit{Ysm})$$ </td> 
#     </tr>    
#     <tr>
#         <td width=10%> <strong style="font-size: 15px;">Reinforcement Learning </strong> </td>
#         <td width=30%> $$\mathit{T}_n = r_{n+1} + \gamma Y_{n+1} \\ \text{ for sequential samples } n  \\ \text{ where } Y_{n+1} \text{ is } Q_{n+1} \text{ value.}$$ </td>
#         <td width=30%> $$\frac{1}{N} \sum_{n=1}^N (\mathit{T}_n - Y_n)^2$$ </td>
#         <td width=30%> $$\frac{-2}{N} (\mathit{T}_n - Y_n) \\ \text{ for each } n \text{ or, }\\  \frac{-2}{N} (\mathit{T} - Y)$$ </td> 
#     </tr>
# 
# </table>

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