\begin{frame}
	\myheading{Module 8.8 : Adding Noise to the outputs}
\end{frame}

\begin{frame}
	\vspace{4em}
	\begin{overlayarea}{\textwidth}{\textheight}
		\begin{block}{Other forms of regularization}
			\begin{itemize}
				\item $l_2$ regularization
				\item Dataset augmentation
				\item Parameter Sharing and tying
				\item Adding Noise to the inputs
				\item \textcolor<1->{red}{Adding Noise to the outputs}
				\item Early stopping
				\item Ensemble methods
				\item Dropout
			\end{itemize}
		\end{block}
	\end{overlayarea}
\end{frame}
			
\begin{frame}
	\begin{columns}
		\column{\textwidth}
		\vspace{1em}
		\begin{overlayarea}{\textwidth}{\textheight}

			\input{modules/Module8/tikz_images/hard_targets}
			\begin{align*}
				\onslide<2->{ \text{minimize}              & : \sum_{i = 0}^{9} p_i \log q_i             \\}
				\onslide<3->{ \text{true distribution}     & : p = \left \{0,0,1,0,0,0,0,0,0,0 \right \} \\}
				\onslide<4->{\text{estimated distribution} & : q}                                        
			\end{align*}
								
			\onslide<5-6>{\begin{block}<5-6>{Intuition}
				\begin{itemize}
					\item<5-6> Do not trust the true labels, they may be noisy
					\item<6> Instead, use soft targets
				\end{itemize}
				\end{block}}
										
		\end{overlayarea}
	\end{columns}
\end{frame}
				
\begin{frame}
	\begin{columns}
		\column{\textwidth}
		% \vspace{1em}
		\begin{overlayarea}{\textwidth}{\textheight}

			\onslide<1->{
				\input{modules/Module8/tikz_images/soft_targets}
			}
			\begin{align*}
				\onslide<2->{ \varepsilon                      & = \text{small positive constant}                                                                              \\}
				\onslide<3->{ \text{minimize}                  & : \sum_{i = 0}^{9} p_i \log q_i                                                                               \\} 
				\onslide<4->{ \text{true distribution + noise} & : p = \left \{\frac{\varepsilon}{9},\frac{\varepsilon}{9},1-\varepsilon,\frac{\varepsilon}{9},\dots \right \} \\ }
				\onslide<5->{ \text{estimated distribution}    & : q}                                                                                                          
			\end{align*}
										
		\end{overlayarea}
	\end{columns}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
%%Lect 3.3
