Create summry

summry

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+Variational Auto Encoders
+Vae are used to generate outputs which are similar to the inputs
+this is achieved with the help of an encoder and a decoder
+to generate an out we need to specify a latent variable which helps in the creation of a specific input let it be z.
+
+this latent variable is then used as an input to the functon f(z;v) where v is a learnable parameter, which produces an output similar to input, we generally prefer it to be a gaussian distribution
+which has mean f(z;v) and variance sigma*I I(identity matrix).
+
+we sample z from a distribution in which each dimension is a gaussian distribution with mean 0 and sd 1
+
+but sampling z from such  distribution is difficult we would like to have a funtion q(z/x) which provides the output(desired gaussian form) basing on the input x which helps in giving 
+a better set of values of z which depend on x
+this functon q helps us in sampling z from a smaller set of values of z which helps us as it removes the difficulty of p(x/z) being 0 most of the time and reducing computation difficulty
+
+the above step is the encoding part which provides us with q(z/x) (preferably gaussian) which outputs us with 1)mean 2)variance(a covariance matrix)
+this is then used to sample(gaussian distr.) and then used as an input to f(z) to produce the output 
+
+the main difficulty here is that during backprop the loss cannot travel back to the encoder part as we are sampling from a gaussian distribtuion
+this problem is solved with the help of reparameterization 
+
+here we take the output from the encoder(mean, covariane matrix) , then we sample from a standard normal distribution N(0,1) (let the variable be r), then we provide the input to the decoder
+as r*variance(from encoder)+mean(from encoder)
+
+by the above step of reparmeterization trick we can form a direct link between the encoder and the decoder which can be used during backprop
+
+now as the output is gaussian T(f(z;v),sigma*I)()where sigma is a hyperparameter the negative log likelihood is dircetly proportional to the square of the distance between f(z) and 
+x but as in the example given in the paper we need to keep the sigma very small so as to make the output more similar to input