Often training a model involves optimizing the likelihood function with respect to. Where is log likelihood of normal function. Taking natural logarithm of left and right terms yields Now the probability of target vector given input can be expressed by , where is mean of the distribution and is calculated by model as This is called standard normal distribution.įor normal distribution model with weight parameter and precision(inverse variance) parameter, the probability of observing a single target t given input x is expressed by the following equation In this case the normal distribution will be, Often in machine learning we deal with distribution with mean 0 and variance 1(Or we transform our data to have mean 0 and variance 1). Gaussian distribution(Normal distribution) with mean and variance is given by From this it follows that the target variable is normally distributed(more on the assumptions of linear regression can be found here and here). One of the assumptions of the linear regression is multi-variant normality. TL DR Use MSE loss if (random) target variable is from Gaussian distribution and categorical cross entropy loss if (random) target variable is from Multinomial distribution. Why cross entropy is used for classification and MSE is used for linear regression?.What is the interpretation of MSE loss and cross entropy loss from probability perspective?.As complement to the accepted answer, I will answer the following questions
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