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what is the formula for log likelihood. These functions are both monotonic because as you go from left to right on the x-axis the y value always increases. Lets say we have some continuous data and we assume that it is normally distributed.
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So we can enter this as a formula in Excel that equals y is 72 times the log of theta value from this row. Li f k Li pk pk f k 1 pkpk 1 pk pk 1 L i f k L i p k p k f k 1 p k p k 1 p k p k 1 And thus we have differentatied the negative log likelihood with respect to the softmax layer. Lastly we will find the sum of the log likelihoods which is the number we will attempt to maximize to solve for the regression coefficients.
LogLYth XN j1 Y j Tx j2 2s2 N2logp Nlogs 7.
Li f k Li pk pk f k 1 pkpk 1 pk pk 1 L i f k L i p k p k f k 1 p k p k 1 p k p k 1 And thus we have differentatied the negative log likelihood with respect to the softmax layer. By Marco Taboga PhD. Notice on the bottom right that the probability of a dataset given a model is a constant in respect to thetas so we can ignore it in the optimisation process. For a glm fit the family does not have to specify how to calculate the log-likelihood so this is based on using the familys aic function to compute the AIC.
