### Artificial IntelligenceAIMA Exercises

Section logistic-regression-section (page logistic-regression-section) noted that the output of the logistic function could be interpreted as a probability $p$ assigned by the model to the proposition that $f(\textbf{x})1$; the probability that $f(\textbf{x})0$ is therefore $1-p$. Write down the probability $p$ as a function of $\textbf{x}$ and calculate the derivative of $\log p$ with respect to each weight $w_i$. Repeat the process for $\log (1-p)$. These calculations give a learning rule for minimizing the negative-log-likelihood loss function for a probabilistic hypothesis. Comment on any resemblance to other learning rules in the chapter.

Section logistic-regression-section (page logistic-regression-section) noted that the output of the logistic function could be interpreted as a probability $p$ assigned by the model to the proposition that $f(\textbf{x})1$; the probability that $f(\textbf{x})0$ is therefore $1-p$. Write down the probability $p$ as a function of $\textbf{x}$ and calculate the derivative of $\log p$ with respect to each weight $w_i$. Repeat the process for $\log (1-p)$. These calculations give a learning rule for minimizing the negative-log-likelihood loss function for a probabilistic hypothesis. Comment on any resemblance to other learning rules in the chapter.

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