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1 question from Linear Models & Regularization

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mediumAI-checkedLinear Models & Regularization

To predict the number of apples $k$ sold per day, you model $k \sim \mathrm{Poisson}(\lambda)$ with $p(k \mid \lambda) = \lambda^k e^{-\lambda} / k!$ , and the network outputs $\theta = \log\lambda$ . Which per-example loss is the negative log-likelihood, up to a constant?

$-k\theta$ 1
$\theta - k\log\theta$ 2
$e^{\theta} - k\theta$ 3
$(k - e^{\theta})^2$ 4

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