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Suppose that you have trained a logistic regression classifier $h_{\theta}(x) = \sigma(1 - x)$ where $\sigma(.)$ is the logistic/sigmoid function. What does its output on a new example $x = 2$ mean? Check all that apply.
(Hint: $\sigma(-1) = 0.27$)

  1. Your estimate for $P(y = 1|x; \theta)$ is about 0.73.
  2. Your estimate for $P(y = 0|x; \theta)$ is about 0.27.
  3. Your estimate for $P(y = 1|x; \theta)$ is about 0.27.
  4. Your estimate for $P(y = 0|x; \theta)$ is about 0.73.

1 Answer

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$P(y = 1|x)$ is estimated by $h_o(x)$. So when $x = 2, P(y = 1|x = 2)$ is estimated by $h_{\theta}(2) = \sigma (-1) \approx 0.27$, also meaning that $P(y = 0 | x = 2) \approx 1 - 0.27 = 0.73$.
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