Symbol in context

$p_\theta$

This entry links every published equation using this exact notation. Its meaning may change between equations.

Used in 6 equations

\hat{s}_{t+1} = f_\theta(s_t, a_t), \qquad \hat{o}_{t+1} \sim p_\theta(o \mid \hat{s}_{t+1})

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

\mathcal{L}_{\text{seq}} = -\sum_{t=1}^{T} \log p_\theta\!\left(z_t \mid z_{<t}\right), \qquad z_t \in \{0, 1, \dots, V-1\}

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\, p_\theta(y \mid x, z),

This equation gives an approximation: it relates the quantities while allowing an approximation.

p(y \mid x) \approx \sum_{z \in \mathrm{top}\text{-}k\left(p_\eta(\cdot \mid x)\right)} p_\eta(z \mid x) \, p_\theta(y \mid x, z),

This equation gives an approximation: it relates the quantities while allowing an approximation.

p(y \mid x) \approx \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x) \prod_{i=1}^{|y|} p_\theta\left(y_i \mid x, z, y_{1:i-1}\right)

This equation gives an approximation: it relates the quantities while allowing an approximation.

p(y \mid x) = \sum_{z \in \mathcal{Z}_k(x)} p_\eta(z \mid x)\,p_\theta(y \mid x,z),

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.