diff --git a/examples/notebooks/Deep Generative Model.ipynb b/examples/notebooks/Deep Generative Model.ipynb index d9362dd..55ed9e6 100644 --- a/examples/notebooks/Deep Generative Model.ipynb +++ b/examples/notebooks/Deep Generative Model.ipynb @@ -129,7 +129,7 @@ "\n", "\\begin{align}\n", "\\log p(x) &= \\log \\sum_{y} \\int q(z,y|x) \\frac{p(x, y, z)}{q(z,y|x)} \\ dz \\geq \\sum_{y} q(y|x) \\int q(z|x, y) \\log \\frac{p(x, y, z)}{q(z,y|x)} \\ dz\\\\\n", - "&= \\sum_{y} q(y|x) \\int q(z|x, y) \\log \\frac{p(x, y, z)}{q(z,y|x)} \\ dz + \\sum_{y} q(y|x) \\log q(y|x) \\int q(z|x, y) \\ dz\\\\\n", + "&= \\sum_{y} q(y|x) \\int q(z|x, y) \\log \\frac{p(x, y, z)}{q(z|x,y)} \\ dz - \\sum_{y} q(y|x) \\log q(y|x) \\int q(z|x, y) \\ dz\\\\\n", "&= \\sum_{y} q(y|x) (- \\mathcal{L}(x,y)) + \\mathcal{H}(q(y|x)) = - \\mathcal{U}(x)\n", "\\end{align}\n", "\n",