typo on expectation
"$$\\mathbb{E}_{q_{\\phi}({\\bf z})} \\left [f_{\\phi}({\\bf z}) \\right]\n",
"=\\mathbb{E}_{q({\\bf \\epsilon})} \\left [f_{\\phi}(g_{\\phi}({\\bf \\epsilon})) \\right]$$\n",
"\n",
- "Crucially we've moved all the $\\phi$ dependence inside of the exectation; $q({\\bf \\epsilon})$ is a fixed distribution with no dependence on $\\phi$. This kind of reparameterization can be done for many distributions (e.g. the normal distribution); see reference [3] for a discussion. In this case we can pass the gradient straight through the expectation to get\n",
+ "Crucially we've moved all the $\\phi$ dependence inside of the expectation; $q({\\bf \\epsilon})$ is a fixed distribution with no dependence on $\\phi$. This kind of reparameterization can be done for many distributions (e.g. the normal distribution); see reference [3] for a discussion. In this case we can pass the gradient straight through the expectation to get\n",
"\n",
"$$\\nabla_{\\phi}\\mathbb{E}_{q({\\bf \\epsilon})} \\left [f_{\\phi}(g_{\\phi}({\\bf \\epsilon})) \\right]=\n",
"\\mathbb{E}_{q({\\bf \\epsilon})} \\left [\\nabla_{\\phi}f_{\\phi}(g_{\\phi}({\\bf \\epsilon})) \\right]$$\n",
