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brendancooleyOlaRonning
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Fix math rendering in variationally inferred parameterization tutorial (pyro-ppl#1767)
* fix math rendering in variationally inferred parameterization tutorial * ruff format
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notebooks/source/variationally_inferred_parameterization.ipynb

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@@ -751,10 +751,10 @@
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"## **2. Model**\n",
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"We will be using a logistic regression model with hierarchical prior on coefficient scales\n",
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"\n",
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"\\begin{aligned}\n",
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"\\begin{align}\n",
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"\\log \\tau_0 & \\sim \\mathcal{N}(0,10) & \\log \\tau_i & \\sim \\mathcal{N}\\left(\\log \\tau_0, 1\\right) \\\\\n",
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"\\beta_i & \\sim \\mathcal{N}\\left(0, \\tau_i\\right) & y & \\sim \\operatorname{Bernoulli}\\left(\\sigma\\left(\\beta X^T\\right)\\right)\n",
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"\\end{aligned}"
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"\\end{align}"
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"source": [
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"Thus, using the above transformation the joint density can be transformed as follows:\n",
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"\\begin{aligned}\n",
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"\\begin{align}\n",
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"p(\\theta, \\hat{\\mu}, \\mathbf{y}) & =\\mathcal{N}(\\theta \\mid 0,1) \\times\n",
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"\\mathcal{N}\\left(\\mu \\mid \\theta, \\sigma_\\mu\\right) \\times \\mathcal{N}(\\mathbf{y} \\mid \\mu, \\sigma)\n",
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"\\end{aligned}\n",
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"\\end{align}\n",
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"\n",
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"\\begin{aligned}\n",
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"\\begin{align}\n",
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"p(\\theta, \\hat{\\mu}, \\mathbf{y}) & =\\mathcal{N}(\\theta \\mid 0,1) \\times \\mathcal{N}\\left(\\hat{\\mu} \\mid \\lambda \\theta, \\sigma_\\mu^\\lambda\\right) \\times \\mathcal{N}\\left(\\mathbf{y} \\mid \\theta+\\sigma_\\mu^{1-\\lambda}(\\hat{\\mu}-\\lambda \\theta), \\sigma\\right)\n",
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"\\end{aligned}\n"
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"\\end{align}\n"
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]
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