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Merge pull request #43 from EiffL/UdeM2021
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EiffL committed Feb 22, 2021
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12 changes: 7 additions & 5 deletions UdeM2021/index.html
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Expand Up @@ -805,7 +805,6 @@ <h3 class="slide-title">Going one step further: generative models as data-driven
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$\mathbf{A}$ is known and encodes our physical understanding of the problem.
<span class="fragment"><br>$\Longrightarrow$ When non-invertible or ill-conditioned, the inverse problem is ill-posed with no unique solution $x$</span>
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Expand Down Expand Up @@ -1294,14 +1293,17 @@ <h3 class="slide-title">Annealed Langevin samples from DSM model in Song & Ermon

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<h3 class="slide-title">Back to the convergence map log posterior</h3>

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$$ \log p( \kappa | e) = \underbrace{\log p(e | \kappa)}_{\simeq -\frac{1}{2} \parallel e - P \kappa \parallel_\Sigma^2} + \log p(\kappa) +cst $$

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<li> The likelihood term (and its score) are known analytically.
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<li> There is <b class="alert">no close form expression for the full non-Gaussian prior</b> of the convergence.
<!-- <li> There is <b class="alert">no close form expression for the full non-Gaussian prior</b> of the convergence.
<br> However:
<ul>
<li> <b>We do have an analytic prior on its 2pt function</b>, and that prior is accurate on large scales.
Expand All @@ -1311,7 +1313,7 @@ <h3 class="slide-title">Back to the convergence map log posterior</h3>
<li> <b>We do have access to samples of full prior</b> through simulations.
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</li>
</li> -->
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<li class="fragment fade-up"><b class="alert">Learning a Hybrid score</b>: theoretical Gaussian on large scale, data-driven on small scales using N-body simulations.
$$\underbrace{\nabla_{\boldsymbol{\kappa}} \log p(\boldsymbol{\kappa})}_\text{full prior} = \underbrace{\nabla_{\boldsymbol{\kappa}} \log p_{th}(\boldsymbol{\kappa})}_\text{gaussian prior} +
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