1. Matching in Observational Studies

    A 'matching' quasi-experimental design controls for confounder variables \(x\) by estimating what the control outcomes \(y\) would be if the control population had the same values of \(x\) as the treatment population. To do this, we regress outcomes in the control population on \(x\), and apply this regression model to …

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  2. Graph SLAM

    For a robot to navigate autonomously, it needs to learn both its own location, as well as the locations of any potential obsticles around it, given its sensors' observations of the world. We'll create a probabilistic model of our environment and get a MAP estimate of these unknown quantities.

    • Let …
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  3. Finite Basis Gaussian Processes

    By Mercer's theorem, every positive definite kernel \(k(x, y) : \mathcal{X} \to \mathcal{X} \to \mathbb{R}\) that we might want to use in a Gaussian Process corresponds to some inner product \(\langle \phi(x), \phi(y) \rangle\), where \(\phi : \mathcal{X} \to \mathcal{V}\) maps our inputs into …

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