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the inverse transform of the standard deviation is wrong. Mean and standard variation have to be transformed differently. Here's a brief explanation: Transform Let's assume random variable $Y$ with mean $\mu_Y$ and variance $\sigma^2_Y.$ The "Scaler" subtracts some constant $a$ and divides the result by a factor $b.$ The transformed variable equals $Z = \...


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I'll provide the derivation for a general random process (with finite second moments). As the author's random process is a simple random process (stochastic part doesn't depend on time), the direct differentiation (what the author did) is also correct. The derivation is based on the book [Natan, Gorbachev, Guz, The basics of random process theory, 2003] (in ...


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For me the biggest advantage of Gaussian Processes is the inherent ability to model the uncertainty of the model. This is incredibly useful because, given the expected value of a function and the corresponding variance I can define a metric (i.e. an Aquisition function) that can tell me e.g. what's the point $x$ that, I should evaluate my underlying ...


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Some disadvantages of LOWESS vs GP are the following: LOWESS will fail even for a moderate input dimension of data, while GP works in this case for right kernel selected For LOWESS to work we need a dense training sample of points over the whole design space. For GP the requirements are less strict We need additional tricks to control outliers Some ...


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Acquisition functions are not about a specific surrogate model. They can be calculated for many of them given that the output of a surrogate model is not a single prediction $\hat{y}(x)$, but a probability distribution $\hat{p}(x)$. In case, of the Gaussian process regression, we assume that the output is Gaussian distribution. So it is sufficient to ...


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Your idea about using a hold-out set for comparing the RMSE is fine. I would note though that if we do not have rather a large hold-out sample, using a repeated cross-validation approach instead of a fixed hold-out set will mitigate finite-sample variance issues; repeated CV is preferable because it allows to also estimate the variability of our test ...


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The f is itself a random variable with density q. When drawing a sample of the predictive distribution of f*, we first draw an f according to to the q-density, and then we draw an f* given f according to the posterior process gaussian distribution. See e.g. the law of total variance.


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One way to construct kernels over discrete spaces is by considering a graph representation of the data and defining a smooth function over nodes of graphs via graph fourier transform. This class of kernels (introduced by Kondor and Lafferty) is called as diffusion kernels. Concretely, the kernel over the graph nodes $V$ is given by: \begin{align} K(V,V) = \...


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