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Gaussian processes refer to stochastic processes whose realization consists of normally distributed random variables, with the additional property that any finite collection of these random variables have a multivariate normal distribution. The machinery of Gaussian processes can be employed in regression and classification problems.

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18 views

What is the significance of a high value of $x^\top A^{-1} x$ as it relates to Gaussian proc...

I am just trying to gain some intuition behind some of the calculations in Gaussian processes. In chapter 2 of the linked book, equation 2.26 calculates the predictive variance as, $$ \mathbb{V}[f_*] …
Joff's user avatar
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1 vote
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52 views

effect of multiplying by Tikhonov regularization factor after an inverse?

I came across a repository which uses Tikhonov regularization to compute an inverse, but then in the inference step they multiply by the Tikhonov factor again... Compute $\Phi\Phi^T$ Compute the inve …
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2 votes
0 answers
382 views

Pyro Gaussian processes regression achieves a low error, but then always outputs the same pr...

I have tried experimenting with high dimensional Gaussian processes multiple times and I always get the same result. The model trains, and then when it comes time to predict with some new data (or eve …
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1 vote
1 answer
711 views

What is the difference between a covariance matrix created by an RBF kernel and a covariance...

I can't explain something simple to myself and it is probably a matter of vocabulary, I am not sure... If I create and random normal $Z \in \mathbb{R}^{3\times5}$, each row and column has a mean of 0. …
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11 votes
3 answers
2k views

What does it mean that a Gaussian process is 'infinite dimensional?'

I have glossed over this phrase many times without really understanding what it means. According to Wikipedia - Gaussian process Gaussian processes can be seen as an infinite-dimensional generalizati …
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1 vote
0 answers
33 views

A question about linear inference in random Fourier feature kernels [duplicate]

In Ali Rahimi's and Ben Recht's paper "Random Features for Large-Scale Kernel Machines," there is a line near the bottom of the introduction which I can not reason about... In addition to giving us a …
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1 vote
0 answers
359 views

Random Fourier Features approximating a kernel inverse?

There is a method I have been studying called Spectral Normalised Neural Gaussian Processes which leaves me with a question I cannot answer. In this method, they utilize Random Fourier Features but in …
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368 views

Why is the Hessian in the Laplace approximation negative

The Laplace approximation builds from the Taylor expansion of the MAP estimate, where the first derivative is 0. The second order Taylor series goes... $$ f(a) + \frac{f'(a)}{1!}(x - a) + \frac{f''(a) …
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6 votes
1 answer
2k views

Cholesky decomposition lower triangular in Gaussian process sampling

I am trying to intuitively understand the Cholesky decomposition in gaussian process function sampling. I understand it as as the square root of the covariance matrix being the multivariate generaliza …
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