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16 May 2024: The Geometry of Random Features. Krzysztof Choromanski1 Mark Rowland2 Tamas Sarlos1 Vikas Sindhwani1 Richard E. Turner2 Adrian Weller231Google Brain, NY 2University of Cambridge, UK 3The Alan Turing Institute, UK. Abstract. We present an in-depth

27 Jan 2023: The EM-EP Algorithm forGaussian Process Classification. Hyun-Chul Kim. and Zoubin Ghahramani. Gatsby Computational Neuroscience Unit, UCL,London, WC1N 3AR, UK,. hckim,zoubin @gatsby.ucl.ac.uk,http://www.gatsby.ucl.ac.uk. Abstract. Gaussian process

13 Feb 2023: W. A). Ken. nedy. (D. M. A). Aka. ka (. D.

27 Jan 2023: W. A). Ken. nedy. (D. M. A). Aka. ka (. D.

13 Feb 2023: where we have introduced the shorthand notation4 Qa,b , Ka,uK1u,uKu,b. We. ... For FITC see Remark 7. Recall that we have definedQa,b , Ka,uK.

13 Feb 2023: namely that if:. p. ([a. b. ])= N. ([µa. µb. ],. [Ka,a Ka,b. Kb,a Kb,b. ]), (1.17). then the means and covariances of marginals are simply the relevant subvectors ... and. submatrices of the joint mean and covariance respectively, i.e., p(a) = N(µa, Ka

13 Feb 2023: Cov(Ea(xi,yi),Ea(x′i,y′i)) = ka((xi,yi),(x. ′i,y′i)). Cov(Eb(yi,y′′i ),Eb(y. ′i,y′′′i )) = kb((y,y. ′′),(y′,y′′′)). ... We use ka(, ) and kb(, ) to denote a positive definite ker-nel function (Schölkopf & Smola, 2001).

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13 Feb 2023: We use a squared exponential covari-ance function ka(x̃, x̃′) = s2a exp((x̃x̃′)T Λ1a (x̃x̃′)),where sa and Λ = diag([la1, la2,. ,

13 Feb 2023: qai =. ka(x̃i, x̃t1)N. (x̃t1 | µ̃t1, Σ̃t1. )dx̃t1. =α2a. |Σ̃t1Λ1a I|exp. ( ... Qij =ka(x̃i,µ̃t1)kb(x̃j,µ̃t1). |R|exp. (12 z>ijR1Σ̃t1zij. )(22). where we defined R := Σ̃t1(Λ1a Λ.