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13 Feb 2023: l. 2a,DF ]), and signal variance s. 2a:. ka(x̃i, x̃j) = s2a exp. ( ... where the E squared exponential covariance functions are. ka(x,x′) = s2aq(x,x. ′,

6 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

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27 Jan 2023: ǩt = [Ka(xt, x1), Ka(xt, x2),. , Ka(xt, xn)].5 Themean of the predictive distribution P(fa(xt)|E, θ) canbe approximated as E[fa(xt)] = ǩtβa where βa is

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.

27 Jan 2023: "$#. %'&)(,.-0/21435768(9&)(9:;14<=&?>A@CBD68E14GFD:HBI<7FDBKJC<8:;(L 14<7M814<N BD>;>H:;<7OQPO.&)(,.-4RS67FD>TRU&)F?RS67VW X ZY8 = '[AY=] _baTcedgfih]jgkflfnmAopmqdrjUjfsaltvuxwzyZ{xuxoGjUf|}{ZmqcedghcbaTceo{)foGTIoGukvux{IykldUkejrofkToh]{IDaTdUDtv

13 Feb 2023: K1A{x} =. (U VV T 1w. ),. where. w = K{x} K{x},AK1A KA,{x},. ... U = K1A 1. wK1A KA,{x}K{x},AK. 1A ,. V = 1wK1A KA,{x}.

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).

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.