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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. ′,

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13 Feb 2023: PYáN247L,I <7=Ka 246 2UI > I > 573T3 ã D < 6NL.246 abN= LL,I a L áI? ... DFE MÛUØUZJLNYZMSM 62TJ;á <7=Ka 5X6 a 24II > LÒ246 > Im246 VGM 24IÌà bN<Y< Im246.

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.

13 Feb 2023: Analytic Moment-based Gaussian Process Filtering. Marc Peter Deisenroth mpd37@cam.ac.ukComputational and Biological Learning Lab (CBL), University of Cambridge, UKIntelligent Sensor-Actuator-Systems Laboratory (ISAS), Universität Karlsruhe (TH),

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

27 Jan 2023: βk Beta(1 a, b ka). Note: mean of a Beta(a, b) is a/(a b).

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.

13 Feb 2023: Bayesian Learning forData-Efficient Control. Rowan McAllister. Supervisor: Prof. C.E. Rasmussen. Advisor: Prof. Z. Ghahramani. Department of EngineeringUniversity of Cambridge. This dissertation is submitted for the degree ofDoctor of Philosophy.

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

13 Feb 2023: With βxa =(Ka σ. 2wa I). 1ya and mfa (xt1) = kfa (X, xt1)>βxa, we obtain.

27 Jan 2023: "$#%&%&')(,.-%. /102 35476987:<; =4?>A@$:<BDCFE0EAGH02I0B$:. JHKMLONQPMRTSAUWVMLHXZY.R[?]_T7acb?SY7dfegX.hTijeahegX7klnmOo'p'qTrsutwvyxMzQo mOo {|tw}mc1 zQ'twp{}M }Q{|o. }M{|c'p{|orsutcwntw}MMtc}y zM}7Zzmcc?tw}MMtw}s cn }Q{|o n{|}MwMtcv. o'twq?

13 Feb 2023: IEEE/ACM Transactions on Computa-tional Biology and Bioinformatics 2007 [http://doi.ieeecomputersociety.org/10.1109/TCBB.2007.70269]. 19. Heller KA, Ghahramani Z: Bayesian Hierarchical Clustering.Twenty-second International Conference

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,. ,