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13 Feb 2023: the approximateprior variances are replaced by the true prior variances. The predictive distribution of the FITC is identical to that of PITC (24),except for the alternative definition of Λ =

13 Feb 2023: Bt|t N(Mt|t, V̄t|t), and Mt|t N(µmt|t, Σmt|t), (24). or equivalently the joint[Bt|tMt|t. ]

13 Feb 2023: student course f aculty projectcornell 0.87 0.82 0.87 0.82 0.80 0.19 0.18 0.24 0.18 0.18texas 0.62 0.32 0.77 ... 0.55 0.54 0.24 0.21 0.29 0.12 0.12.

13 Feb 2023: E[(. [µ̂hf(X) µhf(X)](z). )2]dz. Cn12c r=R‖f‖K. rs22e2re(s2d′)2/(4r) dr. Cn12ce(s2d. ′)24(R‖f‖K). r=R‖f‖K. ... Cn12ce(s2d. ′)24(R‖f‖K) e2(R‖f‖K)(R‖f‖K). s22. (for R ‖f‖K 1) (18) Cn12c(R‖f‖K). s22e2(R‖f‖K) (19).

27 Jan 2023: 26. 24. 22. 20. 18. 16. α2α1. %(. 0.1. 0.08. 0.06. ... 150. 100. 50. 0 0.6. 0.8. 1. 28. 26. 24. 22.

13 Feb 2023: HG beta. /?1& 5/, B1&0?; Q6=IRB.8+& 562+;,1&0K%/&0;-0&0,:U 8G&? <0O',.-<=5& ;(-<B.&,JB18G& ;L/ 24&?E6=IB. ... 6? <B16;)6;5 O? 18B%7 B.8B.8+&;-05/,.6; 6=I,.B?1/-CB./?<=54;GI 6? <B.6;VUL&0K%/&0;-0&5D<=24&05,6;

27 Jan 2023: Cells were collected in 300 µl ofRTL lysing solution (Qiagen) at the following times aftertreatment: 0, 2, 4, 6, 8, 18, 24, 32, 48, 72 h. ... Thecells used in this experiment were all expressing the T-cellreceptor (detected with anti CD3 antibodies) and

27 Jan 2023: Itsgeneralized version which is convergent but slower hasbeen proposed [24]. 3.2 EP for Gaussian Process Classification. ... 00 0. CfJ. 24. 35; ð37Þ. where Cfj is a covariance matrix of latent values related to.

13 Feb 2023: ȳ(x)i =k. E(Wik)E[fk] (24). cov(y(x))ij =k. [E(Wik)E(Wjk)var(fk) δij(var(Wik)E(f2k ))] δijσ2y (25).

13 Feb 2023: HG beta. /?1& 5/, B1&0?; Q6=IRB.8+& 562+;,1&0K%/&0;-0&0,:U 8G&? <0O',.-<=5& ;(-<B.&,JB18G& ;L/ 24&?E6=IB. ... 6? <B16;)6;5 O? 18B%7 B.8B.8+&;-05/,.6; 6=I,.B?1/-CB./?<=54;GI 6? <B.6;VUL&0K%/&0;-0&5D<=24&05,6;

27 Jan 2023: 0 226 0 98 310 0 14 322 0 214 24 0 1 23 0 2 4 0 21 16 0 9 24 0 115 205 51 20 265 0 11 ... 0 36 20 0 32 17 0 3518 28 23 0 28 0 23 23 0 28 27 0 24 28 0 2319 22 10 8 32 0 8 30 0

27 Jan 2023: Curriculum Vitae. Zoubin Ghahramani FRS. CONTACT DETAILS. Department: Department of EngineeringUniversity of CambridgeTrumpington StreetCambridge CB2 1PZ, UK. Tel: 44 (0)1223 748 531Email: zoubin@eng.cam.ac.ukWWW: http://learning.eng.cam.ac.uk/zoubin

27 Jan 2023: '-"-. ; Cahiers de Psychologie Cognitive/ Current Psychology of Cognition:;i; 2002, 21 (4-5), 537-564. ,'. A Bayesian view of motor adaptation. Alexander T. Korenberg and Zoubin Ghahramani. University College London, U.K. Abstract.The adaptability

13 Feb 2023: Bayesian nonparametrics andthe probabilistic approach to modelling. Zoubin Ghahramani. Department of EngineeringUniversity of Cambridge, UK. zoubin@eng.cam.ac.ukhttp://mlg.eng.cam.ac.uk/zoubin. Modelling is fundamental to many fields of science and

13 Feb 2023: The existence of correlated side chain mutations in -heliceshas been well studied [20], [24].

13 Feb 2023: ÿ Y yz vOzNE EdpÒvkppwiA N yg|shdpYÓ+Xshi Ò ÔAy}yqtkwKqtshp. 8 16 24 32.

27 Jan 2023: 0.67 9.81 2.55Exact 1.02 1.04 1.26 0.99Gibbs 2.21 0.91 2.50 0.87CFVA 1.24 1.50 1.50 1.53SVA

27 Jan 2023: B( αK , 1) =Γ( αK ). Γ(1 αK )= Kα , (24).

13 Feb 2023: ξt (I At )ξt1 ̂t At µt1 Sx δt. (24)Hence, under this approximation the random variableξt isagain Gaussian distributed. ... Its mean is obtained by replacingξt andδt in eq. (24) by their respective means:.

13 Feb 2023: ðB23Þ. B.5. QðZlmÞ. Using Eqs. (6) and (24). QðZlmÞ / expfklog pðD; Zlw; m; S; W; b; mÞlQðm;S;W;blmÞg.

13 Feb 2023: ξt (I At )ξt1 ̂t At µt1 Sx δt. (24)Hence, under this approximation the random variableξt isagain Gaussian distributed. ... Its mean is obtained by replacingξt andδt in eq. (24) by their respective means:.

27 Jan 2023: E[A|X, Z] = (ZT Z σ2Xσ2A. I)1ZT X. (24). 1This simple toy example was inspired by the “shapes problem” in (Ghahramani, 1995);a larger scale example with real images

13 Feb 2023: 2.50 0.87CFVA 1.24 1.50 1.50 1.53SVA 0.64 0.88 0.90 0.84.

13 Feb 2023: f (x) = maxλ{λT x f (λ)}, (23). where. f (λ) = maxx{λT x f (x)} (24).

27 Jan 2023: The existence of correlated side chain mutations in -heliceshas been well studied [20], [24].

13 Feb 2023: Flexible Latent Variable Models for Multi-Task. Learning. Jian Zhang1, Zoubin Ghahramani2,3, and Yiming Yang3. 1 Department of Statistics, Purdue University, West Lafayette, IN 47907jianzhan@stat.purdue.edu. 2 Department of Engineering, University

13 Feb 2023: 25 2973.7 -2.247. 5 163.24 -1.066. Finite Variational 10 767.1 -0.908.

13 Feb 2023: Figure 10 about here.]. 24. Empirical analysis of HGDP data To illustrate our method on real data, we applied it. ... proportion of 0.24 in Native American ancestry. Although only one or two populations are.

27 Jan 2023: The model can again be writtenas in (24):. P (s1:T , y1:T |θ) =T. ... HMMs can be extended by allowing a vector of discretestate variables, in an architecture known as a factorial HMM [24].

13 Feb 2023: 346 7 283 32HEP P H 34,546 420,899 24 846 61.

27 Jan 2023: The model can again be writtenas in (24):. P (s1:T , y1:T |θ) =T. ... HMMs can be extended by allowing a vector of discretestate variables, in an architecture known as a factorial HMM [24].

27 Jan 2023: The model can again be writtenas in (24):. P (s1:T , y1:T |θ) =T. ... HMMs can be extended by allowing a vector of discretestate variables, in an architecture known as a factorial HMM [24].

13 Feb 2023: p(x1:T , y1:T |θ) =T. t=1. p(xt|xt1, θ)p(yt|xt, θ) (24). In order words, the observations are assumed to have been generated fromthe hidden ... We assume that st can take discrete values in {1,. , K}.The model can again be written as in (24):.

13 Feb 2023: LETTER Communicated by Joris Mooij. Model Reductions for Inference: Generality of Pairwise,Binary, and Planar Factor Graphs. Frederik Eatonfrederik@ofb.netZoubin Ghahramanizoubin@eng.cam.ac.ukDepartment of Engineering, University of Cambridge,

13 Feb 2023: E[A|X, Z] = (ZT Z σ2Xσ2A. I)1ZT X. (24). 1This simple toy example was inspired by the “shapes problem” in (Ghahramani, 1995);a larger scale example with real images

27 Jan 2023: ðB23Þ. B.5. QðZlmÞ. Using Eqs. (6) and (24). QðZlmÞ / expfklog pðD; Zlw; m; S; W; b; mÞlQðm;S;W;blmÞg.

13 Feb 2023: ARTICLE IN PRESS. Neurocomputing 72 (2009) 1508–1524. Contents lists available at ScienceDirect. Neurocomputing. 0925-23. doi:10.1. CorrTrumpi. E-m. journal homepage: www.elsevier.com/locate/neucom. Gaussian process dynamic programming. Marc Peter

13 Feb 2023: K1mm K. nm Z. Knmθi. ],. log |Q̃|σ2. =n m. σ2+ Tr [Zmm] ,. (24)where we have introduced Z Knm. [Knm Knm σ. 2 Kmm]1.

27 Jan 2023: m) (23)q(m)t = exp 12T Yt C(m)X(m)t 0 R1 Yt C(m)X(m)t : (24)Here T is a temperature parameter, whi h is

13 Feb 2023: Max–Planck–Institut f ür biologische KybernetikMax Planck Institute for Biological Cybernetics. Technical Report No. 136. Approximate Inference forRobust Gaussian Process. Regression. Malte Kuss1, Tobias Pfingsten1,2, Lehel Csató1,Carl E.

27 Jan 2023: we have:f(x) = max fTx f()g; (23)where f() = maxx fTx f(x)g (24)is the conjugate function.We have focused on linear bounds in this section, but ... 24 MICHAEL I. JORDAN ET AL.calculate the conjugate function. If the function is not convex or concave,then

27 Jan 2023: ln p(y |m)BIC = ln p(y | θ̂) d(m). 2ln n ln S (24).

13 Feb 2023: Journal of Machine Learning Research 12 (2011) 1185-1224 Submitted 3/10; Revised 3/11; Published 4/11. The Indian Buffet Process: An Introduction and Review. Thomas L. Griffiths TOM GRIFFITHS@BERKELEY.EDUDepartment of PsychologyUniversity of

13 Feb 2023: 60. Denotational Validation of Higher-Order Bayesian Inference. ADAM ŚCIBIOR, University of Cambridge, England, UK and Max Planck Institute for Intelligent Systems,Germany. OHAD KAMMAR, University of Oxford, England, UKMATTHIJS VÁKÁR, University

13 Feb 2023: Journal of Machine Learning Research 10 (2009) 1187-1238 Submitted 4/08; Revised 11/08; Published 6/09. The Hidden Life of Latent Variables:Bayesian Learning with Mixed Graph Models. Ricardo Silva RICARDO@STATS.UCL.AC.UKDepartment of Statistical

13 Feb 2023: Journal of Machine Learning Research 11 (2010) 985-1042 Submitted 12/08; Revised 8/09; Published 2/10. Kronecker Graphs: An Approach to Modeling Networks. Jure Leskovec JURE@CS.STANFORD.EDUComputer Science DepartmentStanford UniversityStanford, CA

13 Feb 2023: e a d e r t o relevant t e x t s [41, 24, 19] for details. ... 21). (22) (23) (24) (25). where X and V are the prior m e a n and covariance o f t h e state, which are m o d e l

13 Feb 2023: 1.24). Note that the posterior over f is also an N-dimensional Gaussian as it is also con-.

13 Feb 2023: 24). The Hamiltonian can be seen as the log of the augmented distribution to be sampledfrom: p(θ, u|ψ) = p(θ|ψ)N(u|0, I).

13 Feb 2023: 24. 4 Accelerated Sampling in Conjugate Models 26. 4.1 Intuition. 27. ... poor modes early on. Chapter 3: Inference 24. Applied to the IBP, we can think of particle filtering as considering a num-.