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  2. Large Scale Nonparametric Bayesian Inference:Data Parallelisation in…

    https://mlg.eng.cam.ac.uk/pub/pdf/DosKnoMohGha09.pdf
    13 Feb 2023: Initially, a largenumber of features are added, which provides improvements in the test likelihood. ... Table 2 summarises the data and shows thatall approaches had similar test-likelihood performance.
  3. paper.dvi

    https://mlg.eng.cam.ac.uk/pub/pdf/KimGha08.pdf
    13 Feb 2023: Figure 1 shows the training points, test points, decision boundary from GPCand decision boundary from robust GPC. ... We created 10 pairs of training and test sets by randomlydividing the whole data set into two.
  4. Bayesian Classifier Combination Zoubin Ghahramani and Hyun-Chul Kim∗…

    https://mlg.eng.cam.ac.uk/zoubin/papers/GhaKim03.pdf
    27 Jan 2023: Satellitehas a training set of 4435, a test set of 2000 with 6 classes and 36 variables. ... UCI digit data set has a trainingset of 3823, a test set of 1797, 10 classes and 64 variables.
  5. - 4F13: Machine Learning

    https://mlg.eng.cam.ac.uk/teaching/4f13/0708/lect06.pdf
    19 Nov 2023: Constraint-Based Learning: Use statistical tests of marginal and conditionalindependence. Find the set of DAGs whose d-separation relations match theresults of conditional independence tests.
  6. Manifold Gaussian Processes for Regression Roberto Calandra∗, Jan…

    https://mlg.eng.cam.ac.uk/pub/pdf/CalPetRasDei16.pdf
    13 Feb 2023: Additionally, for the test set, wemake use of the Negative Log Predictive Probability (NLPP). ... For training we extract 400consecutive data points, while we test on the following 500data points.
  7. LNCS 5342 - Outlier Robust Gaussian Process Classification

    https://mlg.eng.cam.ac.uk/pub/pdf/KimGha08a.pdf
    13 Feb 2023: Figure 1 shows the training points, test points, decision boundary from GPCand decision boundary from robust GPC. ... We created 10 pairs of training and test sets by randomlydividing the whole data set into two.
  8. Randomized Nonlinear Component Analysis

    https://mlg.eng.cam.ac.uk/pub/pdf/LopSraSmo14a.pdf
    13 Feb 2023: Results are statistically significantrespect to a paired Wilcoxon test on a 95% confidence inter-val. ... Figure 3. Autoencoder reconstructions of unseen test images forthe MNIST (top) and CIFAR-10 (bottom) datasets.
  9. 13 Feb 2023: The test data is created by randomlyselecting 10% of the data points and setting them as missing. ... 0.5. 1. 1.5. 2. 2.5. 3. PARAFAC. Probabilistic NTF. Test Train.
  10. Local and global sparse Gaussian process approximations Edward…

    https://mlg.eng.cam.ac.uk/zoubin/papers/aistats07localGP.pdf
    27 Jan 2023: The nearestblock’s GP is used to predict at a given test point. ... At test time, a test point is simply assigned tothe nearest cluster center.
  11. BIOINFORMATICS ORIGINAL PAPER Vol. 21 no. 16 2005, pages ...

    https://mlg.eng.cam.ac.uk/pub/pdf/ChuGhaFal05a.pdf
    13 Feb 2023: Non-parametric tests,e.g. the Wilcoxon rank sum test, are superior to the t -test in this case. ... The integers in the parantheses is the total test error numberover the 10 folds.
  12. /users/joe/src/tops/dvips

    https://mlg.eng.cam.ac.uk/pub/pdf/UedNakGha00a.pdf
    13 Feb 2023: improve the likelihood of both the training dataand of held-out test data. ... The split criterion defined by equation 3.13 can be viewed as a likelihoodratio test.
  13. Infinite Hidden Markov Models and extensions

    https://mlg.eng.cam.ac.uk/zoubin/talks/BayesHMMs10.pdf
    27 Jan 2023: IHMM evaluation in (Beal et al.,2002) is more elaborate: it allows the IHMM to con-tinue learning about new data encountered during test-ing. ... Subjecting theseresults to the same analysis as the artificial data re-veals similar compared test-set
  14. standalone.dvi

    https://mlg.eng.cam.ac.uk/pub/pdf/QuiRasWil07.pdf
    13 Feb 2023: test conditional: p(f|u) = N (K,uK1. u,uu, K, Q,) , (10b). ... Lower graph: assumption of conditional independencebetween training and test function values given u.
  15. Variational Inference for the Indian Buffet Process Finale…

    https://mlg.eng.cam.ac.uk/pub/pdf/DosMilVanTeh09.pdf
    13 Feb 2023: Table 1: Running times in seconds and test log-likelihoods for the Yale Faces dataset. ... Algorithm K Time Test Log-Likelihood. 2 56 -0.7444Finite Gibbs 5 120 -0.4220.
  16. A Kernel Approach to Tractable Bayesian Nonparametrics

    https://mlg.eng.cam.ac.uk/pub/pdf/HusLac11.pdf
    13 Feb 2023: We foundthat kst outperformed both competing methods sig-nificantly (p < 0.01, two sample T-test). ... 3. As measureof performance, we used average confusion, i. e. thefraction of misclassified test images.
  17. PILCO: A Model-Based and Data-Efficient Approach to Policy Search

    https://mlg.eng.cam.ac.uk/pub/pdf/DeiRas11.pdf
    13 Feb 2023: 3)–(5). Doing this properlyrequires mapping uncertain test inputs through theGP dynamics model. ... b) Histogram (after 1,000 test runs)of the distances of the flywheel frombeing upright.
  18. Recent Advanced in Causal Modelling Using Directed Graphs

    https://mlg.eng.cam.ac.uk/zoubin/SALD/scheines.ppt
    27 Jan 2023: Can be applied to distributions where tests of conditional independence are known, but scores aren’t. ... 2) X1 - X2 into X2. Test. Test Conditions. X3. X2.
  19. 13 Feb 2023: Secondly, our empirical results (see Section 3)indicate, that the test set performance is simply not good. ... Table 1. Average log test densities over 10 random splits of the data.
  20. Prediction on Spike DataUsing Kernel Algorithms Jan Eichhorn, Andreas …

    https://mlg.eng.cam.ac.uk/pub/pdf/EicTolZieetal04.pdf
    13 Feb 2023: Finallywe train the best model on these four folds and compute an independent test error on theremaining fold. ... Table 1 Mean test error and standard error on the low contrast dataset.
  21. 13 Feb 2023: the test log-likelihood on a symmetric logscale as the discrepancy is very large. ... Test MSE on real-world regression problems (lower isbetter). 5.2. Approximation quality.
  22. 13 Feb 2023: Figure 8(a) shows test set log likelihoods for 10 ran-dom divisions of the data into training and test sets. ... test. dat. a. SFAAFA NS. FA. Fig 9. Test set log likelihoods on Prostate cancer dataset from Yu et al.
  23. Inferring a measure of physiological age frommultiple ageing related…

    https://mlg.eng.cam.ac.uk/pub/pdf/KnoParGlaWin11.pdf
    13 Feb 2023: Table 2: Hold out test. Values are log10(p) where p is the p-value for the Spearman rank correlationhypothesis test. ... The results are shown in Figure 2.2, where we are also able to include binary variables unlikefor the Spearman test.
  24. MODEL BASED LEARNING OF SIGMA POINTS IN UNSCENTED KALMAN ...

    https://mlg.eng.cam.ac.uk/pub/pdf/TurRas10.pdf
    13 Feb 2023: 11). 2If we want to integrate the parameters out we must run the UKF witheach sample of θ|y1:T during test and average. ... 6.5. Computational Complexity. The UKF-L, UKF, and EKF have test set computationaltime O(DT(D2 M)).
  25. Scaling the Indian Buffet Process via Submodular Maximization

    https://mlg.eng.cam.ac.uk/pub/pdf/ReeGha13a.pdf
    13 Feb 2023: aibp. t-aibp. f-vibpi-vibp. seconds. test. log-likelihood ugibbs. t-ugibbs. t-aibp. aibp. bnmf. ... test. log-likelihood. Piano. meibp. ugibbs. aibp. bnmf. f-vibp. i-vibp. 103 104 1054.95.
  26. PROPAGATION OF UNCERTAINTY IN BAYESIAN KERNEL MODELS— APPLICATION TO…

    https://mlg.eng.cam.ac.uk/pub/pdf/QuiGirLarRas03.pdf
    13 Feb 2023: Thiscorresponds to using the model in recall/test phase under uncer-tain input. ... 3. PREDICTION WITH UNCERTAIN INPUT. Assume that the test inputx can not be observed directly and theuncertainty is modeled asx p(x) = N (u, S), with meanuand covariance
  27. Gaussian Process Change Point Models

    https://mlg.eng.cam.ac.uk/pub/pdf/SaaTurRas10.pdf
    13 Feb 2023: Weevaluated the models’ ability to predict next day snow-fall using 35 years of test data. ... Method Negative Log Likelihood p-value MSE p-valueNile Data (200 Training Points, 462 Test Points).
  28. Variable noise and dimensionality reduction forsparse Gaussian…

    https://mlg.eng.cam.ac.uk/zoubin/papers/snelson_uai.pdf
    27 Jan 2023: We have triedto implement both versions efficiently. Validation Time /s. Method NLPD MSE Train Test. ... To test this weused PCA to reduce the dimension to 5, before usingthe SPGP.
  29. Adaptive Sequential Bayesian Change Point Detection Ryan…

    https://mlg.eng.cam.ac.uk/pub/pdf/TurSaaRas09.pdf
    13 Feb 2023: We also include the 95% error bars on the NLL and the p-value that the joint model/learned hypers hasa higher NLL using a one sided t-test. ... Industry: We test on the last 8455 points of the portfolio data, 3 July 1975–31 December 2008.
  30. 4F13 Machine Learning: Coursework #4: Reinforcement Learning Zoubin…

    https://mlg.eng.cam.ac.uk/teaching/4f13/0910/cw/coursework4.pdf
    19 Nov 2023: Test yourvalueIteration algorithm.
  31. 4F13 Machine Learning: Coursework #4: Reinforcement Learning Zoubin…

    https://mlg.eng.cam.ac.uk/teaching/4f13/1011/cw/coursework4.pdf
    19 Nov 2023: Test yourvalueIteration algorithm.
  32. G:\bioinformatics\Bioinfo-26(7)issue\btq053.dvi

    https://mlg.eng.cam.ac.uk/pub/pdf/LipGhaBor10.pdf
    13 Feb 2023: A two-sample test tries to decide whether twosamples, in our case x and DC , have been generated by the samedistribution or not. ... edge,and might artificially boost prediction accuracy if they appear in both trainingand test set.
  33. Relational Learning with Gaussian Processes Wei ChuCCLS Columbia…

    https://mlg.eng.cam.ac.uk/pub/pdf/ChuSinGhaetal07.pdf
    13 Feb 2023: in the input space and provides proba-bilistic induction over unseen test points. ... K̃(zm, zt)]T. One can computethe Bernoulli distribution over the test labelyt by.
  34. 4F13 Machine Learning: Coursework #1: Gaussian Processes Carl Edward…

    https://mlg.eng.cam.ac.uk/teaching/4f13/1314/cw/coursework1.pdf
    19 Nov 2023: Show and comment on the fit and the hypers, and the predictions forthe test data.
  35. Gaussian Process Model Based Predictive Control

    https://mlg.eng.cam.ac.uk/pub/pdf/KocMurRasGir04.pdf
    13 Feb 2023: 4. Fitting of theresponse for validation signal:• average absolute test error. AE = 0.1276 (14). • ... average squared test error. SE = 0.0373 (15). 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100002.
  36. Relational Learning with Gaussian Processes Wei ChuCCLS Columbia…

    https://mlg.eng.cam.ac.uk/zoubin/papers/relationalgp.pdf
    27 Jan 2023: in the input space and provides proba-bilistic induction over unseen test points. ... K̃(zm, zt)]T. One can computethe Bernoulli distribution over the test labelyt by.
  37. The Infinite Hidden Markov Model Matthew J. Beal Zoubin ...

    https://mlg.eng.cam.ac.uk/zoubin/papers/ihmm.pdf
    27 Jan 2023: We propose estimating the likelihood of a test sequence given a learned model using particlefiltering. ... 6Different particle initialisations apply if we do not assume that the test sequence immediatelyfollows the training sequence.
  38. Determinantal Clustering Process - A Nonparametric BayesianApproach…

    https://mlg.eng.cam.ac.uk/pub/pdf/ShaGha13a.pdf
    13 Feb 2023: Next anyparameters of the density model can be integrated outto produce a predictive clustering of unseen test data. ... lected wheat types) and leave 5 data points from eachwheat type as unobserved test points.
  39. 544 The Block Diagonal Infinite Hidden Markov Model Thomas ...

    https://mlg.eng.cam.ac.uk/pub/pdf/SteGhaGoretal09.pdf
    13 Feb 2023: Each dataset had 2000 stepsof training data and 2000 steps of test data. ... these were not significantly different (two sam-ple t-test, p = 0.3).
  40. The Supervised IBP: Neighbourhood PreservingInfinite Latent Feature…

    https://mlg.eng.cam.ac.uk/pub/pdf/QuaShaKnoGha13.pdf
    13 Feb 2023: the in-ferred test latent variable z with respect to the train-ing latent variables Z. ... boldface is significant using a one-sided paired t-test with 95% confidence.
  41. 1 Learning the Structure of Deep Sparse Graphical Models ...

    https://mlg.eng.cam.ac.uk/pub/pdf/AdaWalGha10.pdf
    13 Feb 2023: c) (d)Figure 4: Olivetti faces a) Test images on the left, withreconstructed bottom halves on the right. ... Fig 4ashows six bottom-half test set reconstructions on theright, compared to the ground truth on the left.
  42. chu05a.dvi

    https://mlg.eng.cam.ac.uk/pub/pdf/ChuGha05a.pdf
    13 Feb 2023: 0.23370.0072. Table 2: Test results of the three algorithms using a Gaussian kernel. ... Figure 4 presents the test results of the three algorithms for different numbers ofselected genes.
  43. Archipelago: Nonparametric Bayesian Semi-Supervised Learning Ryan…

    https://mlg.eng.cam.ac.uk/pub/pdf/AdaGha09.pdf
    13 Feb 2023: In almost all of our tests, Archipelagohad lower test classification error than the NCNM. ... Itimproves over mixture-based Bayesian approaches toSSL while still modeling complex density functions.In empirical tests, our model compares favorably
  44. - IB Paper 7: Probability and Statistics

    https://mlg.eng.cam.ac.uk/teaching/1BP7/1819/lect01.pdf
    19 Nov 2023: Why do we need this, is it useful?• Make inference about uncertain events• Form the basis of information theory• Test the strength of statistical evidence. •
  45. Dependent Indian Buffet Processes Sinead Williamson Peter Orbanz…

    https://mlg.eng.cam.ac.uk/pub/pdf/WilOrbGha10.pdf
    13 Feb 2023: The data was randomly split into atraining set of 130 countries, and a test set of 14 coun-tries. ... For each test country, one randomly selectedindicator was observed, and the remainder held outfor prediction.
  46. Learning to Control a Low-Cost Manipulator usingData-Efficient…

    https://mlg.eng.cam.ac.uk/pub/pdf/DeiRasFox11.pdf
    13 Feb 2023: Althoughdeposit failure feedback was not available to the learner, thedeposit success is good across 10 test trials and four differenttraining setups. ... Second, Tab. III reports the block-deposit success rates for10 test runs (and four different
  47. Probabilistic Modelling, Machine Learning,and the Information…

    https://mlg.eng.cam.ac.uk/zoubin/talks/mit12csail.pdf
    27 Jan 2023: Some Comparisons. Table 1: Test errors and predictive accuracy (smaller is better) for the GP classifier, the supportvector machine, the informative vector machine, and the sparse pseudo-inputGP classifier. ... Data set GPC SVM IVM SPGPC. name train:test
  48. Gibbs sampling (an MCMC method) and relations to EM

    https://mlg.eng.cam.ac.uk/zoubin/SALD/week7at.pdf
    27 Jan 2023: Uniform U(0, θ] distribution, θ > 0. We select at random m n disks, having a common θ for failure We select n of these (at random) and test them until
  49. Approximate inference for the loss-calibrated Bayesian

    https://mlg.eng.cam.ac.uk/pub/pdf/LacHusGha11.pdf
    13 Feb 2023: We also assume. the transductive scenario where we are given a test setS of S points {xs}Ss=1, i.e. ... of the shift between the test and trainingdistributions (columns) and the asymmetry of loss (rows).
  50. LNAI 3944 - Evaluating Predictive Uncertainty Challenge

    https://mlg.eng.cam.ac.uk/pub/pdf/QuiRasSinetal06.pdf
    13 Feb 2023: The participants could then usethem to train their algorithms before submitting the test predictions. ... The test results were made public on December 11. The website remainsopen for submission.
  51. Bayesian Hierarchical Clustering Katherine A. Heller…

    https://mlg.eng.cam.ac.uk/zoubin/papers/bhcnew.pdf
    27 Jan 2023: As we will see, the main difference isthat our algorithm uses a statistical hypothesis test tochoose which clusters to merge. ... Sec-ond our algorithm is derived from Dirichlet processmixtures. Third the hypothesis test at the core ofour algorithm tests

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