### Table 1: Performance of the regression mapping from XY to the latent space

"... In PAGE 3: ... We performed leave one out cross validation and report the mean absolute error. Table1 shows results on test and training set for the 3 models. Notice that quadratic model performs best and the cubic model overfits the data.... ..."

### Table 2: Comparing Dimensions in the Latent Space Social Network Model. q is the dimension of the latent space, lscriptmax is the maximized loglike- lihood from a numerical optimisation routine, and # par is the total number of parameters estimated, including the latent position coordinates. The best values of BICM and AICM are shown in bold.

in Summary

"... In PAGE 21: ... (32) Note that the values of n1 and n2 chosen do not affect model selection, because the corresponding terms cancel in computing differences between BICM values for different models, which are what matter for model comparisons. The results are shown in Table2 . In addition to our estimates of the maximized likelihood, estimates of the maximized loglikelihood by numerical optimization are shown.... In PAGE 22: ... Again it seems reasonable that the Young Turks have a more central position, suggesting that a one-dimensional latent space captures most of the main features of the data, as suggested by the relatively small differences in BICM and AICM between the one- and two-dimensional models. Our method provides standard errors for BICM and AICM, and these are also shown in Table2 . These increase rapidly, and roughly proportionally with the num- ber of parameters.... ..."

### Table 2: Comparing Dimensions in the Latent Space Social Network Model. q is the dimension of the latent space, lscriptmax is the maximized loglike- lihood from a numerical optimisation routine, and # par is the total number of parameters estimated, including the latent position coordinates. The best values of BICM and AICM are shown in bold.

in Summary

"... In PAGE 21: ... (32) Note that the values of n1 and n2 chosen do not affect model selection, because the corresponding terms cancel in computing differences between BICM values for different models, which are what matter for model comparisons. The results are shown in Table2 . In addition to our estimates of the maximized likelihood, estimates of the maximized loglikelihood by numerical optimization are shown.... In PAGE 22: ... Again it seems reasonable that the Young Turks have a more central position, suggesting that a one-dimensional latent space captures most of the main features of the data, as suggested by the relatively small differences in BICM and AICM between the one- and two-dimensional models. Our method provides standard errors for BICM and AICM, and these are also shown in Table2 . These increase rapidly, and roughly proportionally with the num- ber of parameters.... ..."

### Table 2: Comparing Dimensions in the Latent Space Model Using the Integrated Likelihood. q is the dimension of the latent space. lscriptmax is the maximized loglikelihood from a numerical optimisation routine, and # par is the total number of parameters estimated, including the latent position coordinates.

2007

"... In PAGE 26: ... In fact, the same model would be chosen no matter which of these values of n was chosen. The results are shown in Table2 . In addition to our estimates, estimates of the maximized loglikelihood by numerical optimization are shown.... ..."

Cited by 2

### Table 2: Comparing Dimensions in the Latent Space Model Using the Integrated Likelihood. q is the dimension of the latent space. lscriptmax is the maximized loglikelihood from a numerical optimisation routine, and # par is the total number of parameters estimated, including the latent position coordinates.

2007

"... In PAGE 26: ... In fact, the same model would be chosen no matter which of these values of n was chosen. The results are shown in Table2 . In addition to our estimates, estimates of the maximized loglikelihood by numerical optimization are shown.... ..."

Cited by 2

### Table 2: Comparing Dimensions in the Latent Space Social Network Model. q is the dimen- sion of the latent space, lscriptmax is the maximized loglikelihood from a numerical optimisation routine, and # par is the total number of parameters estimated, including the latent position coordinates. The best values of BICM and AICM are shown in bold.

2007

"... In PAGE 28: ...The results are shown in Table2 . In addition to our estimates of the maximized likelihood, estimates of the maximized loglikelihood by numerical optimization are shown.... In PAGE 29: ... This is why the choice is sensitive to the precise definition of the model comparison criterion. Our method provides standard errors for BICM and AICM, and these are also shown in Table2 . These increase rapidly, and roughly proportionally with the number of parameters.... ..."

Cited by 2

### Table 1. Nearest neighbour errors in latent space for the vowels data (in data space 24 errors). Method Isomap GP-LVM BC-GP-LVM

2006

"... In PAGE 7: ... The back con- strained GP-LVM obtains good separation between the different vowels, while keeping neighbourhood structure. Table1 offers a quantitative comparison. 7.... ..."

Cited by 12

### Table 2: Number k of neighbors, dimension d of the latent space and misclassification rate (with standard errors in brackets) of the best classifier for each considered data sets. Number of Embedding Misclassification

"... In PAGE 3: ... Different classifiers have been obtained according to several values for the number k of elements in the neighborhood of each units and for the embedding di- mension d. In the first two column of Table2 , the values of k and d corresponding to the classifiers with the best performance in the four training sets are reported. In the third column of the table the cross-validated error rates of the best classifiers are shown.... ..."

### Table 1: Automatic estimation of the dimensionality (D 1) of the latent space of motion and automatic estimation of the number of components K in the GMM, for the 10 gestures used in the experiment. Gesture ID 1 2 3 4 5 6 7 8 9 10

2007

"... In PAGE 5: ... 3.3 Experimental results The dimensionality of the latent space and the number of Gaussian components used to encode the data, estimated automatically by the system, are presented in Table1 . Only the rst demonstration observed is used to nd the optimal number of components.... ..."

Cited by 6