?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Bayesian+Manifold+Learning%3A+The+Locally+Linear+Latent+Variable+Model+(LL-LVM)&rft.creator=Park%2C+M&rft.creator=Jitkrittum%2C+W&rft.creator=Qamar%2C+A&rft.creator=Szabo%2C+Z&rft.creator=Buesing%2C+L&rft.creator=Sahani%2C+M&rft.description=We+introduce+the+Locally+Linear+Latent+Variable+Model+(LL-LVM)%2C+a+probabilistic+model+for+non-linear+manifold+discovery+that+describes+a+joint+distribution+over+observations%2C+their+manifold+coordinates+and+locally+linear+maps+conditioned+on+a+set+of+neighbourhood+relationships.+The+model+allows+straightforward+variational+optimisation+of+the+posterior+distribution+on+coordinates+and+locally+linear+maps+from+the+latent+space+to+the+observation+space+given+the+data.+Thus%2C+the+LL-LVM+encapsulates+the+local-geometry+preserving+intuitions+that+underlie+non-probabilistic+methods+such+as+locally+linear+embedding+(LLE).+Its+probabilistic+semantics+make+it+easy+to+evaluate+the+quality+of+hypothesised+neighbourhood+relationships%2C+select+the+intrinsic+dimensionality+of+the+manifold%2C+construct+out-of-sample+extensions+and+to+combine+the+manifold+model+with+additional+probabilistic+models+that+capture+the+structure+of+coordinates+within+the+manifold.&rft.publisher=Neural+Information+Processing+Systems+Foundation&rft.date=2014-12-12&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A++Advances+in+Neural+Information+Processing+Systems+28+(NIPS+2015).++++Neural+Information+Processing+Systems+Foundation%3A+Montreal%2C+Canada.+(2014)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F1452736%2F1%2FSzabo_5973-bayesian-manifold-learning-the-locally-linear-latent-variable-model-ll-lvm.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F1452736%2F&rft.rights=open