?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Bayesian+online+change+point+detection+with+Hilbert+space+approximate+Student-t+process&rft.creator=Sellier%2C+J&rft.creator=Dellaportas%2C+P&rft.description=In+this+paper%2C+we+introduce+a+variant+of+Bayesian+online+change+point+detection+with+a+reduced-rank+Student-t+process+(TP)+and+dependent+Student-t+noise%2C+as+a+nonparametric+time+series+model.+Our+method+builds+and+improves+upon+the+state-of-the-art+Gaussian+process+(GP)+change+point+model+benchmark+of+Saat%C3%A7i+et+al.+(2010).+The+Student-t+process+generalizes+the+concept+of+a+GP+and+hence+yields+a+more+flexible+alternative.+Additionally%2C+unlike+a+GP%2C+the+predictive+variance+explicitly+depends+on+the+training+observations%2C+while+the+use+of+an+entangled+Student-t+noise+model+preserves+analytical+tractability.+Our+approach+also+uses+a+Hilbert+space+reduced-rank+representation+of+the+TP+kernel%2C+derived+from+an+eigenfunction+expansion+of+the+Laplace+operator+(Solin+%26+S%C3%A4rkk%C3%A4%2C+2020)%2C+to+alleviate+its+computational+complexity.+Improvements+in+prediction+and+training+time+are+demonstrated+with+real-world+data+sets.&rft.publisher=PMLR+(Proceedings+of+Machine+Learning+Research)&rft.date=2023&rft.type=Proceedings+paper&rft.language=eng&rft.source=+++++In%3A++Proceedings+of+the+40th+International+Conference+on+Machine+Learning.++(pp.+pp.+30553-30569).++PMLR+(Proceedings+of+Machine+Learning+Research)+(2023)+++++&rft.format=application%2Fpdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10180942%2F1%2Fsellier23a.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10180942%2F&rft.rights=open