<XML><RECORDS><RECORD><REFERENCE_TYPE>10</REFERENCE_TYPE><REFNUM>7022</REFNUM><AUTHORS><AUTHOR>Girard,A.</AUTHOR><AUTHOR>Murray-Smith,R.</AUTHOR></AUTHORS><YEAR>2003</YEAR><TITLE>Learning a Gaussian Process Model with Uncertain Inputs</TITLE><PLACE_PUBLISHED>DCS Tech Report</PLACE_PUBLISHED><PUBLISHER>N/A</PUBLISHER><PAGES>10</PAGES><ISBN>TR-2003-144</ISBN><LABEL>Girard:2003:7022</LABEL><KEYWORDS><KEYWORD>Gaussian Process</KEYWORD></KEYWORDS<ABSTRACT>Learning with uncertain inputs is well-known to be a difficult task. In order to achieve this analytically using a Gaussian Process prior model, we expand the original process around the input mean (Delta method), assuming the random input is normally distributed. We thus derive a new process whose covariance function accounts for the randomness of the input. We illustrate the effectiveness of the proposed model on a simple static simulation example and on the modelling of a nonlinear noisy time-series. </ABSTRACT></RECORD></RECORDS></XML>