# PCA from Noisy Linearly Reduced Measurements

Tuesday, September 27, 2016 - 1:25pm - 2:25pm

Lind 305

Amit Singer (Princeton University)

We consider the problem of estimating the covariance of X from measurements of the form y_i = A_i*x_i + e_i (for i = 1, . . . , n) where x_i are i.i.d. unobserved samples of X, A_i are given linear operators, and e_i represent noise. Our estimator is constructed efficiently via a simple linear inversion using conjugate gradient performed after eigenvalue shrinkage motivated by the spike model in high dimensional PCA. Applications to 2D image denoising, 3D ab-initio modelling, and 3D structure classification in single particle cryo-electron microscopy will be discussed.

Amit Singer is a Professor of Mathematics and member of the Executive Committee of the Program in Applied and Computational Mathematics (PACM) and of the Executive Committee for the Center for Statistics and Machine Learning (CSML) at Princeton University. He joined Princeton as an Assistant Professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University. Singer received the BSc degree in Physics and Mathematics and the PhD degree in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005, respectively. He served in the Israeli Defense Forces during 1997-2003. His list of awards includes a National Finalist for Blavatnik Awards for Young Scientists (2016), Moore Investigator in Data-Driven Discovery (2014), the Simons Investigator Award (2012), the Presidential Early Career Award for Scientists and Engineers (2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu Prize for Best PhD in Mathematics in Israel (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.

Amit Singer is a Professor of Mathematics and member of the Executive Committee of the Program in Applied and Computational Mathematics (PACM) and of the Executive Committee for the Center for Statistics and Machine Learning (CSML) at Princeton University. He joined Princeton as an Assistant Professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University. Singer received the BSc degree in Physics and Mathematics and the PhD degree in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005, respectively. He served in the Israeli Defense Forces during 1997-2003. His list of awards includes a National Finalist for Blavatnik Awards for Young Scientists (2016), Moore Investigator in Data-Driven Discovery (2014), the Simons Investigator Award (2012), the Presidential Early Career Award for Scientists and Engineers (2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu Prize for Best PhD in Mathematics in Israel (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.