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Bi-fidelity Variational Auto-encoder for Uncertainty Quantification
Nuojin Cheng, Osman Asif Malik, Subhayan De +2
Quantifying the uncertainty of quantities of interest (QoIs) from physical systems is a primary objective in model validation. However, achieving this goal entails balancing the ne…
Improved Fixed-Rank Nyström Approximation via QR Decomposition: Practical and Theoretical Aspects
Farhad Pourkamali-Anaraki, Stephen Becker
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning…
Randomized Clustered Nystrom for Large-Scale Kernel Machines
Farhad Pourkamali-Anaraki, Stephen Becker
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nyst…
A Randomized Approach to Efficient Kernel Clustering
Farhad Pourkamali-Anaraki, Stephen Becker
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory re…
Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition
Aleksandr Y. Aravkin, Stephen Becker
We focus on the robust principal component analysis (RPCA) problem, and review a range of old and new convex formulations for the problem and its variants. We then review dual smoo…
Preconditioned Data Sparsification for Big Data with Applications to PCA and K-means
Farhad Pourkamali-Anaraki, Stephen Becker
We analyze a compression scheme for large data sets that randomly keeps a small percentage of the components of each data sample. The benefit is that the output is a sparse matrix…