Scalable message passing for ridge regression signal processing

A non-transitory computer readable storage medium for use in conjunction with a computer system, the computer readable storage medium storing one or more programs including instructions for execution by the computer system, the one or more programs when executed by the computer system cause the computer system to perform operations comprising:

• receiving at a computer system an input of data for a matrix where the matrix is a real valued matrix of m rows and n columns, and said matrix having a real-valued column vector y of length m;
• approximating an approximation of the column vector y by linearly combining all columns of the matrix by minimizing an approximation error which is the sum of the squared differences of the approximation and the complexity of the combining coefficients, where minimizing the approximation error further comprises instructions for computing the reweight factor using a power iteration method,
• continuing iterating the power iteration method until a convergence stopping criterion is met;
• and
• storing in the memory an optimal vector for the approximation based on the values of the approximation when the convergence stopping criterion is met.

A computer system for ridge regression of data comprising:

• a computer having a memory and one or more processors;
• one or more programs, stored in the memory and executed by the one or more processors, where the one or more programs include,
• instructions for receiving at a computer system an input of data for a matrix where the matrix is a real valued matrix of m rows and n columns, and said matrix having a real-valued column vector y of length m and where the data for said matrix is a type of data selected from a group of types of data consisting of signal data, statistical data, and image data;
• instructions for approximating an approximation of the column vector y by linearly combining all columns of the matrix by minimizing an approximation error which is the sum of the squared differences of the approximation and the complexity of the combining coefficients, where minimizing the approximation error further comprises instructions for computing the reweight factor using a power iteration method,
• continuing iterating the power iteration method until a convergence stopping criterion is met;
• and
• instructions for storing in the memory an optimal vector for the approximation based on the values of the approximation when the convergence stopping criterion is met.