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Bayes theorem (1)

Completely positive matrices (1)

Convex analysis (1)

Doubly nonnegative cone (1)

Nonnegative matrix factorization (1)

communication-efficient algorithms (1)

compressed sensing (1)

conditional gradient (1)

dictionary learning (1)

distributed optimization (2)

duality (1)

linear programming (1)

low-rank (1)

matrix (1)

multitask learning (2)

online optimization (1)

optimization (1)

polar sets (1)

semidefinite programming (1)

singular values (1)

smoothing (1)

sparsity (1)

tensor decomposition (1)

Duality of Faces in Polar Sets

Convex analysis

polar sets

In this blog post we introduce a notion of duality between faces of polar convex sets. Our purpose is to show through the simplicity of this introduction that this notion of…

Bayesian signal recovery

compressed sensing

Bayes theorem

The field of compressed sensing consists of quantifying how many linear measurements are required to locate an unknown signal within a known prior set. The a priori knowledge…

Approximate Matrix Rank

matrix

singular values

low-rank

Finding the rank of a matrix is straightforward (but not necessarily cheep!): compute a singular value decomposition, and count the number of nonzero singular values. But…

Nicholas Richardson

Alternating Direction Method of Multipliers for distributed subgroup analysis

distributed optimization

multitask learning

This post briefly introduces how to apply Alternating Direction Method of Multipliers (ADMM) to solve the distributed subgroup analysis, particularly the one regularized by fused lasso.

Communication-efficient algorithms for online distributed multitask learning

online optimization

distributed optimization

multitask learning

communication-efficient algorithms

This is a short review for the communication-efficient algorithms for online distributed multitask learning.

Spatial Transcriptomics Tensor Decomposition

tensor decomposition

Suppose we rearrange the gene expression matrix by expanding the first (spatial) dimension into 2-dimensional grid, so that

Atomic Dictionary Learning

I want a GPU for Christmas!

dictionary learning

sparsity

conditional gradient

The conditional gradient method seems an effective way to approximate a vector as a sum of atoms from a given atomic set. What if we don’t know what’s the right atomic set…

Michael P. Friedlander

Asymptotic Smoothing

duality

smoothing

optimization

semidefinite programming

linear programming

This note explores some duality relations that arise in the context of asymptotic smoothing and its possible application to linear and semidefinite programming.

Michael P. Friedlander

Convex formulations for nonnegative matrix factorization

Nonnegative matrix factorization

Completely positive matrices

Doubly nonnegative cone

The analysis of data sets often requires the identification of components that capture the most significant features of the data. Principle component analysis (PCA) is one…

Sam Burer, Michael P. Friedlander