64 citations · 111 across the 11 of their papers we have counts for
12 papers
iPCA and stability of star quivers
Cole Franks, Visu Makam
Integrated principal components analysis, or iPCA, is an unsupervised learning technique for grouped vector data recently defined by Tang and Allen. Like PCA, iPCA computes new axe…
Shrunk subspaces via operator Sinkhorn iteration
Cole Franks, Tasuku Soma, Michel X. Goemans
A recent breakthrough in Edmonds' problem showed that the noncommutative rank can be computed in deterministic polynomial time, and various algorithms for it were devised. However,…
Near optimal sample complexity for matrix and tensor normal models via geodesic convexity
Cole Franks, Rafael Oliveira, Akshay Ramachandran +1
The matrix normal model, i.e., the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower dimensional factors, is frequent…
Minimal length in an orbit closure as a semiclassical limit
Cole Franks, Michael Walter
Consider the action of a connected complex reductive group on a finite-dimensional vector space. A fundamental result in invariant theory states that the orbit closure of a vector…
Rigorous Guarantees for Tyler's M-estimator via quantum expansion
Cole Franks, Ankur Moitra
Estimating the shape of an elliptical distribution is a fundamental problem in statistics. One estimator for the shape matrix, Tyler's M-estimator, has been shown to have many appe…
Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes
Peter Bürgisser, Cole Franks, Ankit Garg +3
This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which deve…
A simplified disproof of Beck's three permutations conjecture and an application to root-mean-squared discrepancy
Cole Franks
A -permutation family on vertices is a set system consisting of the intervals of permutations of the integers through . The discrepancy of a set system is the min…
On the Discrepancy of Random Matrices with Many Columns
Cole Franks, Michael Saks
Motivated by the Komlós conjecture in combinatorial discrepancy, we study the discrepancy of random matrices with rows and independent columns drawn from a bounded lattice…
Efficient algorithms for tensor scaling, quantum marginals and moment polytopes
Peter Bürgisser, Cole Franks, Ankit Garg +3
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence o…
Graph Labeling with Distance Conditions and the Delta Squared Conjecture
Cole Franks
We give bounds on the L(2,1)-labeling number of a simple graph in terms of its order and its maximum degree. We also describe an infinite class of graphs of which the elements have…
Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones
Philip Chodrow, Cole Franks, Brian Lins
We define upper bound and lower bounds for order-preserving homogeneous of degree one maps on a proper closed cone in in terms of the cone spectral radius. We also define we…
On the structure group of a decomposable model space
Corey Dunn, Cole Franks, Joseph Palmer
We study the structure group of a canonical algebraic curvature tensor built from a symmetric bilinear form, and show that in most cases it coincides with the isometry group of the…