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02/19/2023
iPCA and stability of star quivers
Integrated principal components analysis, or iPCA, is an unsupervised le...
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09/28/2022
The minimal canonical form of a tensor network
Tensor networks have a gauge degree of freedom on the virtual degrees of...
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06/10/2022
Generic Reed-Solomon codes achieve list-decoding capacity
In a recent paper, Brakensiek, Gopi and Makam introduced higher order MD...
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05/30/2022
Subrank and Optimal Reduction of Scalar Multiplications to Generic Tensors
Since the seminal works of Strassen and Valiant it has been a central th...
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08/23/2021
Symmetries in Directed Gaussian Graphical Models
We define Gaussian graphical models on directed acyclic graphs with colo...
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07/22/2021
Lower Bounds for Maximally Recoverable Tensor Code and Higher Order MDS Codes
An (m,n,a,b)-tensor code consists of m× n matrices whose columns satisfy...
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02/15/2021
Polynomial time algorithms in invariant theory for torus actions
An action of a group on a vector space partitions the latter into a set ...
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11/07/2020
Maximum likelihood estimation for tensor normal models via castling transforms
In this paper, we study sample size thresholds for maximum likelihood es...
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07/20/2020
Maximum likelihood estimation for matrix normal models via quiver representations
In this paper, we study the log-likelihood function and Maximum Likeliho...
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10/02/2019
Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings
We consider the problem of outputting succinct encodings of lists of gen...
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09/02/2019
Singular tuples of matrices is not a null cone (and, the symmetries of algebraic varieties)
The following multi-determinantal algebraic variety plays a central role...
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04/08/2019
More barriers for rank methods, via a "numeric to symbolic" transfer
We prove new barrier results in arithmetic complexity theory, showing se...
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02/27/2019
An exponential lower bound for the degrees of invariants of cubic forms and tensor actions
Using the Grosshans Principle, we develop a method for proving lower bou...
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01/06/2018
Algorithms for orbit closure separation for invariants and semi-invariants of matrices
We consider two group actions on m-tuples of n × n matrices. The first i...
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01/01/2018