arXiv subjects

Elina Robeva

Publications and source records attributed to Elina Robeva.

42 records · Page 3Linked to original sources

arXiv2015

Orthogonal Decomposition of Symmetric Tensors

A real symmetric tensor is orthogonally decomposable (or odeco) if it can be written as a linear combination of symmetric powers of $n$ vectors which form an orthonormal basis of $\mathbb R^n$. Motivated by the spectral theorem for real symmetric matrices, we study the properties of odeco tensors. We give a formula for all of the eigenvectors of an odeco tensor. Moreover, we formulate a set of polynomial equations that vanish on the odeco variety and we conjecture that these polynomials generate its prime ideal. We prove this conjecture in some cases and give strong evidence for its overall correctness.

math.AG↗

arXiv2015

Decomposing Tensors into Frames

A symmetric tensor of small rank decomposes into a configuration of only few vectors. We study the variety of tensors for which this configuration is a unit norm tight frame.

math.AG↗

arXiv2015

Fixed points of the EM algorithm and nonnegative rank boundaries

Mixtures of $r$ independent distributions for two discrete random variables can be represented by matrices of nonnegative rank $r$. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the set of fixed points of the Expectation-Maximization algorithm, and we study the boundary of the space of matrices with nonnegative rank at most $3$. Both of these sets correspond to algebraic varieties with many irreducible components.

math.ST↗

arXiv2013

Robust Toric Ideals

We call an ideal in a polynomial ring robust if it can be minimally generated by a universal Gröbner basis. In this paper we show that robust toric ideals generated by quadrics are essentially determinantal. We then discuss two possible generalizations to higher degree, providing a tight classification for determinantal ideals, and a counterexample to a natural extension for Lawrence ideals. We close with a discussion of robustness of higher Betti numbers.

math.AC↗

arXiv2012

A tropical proof of the Brill-Noether Theorem

We produce Brill-Noether general graphs in every genus, confirming a conjecture of Baker and giving a new proof of the Brill-Noether Theorem, due to Griffiths and Harris, over any algebraically closed field.

math.AG↗

arXiv2008

Artificial intelligence for Bidding Hex

We present a Monte Carlo algorithm for efficiently finding near optimal moves and bids in the game of Bidding Hex. The algorithm is based on the recent solution of Random-Turn Hex by Peres, Schramm, Sheffield, and Wilson together with Richman's work connecting random-turn games to bidding games.

math.CO↗