About

Ioana Dumitriu holds a BA in Mathematics from New York University (1999) and a PhD in Applied Mathematics from the Massachusetts Institute of Technology (2003). Following her doctoral studies, she completed a Miller Research Fellowship at the University of California, Berkeley (2003-2006). She then served as a faculty member in the Department of Mathematics at the University of Washington, Seattle, from 2006 to 2019, before joining the University of California, San Diego in 2019. Her research spans various areas within data science, including numerical linear algebra, scientific computing, and stochastic eigenanalysis, also known as random matrix theory. She works on discrete probability and the spectra of random graphs, with applications in machine learning, particularly in clustering and community detection. Dumitriu's contributions are recognized through honors such as being a Fellow of the American Mathematical Society, receiving an NSF CAREER Award, winning the Leslie Fox Prize in Numerical Analysis, and earning an honorable mention for the Householder Prize in Numerical Linear Algebra.

Research topics

• Algorithm
• Mathematics
• Artificial Intelligence
• Computer Science
• Combinatorics
• Discrete mathematics
• Physics
• Statistics
• Mathematical optimization

Selected publications

• BBP Phase Transition for a Doubly Sparse Deformed Model

  Open MIND · 2026-03-05

  preprint1st authorCorresponding

  We prove the equivalent of the Baik, Ben Arous, Péché (2004) phenomenon for a novel, doubly sparse model where both the Wigner noise matrix and signal vector(s) are sparse. Specifically, we consider a deformed sub-Gaussian sparse Wigner ensemble with a fixed number of sub-Gaussian spike vectors of the same-order sparsity added. We show that spike vectors with signals greater than one are correlated with the top eigenvectors of the deformed ensemble and that each spike vector of signal greater than one induces an outlier eigenvalue. Notably, our results hold in the supercritical sparsity regime for the Wigner matrix ($q \gg \frac{\log n}{n}$) and for any sparse spike vector with an unbounded number of entries ($np\to \infty$). No further relationship between the sparsities of the noise matrix ($q$) and spike vectors ($p$) is necessary. This generalizes the work of Benaych-Georges and Nadakuditi (2010) and Péché (2005).

  DOI

• Rank One Completion for Higher Order Tensors

  arXiv (Cornell University) · 2026-04-25

  preprintOpen access

  We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This algorithm only requires solving linear systems and computing singular vectors. In the absence of noise, it produces a unique rank one completion under some assumptions. In the presence of noise, we show that the computed rank one tensor completion is close to the exact one when the noise is sufficiently small. Numerical experiments demonstrate the efficiency and accuracy of the proposed method.

  PublisherDOI

• BBP Phase Transition for a Doubly Sparse Deformed Model

  ArXiv.org · 2026-03-05

  articleOpen access1st authorCorresponding

  We prove the equivalent of the Baik, Ben Arous, Péché (2004) phenomenon for a novel, doubly sparse model where both the Wigner noise matrix and signal vector(s) are sparse. Specifically, we consider a deformed sub-Gaussian sparse Wigner ensemble with a fixed number of sub-Gaussian spike vectors of the same-order sparsity added. We show that spike vectors with signals greater than one are correlated with the top eigenvectors of the deformed ensemble and that each spike vector of signal greater than one induces an outlier eigenvalue. Notably, our results hold in the supercritical sparsity regime for the Wigner matrix ($q \gg \frac{\log n}{n}$) and for any sparse spike vector with an unbounded number of entries ($np\to \infty$). No further relationship between the sparsities of the noise matrix ($q$) and spike vectors ($p$) is necessary. This generalizes the work of Benaych-Georges and Nadakuditi (2010) and Péché (2005).

  PublisherOA PDF

• Rank One Completion for Higher Order Tensors

  ArXiv.org · 2026-04-25

  articleOpen access

  We study the rank one completion problem for tensors of arbitrary orders. The notion of rank one determinable tensors is introduced. We explore its properties and propose a recursive algorithm for computing rank one tensor completion. This algorithm only requires solving linear systems and computing singular vectors. In the absence of noise, it produces a unique rank one completion under some assumptions. In the presence of noise, we show that the computed rank one tensor completion is close to the exact one when the noise is sufficiently small. Numerical experiments demonstrate the efficiency and accuracy of the proposed method.

  PublisherOA PDF

• Fast and Inverse-Free Algorithms for Deflating Subspaces

  Linear Algebra and its Applications · 2026-01-01

  article
  PublisherDOI

• Optimal and exact recovery on the general nonuniform Hypergraph Stochastic Block Model

  The Annals of Statistics · 2026-02-01

  article1st authorCorresponding
  PublisherDOI

• Singular values of sparse random rectangular matrices: Emergence of outliers at criticality

  ArXiv.org · 2025-08-02

  preprintOpen access1st authorCorresponding

  Consider the random bipartite Erdős-Rényi graph $\mathbb{G}(n, m, p)$, where each edge with one vertex in $V_{1}=[n]$ and the other vertex in $V_{2} =[m]$ is connected with probability $p$, and $n=\lfloor γm\rfloor$ for a constant aspect ratio $γ\geq 1$. It is well known that the empirical spectral measure of its centered and normalized adjacency matrix converges to the Marčenko-Pastur (MP) distribution. However, largest and smallest singular values may not converge to the right and left edges, respectively, especially when $p = o(1)$. Notably, it was proved by Dumitriu and Zhu (2024) that there are almost surely no singular value outside the compact support of the MP law when $np = ω(\log(n))$. In this paper, we consider the critical sparsity regime where $p = b\log(n)/\sqrt{mn}$ for some constant $b>0$. We quantitatively characterize the emergence of outlier singular values as follows. For explicit $b_{*}$ and $b^{*}$ as functions of $γ$, we prove that when $b > b_{*}$, there is no outlier outside the bulk; when $b^{*}< b < b_{*}$, outliers are present only outside the right edge of the MP law; and when $b < b^{*}$, outliers are present on both sides, all with high probability. Moreover, the locations of those outliers are precisely characterized by a function depending on the largest and smallest degree vertices of the random graph. We estimate the number of outliers as well. Our results follow the path forged by Alt, Ducatez and Knowles (2021), and can be extended to sparse random rectangular matrices with bounded entries.

  PublisherOA PDFDOI

• Structured Divide-and-Conquer for the Definite Generalized Eigenvalue Problem

  ArXiv.org · 2025-05-28

  preprintOpen access

  This paper presents a fast, randomized divide-and-conquer algorithm for the definite generalized eigenvalue problem, which corresponds to pencils $(A,B)$ in which $A$ and $B$ are Hermitian and the Crawford number $γ(A,B) = \min_{||x||_2 = 1} |x^H(A+iB)x|$ is positive. Adapted from the fastest known method for diagonalizing arbitrary matrix pencils [Foundations of Computational Mathematics 2024], the algorithm is both inverse-free and highly parallel. As in the general case, randomization takes the form of perturbations applied to the input matrices, which regularize the problem for compatibility with fast, divide-and-conquer eigensolvers -- i.e., the now well-established phenomenon of pseudospectral shattering. We demonstrate that this high-level approach to diagonalization can be executed in a structure-aware fashion by (1) extending pseudospectral shattering to definite pencils under structured perturbations (either random diagonal or sampled from the Gaussian Unitary Ensemble) and (2) formulating the divide-and-conquer procedure in a way that maintains definiteness. The result is a specialized solver whose complexity, when applied to definite pencils, is provably lower than that of general divide-and-conquer.

  PublisherOA PDFDOI

• Partial recovery and weak consistency in the non-uniform hypergraph stochastic block model

  Combinatorics Probability Computing · 2024-10-09 · 2 citations

  articleOpen access1st author

  Abstract We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a $\gamma$ fraction of the vertices classified correctly, where $\gamma \in (0.5,1)$ depends on the signal-to-noise ratio (SNR) of the model. When the SNR grows slowly as the number of vertices goes to infinity, our algorithm achieves weak consistency, which improves the previous results in Ghoshdastidar and Dukkipati ((2017) Ann. Stat. 45 (1) 289–315.) for non-uniform HSBMs. Our spectral algorithm consists of three major steps: (1) Hyperedge selection: select hyperedges of certain sizes to provide the maximal signal-to-noise ratio for the induced sub-hypergraph; (2) Spectral partition: construct a regularised adjacency matrix and obtain an approximate partition based on singular vectors; (3) Correction and merging: incorporate the hyperedge information from adjacency tensors to upgrade the error rate guarantee. The theoretical analysis of our algorithm relies on the concentration and regularisation of the adjacency matrix for sparse non-uniform random hypergraphs, which can be of independent interest.

  PublisherOA PDFDOI

• Extreme singular values of inhomogeneous sparse random rectangular matrices

  Bernoulli · 2024-07-30 · 2 citations

  article1st authorCorresponding

  We develop a unified approach to bounding the largest and smallest singular values of an inhomogeneous random rectangular matrix, based on the non-backtracking operator and the Ihara-Bass formula for general random Hermitian matrices with a bipartite block structure. We obtain probabilistic upper (respectively, lower) bounds for the largest (respectively, smallest) singular values of a large rectangular random matrix X. These bounds are given in terms of the maximal and minimal ℓ2-norms of the rows and columns of the variance profile of X. The proofs involve finding probabilistic upper bounds on the spectral radius of an associated non-backtracking matrix B. The two-sided bounds can be applied to the centered adjacency matrix of sparse inhomogeneous Erdős-Rényi bipartite graphs for a wide range of sparsity, down to criticality. In particular, for Erdős-Rényi bipartite graphs G(n,m,p) with p=ω(logn)∕n, and m∕n→y∈(0,1), our sharp bounds imply that there are no outliers outside the support of the Marčenko-Pastur law almost surely. This result extends the Bai-Yin theorem to sparse rectangular random matrices.

  PublisherDOI

Recent grants

• Spectra of Large Random Graphs And Applications In Community Detection

  NSF · $65k · 2019–2021

• Spectra of Large Random Graphs And Applications In Community Detection

  NSF · $150k · 2017–2019

• CAREER: Synergistic interactions between Numerical Linear Algebra and Stochastic Eigenanalysis (Random Matrix Theory)

  NSF · $408k · 2009–2014

Frequent coauthors

• James Demmel

  11 shared

• Kavita Ramanan

  9 shared

• Todd Kemp

  9 shared

• Olga Holtz

  University of California, Berkeley

  8 shared

• Yizhe Zhu

  University of California, Irvine

  8 shared

• Elliot Paquette

  7 shared

• Gerandy Brito

  Georgia Institute of Technology

  6 shared

• Alan Edelman

  Massachusetts Institute of Technology

  5 shared

Awards & honors

• Fellow of the American Mathematical Society
• NSF CAREER Award
• Winner of the Leslie Fox Prize in Numerical Analysis
• Honorable Mention for the Householder Prize in Numerical Lin…