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Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…
Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…
Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…
Deep neural networks (DNNs) have demonstrated remarkable success, yet their wide adoption is often hindered by their opaque decision-making. To address this, attribution methods have been proposed to assign relevance values to each part of…
As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
We establish a general statistical optimality theory for estimation problems where the target parameter is a linear functional of an unknown nuisance component that must be estimated from data. This formulation covers many causal and…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability…
Variational quantum computing offers a powerful framework with applications across diverse fields such as quantum chemistry, machine learning, and optimization. However, its scalability is hindered by the exponential concentration of the…
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…
With increased adoption of supervised deep learning methods for processing and analysis of cosmological survey data, the assessment of data perturbation effects (that can naturally occur in the data processing and analysis pipelines) and…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of probabilistic…
Computation plays a key role in predicting and analyzing natural phenomena. There are two fundamental barriers to our ability to computationally understand the long-term behavior of a dynamical system that describes a natural process. The…
Noise on quantum devices is much more complex than it is commonly given credit. Far from usual models of decoherence, nearly all quantum devices are plagued both by a continuum of environments and temporal instabilities. These induce noisy…
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…
In this paper, we explore the two-point zeroth-order gradient estimator and identify the distribution of random perturbations that minimizes the estimator's asymptotic variance as the perturbation stepsize tends to zero. We formulate it as…