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03/28/2023
Diffusion Maps for Group-Invariant Manifolds
In this article, we consider the manifold learning problem when the data...
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01/22/2023
Moment Varieties for Mixtures of Products
The setting of this article is nonparametric algebraic statistics. We st...
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10/25/2022
Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition
We present an alternating least squares type numerical optimization sche...
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10/20/2022
Snapshot of Algebraic Vision
In this survey article, we present interactions between algebraic geomet...
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09/21/2022
Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms
The number of noisy images required for molecular reconstruction in sing...
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07/07/2022
The effect of smooth parametrizations on nonconvex optimization landscapes
We develop new tools to study the landscapes of nonconvex optimization p...
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04/22/2022
Scalable symmetric Tucker tensor decomposition
We study the best low-rank Tucker decomposition of symmetric tensors, ad...
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02/14/2022
Tensor Moments of Gaussian Mixture Models: Theory and Applications
Gaussian mixture models (GMM) are fundamental tools in statistical and d...
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12/29/2021
On the Instability of Relative Pose Estimation and RANSAC's Role
In this paper we study the numerical instabilities of the 5- and 7-point...
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10/29/2021
Landscape analysis of an improved power method for tensor decomposition
In this work, we consider the optimization formulation for symmetric ten...
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07/08/2021
Finding stationary points on bounded-rank matrices: A geometric hurdle and a smooth remedy
We consider the problem of provably finding a stationary point of a smoo...
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03/10/2021
Symmetry Breaking in Symmetric Tensor Decomposition
In this note, we consider the optimization problem associated with compu...
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12/28/2020
Manifold learning with arbitrary norms
Manifold learning methods play a prominent role in nonlinear dimensional...
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12/09/2019
Subspace power method for symmetric tensor decomposition and generalized PCA
We introduce the Subspace Power Method (SPM) for decomposing symmetric e...
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07/11/2019
Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles
Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is ...
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05/29/2019
On the Expressive Power of Deep Polynomial Neural Networks
We study deep neural networks with polynomial activations, particularly ...
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10/23/2017
3D ab initio modeling in cryo-EM by autocorrelation analysis
Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-E...
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03/15/2017
A clever elimination strategy for efficient minimal solvers
We present a new insight into the systematic generation of minimal solve...
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11/18/2016
Minimal Problems for the Calibrated Trifocal Variety
We determine the algebraic degree of minimal problems for the calibrated...
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10/10/2016
Numerical Implicitization for Macaulay2
We present the Macaulay2 package NumericalImplicitization, which allows ...
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10/06/2016
Distortion Varieties
The distortion varieties of a given projective variety are parametrized ...
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04/15/2016
The Chow Form of the Essential Variety in Computer Vision
The Chow form of the essential variety in computer vision is calculated....
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09/10/2015