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Found 22 papers, 5 papers with code
Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data
We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition.
Reliable Generation of Privacy-preserving Synthetic EHR Time Series via Diffusion Models
The proposed diffusion-model-based method can reliably and efficiently generate synthetic EHR time series, which facilitates the downstream medical data analysis.
Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Model
The MOP-UP algorithm consists of two steps: Average Subspace Capture (ASC) and Alternating Projection (AP).
Phase transition for detecting a small community in a large network
Using a degree-corrected block model (DCBM), we establish phase transitions of this testing problem concerning the size of the small community and the edge densities in small and large communities.
Enhancing convolutional neural network generalizability via low-rank weight approximation
With the proposed design, we are able to characterize our denoiser with fewer parameters and train it based on a single image, which considerably improves the model's generalizability and reduces the cost of data acquisition.
Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E 2.
Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplay
We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank.
Learning Polynomial Transformations
Our first main result is a polynomial-time algorithm for learning quadratic transformations of Gaussians in a smoothed setting.
On Geometric Connections of Embedded and Quotient Geometries in Riemannian Fixed-rank Matrix Optimization
By applying the general procedure to the fixed-rank positive semidefinite (PSD) and general matrix optimization, we establish an exact Riemannian gradient connection under two geometries at every point on the manifold and sandwich inequalities between the spectra of Riemannian Hessians at Riemannian first-order stationary points (FOSPs).
Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization
In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matrix optimization.
Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence
In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements.
Inference for Low-rank Tensors -- No Need to Debias
In all these models, we observe that different from many matrix/vector settings in existing work, debiasing is not required to establish the asymptotic distribution of estimates or to make statistical inference on low-rank tensors.
Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit
High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc.
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
In this paper, we propose {\it \underline{R}ecursive} {\it \underline{I}mportance} {\it \underline{S}ketching} algorithm for {\it \underline{R}ank} constrained least squares {\it \underline{O}ptimization} (RISRO).
Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration
This paper studies a general framework for high-order tensor SVD.
Open Problem: Average-Case Hardness of Hypergraphic Planted Clique Detection
We note the significance of hypergraphic planted clique (HPC) detection in the investigation of computational hardness for a range of tensor problems.
A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration
Rate matching deterministic lower bound for tensor reconstruction, which demonstrates the optimality of HOOI, is also provided.
Tensor Clustering with Planted Structures: Statistical Optimality and Computational Limits
We also develop the tight computational thresholds: when the signal-to-noise ratio is below these thresholds, we prove that polynomial-time algorithms cannot solve these problems under the computational hardness conjectures of hypergraphic planted clique (HPC) detection and hypergraphic planted dense subgraph (HPDS) recovery.
An Optimal Statistical and Computational Framework for Generalized Tensor Estimation
Under mild conditions on the loss function, we establish both an upper bound on statistical error and the linear rate of computational convergence through a general deterministic analysis.
Sparse Group Lasso: Optimal Sample Complexity, Convergence Rate, and Statistical Inference
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse.
On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning.
Heteroskedastic PCA: Algorithm, Optimality, and Applications
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced.
