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Found 15 papers, 1 papers with code
Estimating Higher-Order Mixed Memberships via the $\ell_{2,\infty}$ Tensor Perturbation Bound
Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has a community membership associated with it.
Learning Good State and Action Representations via Tensor Decomposition
The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure.
ISLET: Fast and Optimal Low-rank Tensor Regression via Importance Sketching
In this paper, we develop a novel procedure for low-rank tensor regression, namely \emph{\underline{I}mportance \underline{S}ketching \underline{L}ow-rank \underline{E}stimation for \underline{T}ensors} (ISLET).
Learning Markov models via low-rank optimization
We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states.
Optimal Sparse Singular Value Decomposition for High-dimensional High-order Data
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure.
Estimation of Markov Chain via Rank-Constrained Likelihood
This paper studies the estimation of low-rank Markov chains from empirical trajectories.
Spectral State Compression of Markov Processes
Model reduction of Markov processes is a basic problem in modeling state-transition systems.
Sparse and Low-rank Tensor Estimation via Cubic Sketchings
In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings.
Multi-sample Estimation of Bacterial Composition Matrix in Metagenomics Data
Metagenomics sequencing is routinely applied to quantify bacterial abundances in microbiome studies, where the bacterial composition is estimated based on the sequencing read counts.
Methodology Applications Computation
Tensor SVD: Statistical and Computational Limits
In this paper, we propose a general framework for tensor singular value decomposition (tensor SVD), which focuses on the methodology and theory for extracting the hidden low-rank structure from high-dimensional tensor data.
Cross: Efficient Low-rank Tensor Completion
The proposed procedure is efficient and easy to implement.
Semi-supervised Inference: General Theory and Estimation of Means
Estimators are proposed along with corresponding confidence intervals for the population mean.
Structured Matrix Completion with Applications to Genomic Data Integration
Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering.
ROP: Matrix recovery via rank-one projections
In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case.
Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices
It is shown that for any given constant $t\ge {4/3}$, in compressed sensing $\delta_{tk}^A < \sqrt{(t-1)/t}$ guarantees the exact recovery of all $k$ sparse signals in the noiseless case through the constrained $\ell_1$ minimization, and similarly in affine rank minimization $\delta_{tr}^\mathcal{M}< \sqrt{(t-1)/t}$ ensures the exact reconstruction of all matrices with rank at most $r$ in the noiseless case via the constrained nuclear norm minimization.
