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Found 28 papers, 1 papers with code
High Dimensional Factor Analysis with Weak Factors
This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units, i. e., $\boldsymbol{\Lambda}^{0\top} \boldsymbol{\Lambda}^0 / N^\alpha$ is positive definite in the limit for some $\alpha \in (0, 1)$.
Multiple Testing of Linear Forms for Noisy Matrix Completion
Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion.
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).
Large Dimensional Independent Component Analysis: Statistical Optimality and Computational Tractability
Our method is fairly easy to implement and numerical experiments are presented to further demonstrate its practical merits.
On Recovering the Best Rank-r Approximation from Few Entries
In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries.
On Estimating Rank-One Spiked Tensors in the Presence of Heavy Tailed Errors
In this paper, we study the estimation of a rank-one spiked tensor in the presence of heavy tailed noise.
Assessing Fairness in Classification Parity of Machine Learning Models in Healthcare
Fairness in AI and machine learning systems has become a fundamental problem in the accountability of AI systems.
Detecting Structured Signals in Ising Models
In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way.
Probability Statistics Theory Statistics Theory 62G10, 62G20, 62C20
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.
Perturbation Bounds for (Nearly) Orthogonally Decomposable Tensors
We develop deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors, in a spirit similar to classical results for matrices such as those due to Weyl, Davis, Kahan and Wedin.
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).
On the Optimality of Gaussian Kernel Based Nonparametric Tests against Smooth Alternatives
In addition, our analysis also pinpoints the importance of choosing a diverging scaling parameter when using Gaussian kernels and suggests a data-driven choice of the scaling parameter that yields tests optimal, up to an iterated logarithmic factor, over a wide range of smooth alternatives.
Statistical Inferences of Linear Forms for Noisy Matrix Completion
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries.
Joint Demosaicing and Denoising with Perceptual Optimization on a Generative Adversarial Network
Image demosaicing - one of the most important early stages in digital camera pipelines - addressed the problem of reconstructing a full-resolution image from so-called color-filter-arrays.
Finding Differentially Covarying Needles in a Temporally Evolving Haystack: A Scan Statistics Perspective
Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources.
Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries
To fill in this void, in this article, we characterize the fundamental statistical limits of noisy tensor completion by establishing minimax optimal rates of convergence for estimating a $k$th order low rank tensor under the general $\ell_p$ ($1\le p\le 2$) norm which suggest significant room for improvement over the existing approaches.
Effective Tensor Sketching via Sparsification
In particular, we show that for a $k$th order $d\times\cdots\times d$ cubic tensor of {\it stable rank} $r_s$, the sample size requirement for achieving a relative error $\varepsilon$ is, up to a logarithmic factor, of the order $r_s^{1/2} d^{k/2} /\varepsilon$ when $\varepsilon$ is relatively large, and $r_s d /\varepsilon^2$ and essentially optimal when $\varepsilon$ is sufficiently small.
On the Optimality of Kernel-Embedding Based Goodness-of-Fit Tests
The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years.
Characterizing Spatiotemporal Transcriptome of Human Brain via Low Rank Tensor Decomposition
An application of our method to a spatiotemporal brain expression data provides insights on gene regulation patterns in the brain.
Methodology
On Polynomial Time Methods for Exact Low Rank Tensor Completion
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries.
Non-Convex Projected Gradient Descent for Generalized Low-Rank Tensor Regression
The two main differences between the convex and non-convex approach are: (i) from a computational perspective whether the non-convex projection operator is computable and whether the projection has desirable contraction properties and (ii) from a statistical upper bound perspective, the non-convex approach has a superior rate for a number of examples.
Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion
In this paper, we investigate the sample size requirement for a general class of nuclear norm minimization methods for higher order tensor completion.
Human Memory Search as Initial-Visit Emitting Random Walk
In this paper, we propose the first efficient maximum likelihood estimate (MLE) for INVITE by decomposing the censored output into a series of absorbing random walks.
Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse.
Distance Shrinkage and Euclidean Embedding via Regularized Kernel Estimation
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown.
Rate-Optimal Detection of Very Short Signal Segments
Motivated by a range of applications in engineering and genomics, we consider in this paper detection of very short signal segments in three settings: signals with known shape, arbitrary signals, and smooth signals.
On Tensor Completion via Nuclear Norm Minimization
To establish our results, we develop a series of algebraic and probabilistic techniques such as characterization of subdifferetial for tensor nuclear norm and concentration inequalities for tensor martingales, which may be of independent interests and could be useful in other tensor related problems.
Learning Networks of Heterogeneous Influence
However, the underlying transmission networks are often hidden and incomplete, and we observe only the time stamps when cascades of events happen.
