19 citations · 59 across the 16 of their papers we have counts for
19 papers
Improving Generalization of Complex Models under Unbounded Loss Using PAC-Bayes Bounds
Xitong Zhang, Avrajit Ghosh, Guangliang Liu +1
Previous research on PAC-Bayes learning theory has focused extensively on establishing tight upper bounds for test errors. A recently proposed training procedure called PAC-Bayes t…
Implicit regularization in Heavy-ball momentum accelerated stochastic gradient descent
Avrajit Ghosh, He Lyu, Xitong Zhang +1
It is well known that the finite step-size () in Gradient Descent (GD) implicitly regularizes solutions to flatter minima. A natural question to ask is "Does the momentum parame…
Neural Network Approximation of Continuous Functions in High Dimensions with Applications to Inverse Problems
Santhosh Karnik, Rongrong Wang, Mark Iwen
The remarkable successes of neural networks in a huge variety of inverse problems have fueled their adoption in disciplines ranging from medical imaging to seismic analysis over th…
Perturbation of invariant subspaces for ill-conditioned eigensystem
He Lyu, Rongrong Wang
Given a diagonalizable matrix , we study the stability of its invariant subspaces when its matrix of eigenvectors is ill-conditioned. Let be some invariant subsp…
On the -norms of the Singular Vectors of Arbitrary Powers of a Difference Matrix with Applications to Sigma-Delta Quantization
Theodore Faust, Mark Iwen, Rayan Saab +1
Let denote the maximum magnitude of entries of a given matrix . In this paper we show that $$\max \left\{ \|U_r \|_{\max},\|V_r\|_{\max}…
An exact formula for matrix perturbation analysis and its applications
He Lyu, Rongrong Wang
In this paper, we establish a useful set of formulae for the distance between the original and the perturbed singular subspaces. These formulae explicitly show that how the…
Linear Convergent Decentralized Optimization with Compression
Xiaorui Liu, Yao Li, Rongrong Wang +2
Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DG…
Sigma Delta quantization for images
He Lyu, Rongrong Wang
In signal quantization, it is well-known that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, ad…
Manifold Denoising by Nonlinear Robust Principal Component Analysis
He Lyu, Ningyu Sha, Shuyang Qin +3
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn f…
Capacity Preserving Mapping for High-dimensional Data Visualization
Rongrong Wang, Xiaopeng Zhang
We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By…
From compressed sensing to compressed bit-streams: practical encoders, tractable decoders
Rayan Saab, Rongrong Wang, Ozgur Yilmaz
Compressed sensing is now established as an effective method for dimension reduction when the underlying signals are sparse or compressible with respect to some suitable basis or f…
Sigma Delta quantization with Harmonic frames and partial Fourier ensembles
Rongrong Wang
Sigma Delta quantization, a quantization method which first surfaced in the 1960s, has now been used widely in various digital products such as cameras, cell phones, radars, etc. T…
Restricted isometry property of random subdictionaries
Alexander Barg, Arya Mazumdar, Rongrong Wang
We study statistical restricted isometry, a property closely related to sparse signal recovery, of deterministic sensing matrices of size . A matrix is said to have a s…
The gap between the null space property and the restricted isometry property
Jameson Cahill, Xuemei Chen, Rongrong Wang
The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the…
Quantization of compressive samples with stable and robust recovery
Rayan Saab, Rongrong Wang, Ozgur Yilmaz
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent rec…
Measures of scalability
Xuemei Chen, Gitta Kutyniok, Kasso A. Okoudjou +2
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximat…
A null space analysis of the L1 synthesis method in dictionary-based compressed sensing
Xuemei Chen, Haichao Wang, Rongrong Wang
An interesting topic in compressed sensing aims to recover signals with sparse representations in a dictionary. Recently the performance of the L1-analysis method has been a focus,…
Random Subdictionaries and Coherence Conditions for Sparse Signal Recovery
Alexander Barg, Arya Mazumdar, Rongrong Wang
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals.…
A null space property approach to compressed sensing with frames
Xuemei Chen, Haichao Wang, Rongrong Wang
An interesting topic in compressive sensing concerns problems of sensing and recovering signals with sparse representations in a dictionary. In this note, we study conditions of se…