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Found 39 papers, 13 papers with code
TpopT: Efficient Trainable Template Optimization on Low-Dimensional Manifolds
In this work, we study TpopT (TemPlate OPTimization) as an alternative scalable framework for detecting low-dimensional families of signals which maintains high interpretability.
Boosting the Efficiency of Parametric Detection with Hierarchical Neural Networks
Various approaches have been proposed for improving the efficiency of the detection scheme, with hierarchical matched filtering being an important strategy.
Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization
Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems.
Deep Networks Provably Classify Data on Curves
Data with low-dimensional nonlinear structure are ubiquitous in engineering and scientific problems.
Square Root Principal Component Pursuit: Tuning-Free Noisy Robust Matrix Recovery
We show that a single, universal choice of the regularization parameter suffices to achieve reconstruction error proportional to the (a priori unknown) noise level.
ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction
This work attempts to provide a plausible theoretical framework that aims to interpret modern deep (convolutional) networks from the principles of data compression and discriminative representation.
Generalized Approach to Matched Filtering using Neural Networks
Moreover, we show that the proposed neural network architecture can outperform matched filtering, both with or without knowledge of a prior on the parameter distribution.
Deep Networks from the Principle of Rate Reduction
The layered architectures, linear and nonlinear operators, and even parameters of the network are all explicitly constructed layer-by-layer in a forward propagation fashion by emulating the gradient scheme.
Deep Networks and the Multiple Manifold Problem
Our analysis demonstrates concrete benefits of depth and width in the context of a practically-motivated model problem: the depth acts as a fitting resource, with larger depths corresponding to smoother networks that can more readily separate the class manifolds, and the width acts as a statistical resource, enabling concentration of the randomly-initialized network and its gradients.
From Symmetry to Geometry: Tractable Nonconvex Problems
We highlight the key role of symmetry in shaping the objective landscape and discuss the different roles of rotational and discrete symmetries.
Short and Sparse Deconvolution --- A Geometric Approach
Short-and-sparse deconvolution (SaSD) is the problem of extracting localized, recurring motifs in signals with spatial or temporal structure.
Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine learning.
Gemmini: Enabling Systematic Deep-Learning Architecture Evaluation via Full-Stack Integration
DNN accelerators are often developed and evaluated in isolation without considering the cross-stack, system-level effects in real-world environments.
Short-and-Sparse Deconvolution -- A Geometric Approach
This paper is motivated by recent theoretical advances, which characterize the optimization landscape of a particular nonconvex formulation of SaSD.
Complete Dictionary Learning via $\ell^4$-Norm Maximization over the Orthogonal Group
Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms, usually without theoretical guarantees for either optimality or complexity.
On the Global Geometry of Sphere-Constrained Sparse Blind Deconvolution
Blind deconvolution is the problem of recovering a convolutional kernel $\boldsymbol a_0$ and an activation signal $\boldsymbol x_0$ from their convolution $\boldsymbol y = \boldsymbol a_0 \circledast \boldsymbol x_0$.
Geometry and Symmetry in Short-and-Sparse Deconvolution
We study the $\textit{Short-and-Sparse (SaS) deconvolution}$ problem of recovering a short signal $\mathbf a_0$ and a sparse signal $\mathbf x_0$ from their convolution.
Structured Local Minima in Sparse Blind Deconvolution
We assume the short signal to have unit $\ell^2$ norm and cast the blind deconvolution problem as a nonconvex optimization problem over the sphere.
Structured Local Optima in Sparse Blind Deconvolution
We assume the short signal to have unit $\ell^2$ norm and cast the blind deconvolution problem as a nonconvex optimization problem over the sphere.
Convolutional Phase Retrieval via Gradient Descent
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.
Convolutional Phase Retrieval
We study the convolutional phase retrieval problem, which asks us to recover an unknown signal ${\mathbf x} $ of length $n$ from $m$ measurements consisting of the magnitude of its cyclic convolution with a known kernel $\mathbf a$ of length $m$.
Which Distribution Distances are Sublinearly Testable?
Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far?
A Geometric Analysis of Phase Retrieval
complex Gaussian) and the number of measurements is large enough ($m \ge C n \log^3 n$), with high probability, a natural least-squares formulation for GPR has the following benign geometric structure: (1) there are no spurious local minimizers, and all global minimizers are equal to the target signal $\mathbf x$, up to a global phase; and (2) the objective function has a negative curvature around each saddle point.
Complete Dictionary Recovery over the Sphere II: Recovery by Riemannian Trust-region Method
We consider the problem of recovering a complete (i. e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb{R}^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.
Complete Dictionary Recovery over the Sphere I: Overview and the Geometric Picture
We give the first efficient algorithm that provably recovers $\mathbf A_0$ when $\mathbf X_0$ has $O(n)$ nonzeros per column, under suitable probability model for $\mathbf X_0$.
When Are Nonconvex Problems Not Scary?
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature.
Complete Dictionary Recovery over the Sphere
We consider the problem of recovering a complete (i. e., square and invertible) matrix $\mathbf A_0$, from $\mathbf Y \in \mathbb R^{n \times p}$ with $\mathbf Y = \mathbf A_0 \mathbf X_0$, provided $\mathbf X_0$ is sufficiently sparse.
A Batchwise Monotone Algorithm for Dictionary Learning
Unlike the state-of-the-art dictionary learning algorithms which impose sparsity constraints on a sample-by-sample basis, we instead treat the samples as a batch, and impose the sparsity constraint on the whole.
Finding a sparse vector in a subspace: Linear sparsity using alternating directions
In this paper, we focus on a **planted sparse model** for the subspace: the target sparse vector is embedded in an otherwise random subspace.
Scalable Robust Matrix Recovery: Frank-Wolfe Meets Proximal Methods
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning.
Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the tensor.
Toward Guaranteed Illumination Models for Non-Convex Objects
Illumination variation remains a central challenge in object detection and recognition.
Learning with Partially Absorbing Random Walks
We prove that under proper absorption rates, a random walk starting from a set $\mathcal{S}$ of low conductance will be mostly absorbed in $\mathcal{S}$.
Efficient Point-to-Subspace Query in $\ell^1$ with Application to Robust Object Instance Recognition
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in $\ell^1$ distance.
Compressive Principal Component Pursuit
We consider the problem of recovering a target matrix that is a superposition of low-rank and sparse components, from a small set of linear measurements.
Information Theory Information Theory
Sparsity and Robustness in Face Recognition
This report concerns the use of techniques for sparse signal representation and sparse error correction for automatic face recognition.
Stable Principal Component Pursuit
We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entrywise noise and robust to gross sparse errors.
Information Theory Information Theory
Robust Principal Component Analysis?
This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted.
Information Theory Information Theory
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization
Principal component analysis is a fundamental operation in computational data analysis, with myriad applications ranging from web search to bioinformatics to computer vision and image analysis.
