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Found 32 papers, 1 papers with code
Early Directional Convergence in Deep Homogeneous Neural Networks for Small Initializations
This paper studies the gradient flow dynamics that arise when training deep homogeneous neural networks assumed to have locally Lipschitz gradients and an order of homogeneity strictly greater than two.
Directional Convergence Near Small Initializations and Saddles in Two-Homogeneous Neural Networks
This paper examines gradient flow dynamics of two-homogeneous neural networks for small initializations, where all weights are initialized near the origin.
Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectory
This work investigates the problem of estimating the weight matrices of a stable time-invariant linear dynamical system from a single sequence of noisy measurements.
Convexifying Sparse Interpolation with Infinitely Wide Neural Networks: An Atomic Norm Approach
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations.
Provable Online CP/PARAFAC Decomposition of a Structured Tensor via Dictionary Learning
To this end, we develop a provable algorithm for online structured tensor factorization, wherein one of the factors obeys some incoherence conditions, and the others are sparse.
On Tighter Generalization Bounds for Deep Neural Networks: CNNs, ResNets, and Beyond
We propose a generalization error bound for a general family of deep neural networks based on the depth and width of the networks, as well as the spectral norm of weight matrices.
Provable Online Dictionary Learning and Sparse Coding
To this end, we develop a simple online alternating optimization-based algorithm for dictionary learning, which recovers both the dictionary and coefficients exactly at a geometric rate.
A Provably Communication-Efficient Asynchronous Distributed Inference Method for Convex and Nonconvex Problems
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol.
NOODL: Provable Online Dictionary Learning and Sparse Coding
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as coefficients.
A Dictionary-Based Generalization of Robust PCA Part II: Applications to Hyperspectral Demixing
We consider the task of localizing targets of interest in a hyperspectral (HS) image based on their spectral signature(s), by posing the problem as two distinct convex demixing task(s).
TensorMap: Lidar-Based Topological Mapping and Localization via Tensor Decompositions
We propose a technique to develop (and localize in) topological maps from light detection and ranging (Lidar) data.
Target-based Hyperspectral Demixing via Generalized Robust PCA
In this work, we present a technique to localize targets of interest based on their spectral signatures.
A Dictionary Based Generalization of Robust PCA
We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method.
A Dictionary-Based Generalization of Robust PCA with Applications to Target Localization in Hyperspectral Imaging
We consider the decomposition of a data matrix assumed to be a superposition of a low-rank matrix and a component which is sparse in a known dictionary, using a convex demixing method.
On Tighter Generalization Bound for Deep Neural Networks: CNNs, ResNets, and Beyond
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks.
On Landscape of Lagrangian Functions and Stochastic Search for Constrained Nonconvex Optimization
However, due to the lack of convexity, their landscape is not well understood and how to find the stable equilibria of the Lagrangian function is still unknown.
On Quadratic Convergence of DC Proximal Newton Algorithm in Nonconvex Sparse Learning
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions.
Near Optimal Sketching of Low-Rank Tensor Regression
We study the least squares regression problem \begin{align*} \min_{\Theta \in \mathcal{S}_{\odot D, R}} \|A\Theta-b\|_2, \end{align*} where $\mathcal{S}_{\odot D, R}$ is the set of $\Theta$ for which $\Theta = \sum_{r=1}^{R} \theta_1^{(r)} \circ \cdots \circ \theta_D^{(r)}$ for vectors $\theta_d^{(r)} \in \mathbb{R}^{p_d}$ for all $r \in [R]$ and $d \in [D]$, and $\circ$ denotes the outer product of vectors.
Communication-efficient Algorithm for Distributed Sparse Learning via Two-way Truncation
We propose a communicationally and computationally efficient algorithm for high-dimensional distributed sparse learning.
Improved Support Recovery Guarantees for the Group Lasso With Applications to Structural Health Monitoring
This paper considers the problem of estimating an unknown high dimensional signal from noisy linear measurements, {when} the signal is assumed to possess a \emph{group-sparse} structure in a {known,} fixed dictionary.
On Quadratic Convergence of DC Proximal Newton Algorithm for Nonconvex Sparse Learning in High Dimensions
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions.
Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor
In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with one of the factors being sparse.
Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization
We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e. g., low-rank matrix factorization, phase retrieval, and deep linear neural networks)}.
Robust Low-Complexity Randomized Methods for Locating Outliers in Large Matrices
This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements.
On Fast Convergence of Proximal Algorithms for SQRT-Lasso Optimization: Don't Worry About Its Nonsmooth Loss Function
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility.
Nonconvex Sparse Learning via Stochastic Optimization with Progressive Variance Reduction
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints.
A Compressed Sensing Based Decomposition of Electrodermal Activity Signals
The measurement and analysis of Electrodermal Activity (EDA) offers applications in diverse areas ranging from market research, to seizure detection, to human stress analysis.
On Convolutional Approximations to Linear Dimensionality Reduction Operators for Large Scale Data Processing
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by circular shifts.
Noisy Matrix Completion under Sparse Factor Models
This paper examines a general class of noisy matrix completion tasks where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption.
Identifying Outliers in Large Matrices via Randomized Adaptive Compressive Sampling
This paper examines the problem of locating outlier columns in a large, otherwise low-rank, matrix.
Compressive Measurement Designs for Estimating Structured Signals in Structured Clutter: A Bayesian Experimental Design Approach
This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference, and noise is available.
On the Fundamental Limits of Recovering Tree Sparse Vectors from Noisy Linear Measurements
Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a sparse representation in some basis.
