Search Results for author:
Found 28 papers, 3 papers with code
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.
The flare Package for High Dimensional Linear Regression and Precision Matrix Estimation in R
This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, $\ell_q$ Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation (TIGER and CLIME).
Picasso: A Sparse Learning Library for High Dimensional Data Analysis in R and Python
We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e. g., sparse linear regression, sparse logistic regression, sparse Poisson regression and scaled sparse linear regression) combined with efficient active set selection strategies.
Over-parameterized Adversarial Training: An Analysis Overcoming the Curse of Dimensionality
Our work proves convergence to low robust training loss for \emph{polynomial} width instead of exponential, under natural assumptions and with the ReLU activation.
On Computation and Generalization of Generative Adversarial Imitation Learning
Generative Adversarial Imitation Learning (GAIL) is a powerful and practical approach for learning sequential decision-making policies.
On Recoverability of Randomly Compressed Tensors with Low CP Rank
Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model.
On Generalization Bounds of a Family of Recurrent Neural Networks
We remark: (1) Our generalization bound for vanilla RNNs is significantly tighter than the best of existing results; (2) We are not aware of any other generalization bounds for MGU, LSTM, and Conv RNNs in the exiting literature; (3) We demonstrate the advantages of these variants in generalization.
ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization
In this paper, we propose a zeroth-order AdaMM (ZO-AdaMM) algorithm, that generalizes AdaMM to the gradient-free regime.
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.
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).
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.
Deep Hyperspherical Learning
In light of such challenges, we propose hyperspherical convolution (SphereConv), a novel learning framework that gives angular representations on hyperspheres.
Towards Black-box Iterative Machine Teaching
We propose an active teacher model that can actively query the learner (i. e., make the learner take exams) for estimating the learner's status and provably guide the learner to achieve faster convergence.
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.
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.
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 Faster Convergence of Cyclic Block Coordinate Descent-type Methods for Strongly Convex Minimization
In particular, we first show that for a family of quadratic minimization problems, the iteration complexity $\mathcal{O}(\log^2(p)\cdot\log(1/\epsilon))$ of the CBCD-type methods matches that of the GD methods in term of dependency on $p$, up to a $\log^2 p$ factor.
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.
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.
