arXiv research

A new algorithm speeds up EEG source localization using $\ell_1$ regularization.

This paper shows how to use $\ell_1$ regularization effectively in training sparse CNNs.

A neural network solves logistic regression with $\ell_1$ regularization efficiently.

The paper analyzes $\ell_1$-LinR for Ising model selection using statistical mechanics.

New neural network training method uses bi-fidelity data to reduce errors.

In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of $\ell_0$-regularized estimation. In this note, we show that $\ell_1$-regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned …

We investigate the learning rate of multiple kernel learning (MKL) with $\ell_1$ and elastic-net regularizations. The elastic-net regularization is a composition of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total …

We speed up cross-validation in multinomial logistic regression with an $\ell_1$-regularization formula.

Proposes a method to adapt models in nonstationary environments using ℓ1 regularization.

Analytic method optimizes portfolio variance with asymmetric $\ell_1$ constraint.

Multi-task feature learning aims to identity the shared features among tasks to improve generalization. It has been shown that by minimizing non-convex learning models, a better solution than the convex alternatives can be obtained. Therefore, a non-convex model based on the capped-$\ell_{1},\ell_{1}$ regularization wa…

The paper improves ALO for $\ell_1$-regularized models.

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no conne…

Efficiently performs robust and sparse kernel regression.

Method improves SINDy for noisy nonlinear systems.

Study sparse function recovery from indirect noisy observations using $\ell^1$-regularization.

New method learns high-dimensional Poisson DAG models from observational data.

We analyze learning curves of RF models with convex regularization and derive precise asymptotic expressions.

Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized least squares regression can accurately estimate a sparse linear model from $n$ nois…

Study supports recovery of PDEs from noisy data using a specific regularization method.

Unified framework for sparse logistic regression with nonconvex regularization.

Study examines stability of image-reconstruction algorithms using variational regularization.

We introduce a recursive adaptive group lasso algorithm for real-time penalized least squares prediction that produces a time sequence of optimal sparse predictor coefficient vectors. At each time index the proposed algorithm computes an exact update of the optimal $\ell_{1,\infty}$-penalized recursive least squares (R…

We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output SVM. The convergence rates we obtain match, and sometimes improve, state-of-the-…

Regularized linear regression improves binary classification performance, especially with ridge and $\ell_1$ regularization.

We investigate the learning rate of multiple kernel leaning (MKL) with elastic-net regularization, which consists of an $\ell_1$-regularizer for inducing the sparsity and an $\ell_2$-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large but the number of non…

New framework optimizes classification trees with logistic loss and $\ell_1$ regularization.

Paper solves DAG learning from continuous data using integer programming.

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the $\ell_1$-regularized least squares as well as a greedy esti…

Feature selection is a standard approach to understanding and modeling high-dimensional classification data, but the corresponding statistical methods hinge on tuning parameters that are difficult to calibrate. In particular, existing calibration schemes in the logistic regression framework lack any finite sample guara…

New method improves sparse regression interpretability by suppressing correlated variables.

We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered ($SIR$) model for interaction events fal…

We present a generic framework for parallel coordinate descent (CD) algorithms that includes, as special cases, the original sequential algorithms Cyclic CD and Stochastic CD, as well as the recent parallel Shotgun algorithm. We introduce two novel parallel algorithms that are also special cases---Thread-Greedy CD and …

In this paper we consider the problem of grouped variable selection in high-dimensional regression using $\ell_1-\ell_q$ regularization ($1\leq q \leq \infty$), which can be viewed as a natural generalization of the $\ell_1-\ell_2$ regularization (the group Lasso). The key condition is that the dimensionality $p_n$ can…

This paper studies the partial estimation of Gaussian graphical models from high-dimensional empirical observations. We derive a convex formulation for this problem using $\ell_1$-regularized maximum-likelihood estimation, which can be solved via a block coordinate descent algorithm. Statistical estimation performance …

New GLS estimator handles high-dimensional data with autocorrelated errors.

Paper optimizes ES estimation under an $\ell_1$ constraint, reducing estimation errors.

We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-deman…

This paper proposes a method to select relevant features for multi-label learning.

Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, $\ell_1$ regularization is guaranteed t…

Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations between datasets. Despite their wide usage, they have one common limitation that…

A TCL framework improves causal effect estimation in limited data.

A new neural network architecture reduces parameters by 94% while maintaining performance.

Develops exact convex optimization formulations for neural networks.

Trans-Ising combines auxiliary datasets to estimate high-dimensional Ising models.

The paper examines how to protect LASSO-based feature selection from adversarial attacks.

In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each $f(\cdot)$ in the support of $D$ is convex over $\cal K$. The optimization is commonl…