arXiv research

A popular heuristic for improved performance in Generative adversarial networks (GANs) is to use some form of gradient penalty on the discriminator. This gradient penalty was originally motivated by a Wasserstein distance formulation. However, the use of gradient penalty in other GAN formulations is not well motivated.…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are c…

Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradien…

We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…

Accelerated gradient method tackles nonconvex penalties in sparse learning.

New method solves complex bilevel optimization problems.

Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…

Improved penalty-based methods for bilevel optimization with reduced complexity.

Motivated by manifold learning techniques, we give an explicit lower bound for how far a smoothly embedded compact submanifold in ${\mathbb R}^N$ can move in a normal direction and remain an embedding. In addition, given a penalty function $P : \text{Emb}(M,\mathbb{R}^N) \rightarrow \mathbb{R}$ on the space of embeddi…

Gradient descent training of neural networks leads to solutions close to natural cubic splines.

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…

Paper proposes efficient algorithms for designing SLOPE penalty sequences.

New method approximates sampling from smooth potential distributions using a vanishing penalty.

Wasserstein GANs with Gradient Penalty compute a different optimal transport problem called congested transport.

Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.

A new method reduces bias in adaptive Lasso estimates.

Algorithm minimizes loss and constraint violations in online convex optimization with smooth penalties.

New test improves tree ensemble pruning for better model performance.

The conditional gradient method (CGM) has been widely used for fast sparse approximation, having a low per iteration computational cost for structured sparse regularizers. We explore the sparsity acquiring properties of a generalized CGM (gCGM), where the constraint is replaced by a penalty function based on a gauge pe…

Efficiently performs robust and sparse kernel regression.

Study develops a method to select penalty parameters for sparse neural networks without cross-validation.

Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem. Recently, various algorithms using nonconvex penalties have been proposed, among whic…

The paper studies how adding an ℓ2 penalty affects network embeddings.

We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cas…

Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around $1$ in the training process. We propose a new penalty function for…

The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…

Proposes HGP to improve survival analysis models.

As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex l…

The paper proposes a gradient-based method for multi-penalty Ridge regression.

A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic model-based dynamic neural network structure optimization that considers the probabilit…

Proposes spred for solving $L_1$ penalty with SGD.

We show that gradient descent on full-width linear convolutional networks of depth $L$ converges to a linear predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to linearly fully connected networks, where gradient descent converges to the hard margin linear support vector m…

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing spars…

Gradient matching method estimates implicit regularization in complex deep learning systems.

Proposes a gradient-based variable selection method for binary classification in RKHS.

We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regressio…

In this paper, we propose a framework for automatic classification of patients from multimodal genetic and brain imaging data by optimally combining them. Additive models with unadapted penalties (such as the classical group lasso penalty or $L_1$-multiple kernel learning) treat all modalities in the same manner and ca…

Study ablated data augmentation techniques and their mathematical equivalence to penalties.

Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresp…

We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements. We propose and study an iterative algorithm to minimize a penalized least-squares objective, with a penalty given by the "l_0-norm" of the signal's discrete graph gradient. The method proce…

Momentum SGD fails to track nonstationary optima due to drift amplification.

New framework solves dynamic bilevel optimization problems in reinforcement learning.

A new algorithm finds optimal solutions for constrained decision processes.

Study stabilizes adversarial training in neural networks over infinite-dimensional spaces.

AGS-CL selectively updates penalties based on node importance for continual learning.

Multivariate boosted trees improve forecasting and control by capturing correlated predictions.

Kernel-based mean-field games use MMD penalties for interaction and target costs.

A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.