Variable (feature, gene, model, which we use interchangeably) selections for regression with high-dimensional BIGDATA have found many applications in bioinformatics, computational biology, image processing, and engineering. One appealing approach is the L0 regularized regression which penalizes the number of nonzero fe…
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48 results for “L0 regularization”
New method speeds up solving L0-regularized least-squares problems.
problem Solving L0-regularized least-squares problems efficiently.
method Safe peeling for Branch-and-Bound algorithm.
result Significant gains in solving time and node exploration.
Paper proposes SOTL framework for improving transfer learning accuracy and efficiency.
problem Statistical bias and computational efficiency in multi-source domain adaptation.
method Sparse Optimization for Transfer Learning (SOTL) with L0-regularization.
result SOTL significantly improves estimation accuracy and computational speed, especially under adversarial conditions.
We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to determine a locally optimal L0 solution given any L1 regularization solution. We …
Regularization vs. Relaxation: A conic optimization perspective of statistical variable selectioncs.LG
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an l0-norm penalty. Exactly enforcing the l0-no…
L0Learn solves sparse learning problems with millions of features.
problem Sparse learning problems with millions of features.
method Approximate algorithms based on coordinate descent and local combinatorial optimization.
result Achieves competitive run times and statistical performance.
We consider complexity of Deep Neural Networks (DNNs) and their associated massive over-parameterization. Such over-parametrization may entail susceptibility to adversarial attacks, loss of interpretability and adverse Size, Weight and Power - Cost (SWaP-C) considerations. We ask if there are methodical ways (regulariz…
DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measurescs.LG
In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values, but it cannot provide useful gradi…
New L0 norm added to TDA for market analysis.
problem Improving TDA tools for market prediction.
method Defined and applied L0 norm in TDA for four markets.
result Enhanced TDA tools for market analysis.
Improved sample efficiency in learning sparse Ising models.
problem Learning the graph of a sparse Ising model with limited samples.
method Combining L0 and L2 norms to induce sparsity and model non-zero coefficients.
result Improved sample complexity, achieving new state-of-the-art recovery guarantees.
A graph neural network detects beneficial feature interactions for recommender systems.
problem Feature interactions are crucial but not all are beneficial for recommendation accuracy.
method Graph neural network with L0 activation regularization for edge prediction.
result The model outperforms baselines and automatically identifies beneficial feature interactions.
Study compares L1 and VG sparsity priors in inverse problems.
problem Sparse regularization in inverse problems with incomplete or corrupted measurements.
method Compared L1 regularization with Variational Garrote (VG), a probabilistic method approximating L0 sparsity.
result VG often achieves lower minimum generalization error and improved stability in strongly underdetermined regimes.
Robust Nonparametric Regression via Sparsity Control with Application to Load Curve Data Cleansingstat.ML
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive sampling, to robustify nonparametric regression against outliers - that is, data markedl…
Method introduces topological regularization using information filtering networks.
problem Sparse probabilistic modeling and multicollinear regression.
method Topological regularization via information filtering network.
result Direct application to -norm regularized problems.
A new Branch-and-Bound solver tackles L0-penalized problems with flexible loss functions.
problem Solving L0-penalized optimization problems with a broader class of loss functions.
method Generic Branch-and-Bound procedure with closed-form expressions for key quantities.
result El0ps solver achieves state-of-the-art performance and extends computational feasibility.
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically …
Federated Learning with L0 constraint improves sparsity and performance.
problem Inherent sparsity in data and models leads to dense models with poor generalizability.
method L0 constraint on model density achieved through probabilistic gates and federated stochastic gradient descent.
result Achieves target sparsity (rho) in FL with minimal loss in statistical performance.
Linear time dynamic programming for the exact path of optimal models selected from a finite setcs.LG
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
The paper develops a method to dynamically adjust VAE latent space dimensions during training.
problem Under- or overprovisioning of latent space dimensions in VAEs.
method GECO optimizer with -ARM gradient estimator to dynamically adjust latent space dimensions.
result The latent space can be pruned effectively without violating reconstruction error constraints.
The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial invariants of Conway and Jones. These invariants have one striking common feature. If L+, L- and L0 are diagrams of oriente…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the …
Paper proposes a new sparse group k-max regularization for sparsity constraints.
problem Linear inverse problems with sparsity constraints are NP-hard.
method Sparse group k-max regularization, iterative soft thresholding algorithm.
result Approximates l0 norm more closely and enhances group-wise and in-group sparsity.
The aim of this paper is to train an RBF neural network and select centers under concurrent faults. It is well known that fault tolerance is a very attractive property for neural networks. And center selection is an important procedure during the training process of an RBF neural network. In this paper, we devise two n…
Deep neural networks (DNNs) are known vulnerable to adversarial attacks. That is, adversarial examples, obtained by adding delicately crafted distortions onto original legal inputs, can mislead a DNN to classify them as any target labels. In a successful adversarial attack, the targeted mis-classification should be ach…
Proposes sparse QSVM for better generalization and interpretability.
problem Overfitting and difficulty in interpreting full quadratic classifiers.
method Enforces -norm constraint to promote sparsity and develops a penalty decomposition algorithm.
result The proposed model enhances generalization and produces sparse solutions.
Learning the "blocking" structure is a central challenge for high dimensional data (e.g., gene expression data). Recently, a sparse singular value decomposition (SVD) has been used as a biclustering tool to achieve this goal. However, this model ignores the structural information between variables (e.g., gene interacti…
In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and expensive crossvalidatio…
In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and expensive cross-validati…
Study evaluates scikit-learn regularization frameworks for machine learning models.
problem Choosing the right regularization framework for applied machine learning models.
method Empirical evaluation of four canonical frameworks (Ridge, Lasso, ElasticNet, Post-Lasso OLS) across 134,400 simulations.
result Lasso recall is highly fragile under multicollinearity; at high condition numbers (kappa) and low SNR, Lasso recall collapses to 0.18 while ElasticNet maintains 0.93.
Learning causal effects from many randomized experiments using regularized instrumental variablesstat.ML
Scientific and business practices are increasingly resulting in large collections of randomized experiments. Analyzed together, these collections can tell us things that individual experiments in the collection cannot. We study how to learn causal relationships between variables from the kinds of collections faced by m…
Deep neural networks achieve state-of-the-art results on several tasks while increasing in complexity. It has been shown that neural networks can be pruned during training by imposing sparsity inducing regularizers. In this paper, we investigate two techniques for group-wise pruning during training in order to improve …
Entropy-Regularized Probabilistic Gates for Sparse Model Discovery in Scarce-Data Federated Learningcs.LG
Entropy regularization improves sparse model discovery in federated learning.
problem Sparse model discovery in federated learning with limited data.
method Entropy regularization of gate distributions for probabilistic sparse model exploration.
result Entropy regularization leads to better sparse model recovery and performance.
Scoring systems are classification models that only require users to add, subtract and multiply a few meaningful numbers to make a prediction. These models are often used because they are practical and interpretable. In this paper, we introduce an off-the-shelf tool to create scoring systems that both accurate and inte…
We assume data independently sampled from a mixture distribution on the unit ball of the D-dimensional Euclidean space with K+1 components: the first component is a uniform distribution on that ball representing outliers and the other K components are uniform distributions along K d-dimensional linear subspaces restric…
DiffPrune: Neural Network Pruning with Deterministic Approximate Binary Gates and Regularizationstat.ML
A new method prunes neural networks efficiently without losing effectiveness.
problem Efficient pruning of neural networks without sacrificing performance.
method Deterministic approximation of binary gates and regularization.
result Pruning neural networks significantly without loss in effectiveness.
A new framework detects changepoints in complex data.
problem Detecting structural changes in data with various patterns and trends.
method Iteratively Reweighted Fused Lasso (IRFL) for L0 model selection.
result IRFL achieves accurate changepoint detection across various challenging scenarios.
We propose an algorithm for the non-negative factorization of an occurrence tensor built from heterogeneous networks. We use l0 norm to model sparse errors over discrete values (occurrences), and use decomposed factors to model the embedded groups of nodes. An efficient splitting method is developed to optimize the non…
Sparse Singular Value Decomposition (SVD) models have been proposed for biclustering high dimensional gene expression data to identify block patterns with similar expressions. However, these models do not take into account prior group effects upon variable selection. To this end, we first propose group-sparse SVD model…
Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function uses L2 norm or L1 norm on slack variables. The number of support vectors is a me…
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called norm. In this paper we develop a Momentumized Iterative Shrinkage Th…
Deep neural networks are vulnerable against adversarial examples. In this paper, we propose to train and test the networks with randomly subsampled images with high drop rates. We show that this approach significantly improves robustness against adversarial examples in all cases of bounded L0, L2 and L_inf perturbation…
Introduces HTV to measure function complexity in learning schemes.
problem Assessing the complexity of supervised-learning schemes.
method Defines Hessian-Schatten total variation (HTV) as a seminorm to quantify function complexity.
result HTV is invariant to rotations, scalings, and translations, and its minimum value is achieved for linear mappings.
Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimiz…
Bayesian framework for model uncertainty identifies complex heterogeneity without strong assumptions.
problem Identifying complex heterogeneity in factorial data with varying covariates.
method Rashomon Partition Sets (RPS) using l0 prior for robust model uncertainty.
result RPS provides a robust set of models capturing complex heterogeneity without strong assumptions.
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability bounds on the estimated sparsity as well as on the excess misclassification ris…
New method quantifies market shocks and their effects.
problem Quantifying the impact and response to market shocks.
method Sparse probabilistic elliptical model with -norm regularization.
result Shock patterns are related to network structure and sector diversification.
We consider network sparsification as an -norm regularized binary optimization problem, where each unit of a neural network (e.g., weight, neuron, or channel, etc.) is attached with a stochastic binary gate, whose parameters are jointly optimized with original network parameters. The Augment-Reinforce-Merge (ARM),…
Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a Multinomial Logistic Regression model learns a weight vector to differentiate between any …