arXiv research

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 …

Solving logistic regression with L1-regularization in distributed settings is an important problem. This problem arises when training dataset is very large and cannot fit the memory of a single machine. We present d-GLMNET, a new algorithm solving logistic regression with L1-regularization in the distributed settings. …

Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is the LASSO problem, where the l1 norm regularizes a quadratic function. A multil…

A new ICA method adds L1-regularization for better interpretability of fMRI data.

Local graph clustering methods aim to find small clusters in very large graphs. These methods take as input a graph and a seed node, and they return as output a good cluster in a running time that depends on the size of the output cluster but that is independent of the size of the input graph. In this paper, we adopt a…

We consider the class of optimization problems arising from computationally intensive L1-regularized M-estimators, where the function or gradient values are very expensive to compute. A particular instance of interest is the L1-regularized MLE for learning Conditional Random Fields (CRFs), which are a popular class of …

Proposes an L1-regularized functional SVM for binary classification with functional covariates.

Adaptive sparseness enhances robust regression using MCC and ARD.

Large-scale L1-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. High-performance algorithms and implementations are critical to efficiently solving these problems. Building…

A new method solves l1-regularized optimization problems efficiently and sparsely.

We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution. The l1-penalty term can also be interpreted in terms of short sales, on which several financial markets hav…

We propose a novel general algorithm LHAC that efficiently uses second-order information to train a class of large-scale l1-regularized problems. Our method executes cheap iterations while achieving fast local convergence rate by exploiting the special structure of a low-rank matrix, constructed via quasi-Newton approx…

LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform feature selection by promoting sparsity, and thus, are well-suited for high-dim…

The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…

We present a machine learning framework for modeling protein dynamics. Our approach uses L1-regularized, reversible hidden Markov models to understand large protein datasets generated via molecular dynamics simulations. Our model is motivated by three design principles: (1) the requirement of massive scalability; (2) t…

Paper proposes sparse classification method for high-dimensional data.

We introduce Graph-Sparse Logistic Regression, a new algorithm for classification for the case in which the support should be sparse but connected on a graph. We val- idate this algorithm against synthetic data and benchmark it against L1-regularized Logistic Regression. We then explore our technique in the bioinformat…

The choice of the kernel is critical to the success of many learning algorithms but it is typically left to the user. Instead, the training data can be used to learn the kernel by selecting it out of a given family, such as that of non-negative linear combinations of p base kernels, constrained by a trace or L1 regular…

This paper approximates 1-Wasserstein distance using tree-based embedding.

Study compares L1 and VG sparsity priors in inverse problems.

A new efficient test addresses limitations of knockoffs for conditional independence testing.

Long non-coding RNAs (lncRNAs) are a class of non-coding RNAs which play a significant role in several biological processes. RNA-seq based transcriptome sequencing has been extensively used for identification of lncRNAs. However, accurate identification of lncRNAs in RNA-seq datasets is crucial for exploring their char…

We propose a new Bayesian model for flexible nonlinear regression and classification using tree ensembles. The model is based on the RuleFit approach in Friedman and Popescu (2008) where rules from decision trees and linear terms are used in a L1-regularized regression. We modify RuleFit by replacing the L1-regularizat…

Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -…

A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding t…

Feature selection is a technique to screen out less important features. Many existing supervised feature selection algorithms use redundancy and relevancy as the main criteria to select features. However, feature interaction, potentially a key characteristic in real-world problems, has not received much attention. As a…

The paper characterizes SLOPE's trade-off between FDP and TPP, showing its power limit and superiority over Lasso.

A new spectrum attention mechanism improves time series classification.

We outline a representation for discrete multivariate distributions in terms of interventional potential functions that are globally normalized. This representation can be used to model the effects of interventions, and the independence properties encoded in this model can be represented as a directed graph that allows…

Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BO…

We propose a simple and easy to implement neural network compression algorithm that achieves results competitive with more complicated state-of-the-art methods. The key idea is to modify the original optimization problem by adding K independent Gaussian priors (corresponding to the k-means objective) over the network p…

Develops efficient method for nonconvex problems using Regula Falsi.

By reducing optimization to a sequence of smaller subproblems, working set algorithms achieve fast convergence times for many machine learning problems. Despite such performance, working set implementations often resort to heuristics to determine subproblem size, makeup, and stopping criteria. We propose BlitzWS, a wor…

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster …

In application domains such as healthcare, we want accurate predictive models that are also causally interpretable. In pursuit of such models, we propose a causal regularizer to steer predictive models towards causally-interpretable solutions and theoretically study its properties. In a large-scale analysis of Electron…

We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of L1-regularized regression for this problem, and show how to solve it efficiently using the well-known Pool Adjacent Violators Algorithm as its proximal operator. The main ap…

So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined, i.e. when number of model parameters is much higher than the number of data point…

Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regul…

Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work…

Inverse reinforcement learning (IRL) is the problem of finding a reward function that generates a given optimal policy for a given Markov Decision Process. This paper looks at an algorithmic-independent geometric analysis of the IRL problem with finite states and actions. A L1-regularized Support Vector Machine formula…

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the…

The paper extends NSGPs with $L^1$-regularization for sparsity and solves the resulting R-NSGP regression problem.

Sparse prototypes improve clustering of high-dimensional directional data.

The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These…

This paper develops a general theoretical framework to analyze structured sparse recovery problems using the notation of dual certificate. Although certain aspects of the dual certificate idea have already been used in some previous work, due to the lack of a general and coherent theory, the analysis has so far only be…

Sparse transformer architecture improves accuracy and speed in generative modeling and inverse problems.

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be difficult to use and extend in practice: e.g., they can make it difficult to inco…

Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and va…