arXiv research

The solution path of the 1D fused lasso for an $n$-dimensional input is piecewise linear with $\mathcal{O}(n)$ segments (Hoefling et al. 2010 and Tibshirani et al 2011). However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the wei…

The fused lasso penalizes a loss function by the $L_1$ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed in…

The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.

The Lasso is a very well known penalized regression model, which adds an $L_{1}$ penalty with parameter $λ_{1}$ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an $L_{1}$ penalty with parameter $λ_{2}$ on the difference of neighboring coefficients, assuming the…

We study the property of the Fused Lasso Signal Approximator (FLSA) for estimating a blocky signal sequence with additive noise. We transform the FLSA to an ordinary Lasso problem. By studying the property of the design matrix in the transformed Lasso problem, we find that the irrepresentable condition might not hold, …

The paper develops estimators for variance in graph structures using fused lasso.

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to decompose the graph into a set of trails which can then each be solved efficientl…

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are …

We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an…

ABM automates feature engineering and variable selection for loss-based models.

We consider the problem of predicting an outcome variable using $p$ covariates that are measured on $n$ independent observations, in the setting in which flexible and interpretable fits are desirable. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant…

We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani and Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the special cases of trend filte…

This paper converts ADMM to proximal gradient for efficient sparse estimation.

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to changes in these model parameters. This change point detection and estimation pr…

Substantial evidence indicates that major psychiatric disorders are associated with distributed neural dysconnectivity, leading to strong interest in using neuroimaging methods to accurately predict disorder status. In this work, we are specifically interested in a multivariate approach that uses features derived from …

A wide class of regularization problems in machine learning and statistics employ a regularization term which is obtained by composing a simple convex function ωwith a linear transformation. This setting includes Group Lasso methods, the Fused Lasso and other total variation methods, multi-task learning methods and man…

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…

Feature selection has been proven a powerful preprocessing step for high-dimensional data analysis. However, most state-of-the-art methods tend to overlook the structural correlation information between pairwise samples, which may encapsulate useful information for refining the performance of feature selection. Moreove…

We present safe active incremental feature selection~(SAIF) to scale up the computation of LASSO solutions. SAIF does not require a solution from a heavier penalty parameter as in sequential screening or updating the full model for each iteration as in dynamic screening. Different from these existing screening methods,…

Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.

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…

Functional brain networks are well described and estimated from data with Gaussian Graphical Models (GGMs), e.g. using sparse inverse covariance estimators. Comparing functional connectivity of subjects in two populations calls for comparing these estimated GGMs. Our goal is to identify differences in GGMs known to hav…

We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the comp…

Cyanure is an open-source C++ software package with a Python interface. The goal of Cyanure is to provide state-of-the-art solvers for learning linear models, based on stochastic variance-reduced stochastic optimization with acceleration mechanisms. Cyanure can handle a large variety of loss functions (logistic, square…

Unified framework infers time-varying graphs from incomplete signals.

In this work, we consider to improve the model estimation efficiency by aggregating the neighbors' information as well as identify the subgroup membership for each node in the network. A tree-based $l_1$ penalty is proposed to save the computation and communication cost. We design a decentralized generalized alternatin…

During the past years there has been an explosion of interest in learning methods based on sparsity regularization. In this paper, we discuss a general class of such methods, in which the regularizer can be expressed as the composition of a convex function $ω$ with a linear function. This setting includes several metho…

Federated learning on graphs tackles heterogeneity with efficient parameter estimation.

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…

We develop parallel and distributed Frank-Wolfe algorithms; the former on shared memory machines with mini-batching, and the latter in a delayed update framework. Whenever possible, we perform computations asynchronously, which helps attain speedups on multicore machines as well as in distributed environments. Moreover…

We consider the following signal recovery problem: given a measurement matrix $Φ\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = Φθ^* + ε$ where $ε\in \mathbb{R}^{n}$ is the noise vector whose entries follow i.i.d. centered sub-Gaussian distribution, how to recover …

We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, $G$, over the rows and columns. Our main results shows that for …

We present an efficient alternating direction method of multipliers (ADMM) algorithm for segmenting a multivariate non-stationary time series with structural breaks into stationary regions. We draw from recent work where the series is assumed to follow a vector autoregressive model within segments and a convex estimati…

Enhances tensor regression for interpretability and performance.

We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estima…

Clustering with variable selection is a challenging yet critical task for modern small-n-large-p data. Existing methods based on sparse Gaussian mixture models or sparse K-means provide solutions to continuous data. With the prevalence of RNA-seq technology and lack of count data modeling for clustering, the current pr…

Paper proposes a method to model health outcomes using varying-coefficients and KNN-based LASSO.

R package for multi-objective model selection in statistics.

Neuroimage analysis usually involves learning thousands or even millions of variables using only a limited number of samples. In this regard, sparse models, e.g. the lasso, are applied to select the optimal features and achieve high diagnosis accuracy. The lasso, however, usually results in independent unstable feature…

New framework for data-driven hyperparameter tuning with structured loss.

New method recovers relative rates in spatial compositional data from IMS.

We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for $\ell_p$-norm TV. The most important among these is $\ell_1$-norm TV, for whose prox-operator we present a new geometric analysis which unveils a …

In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to e…

New framework models complex spatial data with basis functions and graphical vectors.

A new framework detects changepoints in complex data.

HSIC-based method explains GNN structures.

Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of $\frac12$ for a suitable potential function is related to local linear convergence. Nevertheless, KL exponent is in general extremely hard to estimate. I…

FILTER model uses fusion penalized logistic threshold regression for high-dimensional data with unknown cut points.