Related papers: On l_1 Mean and Variance Filtering

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…

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…

There exist several methods developed for the canonical change point problem of detecting multiple mean shifts, which search for changes over sections of the data at multiple scales. In such methods, estimation of the noise level is often…

This paper studies the recovery of a joint piece-wise linear trend from a time series using L1 regularization approach, called L1 trend filtering (Kim, Koh and Boyd, 2009). We provide some sufficient conditions under which a L1 trend filter…

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…

We study the problem of variance estimation in general graph-structured problems. First, we develop a linear time estimator for the homoscedastic case that can consistently estimate the variance in general graphs. We show that our estimator…

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning…

A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and…

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on…

There has been an explosion of interest in using $l_1$-regularization in place of $l_0$-regularization for feature selection. We present theoretical results showing that while $l_1$-penalized linear regression never outperforms…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

Image segmentation is a fundamental and challenging task in image processing and computer vision. The color image segmentation is attracting more attention due to the color image provides more information than the gray image. In this paper,…

The curse of dimensionality is a recognized challenge in nonparametric estimation. This paper develops a new L0-norm regularization approach to the convex quantile and expectile regressions for subset variable selection. We show how to use…

Prior distributions for Bayesian inference that rely on the $l_1$-norm of the parameters are of considerable interest, in part because they promote parameter fields with less regularity than Gaussian priors (e.g., discontinuities and…

In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…