Related papers: On l_1 Mean and Variance Filtering
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
In this paper we consider the problem of grouped variable selection in high-dimensional regression using $\ell_1-\ell_q$ regularization ($1\leq q \leq \infty$), which can be viewed as a natural generalization of the $\ell_1-\ell_2$…
We propose a general procedure for estimating the variance-covariance matrix of two-step estimates of structural parameters in latent variable models. The method is partially simulation-based, in that it includes drawing simulated values of…
This paper introduces a new latent variable generative model able to handle high dimensional longitudinal data and relying on variational inference. The time dependency between the observations of an input sequence is modelled using…
We study a class of fused lasso problems where the estimated parameters in a sequence are regressed toward their respective observed values (fidelity loss), with $\ell_1$ norm penalty (regularization loss) on the differences between…
Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant…
Machine learning algorithms typically require abundant data under a stationary environment. However, environments are nonstationary in many real-world applications. Critical issues lie in how to effectively adapt models under an…
Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…
We present a new framework for robust estimation and inference on second-order stationary time series and random fields. This framework is based on the Generalized Method of Wavelet Moments which uses the wavelet variance to achieve…
Convolutional neural networks (CNNs) can model complicated non-linear relations between images. However, they are notoriously sensitive to small changes in the input. Most CNNs trained to describe image-to-image mappings generate temporally…
We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the $\ell_1$ minimization method for…
In this study, we explore in depth a few under-studied topics at the intersection of uncertainty estimation and segmentation. Prior work has shown that the quality of uncertainty estimates can be very sensitive to a range of variables. As…
Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…
We introduce a new methodology for analyzing serial data by quantile regression assuming that the underlying quantile function consists of constant segments. The procedure does not rely on any distributional assumption besides serial…
We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…
Mendelian randomization is an instrumental variable method that utilizes genetic information to investigate the causal effect of a modifiable exposure on an outcome. In most cases, the exposure changes over time. Understanding the…