Related papers: Selective inference after convex clustering with $…

Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…

A probabilistic expert system emulates the decision-making ability of a human expert through a directional graphical model. The first step in building such systems is to understand data generation mechanism. To this end, one may try to…

Recent studies of under-determined linear systems of equations with sparse solutions showed a great practical and theoretical efficiency of a particular technique called $\ell_1$-optimization. Seminal works \cite{CRT,DOnoho06CS} rigorously…

Experimental evaluation is a major research methodology for investigating clustering algorithms and many other machine learning algorithms. For this purpose, a number of benchmark datasets have been widely used in the literature and their…

This survey reviews a clustering method based on solving a convex optimization problem. Despite the plethora of existing clustering methods, convex clustering has several uncommon features that distinguish it from prior art. The…

Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a…

In inverse problems, the use of an $\ell_{12}$ analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased…

Predicting clinical variables from whole-brain neuroimages is a high dimensional problem that requires some type of feature selection or extraction. Penalized regression is a popular embedded feature selection method for high dimensional…

Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is…

This study introduces a general semiparametric clusterwise index distribution model to analyze how latent clusters affect the covariate-response relationships. By employing sufficient dimension reduction to account for the effects of…

We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…

Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…

For many applications, it is critical to interpret and validate groups of observations obtained via clustering. A common validation approach involves testing differences in feature means between observations in two estimated clusters. In…

Standard conformal prediction methods provide a marginal coverage guarantee, which means that for a random test point, the conformal prediction set contains the true label with a user-specified probability. In many classification problems,…

In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…

It is common to show the confidence intervals or $p$-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the…

This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the…

We investigate a class of methods for selective inference that condition on a selection event. Such methods follow a two-stage process. First, a data-driven (sub)collection of hypotheses is chosen from some large universe of hypotheses.…

Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to…