Related papers: Regularized zero-inflated Bernoulli regression mod…
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…
Replicated weighted networks often exhibit many structural zeros alongside heterogeneous non-zero edge strengths. In structural connectomics, this zero-inflation coincides with subjects expressing overlapping, rather than discrete,…
This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0. We apply the square-root lasso estimator penalizing the l1-norm…
We study the classical problem of predicting an outcome variable, $Y$, using a linear combination of a $d$-dimensional covariate vector, $\mathbf{X}$. We are interested in linear predictors whose coefficients solve: % \begin{align*}…
Consider a logistic partially linear model, in which the logit of the mean of a binary response is related to a linear function of some covariates and a nonparametric function of other covariates. We derive simple, doubly robust estimators…
In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Many applied settings in empirical economics involve simultaneous estimation of a large number of parameters. In particular, applied economists are often interested in estimating the effects of many-valued treatments (like teacher effects…
This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…
Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic…
This paper looks at effects, due to the boundary, on inference in logistic regression. It shows that first -- and, indeed, higher -- order asymptotic results are not uniform across the model. Near the boundary, effects such as high…
We address the component-based regularisation of a multivariate Generalised Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…
In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…
We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…