arXiv research

CNR uses convex optimization to estimate conditional distributions.

New method for multivariate distribution regression using NPT metric.

We propose a semiparametric approach, named nonparanormal skeptic, for estimating high dimensional undirected graphical models. In terms of modeling, we consider the nonparanormal family proposed by Liu et al (2009). In terms of estimation, we exploit nonparametric rank-based correlation coefficient estimators includin…

Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high dimensional inference. Just as additive models extend linear models by replacing linear …

The paper shows how to infer conditional independence from non-Gaussian data.

In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estima…

Diagonal transformations preserve independence structures in non-Gaussian distributions.

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for presence of edges both locally at a fixed index value and globally over a range…

We study the problem of using i.i.d. samples from an unknown multivariate probability distribution $p$ to estimate the mutual information of $p$. This problem has recently received attention in two settings: (1) where $p$ is assumed to be Gaussian and (2) where $p$ is assumed only to lie in a large nonparametric smooth…

This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and constructing a uniform confidence subgraph. Due to the presence of unknown marginal trans…

Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several co…

New methods estimate brain connectivity from calcium imaging data with missing data.

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new cha…

Semi-supervised learning is a model training method that uses both labeled and unlabeled data. This paper proposes a fully Bayes semi-supervised learning algorithm that can be applied to any multi-category classification problem. We assume the labels are missing at random when using unlabeled data in a semi-supervised …

This paper tackles structure learning in indirect observations of Gaussian and non-Gaussian random vectors.

Ability for accurate hospital case cost modelling and prediction is critical for efficient health care financial management and budgetary planning. A variety of regression machine learning algorithms are known to be effective for health care cost predictions. The purpose of this experiment was to build an Azure Machine…

Efficiently private regression for unbounded data.

This paper studies robust regression in the settings of Huber's $ε$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $ε$-contamination models for various regression problems including nonpa…

This paper studies the nonparametric modal regression problem systematically from a statistical learning view. Originally motivated by pursuing a theoretical understanding of the maximum correntropy criterion based regression (MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is essentially moda…

Proposes FARM model combining latent factor and sparse regression.

Survey of SDR methods for high-dimensional regression and embedding.

This paper reviews SDR methods for multivariate response regression.

Paper introduces semi-supervised linear extremile regression for high-dimensional data.

Improves logistic regression performance with nonconvex programming.

Study improves $H$-consistency bounds for regression analysis.

Prevalidated ridge regression simplifies logistic regression for high-dimensional data.

Introduces a new model for mapping matrices to matrices, subsuming linear regression.

Meta-theorems validate fair regression algorithms under demographic parity constraints.

We analyzed optimism in linear and kernel regression models.

A new optimizer, MVO, improves nonlinear regression performance.

Brenier isotonic regression extends multi-output isotonic regression using optimal transport.

We simplify complex regression coefficients using linearization and feature comparison.

Unified framework for fair regression under demographic parity.

Locally adaptive interpretable regression improves linear regression's predictability.

Huber regression assessed for robustness in statistical learning.

Least Angle Regression is a promising technique for variable selection applications, offering a nice alternative to stepwise regression. It provides an explanation for the similar behavior of LASSO ($\ell_1$-penalized regression) and forward stagewise regression, and provides a fast implementation of both. The idea has…

We analyze coresets for regularized regression problems and propose a modified lasso that yields smaller coresets.

Study uniform consistency in nonparametric mixture models and mixed regression.

We find a convex model for traditional nonlinear regression under L2 loss.

Collider regression improves predictive performance in regression tasks.

We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…

New GP model estimates piecewise continuous functions.

PARC uses piecewise linear predictors for regression and classification.

This work analyzes Fréchet regression using comparison geometry, providing theoretical and practical insights.

Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.

Paper studies ensemble probabilistic regression trees for smooth approximations.

Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of …

pGMM kernel outperforms ordinary ridge regression and RBF kernel ridge regression without tuning.