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Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…
Capturing the conditional covariances or correlations among the elements of a multivariate response vector based on covariates is important to various fields including neuroscience, epidemiology and biomedicine. We propose a new method…
Predictive models make mistakes. Hence, there is a need to quantify the uncertainty associated with their predictions. Conformal inference has emerged as a powerful tool to create statistically valid prediction regions around point…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
Random Forest (RF) is a widely used ensemble learning technique known for its robust classification performance across diverse domains. However, it often relies on hundreds of trees and all input features, leading to high inference cost and…
Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good…
This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the…
Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning and are often viewed as…
Over the past decade, random forest models have become widely used as a robust method for high-dimensional data regression tasks. In part, the popularity of these models arises from the fact that they require little hyperparameter tuning…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based…
The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to…