Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2003.03629

Getting Better from Worse: Augmented Bagging and a Cautionary Tale of Variable Importance

Lucas Mentch·Siyu Zhou
View original source ↗Read source document ↗Export metadata ↓

Abstract

As the size, complexity, and availability of data continues to grow, scientists are increasingly relying upon black-box learning algorithms that can often provide accurate predictions with minimal a priori model specifications. Tools like random forests have an established track record of off-the-shelf success and even offer various strategies for analyzing the underlying relationships among variables. Here, motivated by recent insights into random forest behavior, we introduce the simple idea of augmented bagging (AugBagg), a procedure that operates in an identical fashion to classical bagging and random forests, but which operates on a larger, augmented space containing additional randomly generated noise features. Surprisingly, we demonstrate that this simple act of including extra noise variables in the model can lead to dramatic improvements in out-of-sample predictive accuracy, sometimes outperforming even an optimally tuned traditional random forest. As a result, intuitive notions of variable importance based on improved model accuracy may be deeply flawed, as even purely random noise can routinely register as statistically significant. Numerous demonstrations on both real and synthetic data are provided along with a proposed solution.

Explore related subjects

stat.MLcs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lucas Mentch, Siyu Zhou. 2020-11-09. Getting Better from Worse: Augmented Bagging and a Cautionary Tale of Variable Importance. https://arxiv.org/abs/2003.03629

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Attack-Resistant Uniform Fairness for Linear and Smooth Contextual Bandits

Modern digital platforms use contextual bandits to allocate valuable exposure and opportunities among competing participants. Fair treatment is therefore an important concern, yet reward maximization alone does not ensure that preferential allocation reflects participants' merits. We develop algorithms for linear and smooth contextual bandits under uniform merit-based fairness, requiring the reward ordering to justify preferential allocation across all contexts and rounds, and study how these guarantees are affected by adversarial reward corruption. Our algorithms achieve \((1-\widetilde O(1/T))\)-fairness, with regret that is minimax optimal among fair policies for linear rewards and nearly minimax optimal for smooth rewards. In the linear setting, matching lower bounds identify the price of fairness exactly: minimax regret increases from \(\log T\) to \(\log^2 T\). For smooth rewards, the cost of fairness is at most polylogarithmic. We further establish a separation between regret and fairness robustness: an \(\widetilde O(1)\) corruption budget can cause substantial fairness violations without worsening the regret order. We therefore develop robust algorithms that adapt sampling, estimation, and fairness certification to corruption, which preserve uniform fairness and achieve minimax-optimal and nearly optimal regrets for linear and smooth rewards, respectively. Numerical and semi-synthetic experiments illustrate these findings.

stat.ML↗
arXiv2026

The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy

We study the minimax cost of $(\varepsilon,δ)$-differential privacy for mean estimation and Gaussian linear regression in low and high dimensions. For low-dimensional mean estimation, a resampling reduction to fingerprinting yields the privacy contribution $d^2\log(1/δ)/(n^2\varepsilon^2)$ in the stated polynomial-$δ$ regime. For low-dimensional regression, a tracing argument gives the contribution $d^2/(n^2\varepsilon^2)$ under an explicit approximate-DP remainder condition. For sparse mean estimation and sparse regression, a constant-weight packing and a private Fano lemma produce an effective privacy entropy of order $\min\{s\log(ed/s),[\log((e^\varepsilon-1)/δ)]_+\}$ for $δ>0$, up to universal constants and a fixed threshold; for pure DP it is $s\log(ed/s)$. Thus, when $δ$ is polynomially smaller than $\varepsilon$, the pure-DP dependence is retained up to polylogarithmic factors whenever the effective dimension is polylogarithmic in $n$, including regimes with $\varepsilon=o(1)$. Coordinatewise-clipping estimators for means and split-sample noisy-gradient estimators for regression attain the lower bounds up to explicit logarithmic factors. Simulations and data examples illustrate related implementations.

stat.ML↗
arXiv2026

Robust Mixture Models for Algorithmic Fairness Under Latent Heterogeneity

Machine learning models optimized for average performance can perform poorly on vulnerable subpopulations. Existing approaches often rely on groups specified in advance, yet fairness-relevant subgroup structure may be latent, intersectional, and driven by complex interactions among continuous and discrete attributes. We introduce \textbf{ROME} (\textbf{\underline{RO}}bust \textbf{\underline{M}}ixture \textbf{\underline{E}}nsemble), a framework that learns latent group structure while optimizing worst-group predictive performance. ROME connects latent-variable modeling with distributionally robust optimization (DRO) through two complementary approaches: an Expectation-Maximization formulation with robust aggregation for linear models and a neural Mixture-of-Experts formulation for nonlinear settings. Across simulations and three real-world regression datasets, ROME improves worst-group performance while maintaining competitive overall accuracy, including in comparisons with established group-aware and group-label-free robust learning methods. ROME provides a flexible approach to robust prediction when fairness-relevant attributes are available for subgroup discovery but their direct use in group-specific outcome models is restricted.

stat.ML↗