arXiv subjects

Maya Ramchandran

Publications and source records attributed to Maya Ramchandran.

4 recordsLinked to original sources

arXiv2026

Pooling Versus Ensembling for Ridge Regression Under Covariate Shift

Datasets in many settings naturally partition into clusters arising from sub-populations, batch effects, or aggregation across multiple sources. A common response to such heterogeneity is to ensemble learners trained on each cluster rather than fit a single model to the pooled data. Prior work motivating such approaches has typically considered settings in which both the covariate distribution and the conditional outcome model differ across clusters; the role of cluster-aware partitioning and ensembling based solely on the covariate distribution remains to be explored. We address this case for ridge-regularized least-squares regression under a linear outcome model and consider all ridge penalty values $\lambda \geq 0$, including the special case of the ridgeless predictor at $\lambda = 0$. By considering both fixed-effects and random-effects models, we argue that under random effects, an optimally tuned pooled ridge predictor always outperforms ensembles of individually optimally tuned predictors. For fixed effects, we derive a general formula for the pooled and ensembled predictors to characterize the role of both regression coefficients as well as the predictor distribution shifts. Together, these results generalize prior risk analyses of bagging and random-partition estimation using ridge and ridgeless regression predictors from the i.i.d. setting to encompass covariate shift and heterogeneity-aware partition structure.

math.ST↗

arXiv2022

Reconstructing gene expression and knockout effect scores from DNA mutation (Mut2Ex): methodology and application to cancer prediction problems

Building prediction models for outcomes of clinical relevance when only a limited number of mutational features are available causes considerable challenges due to the sparseness and low-dimensionality of the data. In this article, we present a method to augment the predictive power of these features by leveraging multi-modal associative relationships between an individual's mutational profile and their corresponding gene expression or knockout effect profiles. We can thus reconstruct expression or effect scores for genes of interest from the available mutation features and then use this reconstructed representation directly to model and predict clinical outcomes. We show that our method produces significant improvements in predictive accuracy compared to models utilizing only the raw mutational data, and results in conclusions comparable to those obtained using real expression or effect profiles.

q-bio.GN↗

arXiv2021

On Ensembling vs Merging: Least Squares and Random Forests under Covariate Shift

It has been postulated and observed in practice that for prediction problems in which covariate data can be naturally partitioned into clusters, ensembling algorithms based on suitably aggregating models trained on individual clusters often perform substantially better than methods that ignore the clustering structure in the data. In this paper, we provide theoretical support to these empirical observations by asymptotically analyzing linear least squares and random forest regressions under a linear model. Our main results demonstrate that the benefit of ensembling compared to training a single model on the entire data, often termed 'merging', might depend on the underlying bias and variance interplay of the individual predictors to be aggregated. In particular, under both fixed and high dimensional linear models, we show that merging is asymptotically superior to optimal ensembling techniques for linear least squares regression due to the unbiased nature of least squares prediction. In contrast, for random forest regression under fixed dimensional linear models, our bounds imply a strict benefit of ensembling over merging. Finally, we also present numerical experiments to verify the validity of our asymptotic results across different situations.

math.ST↗

arXiv2021

Cross-Cluster Weighted Forests

Building trustworthy machine learning algorithms for biological applications requires adapting to data heterogeneity from different sources, batches, distributions, or studies. We propose the 'Cross-Cluster Weighted Forest' (CCWF), an ensembling approach that explicitly leverages heterogeneity in the feature distribution to produce more accurate and more generalizable predictors than the standard Random Forest in cases when data can be naturally clustered. CCWF generalizes the RF architecture to an outer unsupervised layer, supervised subtasks, and ensembling. Specifically it involves unsupervised clustering of the training data, fitting a Random Forest on each cluster, and combining the forests via stacked regression weights that reward cross-cluster generalizability. We provide a theoretical analysis of an analytically tractable forest model showing that cluster-based ensembling is asymptotically more accurate than training a single forest on the full data, with the gain driven by bias reduction. In simulations, we find that CCWF is robust across data-generating regimes and outcome models; furthermore, we explore the influence of data partitioning and ensemble weighting strategies on the benefits of our method. Finally, we apply our approach to cancer molecular profiling and gene expression datasets that are naturally divisible into clusters; in both simulations and real data examples, we illustrate that our approach outperforms classic Random Forest by margins of 30-40%, aligning with our theoretical results. Overall, we show that CCWF provides a statistically grounded prediction algorithm for data spanning multiple domains or sub-populations, a structure common in biological applications.

stat.ML↗