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Molecular Relational Learning (MRL) is widely applied in natural sciences to predict relationships between molecular pairs by extracting structural features. The representational similarity between substructure pairs determines the…
Large language models (LLMs) and classical machine learning methods offer complementary strengths for predictive modeling, yet their fundamentally different representations and training paradigms hinder effective integration: LLMs rely on…
This paper analyzes the possibilities of using the generalized ridge regression to mitigate multicollinearity in a multiple linear regression model. For this purpose, we obtain the expressions for the estimated variance, the coefficient of…
The task of hot-refresh model upgrades of image retrieval systems plays an essential role in the industry but has never been investigated in academia before. Conventional cold-refresh model upgrades can only deploy new models after the…
Accurately characterizing the true redshift (true-$z$) distribution of a photometric redshift (photo-$z$) sample is critical for cosmological analyses in imaging surveys. Clustering-based techniques, which include clustering-redshift (CZ)…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
Multivariate regression is a widespread computational technique that may give meaningless results if the explanatory variables are too numerous or highly collinear. Tikhonov regularization, or ridge regression, is a popular approach to…
Multimodal large language models (MLLMs) struggle with numerical regression under long-tailed target distributions. Token-level supervised fine-tuning (SFT) and point-wise regression rewards bias learning toward high-density regions,…
Class imbalance, where certain classes have insufficient data, poses a critical challenge for robust classification, often biasing models toward majority classes. Distribution calibration offers a promising avenue to address this by…
Theoretical guarantees for the robust solution of inverse problems have important implications for applications. To achieve both guarantees and high reconstruction quality, we propose learning a pixel-based ridge regularizer with a…
Consider the classical supervised learning problem: we are given data $(y_i,{\boldsymbol x}_i)$, $i\le n$, with $y_i$ a response and ${\boldsymbol x}_i\in {\mathcal X}$ a covariates vector, and try to learn a model $f:{\mathcal…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
The optimal fingerprinting method for detection and attribution of climate change is based on a multiple regression where each covariate has measurement error whose covariance matrix is the same as that of the regression error up to a known…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
We consider fully row/column-correlated linear regression models and study several classical estimators (including minimum norm interpolators (GLS), ordinary least squares (LS), and ridge regressors). We show that \emph{Random Duality…
We introduce Conformal Interquantile Regression (CIR), a conformal regression method that efficiently constructs near-minimal prediction intervals with guaranteed coverage. CIR leverages black-box machine learning models to estimate outcome…
We present a method that accurately propagates residual uncertainties in photometric redshift distributions into the cosmological inference from weak lensing measurements. The redshift distributions of tomographic redshift bins are…
We consider correlated \emph{factor} regression models (FRM) and analyze the performance of classical ridge interpolators. Utilizing powerful \emph{Random Duality Theory} (RDT) mathematical engine, we obtain \emph{precise} closed form…
Characterization of local minima draws much attention in theoretical studies of deep learning. In this study, we investigate the distribution of parameters in an over-parametrized finite neural network trained by ridge regularized empirical…