Tootfinder

Learning with springs and sticks
Luis Mantilla Calder\'on, Al\'an Aspuru-Guzik
https://arxiv.org/abs/2508.19015 https://arxiv.org/pdf/2508.19015

Learning with springs and sticks
Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks …

Bayes linear estimator in the general linear model
Hirai Mukasa
https://arxiv.org/abs/2506.21192 https://arxiv.org/pdf/2506.21192

Bayes linear estimator in the general linear model
Bayes linear estimators are derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as an ordinary ridge estimator, a typical shrinkage estimator, and a fractional rank estimator are either Bayes linear estimators or their limit points. First, we prove that Bayes linear estimators are linearly complete, but not necessarily linearly sufficient. Second, we derive a necessary and sufficient condition under which two Bayes linear estimators coinc…

Optimal differentially private kernel learning with random projection
Bonwoo Lee, Cheolwoo Park, Jeongyoun Ahn
https://arxiv.org/abs/2507.17544 https://

Optimal differentially private kernel learning with random projection
Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We propose a novel differentially private kernel ERM algorithm based on random projection in the reproducing kernel Hilbert space using Gaussian processes. Our method achieves minimax-optimal excess risk for both the squared loss and Lipschitz-smooth convex loss fu…

General M-estimators of location on Riemannian manifolds: existence and uniqueness
Jongmin Lee, Sungkyu Jung
https://arxiv.org/abs/2508.16149 https://arxiv…

General M-estimators of location on Riemannian manifolds: existence and uniqueness
We study general M-estimators of location on Riemannian manifolds, extending classical notions such as the Frechet mean by replacing the squared loss with a broad class of loss functions. Under minimal regularity conditions on the loss function and the underlying probability distribution, we establish theoretical guarantees for the existence and uniqueness of such estimators. In particular, we provide sufficient conditions under which the population and sample M-estimators exist and are uniquel…

Focus on Texture: Rethinking Pre-training in Masked Autoencoders for Medical Image Classification
Chetan Madan, Aarjav Satia, Soumen Basu, Pankaj Gupta, Usha Dutta, Chetan Arora
https://arxiv.org/abs/2507.10869

Focus on Texture: Rethinking Pre-training in Masked Autoencoders for Medical Image Classification
Masked Autoencoders (MAEs) have emerged as a dominant strategy for self-supervised representation learning in natural images, where models are pre-trained to reconstruct masked patches with a pixel-wise mean squared error (MSE) between original and reconstructed RGB values as the loss. We observe that MSE encourages blurred image re-construction, but still works for natural images as it preserves dominant edges. However, in medical imaging, when the texture cues are more important for classific…

Heavy Lasso: sparse penalized regression under heavy-tailed noise via data-augmented soft-thresholding
The Tien Mai
https://arxiv.org/abs/2506.07790 https:…

Heavy Lasso: sparse penalized regression under heavy-tailed noise via data-augmented soft-thresholding
High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise assumptions but often deteriorates in the presence of heavy-tailed errors or outliers commonly encountered in real data applications such as genomics, finance, and signal processing. To address these challenges, we propose a novel robust regression method, terme…

Fisher Score Matching for Simulation-Based Forecasting and Inference
Ce Sui, Shivam Pandey, Benjamin D. Wandelt
https://arxiv.org/abs/2507.07833 https://…

Fisher Score Matching for Simulation-Based Forecasting and Inference
We propose a method for estimating the Fisher score--the gradient of the log-likelihood with respect to model parameters--using score matching. By introducing a latent parameter model, we show that the Fisher score can be learned by training a neural network to predict latent scores via a mean squared error loss. We validate our approach on a toy linear Gaussian model and a cosmological example using a differentiable simulator. In both cases, the learned scores closely match ground truth for pl…

Orthogonality-Constrained Deep Instrumental Variable Model for Causal Effect Estimation
Shunxin Yao
https://arxiv.org/abs/2506.02790 https://

Orthogonality-Constrained Deep Instrumental Variable Model for Causal Effect Estimation
OC-DeepIV is a neural network model designed for estimating causal effects. It characterizes heterogeneity by adding interaction features and reduces redundancy through orthogonal constraints. The model includes two feature extractors, one for the instrumental variable Z and the other for the covariate X*. The training process is divided into two stages: the first stage uses the mean squared error (MSE) loss function, and the second stage incorporates orthogonal regularization. Experimental res…

Disentangled Feature Importance
Jin-Hong Du, Kathryn Roeder, Larry Wasserman
https://arxiv.org/abs/2507.00260 https://arxiv.org/pdf/2…

Disentangled Feature Importance
Feature importance quantification faces a fundamental challenge: when predictors are correlated, standard methods systematically underestimate their contributions. We prove that major existing approaches target identical population functionals under squared-error loss, revealing why they share this correlation-induced bias. To address this limitation, we introduce \emph{Disentangled Feature Importance (DFI)}, a nonparametric generalization of the classical $R^2$ decomposition via optimal tran…