Exosomes are small vesicles crucial for cell signaling and disease biomarkers. Due to their complexity, an "omics" approach is preferable to individual biomarkers. While Raman spectroscopy is effective for exosome analysis, it requires high sample concentrations and has limited sensitivity to lipids and proteins. Surface-enhanced Raman spectroscopy helps overcome these challenges. In this study, we leverage Neo4j graph databases to organize 3,045 Raman spectra of exosomes, enhancing data generalization. To further refine spectral analysis, we introduce a novel spectral filtering process that integrates the PageRank Filter with optimal Dimensionality Reduction. This method improves feature selection, resulting in superior classification performance. Specifically, the Extra Trees model, using our spectral processing approach, achieves 0.76 and 0.857 accuracy in classifying hyperglycemic, hypoglycemic, and normal exosome samples based on Raman spectra and surface, respectively, with group 10-fold cross-validation. Our results show that graph-based spectral filtering combined with optimal dimensionality reduction significantly improves classification accuracy by reducing noise while preserving key biomarker signals. This novel framework enhances Raman-based exosome analysis, expanding its potential for biomedical applications, disease diagnostics, and biomarker discovery.

While test-time fine-tuning is beneficial in few-shot learning, the need for multiple backpropagation steps can be prohibitively expensive in real-time or low-resource scenarios. To address this limitation, we propose an approach that emulates gradient descent without computing gradients, enabling efficient test-time adaptation. Specifically, we formulate gradient descent as an Euler discretization of an ordinary differential equation (ODE) and train an auxiliary network to predict the task-conditional drift using only the few-shot support set. The adaptation then reduces to a simple numerical integration (e.g., via the Euler method), which requires only a few forward passes of the auxiliary network -- no gradients or forward passes of the target model are needed. In experiments on cross-domain few-shot classification using the Meta-Dataset and CDFSL benchmarks, our method significantly improves out-of-domain performance over the non-fine-tuned baseline while incurring only 6\% of the memory cost and 0.02\% of the computation time of standard fine-tuning, thus establishing a practical middle ground between direct transfer and fully fine-tuned approaches.

Birth weight (BW) is a key indicator of neonatal health, with low birth weight (LBW) linked to increased mortality and morbidity. Early prediction of BW enables timely interventions; however, current methods like ultrasonography have limitations, including reduced accuracy before 20 weeks and operator dependent variability. Existing models often neglect nutritional and genetic influences, focusing mainly on physiological and lifestyle factors. This study presents an attention-based transformer model with a multi-encoder architecture for early (less than 12 weeks of gestation) BW prediction. Our model effectively integrates diverse maternal data such as physiological, lifestyle, nutritional, and genetic, addressing limitations seen in prior attention-based models such as TabNet. The model achieves a Mean Absolute Error (MAE) of 122 grams and an R-squared value of 0.94, demonstrating high predictive accuracy and interoperability with our in-house private dataset. Independent validation confirms generalizability (MAE: 105 grams, R-squared: 0.95) with the IEEE children dataset. To enhance clinical utility, predicted BW is classified into low and normal categories, achieving a sensitivity of 97.55% and a specificity of 94.48%, facilitating early risk stratification. Model interpretability is reinforced through feature importance and SHAP analyses, highlighting significant influences of maternal age, tobacco exposure, and vitamin B12 status, with genetic factors playing a secondary role. Our results emphasize the potential of advanced deep-learning models to improve early BW prediction, offering clinicians a robust, interpretable, and personalized tool for identifying pregnancies at risk and optimizing neonatal outcomes.

This paper presents a Bayesian estimation framework for Wiener models, focusing on learning nonlinear output functions under known linear state dynamics. We derive a closed-form optimal affine estimator for the unknown parameters, characterized by the so-called "dynamic basis statistics" (DBS). Several features of the proposed estimator are studied, including Bayesian unbiasedness, closed-form posterior statistics, error monotonicity in trajectory length, and consistency condition (also known as persistent excitation). In the special case of Fourier basis functions, we demonstrate that the closed-form description is computationally available, as the Fourier DBS enjoys explicit expressions. Furthermore, we identify an inherent inconsistency in the Fourier bases for single-trajectory measurements, regardless of the input excitation. Leveraging the closed-form estimation error, we develop an active learning algorithm synthesizing input signals to minimize estimation error.

A treatment may be appropriate for some group (the ``sick" group) on whom it has a positive effect, but it can also have a detrimental effect on subjects from another group (the ``healthy" group). In a non-targeted trial both sick and healthy subjects may be treated, producing heterogeneous effects within the treated group. Inferring the correct treatment effect on the sick population is then difficult, because the effects on the different groups get tangled. We propose an efficient nonparametric approach to estimating the group effects, called {\bf PCM} (pre-cluster and merge). We prove its asymptotic consistency in a general setting and show, on synthetic data, more than a 10x improvement in accuracy over existing state-of-the-art. Our approach applies more generally to consistent estimation of functions with a finite range.

We prove that either two-layer self-attention or one-layer self-attention followed by a softmax (each equipped only with linear transformations) is capable of approximating any sequence-to-sequence continuous function on a compact domain. Different from previous studies [Y un et al., 2019, Jiang and Li, 2023, Takakura and Suzuki, 2023, Kajitsuka and Sato, 2023, Hu et al., 2024], our results highlight the expressive power of Transformers derived only from the attention module. By focusing exclusively on attention, our analysis demonstrates that the softmax operation itself suffices as a piecewise linear approximator. Furthermore, we extend this framework to broader applications, such as in-context learning [Brown et al., 2020, Bai et al., 2024], using the same attention-only architecture. Prior studies of Transformer-based universality lean on deep attention stacks [Y un et al., 2019] or feed-forward (FFN) sub-layers [Kajitsuka and Sato, 2023, Hu et al., 2024] or strong assumptions on data or architecture [Takakura and Suzuki, 2023, Petrov et al., 2024]. These results make it unclear whether attention alone is essential or auxiliary. To combat this, we develop a new interpolation-based technique for analyzing attention 1 .

In-context learning (ICL)-the ability of transformer-based models to perform new tasks from examples provided at inference time-has emerged as a hallmark of modern language models. While recent works have investigated the mechanisms underlying ICL, its feasibility under formal privacy constraints remains largely unexplored. In this paper, we propose a differentially private pretraining algorithm for linear attention heads and present the first theoretical analysis of the privacy-accuracy trade-off for ICL in linear regression. Our results characterize the fundamental tension between optimization and privacy-induced noise, formally capturing behaviors observed in private training via iterative methods. Additionally, we show that our method is robust to adversarial perturbations of training prompts, unlike standard ridge regression. All theoretical findings are supported by extensive simulations across diverse settings.

Transformers have become a standard architecture in machine learning, demonstrating strong in-context learning (ICL) abilities that allow them to learn from the prompt at inference time. However, uncertainty quantification for ICL remains an open challenge, particularly in noisy regression tasks. This paper investigates whether ICL can be leveraged for distribution-free uncertainty estimation, proposing a method based on conformal prediction to construct prediction intervals with guaranteed coverage. While traditional conformal methods are computationally expensive due to repeated model fitting, we exploit ICL to efficiently generate confidence intervals in a single forward pass. Our empirical analysis compares this approach against ridge regression-based conformal methods, showing that conformal prediction with in-context learning (CP with ICL) achieves robust and scalable uncertainty estimates. Additionally, we evaluate its performance under distribution shifts and establish scaling laws to guide model training. These findings bridge ICL and conformal prediction, providing a theoretically grounded and new framework for uncertainty quantification in transformer-based models.

We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in optimization. Specifically, we give new algorithms for approximating convex polytopes in a stream, sparsification and robust least squares regression, and dueling optimization. In Part II, we give new statistical guarantees for data science problems. In particular, we formulate a new model in which we analyze statistical properties of backdoor data poisoning attacks, and we study the robustness of graph clustering algorithms to ``helpful'' misspecification.

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to solve this problem, leveraging an alternating optimization approach that decomposes the global non-convex problem into a series of convex sub-problems. To improve performance, we explore advanced initialization strategies inspired by the singular value decomposition (SVD) and incorporate acceleration techniques by introducing momentum-based updates. Beyond optimizing the two-matrix case, we also extend the Hadamard decomposition framework to support more than two low-rank matrices, enabling approximations with higher effective ranks while preserving computational efficiency. Finally, we conduct extensive experiments to compare our method with the existing gradient descent-based approaches for the Hadamard decomposition and with traditional low-rank approximation techniques. The results highlight the effectiveness of our proposed method across diverse datasets.