arXiv subjects

Alek Fröhlich

Publications and source records attributed to Alek Fröhlich.

5 recordsLinked to original sources

arXiv2026

Learning Conditional Expectation Operators via Functional Newton Updates

We introduce the Functional Spectral-Newton Method (FSNM) for learning the leading singular structure of a conditional expectation operator without fixing a basis or reproducing kernel Hilbert space. FSNM fits a low-rank representation of the centered joint-to-product density ratio kernel by alternating functional Newton updates. Each update reduces to a preconditioned regression, which we approximate with vector-valued regression trees in a stagewise boosting procedure. At the population level, we establish descent and an $O(1/T)$ best-iterate block-stationarity rate under a relative weak-learner accuracy condition, and show that every nondegenerate local minimum over the full centered $L^2$ spaces is a globally optimal rank-$d$ approximation. Synthetic experiments show that FSNM recovers a low-rank density ratio and its leading spectral structure, and that the same learned kernel can answer multiple conditional queries without refitting.

stat.ML↗

arXiv2026

Representation Learning for Equivariant Inference with Guarantees

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While geometric deep learning has made empirical advances by incorporating symmetry and geometry priors, less attention has been given to statistical learning guarantees. In this paper, we introduce an equivariant representation learning framework that simultaneously addresses regression, conditional probability estimation, and uncertainty quantification while providing first-of-its-kind non-asymptotic statistical learning guarantees. Grounded in operator and group representation theory, our framework approximates the spectral decomposition of the conditional expectation operator, building representations that are both equivariant and disentangled along independent symmetry quotient groups. Empirical evaluations on synthetic datasets and real-world robotics applications confirm the potential of our approach, matching or outperforming existing equivariant baselines in regression while providing well-calibrated uncertainty estimates.

cs.LG↗

arXiv2026

Toward Scalable and Valid Conditional Independence Testing with Spectral Representations

Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural conditions, limiting their validity. Kernel methods using partial covariance operators offer a more principled approach but suffer from limited adaptivity and scalability. In this work, we explore whether representation learning can help address these limitations. Specifically, we focus on representations derived from the singular value decomposition of partial covariance operators and use them to construct a simple test statistic. We also introduce a bi-level contrastive algorithm to learn these representations. Our theory links representation learning error to test performance and establishes asymptotic validity and power guarantees. Experiments on real and synthetic data suggest that this approach offers a principled and statistically grounded path toward scalable CI testing, bridging kernel-based theory with modern representation learning.

cs.LG↗

arXiv2026

Outcome-Aware Spectral Feature Learning for Instrumental Variable Regression

We address the problem of causal effect estimation in the presence of hidden confounders using nonparametric instrumental variable (IV) regression. An established approach is to use estimators based on learned spectral features, that is, features spanning the top singular subspaces of the operator linking treatments to instruments. While powerful, such features are agnostic to the outcome variable. Consequently, the method can fail when the true causal function is poorly represented by these dominant singular functions. To mitigate, we introduce Augmented Spectral Feature Learning, a framework that makes the feature learning process outcome-aware. Our method learns features by minimizing a novel contrastive loss derived from an augmented operator that incorporates information from the outcome. By learning these task-specific features, our approach remains effective even under spectral misalignment. We provide a theoretical analysis of this framework and validate our approach on challenging benchmarks.

stat.ML↗

arXiv2024

PersonalizedUS: Interpretable Breast Cancer Risk Assessment with Local Coverage Uncertainty Quantification

Correctly assessing the malignancy of breast lesions identified during ultrasound examinations is crucial for effective clinical decision-making. However, the current "golden standard" relies on manual BI-RADS scoring by clinicians, often leading to unnecessary biopsies and a significant mental health burden on patients and their families. In this paper, we introduce PersonalizedUS, an interpretable machine learning system that leverages recent advances in conformal prediction to provide precise and personalized risk estimates with local coverage guarantees and sensitivity, specificity, and predictive values above 0.9 across various threshold levels. In particular, we identify meaningful lesion subgroups where distribution-free, model-agnostic conditional coverage holds, with approximately 90% of our prediction sets containing only the ground truth in most lesion subgroups, thus explicitly characterizing for which patients the model is most suitably applied. Moreover, we make available a curated tabular dataset of 1936 biopsied breast lesions from a recent observational multicenter study and benchmark the performance of several state-of-the-art learning algorithms. We also report a successful case study of the deployed system in the same multicenter context. Concrete clinical benefits include up to a 65% reduction in requested biopsies among BI-RADS 4a and 4b lesions, with minimal to no missed cancer cases.

cs.LG↗