The Spectral Structure of Latent Treatment Effects

• URL: http://arxiv.org/abs/2607.10926v1
• Date: Sun, 12 Jul 2026 21:23:13 GMT
• Title: The Spectral Structure of Latent Treatment Effects
• Abstract summary: In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) recover the mixture of treatment effects.<n>We show that this sequence is one projection of a more fundamental object.<n>The resulting estimator handles overcomplete proxy systems.
• Score: 0.48429188360918735
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

Related papers

• Overfitted high-dimensional matrix factorizations via adaptive spectral shrinkage [8.549941732144035]
  We show that textttEigenBayes adapts to the signal-to-noise ratio of each outcome and latent dimension, while shrinking latent components to zero.<n>We demonstrate strong empirical performance in numerical experiments and a genomics application.
  arXiv  Detail & Related papers  (2026-06-17T19:33:03Z)
• Smoothness-Based Derandomization of PAC-Bayes Bounds [48.06655334157014]
  We study PAC-Bayes derandomization for smooth loss functions.<n>We show that unbounded passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost.<n>We specialize the results to linear predictors and smooth neural networks.
  arXiv  Detail & Related papers  (2026-06-17T14:17:44Z)
• Improved Guarantees for Heterogeneous Treatment-Effect Estimation via Matrix Completion [8.03845232151202]
  Estimating heterogeneous treatment effects can then be expressed as obtaining a good estimation of each row's average in this matrix.<n>We give a simple, computationally efficient estimator without knowledge of the propensities and under standard low-rankness and regularity assumptions.<n>Technically, our analysis establishes the first sharp row-wise $ell$-perturbation bound for low-rank approximation.
  arXiv  Detail & Related papers  (2026-05-28T17:55:23Z)
• Causal Inference with Categorical Unobserved Confounder via Mixture Learning [20.542714966688656]
  We show that causal effects are identifiable when the unobserved confounder is categorical under suitable conditions.<n>We propose an estimation procedure based on tensor decomposition, which allows consistent recovery of the latent structure.
  arXiv  Detail & Related papers  (2026-05-18T18:28:16Z)
• Operator ordering as an emergent geometric background in Dirac systems with spatially varying mass [0.0]
  We investigate the spectral consequences of the uniquely determined Hermitian ordering of the Dirac Hamiltonian with spatially varying mass.<n>We show that this contribution modifies the effective kinetic operator and induces a universal deformation of the spectral quantization condition.
  arXiv  Detail & Related papers  (2026-05-13T21:59:17Z)
• MirrorLA: Reflecting Feature Map for Vision Linear Attention [49.41670925034762]
  Linear attention significantly reduces the computational complexity of Transformers from quadratic to linear, yet it consistently lags behind softmax-based attention in performance.<n>We propose MirrorLA, a geometric framework that substitutes passive truncation with active reorientation.<n>MirrorLA achieves state-of-the-art performance across standard benchmarks, demonstrating that strictly linear efficiency can be achieved without compromising representational fidelity.
  arXiv  Detail & Related papers  (2026-02-04T09:14:09Z)
• Preconditioning Benefits of Spectral Orthogonalization in Muon [50.62925024212989]
  We study the effectiveness of a simplified variant of Muon in two case studies: matrix factorization and in-context learning of linear transformers.<n>Our analysis reveals that the Muon dynamics decouple into a collection of independent scalar sequences in the spectral domain, each exhibiting similar convergence behavior.
  arXiv  Detail & Related papers  (2026-01-20T00:08:31Z)
• Efficient Adaptation of Pre-trained Vision Transformer underpinned by Approximately Orthogonal Fine-Tuning Strategy [57.54306942529943]
  We propose an Approximately Orthogonal Fine-Tuning (AOFT) strategy for representing the low-rank weight matrices.<n>Our method achieves competitive performance across a range of downstream image classification tasks.
  arXiv  Detail & Related papers  (2025-07-17T16:09:05Z)
• Demystifying Spectral Feature Learning for Instrumental Variable Regression [21.514407689434364]
  We derive a generalization error bound for a two-stage least squares estimator based on spectral features.<n>We show that performance depends on two key factors, leading to a clear taxonomy of outcomes.
  arXiv  Detail & Related papers  (2025-06-12T17:06:43Z)
• Absorb and Converge: Provable Convergence Guarantee for Absorbing Discrete Diffusion Models [66.0716790920952]
  We provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices.<n>We establish the first convergence guarantees for both the $tau$-leaping and uniformization samplers under absorbing rate matrices.<n>Under suitable assumptions, we provide convergence guarantees without early stopping.
  arXiv  Detail & Related papers  (2025-06-02T23:14:35Z)
• Score-based Causal Representation Learning with Interventions [54.735484409244386]
  This paper studies the causal representation learning problem when latent causal variables are observed indirectly. The objectives are: (i) recovering the unknown linear transformation (up to scaling) and (ii) determining the directed acyclic graph (DAG) underlying the latent variables.
  arXiv  Detail & Related papers  (2023-01-19T18:39:48Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.