Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians

• URL: http://arxiv.org/abs/2604.25295v1
• Date: Tue, 28 Apr 2026 07:03:04 GMT
• Title: Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobians
• Abstract summary: Continuous causal discovery typically represents learning with structural optimization via non-dimensional structural error penalties.<n>We introduce WeSSTS, which allows causal structural analysis graphs up to d-sample estimation of the global score.
• Score: 7.046544692710195
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Continuous causal discovery typically couples representation learning with structural optimization via non-convex acyclicity penalties, which subjects solvers to local optima and restricts scalability in high-dimensional regimes. We propose a decoupled paradigm that shifts the causal discovery bottleneck from non-convex optimization to statistical score estimation. We introduce the Score-Schur Topological Sort (SSTS), an algorithm that extracts topological order directly from unconstrained generative models, bypassing constrained structure optimization. We establish that the causal hierarchy leaves a geometric signature within the score function: iterative graph marginalization is mathematically equivalent to computing the Schur complement of the Score-Jacobian Information Matrix (SJIM) under linear conditions. This translates the acyclicity constraint into an algebraic procedure with a dominant cost of O(d^3) operations. For non-linear systems, we formulate the expectation gap of Schur marginalization and introduce Block-SSTS to compress extraction depth, bounding structural error. Empirically, SSTS allows causal structural analysis on non-linear graphs up to d=1000. At this scale, our framework indicates that once the non-convex optimization bottleneck is mathematically bypassed, the structural fidelity of continuous causal discovery is bounded by the finite-sample estimation variance of the global score geometry. By reducing graph extraction to matrix operations, this work reframes scalable causal discovery from a constrained optimization problem to a statistical estimation challenge.

Related papers

• BOOOM: Loss-Function-Agnostic Black-Box Optimization over Orthonormal Manifolds for Machine Learning and Statistical Inference [0.0]
  We present a systematic exploration of.<n>the set of $p.<n>orthonormal column-orthonormal escape through a.<n>novel applied to data data.<n>problems.<n>We show a diagonal optimization framework showing a.<n>strong, low-rank decomposition, independent decomposition analysis,.<n>and global convergence in under conditions.
  arXiv  Detail & Related papers  (2026-04-23T19:32:27Z)
• Asymptotic Theory for Graphical SLOPE: Precision Estimation and Pattern Convergence [2.5407895016635127]
  This paper studies Graphical SLOPE for precision matrix estimation.<n>In a fixed-dimensional regime, we establish that the root-$n$ scaled estimation error converges to the unique minimizer of a strictly convex optimization problem.<n>We also establish convergence of the induced SLOPE pattern, thereby obtaining an characterization of the clustering structure selected by the estimator.
  arXiv  Detail & Related papers  (2026-04-14T14:10:56Z)
• Smooth, Sparse, and Stable: Finite-Time Exact Skeleton Recovery via Smoothed Proximal Gradients [2.7920588009522755]
  We bridge the gap between continuous optimization and discrete graph structures by proposing the Hybrid-Order Acyclicity Constraint (AHOC) and optimizing it via the Smoothed Proximal Gradient (SPG-AHOC)<n>We prove that under standard identifiability assumptions, SPG-AHOC recovers the exact DAG support (structure) in finite iterations, even when optimizing a smoothed approximation.<n>This result eliminates structural ambiguity, as our algorithm returns graphs with exact zero entries without truncation.
  arXiv  Detail & Related papers  (2026-01-26T06:16:47Z)
• An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decomposition [0.0]
  In this paper, we aim to investigate the sparse low-rank characteristics rectified on non-negative matrices.<n>We propose a novel regularization term incorporating useful structures in clustering and compression tasks.<n>We derive corresponding closed-form solutions while maintaining the $L$-smooth property always holds for any $Lge 1$.
  arXiv  Detail & Related papers  (2025-03-04T08:20:34Z)
• Elucidating Subspace Perturbation in Zeroth-Order Optimization: Theory and Practice at Scale [33.38543010618118]
  Zeroth-order (ZO) optimization has emerged as a promising alternative to gradient-based backpropagation methods.<n>We show that high dimensionality is the primary bottleneck and introduce the notion of textitsubspace alignment to explain how the subspace perturbations reduce gradient noise and accelerate convergence.<n>We propose an efficient ZO method using block coordinate descent (MeZO-BCD), which perturbs and updates only a subset of parameters at each step.
  arXiv  Detail & Related papers  (2025-01-31T12:46:04Z)
• Non-negative Weighted DAG Structure Learning [12.139158398361868]
  We address the problem of learning the true DAGs from nodal observations. We propose a DAG recovery algorithm based on the method that is guaranteed to return ar.
  arXiv  Detail & Related papers  (2024-09-12T09:41:29Z)
• A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrieval [56.67706781191521]
  In this work, we present a robust phase retrieval problem where the task is to recover an unknown signal. Our proposed oracle avoids the need for computationally spectral descent, using a simple gradient step and outliers.
  arXiv  Detail & Related papers  (2024-09-07T06:37:23Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Model-based Causal Bayesian Optimization [78.120734120667]
  We propose model-based causal Bayesian optimization (MCBO) MCBO learns a full system model instead of only modeling intervention-reward pairs. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form.
  arXiv  Detail & Related papers  (2022-11-18T14:28:21Z)
• Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms [71.62575565990502]
  We prove that the generalization error of an optimization algorithm can be bounded on the complexity' of the fractal structure that underlies its generalization measure. We further specialize our results to specific problems (e.g., linear/logistic regression, one hidden/layered neural networks) and algorithms.
  arXiv  Detail & Related papers  (2021-06-09T08:05:36Z)
• Sparse PCA via $l_{2,p}$-Norm Regularization for Unsupervised Feature Selection [138.97647716793333]
  We propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_2,p$-norm regularization. We present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically.
  arXiv  Detail & Related papers  (2020-12-29T04:08:38Z)
• Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization [98.0595480384208]
  We propose a generalization extraient spaces which converges to a stationary point. The algorithm applies not only to general $p$-normed spaces, but also to general $p$-dimensional vector spaces.
  arXiv  Detail & Related papers  (2020-10-31T21:35:42Z)

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.