arXiv subjects

Yuexin Liao

Publications and source records attributed to Yuexin Liao.

4 recordsLinked to original sources

arXiv2026

Random Utility with Aggregation

We study random utility (RU) rationality with aggregation when the underlying alternatives in each aggregate vary across consumers and are unobserved, as is typical for an outside option. RUM over the underlying alternatives is the natural assumption on the data generating process, while an aggregated random utility model (ARUM) is the standard empirical tool. We characterize RU rationality in three frameworks and show its testable implications are substantially weaker than those of an ARUM. We provide two independent conditions for their equivalence: non-overlapping preferences within aggregates and menu-independent aggregation. Simulations show that violating either condition produces meaningful estimation bias when imposing an ARUM.

econ.TH↗

arXiv2025

Tree-Preconditioned Differentiable Optimization and Axioms as Layers

This paper introduces a differentiable framework that embeds the axiomatic structure of Random Utility Models (RUM) directly into deep neural networks. Although projecting empirical choice data onto the RUM polytope is NP-hard in general, we uncover an isomorphism between RUM consistency and flow conservation on the Boolean lattice. Leveraging this combinatorial structure, we derive a novel Tree-Preconditioned Conjugate Gradient solver. By exploiting the spanning tree of the constraint graph, our preconditioner effectively "whitens" the ill-conditioned Hessian spectrum induced by the Interior Point Method barrier, achieving superlinear convergence and scaling to problem sizes previously deemed unsolvable. We further formulate the projection as a differentiable layer via the Implicit Function Theorem, where the exact Jacobian propagates geometric constraints during backpropagation. Empirical results demonstrate that this "Axioms-as-Layers" paradigm eliminates the structural overfitting inherent in penalty-based methods, enabling models that are jointly trainable, provably rational, and capable of generalizing from sparse data regimes where standard approximations fail.

cs.LG↗

arXiv2025

Ergodic Optimization for Open Expanding Multi-valued Topological Dynamical Systems

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to invariant probability measures for such systems can be characterised in terms of maximum time averages on an auxiliary shift space. For all multi-valued expanding systems that are open mappings, we show that every Hölder continuous real-valued function can be modified by a coboundary, of the same Hölder exponent, such that the resulting function is dominated by its maximum ergodic average.

math.DS↗

arXiv2025

Typical Uniqueness in Ergodic Optimization

For ergodic optimization on any topological dynamical system, with real-valued potential function $f$ belonging to any separable Banach space $B$ of continuous functions, we show that the $f$-maximizing measure is typically unique, in the strong sense that a countable collection of hypersurfaces contains the exceptional set of those $f\in B$ with non-unique maximizing measure. This strengthens previous results asserting that the uniqueness set is both residual and prevalent.

math.DS↗