arXiv subjects

Yilin Xie

Publications and source records attributed to Yilin Xie.

6 recordsLinked to original sources

arXiv2026

Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-Linear Kernel Approximation

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms employ sampling- or gradient-based methods, which do not provably converge to global optima. This work investigates mixed-integer programming (MIP) as a paradigm for global acquisition function optimization. Specifically, our Piecewise-linear Kernel Mixed Integer Quadratic Programming (PK-MIQP) formulation introduces a piecewise-linear approximation for Gaussian process kernels and admits a corresponding MIQP representation for acquisition functions. The proposed method is applicable to uncertainty-based acquisition functions for any stationary or dot-product kernel. We analyze the theoretical regret bounds of the proposed approximation, and empirically demonstrate the framework on synthetic functions, constrained benchmarks, and a hyperparameter tuning task.

math.OC↗

arXiv2026

BoGrape: Bayesian optimization over graphs with shortest-path encoded

Graph-structured data are central to many scientific and industrial applications where the goal is to optimize expensive black-box objectives defined over graph structures or node configurations -- as seen in molecular design, supply chains, and sensor placement. Bayesian optimization offers a principled approach for such settings, but existing methods largely focus on functions defined over nodes of a fixed graph. Moreover, graph optimization is often approached heuristically, and it remains unclear how to systematically incorporate structural constraints into BO. To address these gaps, we build on shortest-path graph kernels to develop a principled framework for acquisition optimization over unseen graph structures and associated node attributes. Through a novel formulation based on mixed-integer programming, we enable global exploration of the combinatorial domain over graph structures and explicit embedding of problem-specific constraints. We demonstrate that our method, BoGrape, is competitive both on general synthetic benchmarks and representative molecular design case studies with application-specific constraints.

math.OC↗

arXiv2025

The Catechol Benchmark: Time-series Solvent Selection Data for Few-shot Machine Learning

Machine learning has promised to change the landscape of laboratory chemistry, with impressive results in molecular property prediction and reaction retro-synthesis. However, chemical datasets are often inaccessible to the machine learning community as they tend to require cleaning, thorough understanding of the chemistry, or are simply not available. In this paper, we introduce a novel dataset for yield prediction, providing the first-ever transient flow dataset for machine learning benchmarking, covering over 1200 process conditions. While previous datasets focus on discrete parameters, our experimental set-up allow us to sample a large number of continuous process conditions, generating new challenges for machine learning models. We focus on solvent selection, a task that is particularly difficult to model theoretically and therefore ripe for machine learning applications. We showcase benchmarking for regression algorithms, transfer-learning approaches, feature engineering, and active learning, with important applications towards solvent replacement and sustainable manufacturing.

cs.LG↗

arXiv2025

Global optimization of graph acquisition functions for neural architecture search

Graph Bayesian optimization (BO) has shown potential as a powerful and data-efficient tool for neural architecture search (NAS). Most existing graph BO works focus on developing graph surrogates models, i.e., metrics of networks and/or different kernels to quantify the similarity between networks. However, the acquisition optimization, as a discrete optimization task over graph structures, is not well studied due to the complexity of formulating the graph search space and acquisition functions. This paper presents explicit optimization formulations for graph input space including properties such as reachability and shortest paths, which are used later to formulate graph kernels and the acquisition function. We theoretically prove that the proposed encoding is an equivalent representation of the graph space and provide restrictions for the NAS domain with either node or edge labels. Numerical results over several NAS benchmarks show that our method efficiently finds the optimal architecture for most cases, highlighting its efficacy.

cs.LG↗

arXiv2025

Fixers and stabilizers for Ree groups

Let $G$ be a finite permutation group on $Ω,$ a subgroup $K\leqslant G$ is called a fixer if each element in $K$ fixes some element in $Ω.$ In this paper, we characterize fixers $K$ with $|K|\geqslant |G_ω|$ for each primitive action of almost simple group $G$ with socle ${}^2G_2(q).$

math.GR↗

arXiv2024

Intersecting subsets in finite permutation groups

Let $G\leqslant\mathrm{Sym}(Ω)$ be transitive, and let $S$ be an intersecting subset, namely, the ratio $xy^{-1}$ of any elements $x,y\in S$ fixes some point. An EKR-type problem is to characterize transitive groups $G\leqslant\mathrm{Sym}(Ω)$ such that any intersecting set is upper bounded by $|G_ω|$, where $ω\inΩ$. A nice result of Meagher-Spiga-Tiep (2016) tells us that if $G$ is 2-transitive, then indeed $|S|\leqslant|G_ω|$. A natural next step would be to explore intersecting subsets for primitive groups and quasiprimitive groups. Our study in this paper shows that for quasiprimitive permutation groups, the size $|S|$ can be arbitrarily larger than $|G_ω|$. We conjecture that for quasiprimitve groups, the upperbound for $|S|$ is $O(|G_ω||Ω|^{1\over2})$. As a starting point, we prove that ${|S|/(|G_ω||Ω|^{1\over2}})\leqslant{\sqrt2/2}$ for all quasiprimitive actions of the Suzuki groups $G=\mathrm{Sz}(q)$. To show that our conjectured upper bound is tight, we provide examples of groups for which ${|S|/(|G_ω||Ω|^{1\over2}})$ is arbitrarily close to ${\sqrt2/2}$. As far as general transitive groups concerned, infinity families of examples produced show that the ratio ${|S|/(|G_ω||Ω|^{1\over2}})$ can be arbitrarily large.

math.GR↗