{
  "abstract": "We study the supervised classification problem for interacting particle systems (IPS) from trajectory observations. The IPS belongs to one of K classes, each characterized by a distinct interaction drift. Given a learning dataset, the goal is then to predict the class label of a newly observed system based on the trajectory of a single particle. This setting raises several statistical challenges. First, the particles within each system interact and are therefore dependent. Second, although the full particle system is Markovian, the trajectory of a single particle is not. To address these difficulties, we exploit the McKean-Vlasov limit of the IPS, which describes the dynamics of a typical particle as the number of particles tends to infinity.\n\nWe propose a plug-in classification procedure based on estimating the interaction drift associated with each class from discretely observed trajectory data. Hence, for each class, we provide a new nonparametric estimator of the drifts by minimizing a ridge-regularized least-squares contrast over a B-spline basis. In particular, our theoretical findings reveal that the convergence rate of the resulting classifier is of order N -1/6+ε for any ε > 0, where N denotes the number of particles in each system. Numerical experiments illustrate the performance of the proposed method and show that it outperforms an end-to-end neural network baseline that does not exploit the underlying particle-system structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35374",
  "author_total": 3,
  "authors": [
    {
      "name": "Christophe Denis"
    },
    {
      "name": "Charlotte Dion-Blanc"
    },
    {
      "name": "Yating Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/990qyx5b0kp16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35374",
  "fulltext_url": null,
  "id": "990qyx5b0kp16",
  "issns": [],
  "landing_url": "https://hal.science/hal-05767719v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-st"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7214710982",
  "pdf_url": "https://hal.science/hal-05767719/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/990qyx5b0kp16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:42Z",
      "native_id": "hal-05767719",
      "source": "hal",
      "url": "https://hal.science/hal-05767719v2"
    },
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35374",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35374"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Who Drives the System? Classifying Mean-Field Particle Systems from Trajectory Data",
  "title_text": "Who Drives the System? Classifying Mean-Field Particle Systems from Trajectory Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/990qyx5b0kp16",
  "venue": "HAL",
  "versions": []
}