Leonardo Santoro

Research

ot Statistical Optimal Transport — Optimal transport (OT) arises as a mean for comparing probability measures. It endows the space of probability measures with a peculiar geometrical structure, paving the way for its application in statistics, machine learning, and applied mathematics.
fda Functional Data Analysis — Functional data analysis (FDA) is a branch of statistics that analyses data providing information about curves, surfaces or anything else varying over a continuum. In its most general form, under an FDA framework, each sample element of functional data is considered to be a random function.

In preparation

  1. On Regularity of Bures-Wasserstein barycentres.
    with Adam Q. Jaffe and Yoav Zemel (2024+)
    In preparation

  2. Isotonic regression for partially ordered data.
    with Victor M. Panaretors (2024+)
    In preparation

  3. Covariance Kernel Embeddings.
    with Kartik G. Waghmare, Victor M. Panaretos (2024+)
    In preparation

  4. Functional Registration for Covariance Flows via Local Variation Measure .
    with Victor M. Panaretos (2024+)
    In preparation

  5. Time Dynamics of Covid-19 and Social Distancing: Amplitude and Phase Variation of a pandemic.
    with Tomas Masak and Francesco Tripoli (2024+)
    In preparation

Preprints

  1. Large Deviations for Bures-Wasserstein Barycenters.
    with Adam Q. Jaffe (2024+)
    [ arXiv ]- submitted to Probability Theory and Related Fields

  2. Functional Vasicek Model .
    with Neda M. Jouzdani, Piotr S. Kokoszka, Hong Miao (2024+)
    [ researchgate ] - under review at Mathematical Finance

  3. Statistical Inference for Bures-Wasserstein Flows.
    with Victor M. Panaretos (2024+)
    [ arXiv ]

  4. Large Sample Theory for Bures-Wasserstein Barycenters.
    with Victor M. Panaretos (2024+)
    [ arXiv ] - under review at Annals of Applied Probability.

Accepted papers

  1. Clinical-Pathological Evaluation and Prognostic Analysis of 228 Merkel Cell Carcinomas .
    with Federica M. Santoro et al (2022)
    Endocrine Pathology [ journal ]

  2. A Karhunen–Loève Theorem for Random Flows in Hilbert spaces .
    with Kartik G. Waghmare, Victor M. Panaretos (2023)
    Electronic Communications in Probability [ journal] [ arXiv ]

  3. Nonparametric Estimation for SDE with Sparsely Sampled Paths: an FDA Perspective .
    with Neda M. Jouzdani, Victor M. Panaretos (2024)
    Stochastic Processes and their Applications [ journal] [ arXiv ]

  4. Widths of crossings in Poisson Boolean percolation .
    with Ioan Manolescu (2024)
    Advances in Applied Probability [ arXiv ] (to appear)