arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.
arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.
arXiv:2609.40156v1 Announce Type: cross Abstract: In many statistical settings, the available data and maintained assumptions do not suffice to uniquely identify the model parameters of interest. In...
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
The paper introduces COFM, a framework for consistent optimal transport flow matching that uses partially input convex neural networks (PICNN) to parameterize the transport potential. By adding a Hamilton‑Jacobi residual to the training objective, COFM enforces dynamical consistency and supports both one‑step transport and multi‑step ODE sampling without costly inner optimization. Experiments on benchmark datasets show that COFM achieves competitive performance while reducing L^2‑UVP by over 2× and cutting computational time by about 9× compared to state‑of‑the‑art models.
arXiv:2603. 15384v2 Announce Type: replace-cross Abstract: We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}.
arXiv:2607. 10740v1 Announce Type: cross Abstract: The analysis of Multivariate Time Series (MTS) plays an important role in a lot of real-world practical applications, but it still remains some challenging problem about capturing multi-granularity structural patterns and suppressing noise appropriately.
arXiv:2603.07014v2 Announce Type: replace-cross Abstract: Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univ...
arXiv:2307. 05213v3 Announce Type: replace-cross Abstract: Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.
arXiv:2608. 28262v1 Announce Type: new Abstract: Entropic optimal transport (EOT) has been shown to offer a computationally tractable approximation to exact optimal transport.
arXiv:2608. 15124v1 Announce Type: new Abstract: In contextual optimization, the decision-maker seeks optimal decisions to minimize a cost function, that varies based on observed features.
The paper introduces HELLO, a hierarchical solver for large‑scale discrete optimal transport that reduces the problem to edge localization guided by dual potentials. HELLO uses a coarse‑to‑fine initialization across a recursive subsampling hierarchy and a refinement step that inserts the largest dual violators until a KKT residual tolerance is met, achieving linear memory usage. Experiments show that HELLO outperforms strong baselines by an order of magnitude in runtime while attaining lower transport objectives, and it scales to over a million samples in high‑dimensional settings, supporting various OT variants.