The paper introduces a method for optimizing bin boundaries in multi-dimensional discriminants using a Gaussian Mixture Model (GMM), allowing flexible definition of analysis categories. Two optimization strategies—differentiable and Bayesian—are compared in toy binary and three-class setups, with the differentiable approach excelling in multi-dimensional cases. Applied to the FAIR Universe $H ightarrow au au$ dataset, the GMM-based optimization achieves the highest signal significance, and the tools are released as lightweight Python plugins.
arXiv:2405. 15768v2 Announce Type: replace-cross Abstract: In this paper, we address the classification of instances represented by distributions on a vector space rather than single points.
The paper tackles the challenge of predicting multiple high‑dimensional physical fields that must satisfy linear equality constraints, a common scenario in physics‑informed machine learning. It critiques the conventional approach of deducing one field from others, showing its sensitivity to arbitrary choices and its impact on accuracy and uncertainty. To address this, the authors introduce a symmetric framework that first applies a row‑wise PCA to preserve constraints in a latent space, then trains a linearly‑constrained multi‑output Gaussian process using a specially parametrized kernel, and validate the method on population dynamics and CFD problems involving Reynolds stress tensors.
arXiv:2606. 11469v1 Announce Type: cross Abstract: We study the task of density estimation, where we hope to accurately estimate a probability density from $n$ samples.
arXiv:2312. 14889v4 Announce Type: replace-cross Abstract: In this paper we revisit the classical method of partitioning classification and prove novel convergence rates under relaxed conditions, both for observable (non-privatised) and for privatised data.
arXiv:2502. 00168v5 Announce Type: replace-cross Abstract: Supervised dimensionality reduction maps labeled data into a low-dimensional feature space while preserving class separation.
arXiv:2607. 23480v1 Announce Type: new Abstract: Variational autoencoders (VAEs) transform high-dimensional, often noisy data into a compact latent representation, making downstream optimization more tractable.
The paper presents an exact constrained reformulation for direct metric optimization (DMO) in binary imbalanced classification, focusing on precision, recall, and F1-score under three settings: fixing precision to optimize recall, fixing recall to optimize precision, and optimizing F1-score. Unlike prior approaches that use smooth approximations, the authors introduce exact penalty methods to solve these problems efficiently. Experiments on benchmark datasets show that this exact reformulation and optimization (ERO) framework outperforms state‑of‑the‑art methods for all three DMO tasks.
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
The paper introduces an amortized learning framework for selecting bandwidths in kernel density estimation by optimizing the logarithmic score across a distribution of tasks. It uses a truncated-and-renormalized bounded-support formulation and affine standardization to achieve stable learning and transferability across different intervals. Experiments on Gaussian samples, a multi-family benchmark, and randomized Gaussian mixtures demonstrate that the learned selector outperforms traditional methods such as Silverman’s rule, Sheather–Jones, and least‑squares cross‑validation, especially for small or heterogeneous samples.
arXiv:1907.06994v2 Announce Type: replace-cross Abstract: Mixtures of experts (MoE) are conditional mixture models in which both the mixing proportions and the component densities depend on the predi...
arXiv:2608. 11162v1 Announce Type: new Abstract: The Naive Bayes (NB) classifier remains a standard choice for categorical data, yet its widely used smoothing rules, such as Laplace, Lidstone, Krichevsky-Trofimov, and the $m$-estimate, all prescribe a fixed smoothing strength that ignores feature cardinality, sample size, and class imbalance, inducing a non-vanishing bias on modern high-cardinality tabular data.
arXiv:2607. 24921v1 Announce Type: cross Abstract: Providing a practical and hadron-level definition of multiple jet flavors has been a long-standing challenge in collider physics.