Mathematical Characterization of Better-than-Random Multiclass Models

Authors: Sébastien Foulle

TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We extend these results to any number of classes: for a target variable with m 2 classes, we show that a model does better than chance if and only if the entries of the confusion matrix verify m(m 1) homogeneous polynomial inequalities of degree 2, which can be expressed using generalized likelihood ratios. We also obtain a more theoretical formulation: a model does better than chance if and only if it is a maximum likelihood estimator of the target variable. Our main objective is to obtain a mathematical characterization of multiclass models that do better than chance
Researcher Affiliation Industry Sébastien Foulle EMAIL Marketing, Customer Experience and Institutional Relations Department Abeille Assurances 80 Avenue de l Europe 92270 Bois-Colombes, France
Pseudocode No The paper describes mathematical characterizations, theorems, definitions, and proofs. It does not contain any structured pseudocode or algorithm blocks.
Open Source Code No The paper does not provide any specific links to source code repositories, nor does it explicitly state that code for the described methodology is released or available in supplementary materials.
Open Datasets No The paper uses illustrative confusion matrices and hypothetical data sets (e.g., 'Example 2. The confusion matrix B = ...', 'Example 3. Let D = ...') to demonstrate theoretical concepts. It does not refer to or provide access information for any publicly available or open datasets used in empirical experiments.
Dataset Splits No The paper does not describe any empirical experiments using datasets, and therefore does not provide specific information about dataset splits like training, validation, or test sets.
Hardware Specification No The paper focuses on mathematical characterization and theoretical results. It does not describe any experiments that would require specific hardware, and thus no hardware specifications are mentioned.
Software Dependencies No The paper is theoretical in nature and does not describe experimental implementations. Therefore, it does not provide details on specific ancillary software dependencies with version numbers.
Experiment Setup No The paper presents a mathematical characterization of models and theoretical results. It does not include an experimental section with specific setup details such as hyperparameters, training configurations, or system-level settings.