Tratamento de dados faltantes via Misturas de Gaussianas Subtrativas e Distância Euclidiana Esperada

Resumo

The presence of missing data compromises the quality of statistical analyses and predictive models, as conventional imputation methods often distort the original covariance structure. This work proposes the Gaussian Subtractive Mixture Model (GSMM) as a robust alternative for joint density modeling, grounded in the theory of subtractive mixtures via sum-of-squares (SOS) decomposition. GSMM efficiently represents complex and non-convex distributions and is theoretically valid under both Missing at Random (MAR) and Missing Completely at Random (MCAR) mechanisms. Unlike sampling-based approaches, we derive analytical expressions for the model’s conditional expectation and variance, enabling exact closed-form inference. These derivations support the proposed GSMM-EED-kNN imputation framework, which integrates the model’s moments into the Expected Euclidean Distance (EED) metric. This integration allows the k-NN algorithm to select neighbors in a manner that accounts for uncertainty associated with missing data. To ensure feasibility in moderate-dimensional settings, numerical stabilization strategies and cross-term pruning techniques are introduced. Experiments conducted under the MCAR mechanism on real-world datasets demonstrate the superiority of the proposed method in preserving multivariate structure and reducing imputation error compared to traditional models.

Ficha do documento

Tipo

Dissertação

Ano

2026

Instituição

Fundação Getulio Vargas

Fonte

Repositório da FGV

Idioma

Português

Acesso

Acesso aberto

Identificador

oai:repositorio.fgv.br:10438/39122

Temas

Dados

Palavras-chave

Imputação de dadosConjuntos de dados incompletosMisturas Gaussianas SubtrativasExpected Euclidean DistanceData imputatinIncomplete datasetsGaussian subtractive mixturesMatemáticaEstatística matemáticaAprendizado do computadorProcessos gaussianosAnálise de covariância