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In many practical and theoretical contexts, the exact value of a definite integral may be inaccessible. This limitation typically arises when the antiderivative of a function is either unknown or cannot be expressed in a closed mathematical form. Alternatively, it can occur when a function is defined not by a formula but by a finite set of empirical data points, such as those collected during experiments. In these cases, approximate integration techniques provide a valuable solution.One of the...
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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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Unificación de la Selección de Estadísticas Resumen para el Cálculo Bayesiano Aproximado

Till Hoffmann1, Jukka-Pekka Onnela1

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Minimizar la entropía posterior esperada (EPE) ofrece un principio unificador para extraer estadísticas resumen informativas de grandes conjuntos de datos. Este enfoque permite una inferencia eficiente sin verosimilitud, logrando resultados competitivos o superiores a los métodos tradicionales.

Palabras clave:
Estimación de Densidad CondicionalCompresión de DatosTeoría de la InformaciónInferencia sin VerosimilitudInferencia Basada en Simulación

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Área de la Ciencia:

  • Estadística Computacional
  • Inferencia Estadística
  • Aprendizaje Automático

Sus antecedentes:

  • La resumen eficiente de grandes conjuntos de datos es crucial para la inferencia sin verosimilitud.
  • Los algoritmos de reducción de dimensionalidad requieren un análisis cuidadoso de las estadísticas resumen.

Objetivo del estudio:

  • Desarrollar un principio unificador para estadísticas resumen informativas.
  • Proponer un método práctico para aprender automáticamente estadísticas de alta fidelidad.

Principales métodos:

  • Caracterización de tres clases de estadísticas resumen.
  • Demostración de la minimización de la entropía posterior esperada (EPE) como principio unificador.
  • Desarrollo de un método práctico utilizando la estimación de densidad condicional.

Principales resultados:

  • Minimizar la EPE engloba muchos métodos existentes de estadísticas resumen.
  • El método propuesto se evaluó en diversos modelos, incluidos modelos de genética de poblaciones y de redes.
  • Las estadísticas que minimizan la EPE lograron una inferencia competitiva o superior a los enfoques basados en la verosimilitud.

Conclusiones:

  • Minimizar la EPE proporciona un marco potente y general para estadísticas resumen informativas.
  • El método desarrollado permite el aprendizaje automático de estadísticas de alta fidelidad.
  • Este enfoque mejora la eficiencia y la precisión de la inferencia sin verosimilitud.