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Measuring the differenceDifference between probability distributionsDistribution is a fundamental problem with numerous applications in machine learningLearningmachine learning and statistics. This chapter focuses on Maximum Mean DiscrepancyMaximummaximum mean discrepancy (MMD) (MMD), a powerful kernel-based metric for comparing distributions by embeddingEmbedembedding data intoReproducing kernel Hilbert space aKernelreproducing kernel Hilbert space (RKHS) Reproducing Kernel Hilbert SpaceHilbertreproducing kernel Hilbert space (RKHS) (RKHS) and evaluating the distance between their mean embeddings. MMDMaximummaximum mean discrepancy (MMD) effectively captures differencesDifference across all moments of distributionsDistribution while relying only on the differencesDifference of first momentsReproducing kernel Hilbert space in Kernelreproducing kernel Hilbert space (RKHS) RKHSHilbertreproducing kernel Hilbert space (RKHS), offering both computational tractability and theoretical guarantees. Generative Moment Matching NetworksGenerativegenerative moment matching network (GMMN) (GMMNs)Momentgenerative moment matching network (GMMN), proposed in 2015, leverage MMDMaximummaximum mean discrepancy (MMD) as a training loss to align the generated data distributionDistribution with the training data. This chapter introduces GMMNsGenerativegenerative moment matching network (GMMN) as Momentgenerative moment matching network (GMMN) one of the earliest neural generative modelsGenerativegenerative model trained without likelihoodLikelihood. Developed shortly afterGenerativegenerative adversarial network (GAN) GANsAdversarialgenerative adversarial network (GAN), GMMNsGenerativegenerative moment matching network (GMMN) offeredMomentgenerative moment matching network (GMMN) a non-adversarial, kernel-based approach to distributionDistribution matching. While Momentgenerative moment matching network (GMMN) GMMNs Generativegenerative moment matching network (GMMN) are rarely used today, MMD remains widely useful in modern machine learningLearningmachine learning for tasksTask such as domain adaptation and statisticalStatistical testing. This chapter further introduces some extensionsExtension ofMomentgenerative moment matching network (GMMN) GMMNGenerativegenerative moment matching network (GMMN). ExtensionsExtension such as ConditionalMomentgenerative moment matching network (GMMN) GMMNsGenerativegenerative moment matching network (GMMN) enable generation conditioned on specific attributes or classesClass. Additionally, methods for adversarially optimizing kernel choice to enhanceMomentgenerative moment matching network (GMMN) GMMNGenerativegenerative moment matching network (GMMN) performance, exemplified by MMDGenerativegenerative adversarial network (GAN) GANsAdversarialgenerative adversarial network (GAN), are presented.

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Generative Moment Matching Networks Structure of a chemical compound showing a central six-membered ring with alternating double bonds, connected to a five-membered ring containing two nitrogen atoms. The five-membered ring is attached to a side chain with a nitrogen atom bonded to a carbon atom, which is further connected to a benzene ring. This structure represents a complex molecule with multiple rings and nitrogen atoms, indicating it may be a biologically active compound or pharmaceutical agent.

  • 章节

  • 发表日期：

    2026年

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  • Benyamin Ghojogh,
  • Ali Ghodsi

摘要

Measuring the differenceDifference between probability distributionsDistribution is a fundamental problem with numerous applications in machine learningLearningmachine learning and statistics. This chapter focuses on Maximum Mean DiscrepancyMaximummaximum mean discrepancy (MMD) (MMD), a powerful kernel-based metric for comparing distributions by embeddingEmbedembedding data intoReproducing kernel Hilbert space aKernelreproducing kernel Hilbert space (RKHS) Reproducing Kernel Hilbert SpaceHilbertreproducing kernel Hilbert space (RKHS) (RKHS) and evaluating the distance between their mean embeddings. MMDMaximummaximum mean discrepancy (MMD) effectively captures differencesDifference across all moments of distributionsDistribution while relying only on the differencesDifference of first momentsReproducing kernel Hilbert space in Kernelreproducing kernel Hilbert space (RKHS) RKHSHilbertreproducing kernel Hilbert space (RKHS), offering both computational tractability and theoretical guarantees. Generative Moment Matching NetworksGenerativegenerative moment matching network (GMMN) (GMMNs)Momentgenerative moment matching network (GMMN), proposed in 2015, leverage MMDMaximummaximum mean discrepancy (MMD) as a training loss to align the generated data distributionDistribution with the training data. This chapter introduces GMMNsGenerativegenerative moment matching network (GMMN) as Momentgenerative moment matching network (GMMN) one of the earliest neural generative modelsGenerativegenerative model trained without likelihoodLikelihood. Developed shortly afterGenerativegenerative adversarial network (GAN) GANsAdversarialgenerative adversarial network (GAN), GMMNsGenerativegenerative moment matching network (GMMN) offeredMomentgenerative moment matching network (GMMN) a non-adversarial, kernel-based approach to distributionDistribution matching. While Momentgenerative moment matching network (GMMN) GMMNs Generativegenerative moment matching network (GMMN) are rarely used today, MMD remains widely useful in modern machine learningLearningmachine learning for tasksTask such as domain adaptation and statisticalStatistical testing. This chapter further introduces some extensionsExtension ofMomentgenerative moment matching network (GMMN) GMMNGenerativegenerative moment matching network (GMMN). ExtensionsExtension such as ConditionalMomentgenerative moment matching network (GMMN) GMMNsGenerativegenerative moment matching network (GMMN) enable generation conditioned on specific attributes or classesClass. Additionally, methods for adversarially optimizing kernel choice to enhanceMomentgenerative moment matching network (GMMN) GMMNGenerativegenerative moment matching network (GMMN) performance, exemplified by MMDGenerativegenerative adversarial network (GAN) GANsAdversarialgenerative adversarial network (GAN), are presented.