Learning to Bound: A Generative Cramer-Rao Bound

Review Computer Science, Artificial Intelligence

Normalizing Flows: An Introduction and Review of Current Methods

Ivan Kobyzev et al.

Summary: Normalizing Flows are generative models that can produce tractable distributions, enabling efficient and accurate sampling and density evaluation. This survey article aims to provide a coherent and comprehensive review of the literature on the construction and use of Normalizing Flows for distribution learning, offering context and explanation of the models, reviewing current state-of-the-art literature, and identifying open questions and promising future directions.

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE (2021)

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Article Statistics & Probability

ROBUST MULTIVARIATE MEAN ESTIMATION: THE OPTIMALITY OF TRIMMED MEAN

Gabor Lugosi et al.

Summary: The study focuses on estimating the mean of a random vector using i.i.d. observations and adversarial contamination. A multivariate extension of the trimmed-mean estimator is introduced and shown to have optimal performance under minimal conditions.

ANNALS OF STATISTICS (2021)

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Article Statistics & Probability

Estimating covariance and precision matrices along subspaces

Zeljko Kereta et al.

Summary: This study examines the accuracy of estimating the covariance and precision matrix of a D-variate sub-Gaussian distribution along a prescribed subspace or direction using finite sample covariances. The results show that the estimation accuracy depends mainly on the components of the distribution corresponding to desired subspaces or directions. This has implications for problems where the behavior of data along a lower-dimensional space is of specific interest, such as dimension reduction or structured regression problems.

ELECTRONIC JOURNAL OF STATISTICS (2021)

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Article Engineering, Electrical & Electronic