A brief note on understanding neural networks as Gaussian processes

关于贝叶斯D-最优性准则的简要注记

A brief note on the Bayesian D-optimality criterion

本文针对有限维贝叶斯线性逆问题，简洁推导了D-最优实验设计（最大化期望信息增益）等价于最小化后验协方差对数行列式，并保持通用性以利扩展至无限维。

Brief Report on Estimating Regularized Gaussian Networks from Continuous and Ordinal Data

In recent literature, the Gaussian Graphical model (GGM; Lauritzen, 1996),a network of partial correlation coefficients, has been used to capture potential dynamic relationships between observed variables. The GGM can be estimated using regularization in combination with model selection using the extended Bayesian Information Criterion (Foygel and Drton, 2010). I term this methodology GeLasso, and asses its performance using a plausible psychological network structure with both continuous and ordinal datasets.Simulation results indicate that GeLasso works well as an out-of-the-box method to es…

A few brief notes on the equivalence of two expressions for statistical significance in point source detections

The problem of point source detection in Poisson-limited count maps has been addressed by two recent papers [M. Lampton, ApJ 436, 784 (1994); D. E. Alexandreas, et al., Nucl. Instr. Meth. Phys. Res. A 328, 570 (1993)]. Both papers consider the problem of determining whether there are significantly more counts in a source region than would be expected given the number of counts observed in a background region. The arguments in the two papers are quite different (one takes a Bayesian point of view and the other does not), and the suggested formulas for computing p-values appear to be different a…

关于因果高斯过程经验协方差最小特征值的一个注记

A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processes

本文通过因果分解和基本高斯分布事实，给出了因果高斯过程经验协方差最小特征值的简单证明，并展示了其在向量自回归最小二乘辨识中的性能保证。

A Note on the comparison of Nearest Neighbor Gaussian Process (NNGP) based models

This note is devoted to the comparison between two Nearest-neighbor Gaussian processes (NNGP) based models: the response NNGP model and the latent NNGP model. We exhibit that the comparison based on the Kullback-Leibler divergence (KL-D) from the NNGP based models to their parent GP based model can result in reverse conclusions in different parameter spaces. And we suggest a heuristic explanation on the phenomenon that the latent NNGP model tends to outperform the response NNGP model in approximating their parent GP based model.

Brief Notes on Hard Takeoff, Value Alignment, and Coherent Extrapolated Volition

I make some basic observations about hard takeoff, value alignment, and coherent extrapolated volition, concepts which have been central in analyses of superintelligent AI systems.