Description

Content: Research results of the Instructor over the years, including more recent on Foundations of Data Science for Algorithmic (Black-Box) models, i.e. without model assumptions for the data.  

Topics include: Cluster and Structures detection with the Variance Components Split (VCS) method. Application in the separation of cryptocurrencies from other assets.

EDI-graph: A Tool to determine, via Expected P-values, almost sure identifiability and discrimination of parameters for Black-Box models. Application in the selection of Data-Generating Machines, and in particular Learning Machines.

Residuals Influence Index (RINFIN) is introduced in linear least squares regression of Y on X, with components measuring the local influence of x in the residual and large value flagging a bad leverage case. Large sample properties of RINFIN are presented.   Applications with microarray data and simulated high dimensional data.  

Pathologies of the Bootstrap.

Pathologies of the MLE, with correction using Model Updated MLE (MUMLE) with DECK-principle; D=Data E=Evolves, C=Creates, K=Knowledge. Relation of MUMLE with Wallace’s Minimum Message length method.

Pathologies of the Wasserstein distance in Statistical Inference.

Artificially augmented samples, shrinkage and MSE reduction.  

Additional topics if time permits:

Elegant Nonparametric Estimation of a density and a regression type function, with rates of convergence in Probability. Matching Estimation of a Black-Box parameter, with convergence rates of the estimates using an extension of Wolfowitz’s Minimum Distance Method. Fiducial Approximate Bayesian Computations (F-ABC).  

Prerequisites: 

A course in Mathematical Statistics and Probability, including modes of convergence of random variables/vectors.

References: 

Papers of the instructor and other related material for every topic covered.

Lecture notes：

https://cloud.tsinghua.edu.cn/d/dee3a78487494d9283d1/