Last updated: 2021-09-14

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Overview

Explore functional/smoothed matrix factorization(MF): consider the MF problem \(Y = LF+E\), and assume \(L\) is sparse and \(F\) has smooth rows.

Main Results

EBMPMF

  1. Smoothed EBMF: Wavelet Smoothing + EBMF

  2. Smoothed PMD: Wavelet Smoothing + PMD, compared with 1.

  3. Smoothed EBMF for Poisson data: Wavelet Smoothing + Transformation + EBMF

  4. EBMPMF, EBMPMF2: EBMPMF simple examples.

  5. Smoothed vs Non-smoothed: illustrate how smoothing could help when factors are indeed smooth.

  6. Sparse NMF methods: Try some esixting sparse NMF methods.

  7. VST NMF: does VST work well for NMF?

  8. EBMPMF and nugget effect

  9. Apply stm to gene splicing: 1. looked at 3 genes and compared 6 methods. 2. large reads at the beginning/ending of exons may due to splitting reads.

  10. 5 low expressed genes with 3 topics and structure plot: compare NMF and stm-smashgen.

  11. The other 16 genes with 3 topics and structure plot

  12. Initial analysis on luis data

PTF

  1. Trend Filtering
  2. Trend filtering and dynamic linear model
  3. Examples
  4. Poisson Trend Filtering: first try of the ptf method, implemented optimization-based method to see if it works.
  5. Basis selection in TF

EBPM

  1. Empirical Bayes Poisson Mean large scale
  2. Compare ebpm estimate from different scales
  3. EBPM scale invariant version: when \(s\) is large, little shrinkage compared with MLE.
  4. EBPM mixture of two gamma distributions: fix prior grid at truth.
  5. EBPM mixture of two gamma distributions: closer priors make it harder to shrink.
  6. EBPM mixture of two gamma distributions: same shape diff rate in priors.

Mis

  1. Functional PCA
  2. Summary of meeting on Aug 02
  3. Genome Annotation
  4. EM algorithm for Topic Model
  5. Analysis on Xing’s method
  6. command line and github tips
  7. Principal Curves
  8. Outlier in wavelet smoothing
  9. Robust smashgen

Dynamics

  1. normal-gamma autoregressive (NGAR) process
  2. Dynamic spike and slab(dss) process prior

Ref

  1. Variational EM ppt, Variational EM paper
  2. A Comparative Simulation Study of Wavelet Shrinkage Estimators for Poisson Counts
  3. Multiscale Topic Tomography
  4. Bayesian Multiscale Models for Poisson Processes