ramhiser / paper-hdrda Goto Github PK

• Focus on general high-dimensional data
• See Jieping Ye's papers and follow suit

• Add rda from the klaR package
• Drop Pang's classifier?
• Add kNN and SVM?

Currently, the discussion is weak. Rewrite it. Items that should be discussed:

• Shrinkage includes several methods with the appropriate choice of alpha and gamma
• We allow the differences in covariance matrices to relax the common linear assumptions employed for high-dimensional data (i.e., LDA)
• We do not require the restrictive assumption that features are uncorrelated/independent

The CSDA reviewers made a few comments that lead me to believe the intro should be more clear. With that in mind, we need to finetune the intro and ensure we are communicating the following:

• We modify RDA to gain interpretability
• HDRDA inherently yields dimension reduction
• HDRDA is much faster than RDA
  • Mention savings in terms of Big Oh
  • Timing comparison (from #26)
• HDRDA should be used instead of RDA (for p > N?)
  • Add RDA to classification study?
• HDRDA is competitive in terms of classification performance

Previously, I coded up a timing comparison, comparing simdiag::hdrda vs klaR::rda. We'll bring that back with a more exhaustive comparison and also include the PenalizedLDA::PenalizedLDA from Witten and Tibshirani (2011).

I'll also add the diagonal classifiers but will likely forego including them in the paper. We will need to remark that loosely justifies this. Frankly, the diagonal classifiers will be much faster because they are simpler, but at the cost of classification accuracy.

In the Witten and Tibshirani (2011) paper, they also perform a timing comparison with 4 populations with varying feature dimensions:

• p=20
• p=200
• p=2000
• p=20000

They perform the timing comparison over 25 repetitions and report the mean and standard deviation of the runtimes. We'll do something similar but with a lot more repetitions.

The cover letter to AoAS needs to be updated for CSDA. Straightforward enough.

These two paragraphs immediately follow Proposition 1 and are found on pages 9-10 of AoAS submission.

• Make more concise
• Incorporate computational complexity
• (Optional) Write algorithm for training/model selection (JCGS papers do this)

Although I find classification studies with simulated data largely pointless, I'd rather add roughly two simulation configurations to ensure the paper is published. If a referee desires more than two, so be it. But two should be good enough.

Our proposed classifier clearly does not generalize the RDA classifier but instead improves and modernizes it for high-dimensional data. With this in mind, we need a slick name. The title of the paper should reflect the name somehow.

Mrs. Young is proofreading the paper. After she's finished, apply her edits.

After Mrs. Young proofreads the paper and I've applied the edits, the paper needs to be transitioned to Elsevier's LaTeX template. Instructions are here.

• JAR

  uStudio, Inc.
  1806 Rio Grande St
  Austin, TX 78701

• CKS

  Myeloma Institute
  University of Arkansas for Medical Sciences
  4301 West Markham # 816
  Little Rock, Arkansas 72205

• PDY

  Department of Management and Information Systems
  Baylor University
  One Bear Place #98005
  Waco, Texas 76798-7140

• DMY

  Department of Statistical Science
  Baylor University
  One Bear Place #97140
  Waco, Texas 76798-7140

Examples:

• Precision
• Recall
• F-score
• AUC
• ROC

Summarize in paper. How?

Possibilities:

• Table
• 2D Heatmap

The \oplus notation used in the paper is less conventional and may be a bit confusing. Instead, we'll switch to 2x2 block-diagonal matrices.

For example, in equation 10, we use the notation W_k \oplus \gamma I_{p-q}. Instead, we should replace this with:

\begin{bmatrix}
W_k & 0 \\
0 & \gamma I_{p-q}
\end{bmatrix}

The results will be more intelligible. It will take a bit of effort though to ensure that no orphan notation is introduced.

After #21 and #19 are complete, submit the paper to CSDA. Instructions on CSDA's site.

After the regularization literature review in the introduction, we begin with "Here, we propose the high-dimensional RDA classifier..." I am now of the opinion that this is not the route we want to go. It does not reference to Friedman's (1989) RDA classifier, and at least one reviewer was critical of this.

The wording then needs to change but still maintain a strong presence. Here are working blurbs to add to paragraph or to replace original sentences.

(After brief discussion of Friedman's classifier) We reparameterize Friedman's (1989) RDA classifier so that the resulting covariance-matrix estimator is a convex combination of ... Our parameterization improves the interpretation of the contribution of each observation weighted by the pooling parameter. We show that our parameterization results yields an equivalent, dual decision function that can be efficiently calculated for p >> N.

The idea here is to demonstrate the effect of the tuning parameter lambda. One emphasis in the paper that we are leaning towards is stressing the benefits of relaxing the linearity assumptions of the LDA classifier.

The figure should display the following:

• Contours for approximately 4-5 populations
• The covariance matrices should be obviously different when lamdba = 0
• The contours should be identical for lambda = 1
• Display 5 subfigures each for lamdba = 0, 0.25, 0.5, 0.75, 1.

When lambda is introduced in the paper, add one sentence that says we demonstrate the effect of lambda in the figure.

Mention open-source, reproducible, etc.

Use the rda function from the klaR package as baseline

If effective, demonstrate this and original approaches in paper?

Journal: Journal of Statistical Computation and Simulation

Instructions for authors.

I am not happy with the current abstract. It does not sell the paper well enough.

After Mrs. Young proofreads the paper and I've applied the edits, upload the paper to arXiv before submitting paper to CSDA.

We have stressed that our proposed classifier is much faster. We need to add more details to back up our claim.

• Provide computational complexity for proposed classifier
• Contrast with computational complexity of the original RDA classifier