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You requested: run the method on SRBCT normalized expression data under (A) the paper’s 2308-gene quality-filtered subset vs (B) a larger unfiltered set “available upstream”, then quantify permutation-based FP counts and misclassification variance across many CV splits, to falsify the hypothesis that shrinkage alone explains “tiny FPs”.
Core evidence basis (what the “shrinkage” method is)
A shrinkage-based penalized regression framework for differential expression detection + classification is described by Baolin et al., deriving penalized F-statistics under an L1 (LASSO-like) penalty, connecting shrinkage to nearest shrunken centroids (PAM) and using cross-validation and permutation-based FDR/false positive estimation on SRBCT (2308 genes; 4 classes).
Multiple gene-selection papers on SRBCT also emphasize that reported near-perfect accuracies can be sensitive to evaluation design (e.g., LOOCV usage, filtering/search choices) and that small-sample/high-dimensional settings can yield optimistic estimates without external validation.
A. Data conditions you must implement (critical, falsifiable contrast)
Condition A (filtered subset): Use exactly the method paper’s 2308-gene quality-filtered normalized expression matrix for SRBCT (4 classes, with normalized expression available in the SRBCT supplement/repository described in the shrinkage method paper).
Condition B (unfiltered/larger upstream set): Use the larger upstream normalized SRBCT expression matrix (the “unfiltered set as available upstream”). Because your prompt does not provide the exact upstream access path or the gene count, you must treat this as an implementation-dependent input and document: (i) how the upstream matrix was generated, (ii) whether the same normalization/scaling is used, and (iii) whether any additional gene filtering occurs.
For both A and B, ensure identical label encoding, identical CV split strategy, and identical standardization procedure.
If the method paper’s pipeline uses a particular scaling before penalized regression, apply it identically to both subsets; otherwise you confound “gene-set size” with “scaling differences”. (The shrinkage paper stresses scaling/standardization for the method’s performance.)
Use the same hyperparameter search space and tuning rule across A and B.
B. The statistical test you need to run (quantify tiny FPs in a falsifiable way)
Hypothesis to falsify
H0: the observed “tiny false positives (FPs)” are explained by shrinkage alone (i.e., independent of whether you include only the 2308 filtered genes vs a larger unfiltered gene universe).
What to measure (two layers)
Permutation-based FP count distribution under each condition (A vs B):
Generate many permutations of class labels within each CV training fold.
For each permuted training fold, fit the shrinkage model and compute the paper’s penalized F-statistics and the corresponding FP / FDR estimate as implemented in that framework.
Classification misclassification variance across many CV splits:
Use the shrinkage model’s classification rule (nearest shrunken centroid relationship is discussed in the paper).
Across repeated random CV splits (or repeated k-fold partitions), record the misclassification count/rate on held-out folds.
Compute variance (and optionally CV of misclassification) for each condition and relate it to FP behavior.
C. Experimental protocol (implementation checklist; no placeholders)
Step-by-step
Data ingest & preprocessing
Load SRBCT normalized expression for gene sets A and B.
Verify gene ordering matches across downstream computations; explicitly store gene IDs.
Repeated CV design
Choose k-fold (or repeated splits) such that you can create many independent CV partitions; your prompt asks for “many CV splits”.
For each split: fit the model on training folds only.
Fit shrinkage model with tuning inside each split
Tune the shrinkage parameter using the paper’s cross-validation approach (keep tuning consistent between A and B).
Record selected penalty parameters for every split (this is essential to interpret “shrinkage alone”).
Permutation-based FP evaluation
For each CV training fold, run B label permutations (large enough for stable FP tails).
For each permutation, compute the penalized F-statistics and the paper’s permutation-based FP/FDR criterion.
Aggregate FP counts across permutations to get a distribution per CV split, not just a single number.
Classification misclassification variance
Use the fitted shrinkage model to classify held-out fold samples.
Record misclassification count/rate; then compute variance across CV splits.
Core falsification analysis
Primary test: Compare the permutation FP distributions between Condition A and Condition B using an effect size + uncertainty (e.g., median FP, tail probability, and split-to-split variance).
Decision rule to falsify H0: If FP counts (especially in upper tail) are materially larger under the larger unfiltered gene set, then “shrinkage alone” is insufficient to explain tiny FPs.
Secondary test: If FP behavior changes in tandem with misclassification variance, that suggests evaluation sensitivity or gene-universe effects, not just shrinkage stability.
D. What outcomes would falsify the “shrinkage alone” explanation?
Outcome 1 (FP inflation with unfiltered genes): FP counts (especially upper tail) are consistently higher in Condition B than in A, with non-overlapping uncertainty.
Outcome 2 (changed penalty selection): The tuned shrinkage parameters differ substantially between A and B across splits, implying the model is compensating for altered gene-universe conditions; that contradicts “shrinkage alone” as a stable explanation.
Outcome 3 (misclassification instability): misclassification variance increases in Condition B, indicating that gene-universe expansion changes generalization behavior.
Critical blind spot to guard against
If Condition B includes genes with different preprocessing/measurement noise, then “shrinkage alone” cannot be cleanly separated from “which gene universe is being shrunk.” This is exactly why the permutation-FP distribution must be computed within each fold and compared under identical tuning rules. The shrinkage framework explicitly motivates permutation-based false-positive estimation and tuning inside CV.
E. Minimal metrics table (what you should output)
Condition
FP count summary (per split)
Misclassification (variance across splits)
Tuned penalty distribution
A: 2308-filtered
median/mean, 95% interval, upper-tail prob
Var(misclass rate), IQR
median, IQR of tuned λ/ D
B: unfiltered upstream
median/mean, 95% interval, upper-tail prob
Var(misclass rate), IQR
median, IQR of tuned λ/ D
F. Why this experiment is scientifically capable of falsification
Shrinkage methods can reduce variance and stabilize selection, but your falsification strategy must test whether the “tiny FP” phenomenon persists when the gene universe changes while keeping the method + tuning + evaluation framework fixed. The penalized shrinkage framework explicitly uses permutation-based false positive estimation tied to the penalized statistics and tuning, making FP behavior empirically testable under your A vs B contrast.
Run it locally (or with BGPT’s agent) to get the falsification results
I can’t execute the computation here because the prompt does not include the actual SRBCT “unfiltered upstream” matrix (gene list + normalized values) nor the exact upstream preprocessing steps. The fastest path is to run BGPT’s AI Scientist agent once you upload the upstream normalized gene-expression matrix (or point BGPT to it), plus the 2308-filtered matrix.
It loads SRBCT filtered and upstream normalized gene matrices, runs repeated CV with tuned shrinkage, computes permutation-based false-positive distributions and misclassification variance, then compares A vs B tails.
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