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new 49ea5584 Fix numbered items
49ea5584 is described below
commit 49ea5584f58de70232dfec257bcb4728909405ae
Author: Lee Rhodes <[email protected]>
AuthorDate: Sat Jan 24 15:19:42 2026 -0800
Fix numbered items
---
docs/Sampling/EB-PPS_SamplingSketches.md | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/docs/Sampling/EB-PPS_SamplingSketches.md
b/docs/Sampling/EB-PPS_SamplingSketches.md
index 14775e7a..7e3e491d 100644
--- a/docs/Sampling/EB-PPS_SamplingSketches.md
+++ b/docs/Sampling/EB-PPS_SamplingSketches.md
@@ -152,7 +152,7 @@ The algorithm's efficiency stems from how it handles
incoming items regardless o
Today, strict adherence to the Probability Proportional to Size (PPS)
property—as prioritized by schemes like EB-PPS—is considered vital for
classifier performance in the following high-stakes scenarios:
<a id="training-classifiers"></a>
-#### 1. Training Bayes-Optimal Classifiers
+#### 1: Training Bayes-Optimal Classifiers
For a classifier to be truly "optimal," it must minimize expected risk based
on the data's true underlying distribution.
@@ -160,21 +160,21 @@ For a classifier to be truly "optimal," it must minimize
expected risk based on
* **Direct Training:** When PPS is strictly maintained, you can use standard
training algorithms (optimized for 0-1 loss) to produce Bayes-optimal decision
boundaries. If PPS is violated (as often happens with fixed-size schemes like
VarOpt), the resulting decision boundary shifts, leading to suboptimal
performance unless complex, custom loss-correction is applied.
<a id="class-imbalance"></a>
-#### 2. Handling Severe Class Imbalance
+#### 2: Handling Severe Class Imbalance
In datasets where the minority class is extremely rare (e.g., fraud detection
or rare disease diagnosis), small errors in inclusion probability can cause the
classifier to ignore critical but rare signals.
* **Avoiding "Majority Bias":** Inaccurate sampling often leads a model to
simply predict the majority class for all instances to achieve high "accuracy"
while failing at its actual task.
* **Exact Representation:** Strict PPS ensures that the weight assigned to
these rare cases is exactly preserved in the sample, forcing the model to learn
the minority class features correctly.
<a id="probability-calibration"></a>
-#### 3. Maintaining Probability Calibration
+#### 3: Maintaining Probability Calibration
Calibration refers to the model's ability to provide accurate probability
estimates (e.g., "there is a 70% chance of malignancy") rather than just a 0/1
label.
* **Clinical Utility:** In healthcare, over- or under-estimating risks can
lead to dangerous overtreatment or missed diagnoses.
* **PPS Advantage:** Because EB-PPS does not distort the inclusion
probabilities to force a fixed sample size, the resulting model is inherently
better calibrated. The probabilities it outputs reflect the true risk levels of
the original population.
<a id="legal-ethical-fairness"></a>
-#### 4. Legal and Ethical Fairness
+#### 4: Legal and Ethical Fairness
Today, algorithmic fairness is a major regulatory focus. Biased sampling is a
primary source of "AI bias" that leads to prejudiced outcomes in lending,
hiring, or healthcare.
* **Predictive Parity:** Strict PPS allows for the construction of fair
Bayes-optimal classifiers that satisfy "predictive parity," ensuring that the
model's error rates and accuracy are consistent across different protected
groups (e.g., race, gender).
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