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new 3ae22170 Sub html notation for latex notation
3ae22170 is described below
commit 3ae221701adf5da4d5f629e5e1b421ce90b4662e
Author: Lee Rhodes <[email protected]>
AuthorDate: Sat Jan 24 17:26:27 2026 -0800
Sub html notation for latex notation
---
docs/Density/DensitySketch.md | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/docs/Density/DensitySketch.md b/docs/Density/DensitySketch.md
index 357c0480..d3b9a409 100644
--- a/docs/Density/DensitySketch.md
+++ b/docs/Density/DensitySketch.md
@@ -43,12 +43,12 @@ https://proceedings.mlr.press/v99/karnin19a/karnin19a.pdf
<a id="highlights"></a>
#### Key Highlights:
* **New Complexity Measure:** The authors define "class discrepancy" as a way
to characterize the coreset complexity of different function families, similar
to how Rademacher complexity is used for generalization.
-* **Improved Coreset Sizes:** They prove the existence of
$\epsilon$-approximation coresets of size $O(\sqrt{d}/\epsilon)$ for several
common machine learning problems, including:
+* **Improved Coreset Sizes:** They prove the existence of
ε-approximation coresets of size *O(√d/ε)* for several
common machine learning problems, including:
* Logistic regression
* Sigmoid activation loss
* Matrix covariance
* Kernel density estimation
-* **Gaussian Kernel Resolution:** The paper resolves a long-standing open
problem by matching the lower bound for the coreset complexity of Gaussian
kernel density estimation at $O(\sqrt{d}/\epsilon)$.
+* **Gaussian Kernel Resolution:** The paper resolves a long-standing open
problem by matching the lower bound for the coreset complexity of Gaussian
kernel density estimation at *O(√d/ε)*.
* **Streaming Algorithms:** It introduces an exponential improvement to the
"merge-and-reduce" trick, leading to better streaming sketches for any problem
with low discrepancy.
* **Deterministic Algorithm:** The authors provide a simple, deterministic
algorithm for finding low-discrepancy sequences and coresets for any positive
semi-definite kernel.
@@ -57,7 +57,7 @@ https://proceedings.mlr.press/v99/karnin19a/karnin19a.pdf
The findings allow for significantly faster optimization in large-scale
machine learning. By reducing a massive dataset into a much smaller coreset,
researchers can perform complex calculations (like training a logistic
regression model) with a fraction of the computational cost while maintaining a
high level of accuracy.
<a id="inspiration"></a>
-### Our implementations was inspired by the following implementation, example,
and tests by Edo Liberty:
+### Our implementations was inspired by the following code, example, and tests
by Edo Liberty:
* **Code:**
https://github.com/edoliberty/streaming-quantiles/blob/f688c8161a25582457b0a09deb4630a81406293b/gde.py
* **Example**
https://github.com/edoliberty/streaming-quantiles/blob/f688c8161a25582457b0a09deb4630a81406293b/gde_example_usage.ipynb
* **Tests**
https://github.com/edoliberty/streaming-quantiles/blob/f688c8161a25582457b0a09deb4630a81406293b/gde_test.py
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