Simplify quickstart tutorial by removing redundant diagnostic sections (#328)

Summary:
## Simplify quickstart documentation

- [x] Remove "Diagnostics for comparing distributions" section (cells 29-30)
- [x] Update "Distribution diagnostics (EMD/CVMD/KS)" section title to include "KLD" (cell 27)
- [x] Remove "Compare ASMD (Absolute Standardized Mean Difference)" section (cells 67-68) from "Comparing Adjustment Methods"
- [x] Fix capitalization of KLD to match other diagnostic abbreviations (EMD, CVMD, KS)
- [x] Add KLD description to distribution diagnostics section
- [x] Add kld() code example to distribution diagnostics section
- [x] Include note about raw covariates applying to all diagnostics
- [x] Clarify KLD is a divergence measure (not symmetric distance)
- [x] Remove trailing empty strings from cells
- [x] Run code review and address all feedback
- [x] Run security checks
- [x] Reply to all review comments

Successfully simplified the quickstart tutorial by consolidating distribution diagnostics and addressing all review feedback:

### Changes Made:
1. **Removed redundant sections** (4 cells removed):
   - "Diagnostics for comparing distributions" section (cells 29-30)
   - "Compare ASMD" section from "Comparing Adjustment Methods" (cells 67-68)

2. **Enhanced distribution diagnostics section**:
   - Added KLD to section header: "Distribution diagnostics (KLD/EMD/CVMD/KS)"
   - Added KLD description with clarification that it's a divergence measure (non-symmetric)
   - Added `print(sample_with_target.covars().kld().T)` code example
   - Moved note about raw covariates to separate paragraph applying to all diagnostics
   - Removed trailing empty strings for cleaner notebook formatting

3. **Code review feedback addressed**:
   - Separated note about raw covariates from KLD bullet to apply to all metrics
   - Clarified KLD is a divergence measure vs distance metric
   - Cleaned up formatting issues

**Result**: Cleaner tutorial flow with 4 cells removed (75 → 71), all essential information preserved and better organized.

<details>

<summary>Original prompt</summary>

>
> ----
>
> *This section details on the original issue you should resolve*
>
> <issue_title>[BUG] Simplify quick start further</issue_title>
> <issue_description>Fix this:
> https://import-balance.org/docs/tutorials/quickstart/
>
> Remove the section
> 'Diagnostics for comparing distributions'
> But add the the previous section kld:
> "Distribution diagnostics (EMD/CVMD/KS)"
>
> And remove the section
> "Compare ASMD (Absolute Standardized Mean Difference)"
> From the section "Comparing Adjustment Methods"
> </issue_description>
>
> ## Comments on the Issue (you are copilot in this section)
>
> <comments>
> </comments>
>

</details>

- Fixes #327

 ---

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Pull Request resolved: #328

Differential Revision: D92658641

Pulled By: talgalili

fbshipit-source-id: 60e8e34358d1cbb940a7cb3af8d6b225a2e36226

Author: Copilot

tutorials/balance_quickstart.ipynb

@@ -419,19 +419,23 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Distribution diagnostics (EMD/CVMD/KS)\n",
+    "## Distribution diagnostics (KLD/EMD/CVMD/KS)\n",
     "\n",
-    "Balance also exposes distributional distance diagnostics for covariates.\n",
+    "Balance also exposes distribution diagnostics for covariates.\n",
     "These look beyond mean differences and compare the **full distributions** of covariates in the weighted sample vs. the target.\n",
     "\n",
+    "- **KLD (Kullback-Leibler divergence)** measures the relative entropy between two probability distributions (note: this is a divergence measure, not a symmetric distance).\n",
+    "  (See: https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence)\n",
     "- **EMD (Earth Mover's Distance)** measures the minimum \"cost\" to transform one distribution into another.\n",
     "  (See: https://en.wikipedia.org/wiki/Earth_mover%27s_distance)\n",
     "- **CVMD (Cram\u00e9r\u2013von Mises distance)** measures the integrated squared difference between the empirical CDFs.\n",
     "  (See: https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion)\n",
     "- **KS (Kolmogorov\u2013Smirnov distance)** measures the maximum absolute difference between the empirical CDFs.\n",
     "  (See: https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test)\n",
     "\n",
-    "These diagnostics complement **ASMD**, which only compares means. Use EMD/CVMD/KS when you want to check whether weighting aligns the *shape* of covariate distributions (not just their means).\n"
+    "Note: Distribution diagnostics operate on the raw covariates (with NA indicators), rather than the model matrix, so categorical variables stay intact.\n",
+    "\n",
+    "These diagnostics complement **ASMD**, which only compares means. Use these metrics when you want to check whether weighting aligns the *shape* of covariate distributions (not just their means).\n"
    ]
   },
   {
@@ -440,30 +444,12 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "print(sample_with_target.covars().kld().T)\n",
     "print(sample_with_target.covars().emd().T)\n",
     "print(sample_with_target.covars().cvmd().T)\n",
     "print(sample_with_target.covars().ks().T)\n"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Diagnostics for comparing distributions\n",
-    "\n",
-    "Distribution diagnostics operate on the raw covariates (with NA indicators), rather than the model matrix, so categorical variables stay intact.\n",
-    "We can use KLD (Kullback-Leibler divergence) to compare distributions:\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(sample_with_target.covars().kld().T)"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -947,34 +933,6 @@
     "print(adjusted_hgb_mm.summary())"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Compare ASMD (Absolute Standardized Mean Difference)\n",
-    "\n",
-    "Let's compare the covariate balance achieved by each method using ASMD tables:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(\"\\n=== Default Method (Logistic Regression) ASMD ===\")\n",
-    "print(adjusted_default.covars().asmd().T)\n",
-    "\n",
-    "print(\"\\n=== HistGradientBoosting + Model Matrix ASMD ===\")\n",
-    "print(adjusted_hgb_mm.covars().asmd().T)\n",
-    "\n",
-    "if _sklearn_version >= (1, 4):\n",
-    "    print(\"\\n=== HistGradientBoosting + Raw Covariates ASMD ===\")\n",
-    "    print(adjusted_hgb.covars().asmd().T)\n",
-    "else:\n",
-    "    print(\"\\nHistGradientBoosting + Raw Covariates ASMD skipped (requires scikit-learn >= 1.4)\")"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},