{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Quality-weighted ComBat - deep dive\n", "\n", "`QualityWeightedComBat` replaces ComBat's unweighted per-batch moment estimates with weighted averages, where the weight is a non-negative scalar per sample (typically SNR). The shrinkage formula uses the **effective** (weighted) batch size, so batches dominated by low-quality samples shrink harder towards the prior.\n", "\n", "This notebook fits both correctors, compares their posteriors, and sweeps across SNR regimes reporting three batch-mixing metrics.\n", "\n", "Uses the **MALDI-Kleb-AI** dataset (Rocchi *et al.*, 2026; [Zenodo DOI 10.5281/zenodo.17405072](https://zenodo.org/records/17405072)); see notebook 01 for caching details.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. MALDI-Kleb-AI SNR distribution\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:12.958118Z", "iopub.status.busy": "2026-04-23T12:26:12.957983Z", "iopub.status.idle": "2026-04-23T12:26:34.171812Z", "shell.execute_reply": "2026-04-23T12:26:34.167589Z" } }, "outputs": [ { "data": { "text/plain": [ "count 741.00\n", "mean 112.70\n", "std 65.54\n", "min 19.37\n", "25% 62.76\n", "50% 99.10\n", "75% 147.98\n", "max 415.47\n", "Name: SNR, dtype: float64" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sys, pathlib\n", "sys.path.insert(0, str(pathlib.Path.cwd().parent))\n", "from notebooks._demo import load_maldi_kleb_ai\n", "\n", "ds = load_maldi_kleb_ai(antibiotic='Amikacin')\n", "ds.quality.describe().round(2)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:34.190009Z", "iopub.status.busy": "2026-04-23T12:26:34.189869Z", "iopub.status.idle": "2026-04-23T12:26:34.725100Z", "shell.execute_reply": "2026-04-23T12:26:34.723838Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np, pandas as pd\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "fig, ax = plt.subplots(figsize=(9, 3))\n", "for lvl in ds.batch.unique():\n", " ax.hist(ds.quality[ds.batch == lvl], bins=30, alpha=0.5, label=lvl)\n", "ax.set_xlabel('SNR')\n", "ax.set_ylabel('# spectra')\n", "ax.set_xscale('log')\n", "ax.legend(title='batch', fontsize=8)\n", "ax.set_title('Per-batch SNR distribution (log scale) - MALDI-Kleb-AI')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Fit both ComBat variants\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:34.726966Z", "iopub.status.busy": "2026-04-23T12:26:34.726670Z", "iopub.status.idle": "2026-04-23T12:26:35.987711Z", "shell.execute_reply": "2026-04-23T12:26:35.986338Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "QW-ComBat converged in 3 iterations\n" ] } ], "source": [ "from maldibatchkit import ComBat, QualityWeightedComBat\n", "\n", "combat = ComBat(batch=ds.batch, method='johnson').fit(ds.X)\n", "qw = QualityWeightedComBat(batch=ds.batch, quality=ds.quality).fit(ds.X)\n", "\n", "X_combat = combat.transform(ds.X)\n", "X_qw = qw.transform(ds.X)\n", "print('QW-ComBat converged in', qw.n_iter_, 'iterations')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Diagnostics side-by-side\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:35.989994Z", "iopub.status.busy": "2026-04-23T12:26:35.989672Z", "iopub.status.idle": "2026-04-23T12:26:37.898487Z", "shell.execute_reply": "2026-04-23T12:26:37.897899Z" } }, "outputs": [ { "data": { "text/html": [ "
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beforeComBatQW-ComBat
silhouette0.147-0.0110.009
kbet_acc0.0190.1590.134
lisi1.0151.2661.200
\n", "
" ], "text/plain": [ " before ComBat QW-ComBat\n", "silhouette 0.147 -0.011 0.009\n", "kbet_acc 0.019 0.159 0.134\n", "lisi 1.015 1.266 1.200" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from maldibatchkit.diagnostics import silhouette_batch, kbet, lisi\n", "\n", "def metrics(X):\n", " return pd.Series({\n", " 'silhouette': silhouette_batch(X, ds.batch),\n", " 'kbet_acc': kbet(X, ds.batch, k=20)['acceptance_rate'],\n", " 'lisi': lisi(X, ds.batch, perplexity=30.0),\n", " })\n", "\n", "pd.concat(\n", " {'before': metrics(ds.X), 'ComBat': metrics(X_combat), 'QW-ComBat': metrics(X_qw)},\n", " axis=1,\n", ").round(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Effective batch sizes under quality weighting\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:37.903846Z", "iopub.status.busy": "2026-04-23T12:26:37.903342Z", "iopub.status.idle": "2026-04-23T12:26:37.911590Z", "shell.execute_reply": "2026-04-23T12:26:37.910846Z" } }, "outputs": [ { "data": { "text/html": [ "
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raw_counteffective_size_SNR_weighted
Catania87160.4
Milan184208.4
Rome470372.2
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" ], "text/plain": [ " raw_count effective_size_SNR_weighted\n", "Catania 87 160.4\n", "Milan 184 208.4\n", "Rome 470 372.2" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pd.DataFrame({\n", " 'raw_count': ds.batch.value_counts(),\n", " 'effective_size_SNR_weighted': pd.Series(\n", " qw.effective_batch_sizes_, index=qw.batch_levels_\n", " ),\n", "}).round(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Posterior γ comparison\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:37.915224Z", "iopub.status.busy": "2026-04-23T12:26:37.915017Z", "iopub.status.idle": "2026-04-23T12:26:38.300728Z", "shell.execute_reply": "2026-04-23T12:26:38.300120Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "unw_gamma = combat._model._gamma_star # (n_batches, n_features)\n", "qw_gamma = qw.gamma_star_\n", "\n", "fig, axes = plt.subplots(1, unw_gamma.shape[0], figsize=(4 * unw_gamma.shape[0], 3), sharey=True)\n", "for i, (ax, lvl) in enumerate(zip(axes, qw.batch_levels_, strict=True)):\n", " ax.plot(unw_gamma[i], label='ComBat', alpha=0.8, lw=0.7)\n", " ax.plot(qw_gamma[i], label='QW-ComBat', alpha=0.8, lw=0.7)\n", " ax.set_title(f'batch {lvl}: posterior γ')\n", " ax.axhline(0.0, color='k', lw=0.5)\n", "axes[0].legend(fontsize=8)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. SNR-quantile sensitivity\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2026-04-23T12:26:38.302063Z", "iopub.status.busy": "2026-04-23T12:26:38.301950Z", "iopub.status.idle": "2026-04-23T12:26:43.035601Z", "shell.execute_reply": "2026-04-23T12:26:43.035081Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/ettore/miniconda3/envs/metagenome/lib/python3.10/site-packages/sklearn/base.py:918: UserWarning: Batch sizes are highly imbalanced (ratio 107.0:1). Largest: 'Rome' (321 samples), smallest: 'Catania' (3 samples). Empirical Bayes estimates may be unreliable for small batches.\n", " return self.fit(X, **fit_params).transform(X)\n" ] }, { "data": { "text/html": [ "
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nComBat silhouetteComBat kbet_accComBat lisiQW-ComBat silhouetteQW-ComBat kbet_accQW-ComBat lisi
regime
low-SNR half370-0.1260.7191.067-0.1130.7951.056
high-SNR half371-0.0050.1671.751-0.0010.1701.742
full741-0.0110.1591.2660.0090.1341.200
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" ], "text/plain": [ " n ComBat silhouette ComBat kbet_acc ComBat lisi \\\n", "regime \n", "low-SNR half 370 -0.126 0.719 1.067 \n", "high-SNR half 371 -0.005 0.167 1.751 \n", "full 741 -0.011 0.159 1.266 \n", "\n", " QW-ComBat silhouette QW-ComBat kbet_acc QW-ComBat lisi \n", "regime \n", "low-SNR half -0.113 0.795 1.056 \n", "high-SNR half -0.001 0.170 1.742 \n", "full 0.009 0.134 1.200 " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# How does QW-ComBat compare to ComBat on different SNR regimes?\n", "# Report three batch-mixing metrics so we do not hang the conclusion\n", "# on a single quantity.\n", "import numpy as np\n", "\n", "low = ds.quality < ds.quality.median()\n", "high = ~low\n", "regimes = [\n", " ('low-SNR half', low),\n", " ('high-SNR half', high),\n", " ('full', np.ones(len(ds.X), dtype=bool)),\n", "]\n", "\n", "rows = []\n", "for label, mask in regimes:\n", " X_sub = ds.X.loc[mask]\n", " b_sub = ds.batch.loc[mask]\n", " q_sub = ds.quality.loc[mask]\n", " combat_s = ComBat(batch=b_sub).fit_transform(X_sub)\n", " qw_s = QualityWeightedComBat(batch=b_sub, quality=q_sub).fit_transform(X_sub)\n", " def _metrics(X, batch):\n", " return {\n", " 'silhouette': silhouette_batch(X, batch),\n", " 'kbet_acc': kbet(X, batch, k=20)['acceptance_rate'],\n", " 'lisi': lisi(X, batch, perplexity=30.0),\n", " }\n", " combat_m = _metrics(combat_s, b_sub)\n", " qw_m = _metrics(qw_s, b_sub)\n", " rows.append({'regime': label, 'n': int(mask.sum()),\n", " **{f'ComBat {k}': combat_m[k] for k in combat_m},\n", " **{f'QW-ComBat {k}': qw_m[k] for k in qw_m}})\n", "sweep = pd.DataFrame(rows).set_index('regime')\n", "sweep.round(3)" ] } ], "metadata": { "kernelspec": { "display_name": "maldibatchkit", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.17" } }, "nbformat": 4, "nbformat_minor": 4 }