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Understanding Prediction Powered Inference (PPI) used in ARES
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using Confidence Interval to Calibrate Likert Scale LLMs\n",
"\n",
"ARES uses Confidence Intervals to calibrate LLM judges to human judgments. It requires the use of binary judgments since it leverages the `binomial` distribution internally. In this notebook, we examine if it might be possible to apply similar reasoning to calibrate an LLM that provides judgments on a Likert scale to similar human judgments.\n",
"\n",
"### References\n",
"\n",
"* https://www.statsmodels.org/dev/generated/statsmodels.stats.proportion.multinomial_proportions_confint.html"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"from statsmodels.stats.proportion import multinomial_proportions_confint"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# number of goldset labels\n",
"n = 500\n",
"# number of classes\n",
"m = 5\n",
"# degree of perturbation (can be in range -1 to +1)\n",
"perturb = 0.2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Gold Set synthesis\n",
"\n",
"We build up our goldset labels, representing a balanced goldset of N (N=5) classes."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gold_labels.shape: (500,)\n",
"counts: [100. 100. 100. 100. 100.]\n"
]
}
],
"source": [
"def compute_counts(arr, m):\n",
" idxs, counts = np.unique(arr, return_counts=True)\n",
" idx2count = {i: c for i, c in zip(idxs, counts)}\n",
" counts = np.zeros(m)\n",
" for i in range(m):\n",
" counts[i] = idx2count.get(i, 0)\n",
" return counts\n",
"\n",
"gold_labels = []\n",
"for i in range(m):\n",
" gold_labels.extend([i] * (n // m))\n",
"gold_labels.extend([m] * (n - len(gold_labels)))\n",
"gold_labels = np.array(gold_labels)\n",
"np.random.shuffle(gold_labels)\n",
"\n",
"print(\"gold_labels.shape:\", gold_labels.shape)\n",
"print(\"counts:\", compute_counts(gold_labels, m))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Perturbation\n",
"\n",
"We apply perturbation to the original dataset as directed by the `perturb` variable.\n",
"\n",
"The `perturb` variable takes values between -1 and +1. Positive values make the LLM more lenient (more scores on the higher end of the scale) while negative values make the LLM score more strict (more scores on the lower end of the scale).\n",
"\n",
"For example, a value of 0.3 would move 30% of the variables from the low end to the high end of the scale, and a value of -0.3 would do the reverse."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"pred_labels.shape: (500,)\n",
"counts: [ 55. 45. 100. 145. 155.]\n"
]
}
],
"source": [
"def do_perturbation(gold_labels, m, perturb):\n",
" num_perturbed = int(n * perturb)\n",
" classes = np.arange(m)\n",
" if m % 2 == 0:\n",
" low_classes = classes[0: m // 2]\n",
" high_classes = classes[m // 2:]\n",
" else:\n",
" low_classes = classes[0: m // 2]\n",
" high_classes = classes[(m // 2) + 1:]\n",
"\n",
" assert(len(low_classes) == len(high_classes))\n",
"\n",
" if perturb > 0:\n",
" xfer_idxs = {s: t for s, t in zip(low_classes, high_classes)}\n",
" else:\n",
" num_perturbed = -num_perturbed\n",
" xfer_idxs = {s:t for s, t in zip(high_classes, low_classes)}\n",
"\n",
" pred_labels = gold_labels.copy()\n",
" num_xfered = 0\n",
" for i in range(n):\n",
" if pred_labels[i] in xfer_idxs.keys():\n",
" pred_labels[i] = xfer_idxs[pred_labels[i]]\n",
" num_xfered += 1\n",
" if num_xfered == num_perturbed:\n",
" break\n",
" return pred_labels\n",
"\n",
"pred_labels = do_perturbation(gold_labels, m, perturb)\n",
"\n",
"print(\"pred_labels.shape:\", pred_labels.shape)\n",
"print(\"counts:\", compute_counts(pred_labels, m))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### Visualize Perturbations\n",
"\n",
"The set of bar charts show how the mix of labels changes as the value of `perturb` is varied from -0.5 to +0.5, i.e. from 50% more strict to 50% more lenient compared to the gold set of labels."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 11 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"perturbations = np.arange(-0.5, 0.6, 0.1)\n",
"for i, perturb in enumerate(perturbations):\n",
" if abs(perturb) < 1e-14:\n",
" pred_labels = gold_labels.copy()\n",
" else:\n",
" pred_labels = do_perturbation(gold_labels, m, perturb)\n",
" class_counts = compute_counts(pred_labels, m)\n",
"\n",
" plt.subplot(6, 2, i + 1)\n",
" plt.bar(np.arange(m), class_counts)\n",
" plt.title(\"perturbation: {:.3f}\".format(perturb))\n",
"\n",
"plt.tight_layout()\n",
"_ = plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Visualize Confidence Intervals\n",
"\n",
"We compute the confidence interval for LLM judges that predict these different distributions against the perfectly balanced gold set labels. We want to learn about how the confidence interval changes as a function of the perturbation.\n",
"\n",
"**NOTE:** _We use the `multinomial_proportion_confint` from the `statsmodels` library. Notice that the only input it takes is the class count distribution and the significance level $\\alpha;$, so presumably the gold set would need to be provided as perfectly balanced to get meaningful comparisons._"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(11, 5)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"conf_intervals = []\n",
"perturbations = np.arange(-0.5, 0.6, 0.1)\n",
"for i, perturb in enumerate(perturbations):\n",
" if abs(perturb) < 1e-14:\n",
" pred_labels = gold_labels.copy()\n",
" else:\n",
" pred_labels = do_perturbation(gold_labels, m, perturb)\n",
" class_counts = compute_counts(pred_labels, m)\n",
" # Compute the confidence interval\n",
" ci = multinomial_proportions_confint(class_counts, alpha=0.05, method=\"goodman\")\n",
" diffs = ci[:, 1] - ci[:, 0]\n",
" conf_intervals.append(diffs)\n",
"\n",
"conf_intervals = np.array(conf_intervals)\n",
"conf_intervals.shape"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for j in range(conf_intervals.shape[1]):\n",
" plt.plot(perturbations, conf_intervals[:, j], marker=\"o\", \n",
" label=\"class {}\".format(j))\n",
"plt.legend(loc=\"best\")\n",
"plt.title(\"Per class confidence interval width vs perturbation\")\n",
"_ = plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"avg_conf_intervals = np.mean(conf_intervals, axis=1)\n",
"plt.plot(perturbations, avg_conf_intervals, marker=\"o\")\n",
"plt.title(\"Average confidence interval width vs perturbation\")\n",
"_ = plt.show()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "apollo",
"language": "python",
"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": "3.11.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
-0.50 0.440 0.568 0.434 0.571 0.251 0.307
-0.40 0.431 0.557 0.434 0.571 0.253 0.309
-0.30 0.445 0.559 0.434 0.571 0.327 0.387
-0.20 0.446 0.554 0.434 0.571 0.351 0.411
-0.10 0.428 0.512 0.434 0.571 0.400 0.461
-0.00 0.474 0.536 0.434 0.571 0.474 0.535
0.10 0.472 0.548 0.434 0.571 0.503 0.564
0.20 0.429 0.531 0.434 0.571 0.548 0.609
0.30 0.472 0.588 0.434 0.571 0.656 0.714
0.40 0.445 0.573 0.434 0.571 0.704 0.759
0.50 0.426 0.556 0.434 0.571 0.694 0.750
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