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Posted to commits@datasketches.apache.org by ch...@apache.org on 2024/08/16 09:33:08 UTC
(datasketches-characterization) branch add-python-plotting created (now 47acb66)
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charlie pushed a change to branch add-python-plotting
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at 47acb66 Added readme
This branch includes the following new commits:
new b160991 Added expansion profile
new 47acb66 Added readme
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(datasketches-characterization) 01/02: Added expansion profile
Posted by ch...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
charlie pushed a commit to branch add-python-plotting
in repository https://gitbox.apache.org/repos/asf/datasketches-characterization.git
commit b160991594083e543d1da1359d9f70f7ddd30078
Author: c-dickens <ch...@apache.org>
AuthorDate: Fri Aug 16 09:55:09 2024 +0100
Added expansion profile
---
src/notebooks/ExpansionProfile.ipynb | 908 +
src/notebooks/README.md | 13 +
src/notebooks/qf_probability_sum.py | 21 +
src/notebooks/requirements.txt | 111 +
...entFilterExpansionProfile20240813_090828PST.txt | 61470 +++++++++
...entFilterExpansionProfile20240814_034519PST.txt | 122910 ++++++++++++++++++
6 files changed, 185433 insertions(+)
diff --git a/src/notebooks/ExpansionProfile.ipynb b/src/notebooks/ExpansionProfile.ipynb
new file mode 100644
index 0000000..4e86dae
--- /dev/null
+++ b/src/notebooks/ExpansionProfile.ipynb
@@ -0,0 +1,908 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# False Positive Rate, Fingerprints, and Expansion\n",
+ "\n",
+ "We test the false positive rate and its relation to fingerprint and expansion."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "from typing import Tuple\n",
+ "import matplotlib.pyplot as plt\n",
+ "%matplotlib inline\n",
+ "from qf_probability_sum import qf_probability_sum"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def parse_results(filename:str) -> Tuple[pd.DataFrame, float, int]:\n",
+ " \"\"\"\n",
+ " Takes an input file name in .txt format, strips out the extra strings and returns \n",
+ " the main results in a dataframe.\n",
+ "\n",
+ " The universe size is the largest power of 2 that is used to insert into the sketch and \n",
+ " the capacity is how far along the power of two interval used for maximum cardinality.\n",
+ "\n",
+ " Eg. capacity = 0.9 and lgU = 20 means that we insert 0.9 * 2^20 elements into the sketch.\n",
+ "\n",
+ " Parameters:\n",
+ " - filename (str): The path to the input file in .txt format.\n",
+ "\n",
+ " Returns:\n",
+ " - Tuple[pd.DataFrame, float, int]: A tuple containing the main results in a dataframe, \n",
+ " the number of queries, and the number of false positives per query.\n",
+ " \"\"\"\n",
+ " with open(filename) as f:\n",
+ " lines = f.readlines()[2:]\n",
+ " ignore_from_idx = lines.index(\"PROPERTIES:\\n\")\n",
+ " results = lines[:ignore_from_idx-1] # there is an empty line preceding the ignore_from_idx\n",
+ " results_clean = [r.strip(\"\\n\") for r in results]\n",
+ " results_df = pd.DataFrame(sub.split(\"\\t\") for sub in results_clean[1:])\n",
+ " results_df.columns = results_clean[0].split(\"\\t\")\n",
+ " for col in results_df.columns:\n",
+ " results_df[col] = pd.to_numeric(results_df[col])\n",
+ " num_queries = None\n",
+ " for line in lines:\n",
+ " if \"lgNumQueries\" in line:\n",
+ " num_queries = 2.**int(line.split(\"=\")[-1])\n",
+ " break\n",
+ " results_df[\"trialFPR\"] = results_df[\"NumFalsePositives\"] / num_queries\n",
+ " return results_df, int(num_queries)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1. False Positive Rate Bound for a fixed fingerprint\n",
+ "\n",
+ "First, we check the FPR bound of $2^{-f}$ for a single fingerprint.\n",
+ "The configuration for this experiment is: $m = 2^{21}$ slots, and four points in the octave between $2^{20}$ and $2^{21}$.\n",
+ "For each trial, we generate a new input and query set $Q$ and count the number of false positives when testing the query set against the filter.\n",
+ "The query set has $|Q| = 4096$.\n",
+ "\n",
+ "The number of false positives reported is approximately a Binomial distribution with $Q$ trials and probability $p$ of reporting a false positive as the Binomial success probability.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "single_fingerprint_df, num_queries = parse_results(\"QuotientFilterExpansionProfile20240813_090828PST.txt\")\n",
+ "single_fprint = single_fingerprint_df[\"FPrintLen\"].values[0]\n",
+ "\n",
+ "# ignore any fingerprints that are not the same length as the first fingerprint\n",
+ "single_fingerprint_df = single_fingerprint_df[single_fingerprint_df[\"FPrintLen\"] == single_fprint]\n",
+ "single_fingerprint_df.head()\n",
+ "\n",
+ "input_values = single_fingerprint_df[\"NumInput\"].unique()\n",
+ "num_slots = single_fingerprint_df[\"NumSlots\"].unique()[0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(2097152, 4096)"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "num_slots, num_queries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_mean_entries_fpr(results_df:pd.DataFrame) -> np.ndarray:\n",
+ " \"\"\"\n",
+ " Calculate the mean number of entries and false positive rate for each combination of \"NumSlots\" and \"NumInput\" in the given DataFrame.\n",
+ "\n",
+ " Parameters:\n",
+ " - results_df (pd.DataFrame): The DataFrame containing the results.\n",
+ "\n",
+ " Returns:\n",
+ " - np.ndarray: An array whose columns are the number of slots, mean number of entries in filterinput points and the mean of the number of entries and trial FPR.\n",
+ " # first column is number of slots, second is number of entries, third is trial FPR\n",
+ " \"\"\"\n",
+ " means = []\n",
+ " for gg in results_df.groupby(\"NumSlots\"):\n",
+ " for gdf in gg[1].groupby(\"NumInput\"):\n",
+ " means.append([gg[0], gdf[1][\"NumEntries\"].mean(), gdf[1][\"trialFPR\"].mean(), gdf[1][\"trialFPR\"].median()])\n",
+ " return np.array(means)\n",
+ "\n",
+ "mean_num_entries_fpr = get_mean_entries_fpr(single_fingerprint_df)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[2.09715200e+06, 1.04042699e+06, 1.54996514e-02, 1.53808594e-02],\n",
+ " [2.09715200e+06, 1.08923099e+06, 1.62308216e-02, 1.61132812e-02],\n",
+ " [2.09715200e+06, 1.14030623e+06, 1.69944763e-02, 1.68457031e-02],\n",
+ " [2.09715200e+06, 1.19375406e+06, 1.77892447e-02, 1.78222656e-02],\n",
+ " [2.09715200e+06, 1.24968171e+06, 1.86212659e-02, 1.85546875e-02],\n",
+ " [2.09715200e+06, 1.30820458e+06, 1.94831491e-02, 1.95312500e-02],\n",
+ " [2.09715200e+06, 1.36943901e+06, 2.03975439e-02, 2.02636719e-02],\n",
+ " [2.09715200e+06, 1.43350899e+06, 2.13514566e-02, 2.12402344e-02],\n",
+ " [2.09715200e+06, 1.50054058e+06, 2.23572850e-02, 2.22167969e-02],\n",
+ " [2.09715200e+06, 1.57067088e+06, 2.34036446e-02, 2.31933594e-02],\n",
+ " [2.09715200e+06, 1.64403715e+06, 2.44902968e-02, 2.44140625e-02]])"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "mean_num_entries_fpr"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we will plot the error behaviour as the number of entries in the filter increases."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x14fbeb910>"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABIgAAAGeCAYAAAD/mzriAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOzdeZwcVbnw8V9V9T77viRkEkgICZAFwr4FBGS5IAgqKgKKbMJFQUT0khASFOGCggtGUMGFKKiAV15BkS0gYUsIJiRk3zNrJrP03lV13j8605nOdE9mJtPTPTPPN5/+ZLrqdPfpU13VVU+f8xxNKaUQQgghhBBCCCGEEKOWnu0KCCGEEEIIIYQQQojskgCREEIIIYQQQgghxCgnASIhhBBCCCGEEEKIUU4CREIIIYQQQgghhBCjnASIhBBCCCGEEEIIIUY5CRAJIYQQQgghhBBCjHISIBJCCCGEEEII [...]
+ "text/plain": [
+ "<Figure size 1400x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(14, 4))\n",
+ "\n",
+ "for i, g in enumerate(single_fingerprint_df.groupby(\"NumInput\")):\n",
+ " group = g[0]\n",
+ " group_data = g[1]\n",
+ " fprint_len = group_data[\"FPrintLen\"].values[0]\n",
+ " naive_bound = 2.**(-fprint_len)\n",
+ "\n",
+ " colour = \"C\" + str(group_data[\"FPrintLen\"].values[0] -3)\n",
+ " ax.scatter(group_data[\"NumEntries\"], group_data[\"NumFalsePositives\"], \n",
+ " color=colour, marker=\"o\", s=10, alpha=0.01)\n",
+ " \n",
+ "\n",
+ "# bound function -- plotted at the input values points because the absolute load is a random variable that deviates \n",
+ "# from a deterministic input cardinality.\n",
+ "ff = fprint_len*np.ones_like(input_values)\n",
+ "bound_fct = 2.**(-ff)\n",
+ "ax.plot(input_values, bound_fct*num_queries, \n",
+ " color=\"red\", marker=\"x\", label=r\"$2^{-f}\\cdot |\\{QuerySet\\}|$\", linestyle=\"--\")\n",
+ "ax.plot(input_values, (mean_num_entries_fpr[:,1]/mean_num_entries_fpr[:,0])*bound_fct*num_queries, \n",
+ " label=r\"$\\alpha 2^{-f} \\cdot |\\{QuerySet\\}|$\", color=\"black\", marker=\"x\", linestyle=\"--\")\n",
+ "\n",
+ "\n",
+ "# Mean operator is linear in this setting\n",
+ "ax.plot(mean_num_entries_fpr[:,1], mean_num_entries_fpr[:,2]*num_queries, label=r\"$Mean(FPR)\\cdot |\\{QuerySet\\}|$\")\n",
+ "\n",
+ "# Exact probability sum\n",
+ "exact_probs = np.array([qf_probability_sum(num_slots, n, fprint_len) for n in input_values])\n",
+ "ax.plot(input_values, exact_probs*num_queries, label=\"Exact Probability Sum\", color=\"magenta\", marker=\"*\", linestyle=\"--\")\n",
+ "\n",
+ "# # tidy the axes\n",
+ "ax.set_ylabel(\"Number of FPs\")\n",
+ "ax.set_xlabel(\"Number of input items: $n$\")\n",
+ "\n",
+ "slot_ticks = single_fingerprint_df[\"NumInput\"].unique().tolist()\n",
+ "ax.set_xticks(slot_ticks)\n",
+ "ax.ticklabel_format(style='plain')\n",
+ "ax.grid()\n",
+ "ax.legend(loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=4)\n",
+ "\n",
+ "#fig.savefig(\"single_fp_results_count.pdf\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now subtract the mean to get a better idea of how the variance behaves as input items increase.\n",
+ "We see that the variance is mildly increasing. This is to be expected since each of the independent trials represents a draw from a $Binomial(Q, p)$ distribution\n",
+ "(where $p$ is the probability of a false positive) whose variance is proportional to $p(1-p)$ which is increasing on $(0,\\frac12)$. Indeed we see that the empirical standard deviation closely matches that predicted from the theory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x14fbc3310>"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABI0AAAF3CAYAAAAo+bvsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOzdd3hURdvA4d+WbHoPkEASCJ0QQu9IEwERBPQVBAvYu752bAgoip+I8loQa2wgohRBpEjvPbTQSUiA9N62nvn+WLJhKZK+2TC3Vy7JyezsszPZzTnPmaISQggkSZIkSZIkSZIkSZIk6RJqRwcgSZIkSZIkSZIkSZIk1T4yaSRJkiRJkiRJkiRJkiRdQSaNJEmSJEmSJEmSJEmSpCvIpJEkSZIkSZIkSZIkSZJ0BZk0kiRJkiRJkiRJkiRJkq4gk0aSJEmSJEmSJEmSJEnSFWTSSJIkSZIkSZIkSZIk [...]
+ "text/plain": [
+ "<Figure size 1400x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(14, 4))\n",
+ "\n",
+ "num_fp_means = []\n",
+ "num_fp_stds = []\n",
+ "for i, g in enumerate(single_fingerprint_df.groupby(\"NumInput\")):\n",
+ " group = g[0]\n",
+ " group_data = g[1]\n",
+ " fprint_len = group_data[\"FPrintLen\"].values[0]\n",
+ " load_factor = group_data[\"NumEntries\"] / group_data[\"NumSlots\"]\n",
+ " fps_less_mean = group_data[\"NumFalsePositives\"]- group_data[\"NumFalsePositives\"].mean()\n",
+ " num_fp_means.append(fps_less_mean.mean())\n",
+ " num_fp_stds.append(fps_less_mean.std())\n",
+ " \n",
+ " colour = \"C\" + str(group_data[\"FPrintLen\"].values[0] -3)\n",
+ "\n",
+ " ax.scatter(group_data[\"NumEntries\"], fps_less_mean, \n",
+ " color=colour, marker=\".\", s=10, alpha=0.01)\n",
+ " \n",
+ "\n",
+ "# Binomial error terms\n",
+ "ax.plot(input_values, np.sqrt(exact_probs*(1-exact_probs)*num_queries), label=\"Binomial Error\", color=\"blue\", marker=\"+\", linestyle=\"--\")\n",
+ "ax.plot(input_values, -np.sqrt(exact_probs*(1-exact_probs)*num_queries), color=\"blue\", marker=\"+\", linestyle=\"--\")\n",
+ "\n",
+ "# Mean and standard deviations of FPs less mean\n",
+ "ax.plot(input_values, num_fp_means, label=\"Empirical mean\", color=\"red\", linestyle=\":\")\n",
+ "ax.plot(input_values, num_fp_stds, label=\"Empirical standard deviation\", color=\"red\", marker=\"x\", linestyle=\":\")\n",
+ "ax.plot(input_values, -np.array(num_fp_stds), color=\"red\", marker=\"x\", linestyle=\":\")\n",
+ "\n",
+ "# # tidy the axes\n",
+ "ax.set_ylabel(r\"$\\# \\text{FPs} - Mean(\\# \\text{FPs})$\")\n",
+ "ax.set_xlabel(\"Number of input items: $n$\")\n",
+ "\n",
+ "slot_ticks = single_fingerprint_df[\"NumInput\"].unique().tolist()\n",
+ "ax.set_xticks(slot_ticks)\n",
+ "ax.ticklabel_format(style='plain')\n",
+ "ax.grid()\n",
+ "ax.legend(loc=\"upper left\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[7.86102209, 7.90683742],\n",
+ " [8.05846448, 8.08716986],\n",
+ " [8.25690964, 8.27140107],\n",
+ " [8.4470204 , 8.45959971],\n",
+ " [8.63977779, 8.65182699],\n",
+ " [8.83408323, 8.84815939],\n",
+ " [8.99173992, 9.04866053],\n",
+ " [9.22347582, 9.25340337],\n",
+ " [9.4533194 , 9.46244994],\n",
+ " [9.73107549, 9.67586922],\n",
+ " [9.98112535, 9.89372946]])"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# empirical and mathematical standard deviations\n",
+ "np.c_[num_fp_stds, np.sqrt(exact_probs*(1-exact_probs)*num_queries)]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Now we use the same results to estimate the false positive rate by dividing out the number of query points normalising constant."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x165f0b910>"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABIYAAAJLCAYAAACSSZ1QAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOzdd3xc1Z3//9e9d7p6sy1b7qYb01tIMCQkEAibvqngNJaUXULYJbv5LiaAk7BkU0h+WQIhCXE2gbC76SQQSKGEGopNMcXGtlwkWVaXpt97z++PkcaWVSzbGo3K+6mHHtLce2bm43M113c+c87nWMYYg4iIiIiIiIiIzDh2sQMQEREREREREZHiUGJIRERERERERGSGUmJIRERERERERGSGUmJIRERERERERGSGUmJIRERERERERGSGUmJIRERERERERGSGUmJIRERERERERGSGChQ7ABGR6cDzPLLZ [...]
+ "text/plain": [
+ "<Figure size 1400x600 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(14, 6))\n",
+ "for i, g in enumerate(single_fingerprint_df.groupby(\"NumInput\")):\n",
+ " group = g[0]\n",
+ " group_data = g[1]\n",
+ " fprint_len = group_data[\"FPrintLen\"].values[0]\n",
+ "\n",
+ " naive_bound = 2.**(-fprint_len)\n",
+ "\n",
+ " colour = \"C\" + str(group_data[\"FPrintLen\"].values[0] -3)\n",
+ " ax.scatter(group_data[\"NumEntries\"], group_data[\"NumFalsePositives\"]/num_queries, \n",
+ " color=colour, marker=\"o\", s=10, alpha=0.01)\n",
+ " \n",
+ "\n",
+ "# bound function\n",
+ "ff = fprint_len*np.ones_like(input_values)\n",
+ "bound_fct = 2.**(-ff)\n",
+ "ax.plot(input_values, bound_fct, \n",
+ " color=\"red\", marker=\"x\", label=r\"$2^{-f}\\cdot$\", linestyle=\"--\")\n",
+ "ax.plot(input_values, (mean_num_entries_fpr[:,1]/mean_num_entries_fpr[:,0])*bound_fct, \n",
+ " label=r\"$\\alpha 2^{-f}$\", color=\"black\", marker=\"x\", linestyle=\"--\")\n",
+ "\n",
+ "ax.plot(mean_num_entries_fpr[:,1], mean_num_entries_fpr[:,2], label=r\"$Mean(FPR)$\")\n",
+ "ax.plot(input_values, exact_probs, label=\"Exact Probability Sum\", color=\"magenta\", marker=\"*\", linestyle=\"--\")\n",
+ "\n",
+ "# tidy the axes\n",
+ "ax.set_ylabel(\"False Positive Rate\")\n",
+ "ax.set_xlabel(\"Number of Entries in Filter\")\n",
+ "\n",
+ "slot_ticks = single_fingerprint_df[\"NumInput\"].unique().tolist()\n",
+ "ax.set_xticks(slot_ticks)\n",
+ "ax.ticklabel_format(style='plain')\n",
+ "ax.grid()\n",
+ "ax.set_yscale(\"log\", base=2)\n",
+ "ax.legend(loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=4)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.01550, 0.01526, 0.01550, 0.01526\n",
+ "0.01623, 0.01597, 0.01623, 0.01597\n",
+ "0.01699, 0.01670, 0.01699, 0.01671\n",
+ "0.01779, 0.01747, 0.01779, 0.01747\n",
+ "0.01862, 0.01827, 0.01862, 0.01827\n",
+ "0.01949, 0.01911, 0.01948, 0.01910\n",
+ "0.02041, 0.01999, 0.02040, 0.01998\n",
+ "0.02136, 0.02090, 0.02135, 0.02090\n",
+ "0.02236, 0.02186, 0.02236, 0.02186\n",
+ "0.02340, 0.02286, 0.02340, 0.02286\n",
+ "0.02450, 0.02390, 0.02449, 0.02389\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x165f13310>"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABKoAAAJLCAYAAADHKH4OAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOzdeXxcZb348c85Z/aZTCZLs7dp0nRfaMtSimAVCkVFlqugoIKK6L0uKFzUy/0hsoi4ItyLiqiAeEVQQa7bRQoKIpQC3Zd0SZekbZJmz2RmMut5fn8MmTZdk3YmM5N+37zyKnPm5Mw358zMec73PM/30ZRSCiGEEEIIIYQQQgghskzPdgBCCCGEEEIIIYQQQoAkqoQQQgghhBBCCCFEjpBElRBCCCGEEEIIIYTICZKoEkIIIYQQQgghhBA5QRJVQgghhBBCCCGEECInSKJKCCGEEEIIIYQQQuQESVQJ [...]
+ "text/plain": [
+ "<Figure size 1400x600 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(14, 6))\n",
+ "\n",
+ "fpr_means = []\n",
+ "fpr_stds = []\n",
+ "approx_bound = []\n",
+ "for i, g in enumerate(single_fingerprint_df.groupby(\"NumInput\")):\n",
+ " group = g[0]\n",
+ " group_data = g[1]\n",
+ " fprint_len = group_data[\"FPrintLen\"].values[0]\n",
+ " fps_less_mean = group_data[\"trialFPR\"]- group_data[\"trialFPR\"].mean()\n",
+ " fpr_means.append(fps_less_mean.mean())\n",
+ " fpr_stds.append(fps_less_mean.std())\n",
+ " mean_load = (group_data[\"NumEntries\"] / group_data[\"NumSlots\"]).mean()\n",
+ " p = mean_load*2.**(-fprint_len)\n",
+ " p_emp = group_data[\"trialFPR\"].mean()\n",
+ " print(f\"{p:.5f}, {p*(1-p):.5f}, {p_emp:.5f}, {p_emp*(1-p_emp):.5f}\")\n",
+ " approx_bound.append(mean_load*2.**(-fprint_len) - group_data[\"trialFPR\"].mean())\n",
+ "\n",
+ " colour = \"C\" + str(group_data[\"FPrintLen\"].values[0] -3)\n",
+ " ax.scatter(group_data[\"NumEntries\"], fps_less_mean, color=colour, marker=\"o\", s=10, alpha=0.01)\n",
+ "\n",
+ "\n",
+ "# empirical mean and standard deviations of FPs less mean\n",
+ "ax.plot(input_values, fpr_means, label=\"Empirical mean\", color=\"red\", marker=\"x\", linestyle=\":\")\n",
+ "ax.plot(input_values, fpr_stds, label=\"Empirical standard deviation\", color=\"red\", marker=\"x\", linestyle=\":\")\n",
+ "ax.plot(input_values, -np.array(fpr_stds), color=\"red\", marker=\"x\", linestyle=\":\")\n",
+ "\n",
+ "# add the simple bound back in\n",
+ "ax.plot(input_values, approx_bound, label=r\"$\\alpha 2^{-f} - \\text{Mean}(TrialFPR)$\", color=\"black\", marker=\"v\", markersize=5., linestyle=\"--\")\n",
+ "\n",
+ "# Binomial error terms\n",
+ "ax.plot(input_values, np.sqrt(exact_probs*(1-exact_probs)/num_queries), label=\"Binomial Error\", color=\"blue\", marker=\"+\", linestyle=\"--\")\n",
+ "ax.plot(input_values, -np.sqrt(exact_probs*(1-exact_probs)/num_queries), color=\"blue\", marker=\"+\", linestyle=\"--\")\n",
+ "\n",
+ "# tidy the axes\n",
+ "ax.set_ylabel(\"Empirical FPR - Mean(Empirical FPR)\")\n",
+ "ax.set_xlabel(\"Number of Entries in Filter\")\n",
+ "\n",
+ "slot_ticks = single_fingerprint_df[\"NumInput\"].unique().tolist()\n",
+ "ax.set_xticks(slot_ticks)\n",
+ "ax.ticklabel_format(style='plain')\n",
+ "ax.grid()\n",
+ "#ax.set_yscale(\"log\", base=2)\n",
+ "ax.legend(loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Overall, what we see from this plot is that a slightly more refined bound can be given to the user given information in the filter.\n",
+ "Namely, the load can be calculated and this value can be used to scale the $2^{-f}$ function. The plot above shows that the function \n",
+ "$\\alpha 2^{-f} - \\text{Mean}(TrialFPR)$ is centered on zero, so on average there is little difference between the two functions."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "NumSlots NumInput NumEntries FPrintLen MedNumFPs MaxNumFPs nBadTrial MeanFPR stdFPR WorstFPR Bound \n",
+ "------------------------------------------------------------------------------------------\n",
+ "2097152 1048576 1040426.0 5 63.0 95 0 0.0155 0.0019 0.0232 0.0312 \n",
+ "2097152 1098167 1089232.0 5 66.0 99 0 0.0162 0.0020 0.0242 0.0312 \n",
+ "2097152 1150104 1140308.0 5 69.0 102 0 0.0170 0.0020 0.0249 0.0312 \n",
+ "2097152 1204498 1193754.0 5 73.0 105 0 0.0178 0.0021 0.0256 0.0312 \n",
+ "2097152 1261463 1249681.0 5 76.0 106 0 0.0186 0.0021 0.0259 0.0312 \n",
+ "2097152 1321123 1308203.0 5 80.0 108 0 0.0195 0.0022 0.0264 0.0312 \n",
+ "2097152 1383604 1369436.0 5 83.0 115 0 0.0204 0.0022 0.0281 0.0312 \n",
+ "2097152 1449041 1433508.0 5 87.0 119 0 0.0214 0.0023 0.0291 0.0312 \n",
+ "2097152 1517572 1500540.0 5 91.0 122 0 0.0224 0.0023 0.0298 0.0312 \n",
+ "2097152 1589344 1570671.0 5 95.0 128 0 0.0234 0.0024 0.0312 0.0312 \n",
+ "2097152 1664511 1644037.0 5 100.0 136 6 0.0245 0.0024 0.0332 0.0312 \n"
+ ]
+ }
+ ],
+ "source": [
+ "print(f\"{'NumSlots':<10} {'NumInput':<10} {'NumEntries':<10} {'FPrintLen':<10} {'MedNumFPs':<10} {'MaxNumFPs':<10} {'nBadTrial':<10} {'MeanFPR':<10} {'stdFPR':<10} {'WorstFPR':<10} {'Bound':<10}\")\n",
+ "print(\"-\"*90)\n",
+ "\n",
+ "for g in single_fingerprint_df.groupby(\"NumInput\"):\n",
+ " \n",
+ " num_slots = g[1][\"NumSlots\"].values[0]\n",
+ " fprint_len = g[1][\"FPrintLen\"].values[0]\n",
+ " num_entries = g[1][\"NumEntries\"].median()\n",
+ " med_num_fps = g[1][\"NumFalsePositives\"].median()\n",
+ " max_num_fps = g[1][\"NumFalsePositives\"].max()\n",
+ " mean_fpr = g[1][\"trialFPR\"].mean()\n",
+ " std_fpr = g[1][\"trialFPR\"].std()\n",
+ " worst_fpr = g[1]['trialFPR'].max()\n",
+ " bound = 2.**(-fprint_len)\n",
+ " thld = np.floor(num_queries * bound).astype(int)\n",
+ " g[1][\"BadTrial\"] = g[1][\"NumFalsePositives\"] > thld\n",
+ " num_bad_trials = g[1][\"BadTrial\"].sum() \n",
+ " print(f\"{num_slots:<10} {g[0]:<10} {num_entries:<10} {fprint_len:<10} {med_num_fps:<10} {max_num_fps:<10} {num_bad_trials:<10} {mean_fpr:<10.4f} {std_fpr:<10.4f} {worst_fpr:<10.4f} {bound:<10.4f}\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 2. False Positive Rate Bound for varying fingerprint length\n",
+ "We should see similar behaviour to the above but across all fingerprint lengths."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<div>\n",
+ "<style scoped>\n",
+ " .dataframe tbody tr th:only-of-type {\n",
+ " vertical-align: middle;\n",
+ " }\n",
+ "\n",
+ " .dataframe tbody tr th {\n",
+ " vertical-align: top;\n",
+ " }\n",
+ "\n",
+ " .dataframe thead th {\n",
+ " text-align: right;\n",
+ " }\n",
+ "</style>\n",
+ "<table border=\"1\" class=\"dataframe\">\n",
+ " <thead>\n",
+ " <tr style=\"text-align: right;\">\n",
+ " <th></th>\n",
+ " <th>NumSlots</th>\n",
+ " <th>NumInput</th>\n",
+ " <th>FPrintLen</th>\n",
+ " <th>NumEntries</th>\n",
+ " <th>NumFalsePositives</th>\n",
+ " <th>trialFPR</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>2097152</td>\n",
+ " <td>1048576</td>\n",
+ " <td>5</td>\n",
+ " <td>1040474</td>\n",
+ " <td>72</td>\n",
+ " <td>0.017578</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>2097152</td>\n",
+ " <td>1098167</td>\n",
+ " <td>5</td>\n",
+ " <td>1089276</td>\n",
+ " <td>77</td>\n",
+ " <td>0.018799</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>2</th>\n",
+ " <td>2097152</td>\n",
+ " <td>1150104</td>\n",
+ " <td>5</td>\n",
+ " <td>1140311</td>\n",
+ " <td>79</td>\n",
+ " <td>0.019287</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>3</th>\n",
+ " <td>2097152</td>\n",
+ " <td>1204498</td>\n",
+ " <td>5</td>\n",
+ " <td>1193814</td>\n",
+ " <td>83</td>\n",
+ " <td>0.020264</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>4</th>\n",
+ " <td>2097152</td>\n",
+ " <td>1261463</td>\n",
+ " <td>5</td>\n",
+ " <td>1249723</td>\n",
+ " <td>86</td>\n",
+ " <td>0.020996</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " NumSlots NumInput FPrintLen NumEntries NumFalsePositives trialFPR\n",
+ "0 2097152 1048576 5 1040474 72 0.017578\n",
+ "1 2097152 1098167 5 1089276 77 0.018799\n",
+ "2 2097152 1150104 5 1140311 79 0.019287\n",
+ "3 2097152 1204498 5 1193814 83 0.020264\n",
+ "4 2097152 1261463 5 1249723 86 0.020996"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "multi_fingerprint_df, multi_fp_num_queries = parse_results(\"QuotientFilterExpansionProfile20240814_034519PST.txt\")\n",
+ "\n",
+ "\n",
+ "multi_input_values = multi_fingerprint_df[\"NumInput\"].unique()\n",
+ "multi_num_slots = multi_fingerprint_df[\"NumSlots\"].unique()\n",
+ "\n",
+ "multi_fingerprint_df.head()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def get_fingerprint_lengths(df:pd.DataFrame) -> np.ndarray:\n",
+ " \"\"\"\n",
+ " Get the fingerprint lengths in the given DataFrame.\n",
+ "\n",
+ " Parameters:\n",
+ " - df (pd.DataFrame): The DataFrame containing the fingerprint lengths.\n",
+ "\n",
+ " Returns:\n",
+ " - np.ndarray: An array of the fingerprint lengths.\n",
+ " \"\"\"\n",
+ " num_input_fprint_len_arr = []\n",
+ " for g in df.groupby(\"NumInput\"):\n",
+ " num_input_fprint_len_arr.append([g[0], g[1][\"FPrintLen\"].values[0]])\n",
+ " return np.array(num_input_fprint_len_arr)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "30\n"
+ ]
+ }
+ ],
+ "source": [
+ "unique_triples = multi_fingerprint_df[[\"NumSlots\", \"NumInput\",\t\"FPrintLen\"]].drop_duplicates()\n",
+ "print(len(unique_triples))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "multi_exact_probs = np.zeros((len(unique_triples),), dtype=float)\n",
+ "for i, triple in enumerate(unique_triples.values):\n",
+ " multi_exact_probs[i] = qf_probability_sum(*triple)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x16467e490>"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABH4AAAGjCAYAAABaLdJPAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAAD9VElEQVR4nOzdd3xV5f3A8c85dyU3e5CEBEhYIkOWgIIiuPeqbdXWn1gVxWq1WgdaBQQs7mq1ltaBtmqrddVa9wAHQ2XvHQgkkEH2uuM8vz9OcrPuDQkk54bwffu63nuec+4533u563zzPN9HU0ophBBCCCGEEEIIIUS3o4c7ACGEEEIIIYQQQgjROSTxI4QQQgghhBBCCNFNSeJHCCGEEEIIIYQQopuSxI8QQgghhBBCCCFENyWJHyGEEEIIIYQQQohuShI/QgghhBBCCCGEEN2UJH6EEEIIIYQQQgghuilJ/Agh [...]
+ "text/plain": [
+ "<Figure size 1400x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(14, 4))\n",
+ "\n",
+ "multi_mean_num_entries_fpr = get_mean_entries_fpr(multi_fingerprint_df)\n",
+ "\n",
+ "for i, g in enumerate(multi_fingerprint_df.groupby(\"NumInput\")):\n",
+ " group = g[0]\n",
+ " group_data = g[1]\n",
+ " fprint_len = group_data[\"FPrintLen\"].values[0]\n",
+ " naive_bound = 2.**(-fprint_len)\n",
+ "\n",
+ " colour = \"C\" + str(group_data[\"FPrintLen\"].values[0] -3)\n",
+ " ax.scatter(group_data[\"NumEntries\"], group_data[\"NumFalsePositives\"], \n",
+ " color=colour, marker=\"o\", s=10, alpha=0.01)\n",
+ " \n",
+ "\n",
+ "# bound function -- plotted at the input values points because the absolute load is a random variable that deviates \n",
+ "# from a deterministic input cardinality.\n",
+ "inputs_and_fprint_lens = get_fingerprint_lengths(multi_fingerprint_df)\n",
+ "bound_fct = 2.**(-inputs_and_fprint_lens[:, 1])\n",
+ "ax.plot(inputs_and_fprint_lens[:, 0], bound_fct*multi_fp_num_queries, \n",
+ " color=\"red\", marker=\"x\", label=r\"$2^{-f}\\cdot |\\{QuerySet\\}|$\", linestyle=\"--\")\n",
+ "ax.plot(multi_input_values, (multi_mean_num_entries_fpr[:,1]/multi_mean_num_entries_fpr[:,0])*bound_fct*multi_fp_num_queries, \n",
+ " label=r\"$\\alpha 2^{-f} \\cdot |\\{QuerySet\\}|$\", color=\"black\", marker=\"x\", linestyle=\"--\")\n",
+ "\n",
+ "\n",
+ "# Mean operator is linear in this setting\n",
+ "ax.plot(multi_mean_num_entries_fpr[:,1], multi_mean_num_entries_fpr[:,2]*multi_fp_num_queries, label=r\"$Mean(FPR)\\cdot |\\{QuerySet\\}|$\")\n",
+ "\n",
+ "# Exact probability sum\n",
+ "ax.plot(multi_input_values, multi_exact_probs*num_queries, label=\"Exact Probability Sum\", color=\"magenta\", marker=\"*\", linestyle=\"--\")\n",
+ "\n",
+ "# tidy the axes\n",
+ "ax.set_ylabel(\"Number of FPs\")\n",
+ "ax.set_xlabel(\"Number of input items: $n$\")\n",
+ "ax.set_yscale(\"log\", base=2)\n",
+ "ax.set_xscale(\"log\", base=2)\n",
+ "ax.grid()\n",
+ "ax.legend(loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=4)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.legend.Legend at 0x14ff44f10>"
+ ]
+ },
+ "execution_count": 18,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABIYAAAGjCAYAAABZth4iAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8g+/7EAAAACXBIWXMAAA9hAAAPYQGoP6dpAADwkklEQVR4nOzdd3xb5dXA8d+9GrblvVccxxmE7ARCIKywoYGyRyktgZZRoKWUTUtCSKCBQul8gRIKlFJGW0qhQCmhJYEwQxYJ2cOOE8fx3rbGvc/7x5VkO5ZMnNhXGefLx0j30dXVkRTL0tF5zqMppRRCCCGEEEIIIYQQ4pCjxzoAIYQQQgghhBBCCBEbkhgSQgghhBBCCCGEOERJYkgIIYQQQgghhBDiECWJISGEEEIIIYQQQohDlCSGhBBCCCGEEEIIIQ5RkhgSQgghhBBCCCGEOERJYkgIIYQQQgghhBDiECWJ [...]
+ "text/plain": [
+ "<Figure size 1400x400 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(14, 4))\n",
+ "\n",
+ "multi_mean_num_entries_fpr = get_mean_entries_fpr(multi_fingerprint_df)\n",
+ "\n",
+ "for i, g in enumerate(multi_fingerprint_df.groupby(\"NumInput\")):\n",
+ " group = g[0]\n",
+ " group_data = g[1]\n",
+ " fprint_len = group_data[\"FPrintLen\"].values[0]\n",
+ " naive_bound = 2.**(-fprint_len)\n",
+ "\n",
+ " colour = \"C\" + str(group_data[\"FPrintLen\"].values[0] -3)\n",
+ " ax.scatter(group_data[\"NumEntries\"], group_data[\"trialFPR\"], \n",
+ " color=colour, marker=\"o\", s=10, alpha=0.01)\n",
+ " \n",
+ "\n",
+ "# bound function -- plotted at the input values points because the absolute load is a random variable that deviates \n",
+ "# from a deterministic input cardinality.\n",
+ "inputs_and_fprint_lens = get_fingerprint_lengths(multi_fingerprint_df)\n",
+ "bound_fct = 2.**(-inputs_and_fprint_lens[:, 1])\n",
+ "ax.plot(inputs_and_fprint_lens[:, 0], bound_fct, \n",
+ " color=\"red\", marker=\"x\", label=r\"$2^{-f}$\", linestyle=\"--\")\n",
+ "ax.plot(multi_input_values, (multi_mean_num_entries_fpr[:,1]/multi_mean_num_entries_fpr[:,0])*bound_fct, \n",
+ " label=r\"$\\alpha 2^{-f}$\", color=\"black\", marker=\"x\", linestyle=\"--\")\n",
+ "\n",
+ "\n",
+ "# Mean operator is linear in this setting\n",
+ "ax.plot(multi_mean_num_entries_fpr[:,1], multi_mean_num_entries_fpr[:,2], label=r\"$Mean(FPR)$\")\n",
+ "\n",
+ "# Exact probability sum\n",
+ "ax.plot(multi_input_values, multi_exact_probs, label=\"Exact Probability Sum\", color=\"magenta\", marker=\"*\", linestyle=\"--\")\n",
+ "\n",
+ "# tidy the axes\n",
+ "ax.set_ylabel(\"FPR\")\n",
+ "ax.set_xlabel(\"Number of input items: $n$\")\n",
+ "ax.set_yscale(\"log\", base=2)\n",
+ "ax.set_xscale(\"log\", base=2)\n",
+ "ax.grid()\n",
+ "ax.legend(loc=\"upper center\", bbox_to_anchor=(0.5, 1.15), ncol=4)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We see the same behaviour as for the single fingerprint length even when the filter expands.\n",
+ "Different colours represent different fingerprint lengths. The three groups are $5, 4, 3$ from left to right in green, orange, and blue."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3 (ipykernel)",
+ "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
+}
diff --git a/src/notebooks/README.md b/src/notebooks/README.md
new file mode 100644
index 0000000..32225cb
--- /dev/null
+++ b/src/notebooks/README.md
@@ -0,0 +1,13 @@
+# Python Notebooks
+
+These Python notebooks contain the code for generating the plots from
+some of the JAva characterization experiments.
+The notebooks require basic Python data analysis libraries such as:
+- pandas
+- numpy
+- matplotlib
+- seaborn
+- scipy
+- jupyter
+The packages and their dependencies are included in the
+`requirements.txt` file in case you need to make a new virtual environment.
\ No newline at end of file
diff --git a/src/notebooks/qf_probability_sum.py b/src/notebooks/qf_probability_sum.py
new file mode 100644
index 0000000..9a4e6a3
--- /dev/null
+++ b/src/notebooks/qf_probability_sum.py
@@ -0,0 +1,21 @@
+import numpy as np
+from scipy.stats import binom as binom_dist
+
+def qf_probability_sum(num_slots:int|np.int64, num_elements:int|np.int64, fingerprint_length:int|np.int64) -> float:
+ """
+ This sum is well approximated by alpha*2^(-f) for alpha = num_elements / num_slots
+ :param num_slots: The number of slots in the filter
+ :param num_elements: The number of elements to be inserted into the filter
+ :param fingerprint_length: The length of the fingerprint used in the filter
+ :return: The sum of probabilities
+ """
+ m = num_slots
+ n = num_elements
+ f = fingerprint_length
+ assert isinstance(m, int) | isinstance(f, np.int64), "num_slots must be an integer"
+ assert isinstance(n, int) | isinstance(f, np.int64), "num_elements must be an integer"
+ assert isinstance(f, int) | isinstance(f, np.int64), "fingerprint_length must be an integer"
+ dist = binom_dist(n, 1./m)
+ probs = dist.pmf(np.arange(m+1))
+ probs *= (1. - (1. - 2.**(-f))**np.arange(m+1))
+ return np.sum(probs)
\ No newline at end of file
diff --git a/src/notebooks/requirements.txt b/src/notebooks/requirements.txt
new file mode 100644
index 0000000..d571342
--- /dev/null
+++ b/src/notebooks/requirements.txt
@@ -0,0 +1,111 @@
+anyio==4.4.0
+appnope==0.1.4
+argon2-cffi==23.1.0
+argon2-cffi-bindings==21.2.0
+arrow==1.3.0
+asttokens==2.4.1
+async-lru==2.0.4
+attrs==24.2.0
+babel==2.16.0
+beautifulsoup4==4.12.3
+bleach==6.1.0
+certifi==2024.7.4
+cffi==1.17.0
+charset-normalizer==3.3.2
+comm==0.2.2
+contourpy==1.2.1
+cycler==0.12.1
+debugpy==1.8.5
+decorator==5.1.1
+defusedxml==0.7.1
+executing==2.0.1
+fastjsonschema==2.20.0
+fonttools==4.53.1
+fqdn==1.5.1
+h11==0.14.0
+httpcore==1.0.5
+httpx==0.27.0
+idna==3.7
+ipykernel==6.29.5
+ipython==8.26.0
+ipywidgets==8.1.3
+isoduration==20.11.0
+jedi==0.19.1
+Jinja2==3.1.4
+json5==0.9.25
+jsonpointer==3.0.0
+jsonschema==4.23.0
+jsonschema-specifications==2023.12.1
+jupyter==1.0.0
+jupyter-console==6.6.3
+jupyter-events==0.10.0
+jupyter-lsp==2.2.5
+jupyter_client==8.6.2
+jupyter_core==5.7.2
+jupyter_server==2.14.2
+jupyter_server_terminals==0.5.3
+jupyterlab==4.2.4
+jupyterlab_pygments==0.3.0
+jupyterlab_server==2.27.3
+jupyterlab_widgets==3.0.11
+kiwisolver==1.4.5
+MarkupSafe==2.1.5
+matplotlib==3.9.2
+matplotlib-inline==0.1.7
+mistune==3.0.2
+nbclient==0.10.0
+nbconvert==7.16.4
+nbformat==5.10.4
+nest-asyncio==1.6.0
+notebook==7.2.1
+notebook_shim==0.2.4
+numpy==2.0.1
+overrides==7.7.0
+packaging==24.1
+pandas==2.2.2
+pandocfilters==1.5.1
+parso==0.8.4
+pexpect==4.9.0
+pillow==10.4.0
+platformdirs==4.2.2
+prometheus_client==0.20.0
+prompt_toolkit==3.0.47
+psutil==6.0.0
+ptyprocess==0.7.0
+pure_eval==0.2.3
+pycparser==2.22
+Pygments==2.18.0
+pyparsing==3.1.2
+python-dateutil==2.9.0.post0
+python-json-logger==2.0.7
+pytz==2024.1
+PyYAML==6.0.2
+pyzmq==26.1.0
+qtconsole==5.5.2
+QtPy==2.4.1
+referencing==0.35.1
+requests==2.32.3
+rfc3339-validator==0.1.4
+rfc3986-validator==0.1.1
+rpds-py==0.20.0
+scipy==1.14.0
+seaborn==0.13.2
+Send2Trash==1.8.3
+setuptools==72.2.0
+six==1.16.0
+sniffio==1.3.1
+soupsieve==2.6
+stack-data==0.6.3
+terminado==0.18.1
+tinycss2==1.3.0
+tornado==6.4.1
+traitlets==5.14.3
+types-python-dateutil==2.9.0.20240316
+tzdata==2024.1
+uri-template==1.3.0
+urllib3==2.2.2
+wcwidth==0.2.13
+webcolors==24.8.0
+webencodings==0.5.1
+websocket-client==1.8.0
+widgetsnbextension==4.0.11
diff --git a/src/results/QuotientFilterExpansionProfile20240813_090828PST.txt b/src/results/QuotientFilterExpansionProfile20240813_090828PST.txt
new file mode 100644
index 0000000..2502a28
--- /dev/null
+++ b/src/results/QuotientFilterExpansionProfile20240813_090828PST.txt
@@ -0,0 +1,61470 @@
+START JOB QuotientFilterExpansionProfile
+Date Time: 2024/08/13 09:08:28 PST
+NumSlots NumInput FPrintLen NumEntries NumFalsePositives
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(datasketches-characterization) 02/02: Added readme
Posted by ch...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
charlie pushed a commit to branch add-python-plotting
in repository https://gitbox.apache.org/repos/asf/datasketches-characterization.git
commit 47acb6674fb727a2c0dd6be16538d597122db3b2
Author: c-dickens <ch...@apache.org>
AuthorDate: Fri Aug 16 10:30:26 2024 +0100
Added readme
---
src/notebooks/README.md | 23 ++++++++++-------------
1 file changed, 10 insertions(+), 13 deletions(-)
diff --git a/src/notebooks/README.md b/src/notebooks/README.md
index 32225cb..74851e5 100644
--- a/src/notebooks/README.md
+++ b/src/notebooks/README.md
@@ -1,13 +1,10 @@
-# Python Notebooks
-
-These Python notebooks contain the code for generating the plots from
-some of the JAva characterization experiments.
-The notebooks require basic Python data analysis libraries such as:
-- pandas
-- numpy
-- matplotlib
-- seaborn
-- scipy
-- jupyter
-The packages and their dependencies are included in the
-`requirements.txt` file in case you need to make a new virtual environment.
\ No newline at end of file
+# Quotient Filter Profiles Plotting
+
+This folder contains code for plotting quotient filter profiles.
+The notebooks are used to generate visualizations and analyze the performance of quotient filters.
+
+## Usage
+
+To use the plotting code you may need to install the packages in
+the `requirements.txt` file.
+
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