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   "source": [
    "# A Framework to Understand DP\n",
    "\n",
    "This resource introduces differential privacy from the perspective of the OpenDP programming framework.\n",
    "No prior knowledge is assumed of differential privacy (DP), but you will likely still find this resource useful for understanding DP even if you already have a background in DP.\n",
    "Prior knowledge in basic probability, like random variables, will be useful.\n",
    "\n",
    "Assume we have a vector dataset $u$ where each record contains sensitive information about a different individual."
   ]
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   "source": [
    "# u is a small vector dataset with contributions from:\n",
    "#   [Alice, Jane, John, Jack, ...]\n",
    "u = [12,    10,   8,    7,       ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use differential privacy to collect measurements (statistics such as means and histograms) on this dataset, without revealing information about specific individuals.\n",
    "\n",
    "To understand DP, it is important to first understand:  \n",
    "1. distance between datasets  \n",
    "2. distance between distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distance Between Datasets - Adjacency\n",
    "\n",
    "An adjacent dataset is any dataset that differs from our dataset by a single individual.\n",
    "Returning to our vector dataset example, assume our dataset $u$ has one record that contains information about a person, Alice.\n",
    "Then one adjacent dataset $v$ would contain every row in $u$ except for the row with Alice's information. "
   ]
  },
  {
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   "source": [
    "# v is one (of many) datasets that are adjacent to u\n",
    "#   [Jane, John, Jack, ...] (without Alice!)\n",
    "v = [10,   8,    7,       ]"
   ]
  },
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   "source": [
    "You can construct other datasets adjacent to $u$ by dropping a different row or adding a new row.\n",
    "When one person may contribute up to $k$ rows, adjacent datasets differ by up to $k$ additions and removals. \n",
    "\n",
    "The number of additions/removals between any two datasets is equivalent to the cardinality of the symmetric difference between the multisets $u$ and $v$. We call this metric the symmetric distance.\n",
    "\n",
    "$$d_{\\mathrm{Sym}}(u, v) = |u \\triangle v| = \\sum_x |\\# \\{ i : x = u_i \\} - \\# \\{ i : x = v_i \\}|$$\n",
    "\n",
    "\n",
    "And in code:"
   ]
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  {
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   "execution_count": 3,
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    "execution": {
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       "1"
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   "source": [
    "def d_SymmetricDistance(u, v):\n",
    "    \"\"\"symmetric distance between multisets u and v\"\"\"\n",
    "    # NOT this, as sets are not multisets. Loses multiplicity:\n",
    "    # return len(set(u).symmetric_difference(set(v)))\n",
    "\n",
    "    from collections import Counter\n",
    "    u, v = Counter(u), Counter(v)\n",
    "    # indirectly compute symmetric difference via the union of asymmetric differences\n",
    "    return sum(((u - v) + (v - u)).values())\n",
    "\n",
    "\n",
    "# compute the symmetric distance between our two example datasets:\n",
    "d_SymmetricDistance(u, v)"
   ]
  },
  {
   "attachments": {},
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   "source": [
    "$d_{\\mathrm{Sym}}(\\{12, 10, 8, 7\\}, \\{10, 8, 7\\}) = |\\{12, 10, 8, 7\\} \\triangle \\{10, 8, 7\\}| = |\\{12\\}| = 1$\n",
    "\n",
    "If the second dataset $v$ were to differ from $u$ by changing the 12 to 10, then we would still count the multiplicity of 10:\n",
    "\n",
    "$d_{\\mathrm{Sym}}(\\{12, 10, 8, 7\\}, \\{10, 10, 8, 7\\}) = |\\{12, 10, 8, 7\\} \\triangle \\{10, 10, 8, 7\\}| = |\\{12, 10\\}| = 2$\n",
    "\n",
    "In practice, we never directly compute these distances.\n",
    "In order to apply differentially private methods, you need to establish an upper bound on the distance between adjacent datasets.\n",
    "For example, if each individual person may affect up to five records in the dataset, then setting a distance $d_in = 5$ allows us to ensure individual-level privacy.\n",
    "\n",
    "For instance, in the vector dataset example, it was stipulated that each element contains sensitive information about a different individual. \n",
    "This statement implies that the symmetric distance between adjacent datasets, where one individual is added or removed, is at most one.\n",
    "That is, for any choice of datasets $u$ and $v$ such that $u$ is adjacent to $v$ (denoted $u \\sim_{\\mathrm{Sym}} v$), we have that $d_{\\mathrm{Sym}}(u, v) \\leq 1$. \n",
    "\n",
    "Before moving on, there are some trivial generalizations. \n",
    "A dataset need not be a vector, it could be a dataframe or any other collection with a concept of records. \n",
    "There are also other dataset metrics aside from `SymmetricDistance` (used for unbounded DP), such as `ChangeOneDistance` (used for bounded DP). There are also variations of metrics that are sensitive to data ordering, metrics for describing distances between graphs, and more!\n",
    "\n",
    "You should now have a sense for what an adjacent dataset means, how dataset distances work, and an intuitive understanding of the symmetric distance metric."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distance Between Distributions - Divergence\n",
    "You can think of a measurement $M(\\cdot)$ as a differentially private statistic.\n",
    "Measurements are described by random variables (RVs), that is, they sample from noise distributions.\n",
    "The outputs of a measurement are realizations of a random variable that follow a known probability distribution.\n",
    "Measurements only have one input: a dataset; other parameters are fixed when the measurement is constructed.\n",
    "For context, a Laplace RV has parameters for shift and scale.\n",
    "This section describes how to measure distance between the distributions of measurements on adjacent datasets.\n",
    "\n",
    "A common measurement is the Laplace DP sum, which is a sample from the Laplace distribution centered at the dataset sum with a fixed noise scale.\n",
    "The following plot compares the distribution of the DP sum on dataset $u$ with the distribution of the DP sum on dataset $v$, when the noise scale is fixed to `25`."
   ]
  },
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "scale = 25\n",
    "\n",
    "# while in this case the support theoretically includes all reals, \n",
    "#     we only bother plotting part of the support\n",
    "support = np.arange(sum(v) - scale, sum(u) + scale)\n",
    "\n",
    "def rv_M(x):\n",
    "    \"\"\"returns a random variable, M(x)\"\"\"\n",
    "    from scipy.stats import laplace\n",
    "    return laplace(loc=sum(x), scale=scale)\n",
    "\n",
    "def plot_pdfs(u, v, output_domain):\n",
    "    plt.plot(output_domain, rv_M(u).pdf(output_domain), label=\"$p_{M(u)}(x)$\") # type: ignore\n",
    "    plt.plot(output_domain, rv_M(v).pdf(output_domain), label=\"$p_{M(v)}(x)$\") # type: ignore\n",
    "    plt.ylabel('density: $p_{RV}(x)$')\n",
    "    plt.xlabel('support: x')\n",
    "    plt.legend(prop={'size': 15})\n",
    "plot_pdfs(u, v, support)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are interested in the greatest divergence, a measure of the dissimilarity of these two distributions.\n",
    "While divergences are not necessarily distances, we informally refer to them as distances.\n",
    "A common measure of divergence is based on the log ratio of probabilities:\n",
    "\n",
    "$$D_{\\mathrm{MaxDivergence}}(M(u), M(v)) = \\max\\limits_{S \\subseteq \\mathrm{supp}(M(u))} \\log\\left(\\frac{\\Pr[M(u) \\in S]}{\\Pr[M(v) \\in S]}\\right)$$\n",
    "\n",
    "In this equation we define the distance between the RVs of $M(u)$ and $M(v)$ to be the maximum divergence among all possible subsets of the support.\n",
    "\n",
    "For our DP sum with Laplacian noise example, the output domain of $M(\\cdot)$ is the set of all real numbers, $\\mathbb{R}$.\n",
    "In the plot below, I illustrate this equation for one randomly chosen subset $S$ of the output domain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.439394Z",
     "iopub.status.busy": "2025-06-04T18:17:56.439288Z",
     "iopub.status.idle": "2025-06-04T18:17:56.514596Z",
     "shell.execute_reply": "2025-06-04T18:17:56.514378Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_S(u, v, S):\n",
    "    \"\"\"draw the probability regions spanned by S\"\"\"\n",
    "    plt.fill_between(S, rv_M(u).pdf(S), label=\"$\\\\Pr[M(u) \\\\in S]$\", alpha=.4) # type: ignore\n",
    "    plt.fill_between(S, rv_M(v).pdf(S), label=\"$\\\\Pr[M(v) \\\\in S]$\", alpha=.4) # type: ignore\n",
    "    plt.plot([np.min(S), np.max(S)], [0, 0], label=\"S\")\n",
    "    plt.legend()\n",
    "\n",
    "# re-run this notebook to see different choices of S\n",
    "S = np.arange(*sorted(np.random.choice(support, size=2, replace=False)))\n",
    "\n",
    "plot_pdfs(u, v, support)\n",
    "plot_S(u, v, S)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The area of the blue region is the probability that $M(u)$ is in $S$... and similarly the area of the orange region is $\\Pr[M(v) \\in S]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.515913Z",
     "iopub.status.busy": "2025-06-04T18:17:56.515827Z",
     "iopub.status.idle": "2025-06-04T18:17:56.519453Z",
     "shell.execute_reply": "2025-06-04T18:17:56.519260Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of blue region:   0.2867171279172761\n",
      "area of orange region: 0.3978533407816897\n",
      "divergence for this S: 0.32758733417005853\n"
     ]
    }
   ],
   "source": [
    "def divergence_over_S(u, v, S):\n",
    "    \"\"\"prints the Divergence(M(u), M(v)) over some interval S, assuming M(x) = Laplace(sum(x), scale)\"\"\"\n",
    "\n",
    "    # integrate over both regions\n",
    "    lower, upper = np.min(S), np.max(S)\n",
    "    pr_Mu_in_S = rv_M(u).cdf(upper) - rv_M(u).cdf(lower) # blue\n",
    "    pr_Mv_in_S = rv_M(v).cdf(upper) - rv_M(v).cdf(lower) # orange\n",
    "\n",
    "    print(\"area of blue region:  \", pr_Mu_in_S)\n",
    "    print(\"area of orange region:\", pr_Mv_in_S)\n",
    "    print(\"divergence for this S:\", np.abs(np.log(pr_Mu_in_S / pr_Mv_in_S)))\n",
    "divergence_over_S(u, v, S)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the divergence between the RVs of $M(u)$ and $M(v)$ for one choice of S, but keep in mind that $D_{\\mathrm{MaxDivergence}}(M(u), M(v))$ is the greatest divergence over any choice of $S$.\n",
    "Intuitively, the divergence between the RVs of $M(u)$ and $M(v)$ for the same $S$ must increase if Alice made a greater contribution to the statistic:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.520580Z",
     "iopub.status.busy": "2025-06-04T18:17:56.520500Z",
     "iopub.status.idle": "2025-06-04T18:17:56.596646Z",
     "shell.execute_reply": "2025-06-04T18:17:56.596416Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "area of blue region:   0.008486665039311609\n",
      "area of orange region: 0.3978533407816897\n",
      "divergence for this S: 3.8475873341700586\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# hypothetical: what if Alice's contribution was 100, instead of 12?\n",
    "u_prime = [100, *u[1:]]\n",
    "divergence_over_S(u_prime, v, S)\n",
    "\n",
    "output_domain = np.arange(sum(v) - scale, sum(u_prime) + scale, 1)\n",
    "plot_pdfs(u_prime, v, output_domain)\n",
    "plot_S(u_prime, v, S)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, when the divergence between probability distributions is greater, we can more confidently distinguish which distribution a sample came from. \n",
    "These examples help to form an intuition for how the max divergence measure relates to privacy.\n",
    "\n",
    "Moreso, the max divergence qualifies as a measure of privacy because it provides immunity from post-processing.\n",
    "There is no further computation that can be made on the release that will make it easier to distinguish which distribution a sample came from. \n",
    "That is, the divergence cannot increase after applying $f$ to a release:\n",
    "\n",
    "$$\\forall f \\quad D\\Bigl(M(u), M(v)\\Bigr) \\ge D\\Bigl(f(M(u)), f(M(v))\\Bigr)$$\n",
    "\n",
    "This property is the crucial distinction between measures, as discussed in this section, and metrics, as discussed in the previous section. \n",
    "Measurements and transformations share the same distinction."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of Privacy\n",
    "Now that we have an understanding of distances between datasets, and distances between distributions, we can define the privacy of a measurement, $M(\\cdot)$:\n",
    "\n",
    "> $M(\\cdot)$ is $\\boldsymbol\\epsilon\\textbf{-differentially private}$ at distance $k$ if, \n",
    "> for every pair of datasets $u$ and $v$ such that $d_{\\mathrm{Sym}}(u, v) \\leq k$, \n",
    "> we have that $D_{\\mathrm{MaxDivergence}}(M(u), M(v)) \\leq \\epsilon$.\n",
    "\n",
    "\n",
    "In this definition, we relate a dataset distance $k$ to another distance $\\epsilon$.\n",
    "This $\\epsilon$ is more general than the max divergence we computed in the previous section because it is the greatest divergence over all possible choices of $S$, _and over all possible pairs of adjacent datasets_ $u$ and $v$.\n",
    "$\\epsilon$ is often referred to as a bound on the privacy loss of $M(\\cdot)$.\n",
    "\n",
    "This has a very practical interpretation: Let's say I have a dataset $x$ for which an individual user can contribute at most $k$ rows, and a statistic $M(\\cdot)$ that is $\\epsilon$-DP when user contribution is at most $k$.\n",
    "By the DP guarantee, it is proven that the influence of any one individual on the data release induces a divergence no greater than $\\epsilon$. Thus, assuming a reasonably small choice of $\\epsilon$, the individual's participation in the statistical release is kept private, because their influence on the data release is at most $\\epsilon$-distinguishable."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you have some background in differential privacy you may be more familiar with a definition of privacy worded like this:\n",
    "\n",
    "> $M(\\cdot)$ is $\\boldsymbol\\epsilon\\textbf{-differentially private}$ if, \n",
    "> for every pair of adjacent datasets $u$ and $v$, \n",
    "> we have that $\\Pr[M(u) \\in S] \\leq e^\\epsilon \\cdot \\Pr[M(v) \\in S]$.\n",
    "\n",
    "This is mostly equivalent, because of the way we've defined $D_{\\mathrm{MaxDivergence}}(M(u), M(v))$ in the previous section.\n",
    "However, this formulation of the definition is ambiguous about what makes a dataset adjacent. To obtain well-defined privacy guarantees, it is important to specify the dataset metric and dataset distance."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We further generalize the definition of privacy:\n",
    "\n",
    "> $M(\\cdot)$ is $(d_{in}, d_{out})\\textbf{-differentially private}$ with respect to input metric $MI$ and output measure $MO$ if, \n",
    "> for any choice of datasets $u$ and $v$ such that $d_{MI}(u, v) \\leq d_{in}$, \n",
    "> we have that $D_{MO}(M(u), M(v)) \\leq d_{out}$.\n",
    "\n",
    "The first definition can be reclaimed by letting $MI$ be `SymmetricDistance` and $MO$ be `MaxDivergence`. \n",
    "$MO$ can be set to other measures of divergence to represent approximate ($\\epsilon, \\delta$)-differential privacy, or zero-concentrated $\\rho$-differential privacy.\n",
    "Similarly, our choice of `SymmetricDistance` represents unbounded DP, but we can represent bounded DP by letting $MI$ be `ChangeOneDistance`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distance Between Aggregates - Sensitivity\n",
    "The _sensitivity_ is the greatest amount an aggregate can change when computed on an adjacent dataset.\n",
    "Aggregators are typically deterministic statistics (like the sum or histogram functions), and their exact outputs are aggregates.\n",
    "More generally, a transformation $T(\\cdot)$ is a function from a data domain to a data domain.\n",
    "Aggregators are a kind of transformation in which the output domain consists of aggregates.\n",
    "\n",
    "One example of a sensitivity metric is the `AbsoluteDistance`, which is used to measure the distance between scalar aggregates. \n",
    "$$d_{\\mathrm{Abs}}(a, b) = |a - b|$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.598046Z",
     "iopub.status.busy": "2025-06-04T18:17:56.597914Z",
     "iopub.status.idle": "2025-06-04T18:17:56.599537Z",
     "shell.execute_reply": "2025-06-04T18:17:56.599334Z"
    }
   },
   "outputs": [],
   "source": [
    "def d_Abs(a, b):\n",
    "    \"\"\"absolute distance between a and b\"\"\"\n",
    "    return abs(a - b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the absolute distance metric to express the sensitivity of the sum aggregator.\n",
    "In our vector dataset example, we know each individual can contribute at most one record.\n",
    "Since this record is unbounded, it can perturb the sum an arbitrarily large amount towards positive or negative infinity.\n",
    "This is unfortunate, because it implies that the divergence is also infinite!\n",
    "\n",
    "In order to attain a finite sensitivity, it is customary to clamp— that is, to replace any value less than a lower bound with the lower bound, and any value greater than an upper bound with the upper bound. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.600729Z",
     "iopub.status.busy": "2025-06-04T18:17:56.600652Z",
     "iopub.status.idle": "2025-06-04T18:17:56.602222Z",
     "shell.execute_reply": "2025-06-04T18:17:56.602043Z"
    }
   },
   "outputs": [],
   "source": [
    "def clamped_sum_0_12(x):\n",
    "    \"\"\"a naive function that computes the sum, where each element is clamped within [0, 12]\"\"\"\n",
    "    return sum(np.clip(x, 0, 12))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Broadly speaking, if the transformation clamps data to the interval $[L, U]$, and we know each individual contributes at most $d_{in}$ records, then the clamped sum sensitivity ($d_{out}$) is\n",
    "$$\\max_{u \\sim_{Sym} v} |\\mathrm{clamped\\_sum}(u) - \\mathrm{clamped\\_sum}(v)| = d_{in} \\cdot \\max(|L|, U)$$\n",
    "\n",
    "We can use this to solve for the sensitivity of $clamped\\_sum\\_0\\_12$, by letting $[L, U] = [0, 12]$. Thus its sensitivity is $1 \\cdot max(|0|, 12) = 12$. For any conceivable dataset $u$, adding or removing any individual (to get some dataset $v$) can change the sum by at most $12$.\n",
    "\n",
    "Our current choice of $u$ and $v$ is an example that maximizes the absolute distance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.603290Z",
     "iopub.status.busy": "2025-06-04T18:17:56.603223Z",
     "iopub.status.idle": "2025-06-04T18:17:56.605198Z",
     "shell.execute_reply": "2025-06-04T18:17:56.605000Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(12)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_Abs(clamped_sum_0_12(u), clamped_sum_0_12(v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can even use the `AbsoluteDistance` as the input metric $MI$ of a measurement $M(\\cdot)$ (see the definition of privacy).\n",
    "Let's define a new function $laplace\\_noise$ to illustrate this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2025-06-04T18:17:56.607631Z"
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   "source": [
    "def laplace_noise(x):\n",
    "    \"\"\"a naive function that adds an approximation to Laplace noise\"\"\"\n",
    "    return np.random.laplace(loc=x, scale=scale)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We let $MI$ be `AbsoluteDistance` and $MO$ be `MaxDivergence`.\n",
    "It can be shown that for any choice of $u, v \\in \\mathbb{R}$ such that $d_{\\mathrm{Abs}}(u, v) \\leq d_{in}$, and $d_{out} = d_{in} / scale$, then:\n",
    "$$D_{\\mathrm{MaxDivergence}}(\\mathrm{laplace\\_noise}(u), \\mathrm{laplace\\_noise}(v)) \\leq d_{out}$$\n",
    "Therefore, if the data types in this function had infinite precision, then $laplace\\_noise$ would be a measurement.\n",
    "Other common metrics to express sensitivities are `L1Distance` and `L2Distance`."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of Stability\n",
    "Similar to how we defined the privacy of a measurement $M(\\cdot)$, we can also define the stability of a transformation, $T(\\cdot)$:\n",
    "\n",
    "> $T(\\cdot)$ is $(d_{in}, d_{out})\\textbf{-stable}$ with respect to input metric $MI$ and output metric $MO$ if, for any choice of datasets $u$ and $v$ such that $d_{MI}(u, v) \\leq d_{in}$, we have that $d_{MO}(T(u), T(v)) \\leq d_{out}$.\n",
    "\n",
    "An example is the $clamped\\_sum\\_0\\_12$ function from the previous section.\n",
    "If the data types in $clamped\\_sum\\_0\\_12$ had infinite precision, it would be a stable transformation where $MI$ is `SymmetricDistance` and $MO$ is `AbsoluteDistance`.\n",
    "We've previously shown that when $d_{in} = 1$, the sensitivity $d_{out} = 12$.\n",
    "\n",
    "This stability guarantee does not carry privacy guarantees on its own, but it lets us construct building blocks that can be chained together.\n",
    "If the output metric $MO$ and output domain $DO$ of a transformation $T(\\cdot)$ conform with the input metric $MI$ and input domain $DI$ of a measurement $M(\\cdot)$, then it is valid to construct a new measurement $M_{\\mathrm{chained}}(\\cdot) = M(T(\\cdot))$.\n",
    "We can similarly construct a new transformation $T_{\\mathrm{chained}}(\\cdot) = T_2(T_1(\\cdot))$.\n",
    "\n",
    "Notice that the output domain and metric of the $clamped\\_sum\\_0\\_12$ transformation conform with the input metric and domain of the $laplace\\_noise$ measurement, so we can chain these together:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2025-06-04T18:17:56.610255Z"
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   "source": [
    "def laplace_sum(x):\n",
    "    \"\"\"a naive function that computes the noisy clamped sum\"\"\"\n",
    "    return laplace_noise(clamped_sum_0_12(x))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this function was constructed by chaining a stable transformation and private measurement, it is trivial to prove that it is a private measurement (if the data types had infinite precision).\n",
    "The new chained measurement's $MI$ is `SymmetricDistance`, and $MO$ is `MaxDivergence`, and when the dataset distance $d_{in} = 1$, we have that $\\epsilon = d_{out} = d_{in} \\cdot \\max(|0|, 12) / 25 = d_{in} \\cdot 0.48 = 0.48$.\n",
    "That is, when an individual can contribute at most one record, the maximum observable divergence among the output distributions is $0.48$.\n",
    "\n",
    "\n",
    "## Stability Maps and Privacy Maps\n",
    "\n",
    "A crucial takeaway from this notebook is a high-level understanding that _differential privacy is a system to relate distances_ ($d_{in}$ and $d_{out}$).\n",
    "If you can establish a bound on the distance to adjacent datasets $d_{in}$ (in terms of some metric $MI$) then you can work out the stability or privacy properties $d_{out}$ (in terms of some metric or measure $MO$) of computations made on your data.\n",
    "\n",
    "We encapsulate this relationship between distances with one last abstraction, a _map_.\n",
    "A _map_ is a function, associated with your computation, that computes a $d_{out}$ for any given $d_{in}$. \n",
    "Thus, if $map(d_{in}) \\le d_{out}$, then a computation is $d_{out}$-DP.\n",
    "\n",
    "The stability map for the $clamped\\_sum\\_0\\_12$ function is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
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     "shell.execute_reply": "2025-06-04T18:17:56.617183Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def clamped_sum_0_12_map(d_in):\n",
    "    return d_in * max(abs(0), 12)\n",
    "\n",
    "# find the smallest d_out (absolute distance) of clamped_sum_0_12 when d_in (symmetric distance) is 1\n",
    "clamped_sum_0_12_map(d_in=1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This map is just a repackaging of our previous formula for the clamped sum sensitivity, so that $d_{in}$ can be set later. It is referred to as a _stability_ map because stability is a more general term than sensitivity, \n",
    "namely a bound on on how much outputs can change as a function of input distances.\n",
    "\n",
    "The same pattern holds for the privacy map of the $laplace\\_noise$ measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.619778Z",
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     "shell.execute_reply": "2025-06-04T18:17:56.621378Z"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def laplace_noise_map(d_in):\n",
    "    return d_in / scale\n",
    "\n",
    "# find the smallest d_out (epsilon) of laplace_noise when d_in (absolute distance) is 12\n",
    "laplace_noise_map(d_in=12)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we refer to it as a privacy map, because the output distance is in terms of a privacy measure, which captures distance between output _distributions_ (like `MaxDivergence`) and hence offers privacy guarantees.\n",
    "Now that we have the stability map for the clamped sum transformation and the privacy map for the Laplace noise measurement, we can automatically construct the privacy map for the Laplace sum measurement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-04T18:17:56.622737Z",
     "iopub.status.busy": "2025-06-04T18:17:56.622667Z",
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     "shell.execute_reply": "2025-06-04T18:17:56.624403Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def laplace_sum_map(d_in):\n",
    "    return laplace_noise_map(clamped_sum_0_12_map(d_in))\n",
    "\n",
    "# find the smallest d_out (epsilon) of laplace_noise when d_in (symmetric distance) is 1\n",
    "laplace_sum_map(1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've now come full-circle.\n",
    "In the \"Distance Between Distributions\" section, we computed an example divergence for one choice of $S$.\n",
    "We have now indirectly computed an upper bound for that divergence of $0.48$.\n",
    "You may notice that some choices of $S$ in that section can give divergences very slightly larger than $0.48$.\n",
    "This is because floating-point numbers have finite precision, so intermediate computations were subject to rounding that introduced error.\n",
    "\n",
    "The transformation and measurement examples in this notebook are only $(d_{in}, d_{out})$-differentially private if we assume the data types have infinite precision— and they don't!\n",
    "Building transformations or measurements that have proven stability or privacy properties is nontrivial, especially if you account for finite precision in data types.\n",
    "This is the purpose of the OpenDP library: to help you build robust transformations and measurements with rigorous privacy properties.\n",
    "\n"
   ]
  }
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