Left truncated customer acquisition data

left-truncated-customer-acquisitions.ipynb

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    {
      "cell_type": "markdown",
      "source": "## Summary\n\nThis notebook studies a simplified story of left truncated data that is closely related to a real world example I encountered. We'll use statistical analysis to show how data truncation can distort a metric such as one might create as a feature for use in machine learning.",
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      "cell_type": "markdown",
      "source": "## The story\n\nGood news! Our retail business has been running for 10 years and, under the definition that a custom _acquisition_ is the event of the their first purchase, we've acquired new customers at a steady rate over that period. Even better, every customer that we've acquired has continued to purchase from us.\n\nBad news! We want to use customer acquistion date in the form of a metric counting days since acquisition  as a feature for training a new machine learning model. But, our data warehouse only contains purchasing data starting some years _after_ we opened for business. In statistical terms, our data are left truncated.\n\nWe're left with a situation where, instead of being able to calculate our true customer acquistion dates, we can only calculate \"truncated\" acquisition dates: the dates of their first purchases _after_ our records begin.\n\nCan you guess what we should expect the truncated acquisition date distribution to look like? Should it be uniform like the true acquisition date distribution? Let's follow the following approach to answer this question.\n\n1. Decide on some reasonable theoretical principles for customer acquisitions.\n2. Derive a probability density for truncated acquisition dates.\n3. Create an separate simulation based on the same principles we used for (2).\n4. Plot the derived density function (2) and a histogram of the simulation results (3) to check for agreement.",
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      "source": "## Definitions\n\n- The variable $t \\in [0,10]$ measures time in units of years, with $t = 0$ being our first day of trading and $t = 10$ being the present day.\n- The constant $t_0 \\in [0,10]$ represents the start of our customer purchase records in our data warehouse.\n- The notational convenience $r_0 = t_0 / 10$ is the fractional amount of time before data warehouse records start.\n- The _true_ customer acquisition date $A_{\\mathrm{true}}$ is a random variable following a uniform distribution, i.e. $A_{\\mathrm{true}} \\sim U(0, 10)$.\n- Repeat purchases constitute a Poisson process with rate $\\lambda$, i.e. the number of purchases $N$ in a year follows $N \\sim \\mathrm{Pois}(\\lambda)$. As an example, $\\lambda=4$ gives a customer expected to make one repeat purchase every 3 months.\n- The _truncated_ customer acquisition date $A_{\\mathrm{trunc}}$ is a random variable representing the apparent acquisition dates, defined as the first of their purchases after $t_0$ that we find in our data.",
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      "cell_type": "markdown",
      "source": "## Characteristics of repeat purchasing\n\nThe choice of a Poisson process for repeat purchasing amounts to making the following assumptions.\n\n1. Purchases are independent of each other. The occurrence of one purchase does not affect the probability that another purchase will occur.\n2. The average purchase rate (purchases per time period) is constant.\n3. Two distinct purchases cannot occur at the same time.",
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      "cell_type": "markdown",
      "source": "## Derivation\n\nThe behaviour of $A_{\\mathrm{trunc}}$ divides naturally into two cases\n1. that corresponding to true acquisition dates after $t_0$ and\n2. that corresponding to true acquisition dates before $t_0$.\n\nGiven that $A_{\\mathrm{true}} \\sim U(0, 10)$, case 1 applies with probability $1-r_0$ and case 2 applies with probability $r_0$. The final density function for $A_{\\mathrm{trunc}}$ then corresponds to the mixture distribution of the case 1 and case 2 densities with weights given by the two probabilities just cited.\n\n### Case 1: customers acquired after the start of records ($A_{\\mathrm{true}} >= t_0$)\n\nIn this case, $A_{\\mathrm{trunc}} = A_{\\mathrm{true}}$ and we have only to truncate the distribution of the latter to obtain the distribution of the former. Note that the required rescaling is implicit in the definition of $U(a,b)$.\n\n$$ A_{\\mathrm{trunc}} \\sim U(t_0, 10) $$\n\n### Case 2: customers acquired before the start of records ($A_{\\mathrm{true}} < t_0$)\n\nIn this case, $A_{\\mathrm{true}}$ is determined by the waiting time until the customer's first repurchase after $t_0$. Because repurchasing is a Poisson process, the unconstrained repurchase waiting time follows the exponential distribution $ \\lambda e^{-\\lambda t} $.\n\nWe can now take advantage of the memoryless nature of the exponential distribution: the repurchase waiting time _given_ that we've already waited until $t=t_0$ is unchanged! This, combined with the recognition that we're starting our waiting at $t=t_0$ rather than $t=0$, gives us\n\n$$ A_{\\mathrm{trunc}} \\sim \\lambda e^{-\\lambda (t-t_0)} $$",
      "metadata": {}
    },
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      "cell_type": "markdown",
      "source": "### The mixture distribution of $A_{\\mathrm{trunc}}$\n\nUsing\n 1. the respective probabilities of case 1 and case 2 as weights,\n 2. the lower and upper bounds of the support of $U(t_0, 10)$ and\n 3. the observation that we cannot turn up a truncated acquisition having a date before the start of records\n\nwe can now form the piecewise continuous PDF for $A_{\\mathrm{trunc}}$.\n\n$$\nA_{\\mathrm{trunc}} \\sim \\begin{cases}\n    0 &t < t_0 \\\\\n    r_0 U(t_0, 10) + (1-r_0) \\lambda e^{-\\lambda(t-t_0)} &t_0 \\leq t < 10 \\\\\n    \\lambda e^{-\\lambda(t-t_0)} &10 \\leq t\n\\end{cases}\n$$",
      "metadata": {}
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      "cell_type": "markdown",
      "source": "### The qualitative behaviour of $A_{\\mathrm{trunc}}$\n\n1. We'll never see a truncated customer acquisition before the start of records at $t_0$.\n2. Immediately after $t_0$ we'll see the greatest concentration of truncated acquisitions, where the exponential component of the mixture distribution takes on its largest values.\n3. As we move into the future from $t_0$, the exponential quickly decays and the concentration of truncated acquisitions converges on the uniform distribution of true acquisitions.\n4. Beyond $t=10$, the end of records of true acquisitions in our assumed dataset, we are left with some rapidly fading chance of nevertheless still observing a truncated acquisition. These are discussed further in the next paragraph.",
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      "source": "### The \"unseens\"\n\nThe PDF followed by $A_{\\mathrm{trunc}}$ non-zero on $[10, \\infty)$. This may come as a surprise since we insisted at the outset that $A_{\\mathrm{true}} \\sim U(0, 10)$. How have we now started to expect to see truncated customer acquisitions after year 10 when no true acquistions happened then? These arise from a particular situation in which a customer\n1. is acquired, unnoticed, before $t_0$ then\n2. neglects to repeat purchase until after year 10.\n\nThis customer _will_ repeat purchase eventually, but the probability of their going any number of years before they do is greater than 0 under the assumed Poisson process.\n\nMaking choices of $t_0 = 3$ and $\\lambda=4$, we can calculate the probability that one of these \"unseen\" acquisitions will come about in the 10-year dataset.\n$$\n\\begin{align}\nP(\\mathrm{unseen}) &= P(A_{\\mathrm{true}} < t_0) \\times P(A_{\\mathrm{trunc}} > 10) \\\\\n    &= r_0 \\times e^{-\\lambda t} \\\\\n    &= 0.3 \\times e^{-4 \\cdot 10} \\\\\n    &\\approx 1.274 \\times 10^{-18} \n\\end{align}\n$$\n\nWell... no one's going to see an unseen at that rate (not even if they live forever after $t=10$).",
      "metadata": {}
    },
    {
      "cell_type": "markdown",
      "source": "## Simulation and plots",
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": "import numpy as np\nimport matplotlib.pyplot as plt",
      "metadata": {
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      "outputs": [],
      "execution_count": 3
    },
    {
      "cell_type": "code",
      "source": "# Model\n\nt_0 = 3.0  # years until records start\nr_0 = t_0/10\nlmbda = 4  # repeat purchases per year on average\n\ndef A_trunc_pdf(t):\n    if t < t_0:\n        return 0\n\n    if t < 10:\n        return (1-r_0) * 1/(10-t_0) + r_0 * lmbda * np.exp(-lmbda*(t-t_0))\n\n    return lmbda * np.exp(-lmbda*(t-t_0))\n\n# Insert NaNs at jump discontinuities to stop pylot from interpolating across them\nt = np.concatenate([\n    np.arange(0, t_0, 1e-2),\n    [np.nan],\n    np.arange(t_0, 10, 1e-2),\n    [np.nan],\n    np.arange(10, 15, 1e-2)\n])",
      "metadata": {
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      },
      "outputs": [],
      "execution_count": 4
    },
    {
      "cell_type": "code",
      "source": "# Simulation\n\n# Uniformly distribute true customer acquisition times\nA = np.random.uniform(0, 10, 1000)\n# Convert Poisson rate parameter to the scale factor expected by Numpy's exponential distribution sampler\nexp_scale = 1 / lmbda\n\nfor i in range(len(A)):\n    # For each customer acquired before t_0, simulate repeat purchases until we pass t_0\n    while A[i] < t_0:\n        A[i] += np.random.exponential(exp_scale)",
      "metadata": {
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      "outputs": [],
      "execution_count": 5
    },
    {
      "cell_type": "code",
      "source": "plt.figure(figsize=(9,6))\n\nax = plt.plot(t, [A_trunc_pdf(t_scalar) for t_scalar in t], color='b')\nplt.hist(A, bins=50, density=True, color='orange', alpha=0.3)\n\nplt.title('Probability density of A_trunc')\nplt.xlabel('Time (years)')\nplt.ylim(-0.1, plt.ylim()[1])\nplt.axvline(x=t_0, color='r', ls=':')  # the start of records\nplt.axvline(x=10, color='r', ls=':')  # the end of records\nplt.grid()",
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"
          },
          "metadata": {}
        }
      ],
      "execution_count": 7
    }
  ]
}