Lab_6_ExpFam_Divergences.ipynb

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        "<a href=\"https://colab.research.google.com/github/USCbiostats/PM520/blob/main/Lab_6_ExpFam_Divergences.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# It's a Family Affair, or: Exponential Families, Natural Gradient Descent, & Statistical Divergences\n",
        "\n",
        "[Exponential Families](https://en.wikipedia.org/wiki/Exponential_family) (sometimes abbreviated as ExpFam) provide a [succinct characterization](https://en.wikipedia.org/wiki/Exponential_family#Table_of_distributions) of many distributions (e.g., [Normal](https://en.wikipedia.org/wiki/Normal_distribution), [Gamma](https://en.wikipedia.org/wiki/Gamma_distribution), [Poisson](https://en.wikipedia.org/wiki/Poisson_distribution), [Bernoulli](https://en.wikipedia.org/wiki/Bernoulli_distribution), [Wishart](https://en.wikipedia.org/wiki/Wishart_distribution), etc.). We'll take an informal look at their properties and how to perform inference.\n",
        "\n",
        "We'll also take an informal review of [statistical divergences](https://en.wikipedia.org/wiki/Divergence_%28statistics%29), which reflect notions of a \"distance\" between parametric distributions.\n",
        "\n",
        "Lastly, we look at another means to perform optimization, but different from previous approaches, we show how to generalize notions of \"steepest\" to consider the underlying geometry in a distributional sense through *natural* gradient descent."
      ],
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      "source": [
        "## Exponential Families\n",
        "Let $\\eta = [\\eta_1, \\dotsc, \\eta_k]$ be a $k$-vector of parameters, and $x$ be an observation such that $x \\sim f(\\eta)$. We can define its [PDF](https://en.wikipedia.org/wiki/Probability_density_function) (or [PMF](https://en.wikipedia.org/wiki/Probability_mass_function) in case of discrete $x$) as $$f(x | \\eta) = h(x)\\exp(\\eta \\cdot T(x) - A(\\eta)),$$ where $h(x)$ is a *base measure*, $\\eta$ are the *natural parameters*, $T(x)$ are the [*sufficient statistics*](https://en.wikipedia.org/wiki/Sufficient_statistic), and $A(\\eta)$ is the [*log-partition function*](https://en.wikipedia.org/wiki/Partition_function_%28mathematics%29). If $\\eta$ is *finite*, and the [*support*](https://en.wikipedia.org/wiki/Support_%28mathematics%29%23In_probability_and_measure_theory) of $f$ does not depend on the value of $\\eta$, then $f$ can be said to be a member of the [Exponential Families](https://en.wikipedia.org/wiki/Exponential_family).\n",
        "\n",
        "### Example: Normal Distribution\n",
        "Recall if $x \\sim N(\\mu, \\sigma^2)$, then the PDF of $x$ is given by,\n",
        "$$f(x | \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} \\exp\\left(-\\frac{(x - \\mu)^2}{2 \\sigma^2}\\right).$$ To see that the two-parameter Normal distribution is a member of the Exponential Families, define $\\eta = [\\frac{\\mu}{\\sigma^2}, -\\frac{1}{2\\sigma^2}]$, $h(x) = \\frac{1}{\\sqrt{2\\pi}}$, $T(x) = [x, x^2]^T$, and $A(\\eta) = \\frac{\\mu^2}{2\\sigma^2} + \\log |\\sigma| = -\\frac{\\eta_1^2}{4\\eta_2} + \\frac{1}{2}\\log|\\frac{1}{2\\eta_2}|$. Placing this all together we have,\n",
        "$$\\begin{align*}\n",
        "f(x | \\eta) &= h(x)\\exp(\\eta \\cdot T(x) - A(\\eta)) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp(\\eta \\cdot T(x) - A(\\eta)) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp\\left([\\frac{\\mu}{\\sigma^2}, -\\frac{1}{2\\sigma^2}] \\cdot T(x) - A(\\eta)\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp\\left([\\frac{\\mu}{\\sigma^2}, -\\frac{1}{2\\sigma^2}] \\cdot [x, x^2]^T - A(\\eta)\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp\\left(\\frac{\\mu x}{\\sigma^2} -\\frac{x^2}{2\\sigma^2} - A(\\eta)\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp\\left(\\frac{\\mu x}{\\sigma^2} -\\frac{x^2}{2\\sigma^2} + \\frac{\\eta_1^2}{4\\eta_2} - \\frac{1}{2}\\log\\left|\\frac{1}{2\\eta_2}\\right|\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp\\left(\\frac{\\mu x}{\\sigma^2} -\\frac{x^2}{2\\sigma^2} - \\frac{\\mu^2}{2\\sigma^2} - \\log |\\sigma|\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}} \\exp\\left(-\\frac{(x - \\mu)^2}{2\\sigma^2} - \\log |\\sigma|\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi}\\sigma} \\exp\\left(-\\frac{(x - \\mu)^2}{2\\sigma^2}\\right) \\\\\n",
        "  &= \\frac{1}{\\sqrt{2\\pi\\sigma^2}} \\exp\\left(-\\frac{(x - \\mu)^2}{2\\sigma^2}\\right) \\\\\n",
        "\\end{align*}$$\n",
        "\n",
        "## Expectations\n",
        "A key property of ExpFam distributions is that one can define the [moments](https://en.wikipedia.org/wiki/Moment_%28mathematics%29) of $T(x)$ from the log-partition function $A(\\eta)$. Two key moments to remember are, $\\mathbb{E}[T(x)] = \\frac{\\partial}{\\partial \\eta} A(\\eta)$ and $\\mathbb{V}[T(x)] = \\frac{\\partial^2}{\\partial \\eta \\partial \\eta^T} A(\\eta)$.\n",
        "\n",
        "In the case of scalar Normal variables, we have $\\mathbb{E}[T(x)] = \\mathbb{E}\\left[[x, x^2]\\right] = [\\mu, \\sigma^2 + \\mu^2]$ and $\\mathbb{V}[T(x)] = \\begin{bmatrix} \\sigma^2 & 0 \\\\ 0 & 2\\sigma^4 \\end{bmatrix}$.\n",
        "$$\\begin{align*}\n",
        "\\mathbb{E}[T(x)] &= \\frac{\\partial}{\\partial \\eta} A(\\eta) \\\\\n",
        "  &= \\frac{\\partial}{\\partial \\eta} \\left[-\\frac{\\eta_1^2}{4\\eta_2} + \\frac{1}{2}\\log|\\frac{1}{2\\eta_2}|\\right] \\\\\n",
        "  &= -\\frac{\\partial}{\\partial \\eta} \\frac{\\eta_1^2}{4\\eta_2} + \\frac{\\partial}{\\partial \\eta}\\frac{1}{2}\\log|\\frac{1}{2\\eta_2}| \\\\\n",
        "  &= -\\frac{\\partial}{\\partial \\eta} \\frac{\\eta_1^2}{4\\eta_2} - \\frac{\\partial}{\\partial \\eta}\\frac{1}{2}\\log|2\\eta_2| \\\\\n",
        "\\mathbb{E}[T(x)]_1 &= -\\frac{\\partial}{\\partial \\eta_1} \\frac{\\eta_1^2}{4\\eta_2} - \\frac{\\partial}{\\partial \\eta_1}\\frac{1}{2}\\log|2\\eta_2| \\\\\n",
        "  &= - \\frac{2 \\eta_1}{4 \\eta_2} = -\\frac{\\eta_1}{2 \\eta_2} = -\\frac{\\mu / \\sigma^2}{-2 / (2\\sigma^2)} = \\mu \\\\\n",
        "\\mathbb{E}[T(x)]_2 &= -\\frac{\\partial}{\\partial \\eta_2} \\frac{\\eta_1^2}{4\\eta_2} - \\frac{\\partial}{\\partial \\eta_2}\\frac{1}{2}\\log|2\\eta_2| \\\\\n",
        "  &= \\frac{\\eta^2_1}{\\eta_2^2} - \\frac{1}{2\\eta_2} = \\frac{\\mu^2/\\sigma^4}{1/\\sigma^4} + \\frac{1}{1 / \\sigma^2} = \\mu^2 + \\sigma^2.\n",
        "\\end{align*}$$\n",
        "\n",
        "## MLE Inference for ExpFam\n",
        "Given $x_1, \\dotsc, x_n$ we assume that $x_i \\sim f(\\eta)$ independently and identically distributed under some ExpFam dist $f$ with natural parameters $\\eta$. Our log-likelihood is then given by,\n",
        "$$ \\ell(\\eta) = \\sum_{i=1}^n \\log f(x_i | \\eta).$$ To identify the\n",
        "maximum likelihood estimates we first compute the gradient of $\\ell$ wrt $\\eta$, which is given by\n",
        "$$\\begin{align*}\n",
        "\\nabla \\ell(\\eta) &= \\sum_{i=1}^n \\nabla \\log f(x_i | \\eta) \\\\\n",
        "  &= \\sum_{i=1}^n \\nabla \\log \\left[ h(x_i)\\exp(\\eta \\cdot T(x_i) - A(\\eta))\\right] \\\\\n",
        "  &= \\sum_{i=1}^n \\nabla \\left[\\log h(x_i) + \\log \\exp(\\eta \\cdot T(x_i) - A(\\eta))\\right] \\\\\n",
        "  &= \\sum_{i=1}^n \\nabla \\log h(x_i) + \\nabla \\log \\exp(\\eta \\cdot T(x_i) - A(\\eta)) \\\\\n",
        "  &= \\sum_{i=1}^n \\nabla [\\eta \\cdot T(x_i)] - \\nabla A(\\eta) \\\\\n",
        "  &= \\sum_{i=1}^n T(x_i) - \\mathbb{E}[T(x_i)],\n",
        "\\end{align*}$$\n",
        "where we used the fact that  $\\nabla A(\\eta) = \\mathbb{E}[T(x)]$. Setting this to zero and solving implies, we would like to find values $\\eta$ such that $\\sum_i T(x_i) = \\sum_i \\mathbb{E}[T(x_i)] = n \\mathbb{E}[T(X)] ⇒ \\frac{1}{n} \\sum_i T(x_i) = \\mathbb{E}[T(X)]$! In other words, MLE under ExpFam seeks values of $\\eta$ that *match the empirical mean of the observed sufficient statistics to their expectation*!"
      ],
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      "cell_type": "markdown",
      "source": [
        "## It's an Equinox for all seasons\n",
        "TBD: Information on `equinox`, (functional) objective oriented programming, abstract base classes. More documentation on `Normal` class."
      ],
      "metadata": {
        "id": "4cm1S74tRxqA"
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    },
    {
      "cell_type": "code",
      "source": [
        "!pip install equinox"
      ],
      "metadata": {
        "id": "ykn-OzCv3xjQ"
      },
      "execution_count": null,
      "outputs": []
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      "cell_type": "code",
      "source": [
        "from abc import abstractmethod\n",
        "\n",
        "import equinox as eqx\n",
        "import jax\n",
        "import jax.numpy as jnp\n",
        "from jaxtyping import Array, ArrayLike\n",
        "\n",
        "\n",
        "class ExpFam(eqx.Module):\n",
        "  \"\"\"\n",
        "  Simple base class for Exponential Families. Will keep track of\n",
        "  observations as internal state and provide means to evaluate\n",
        "  the loglikelihood of downstream implementations.\n",
        "\n",
        "  x: Array, our observations\n",
        "  \"\"\"\n",
        "\n",
        "  x: Array\n",
        "\n",
        "  @abstractmethod\n",
        "  def base_measure(self) -> Array:\n",
        "    \"\"\"\n",
        "    Computes the base measure for an implementation of ExpFam.\n",
        "\n",
        "    Returns:\n",
        "      The base measure for an implementation of ExpFam.\n",
        "    \"\"\"\n",
        "    ...\n",
        "\n",
        "  @abstractmethod\n",
        "  def sufficient_statistics(self) -> Array:\n",
        "    \"\"\"\n",
        "    Computes the sufficient statistics (i.e. $T(x)$) for an implementation\n",
        "    of ExpFam.\n",
        "\n",
        "    Returns:\n",
        "      The sufficient statistics for each observation under an implementation\n",
        "      of ExpFam.\n",
        "    \"\"\"\n",
        "    ...\n",
        "\n",
        "  @abstractmethod\n",
        "  def log_partition(self, eta: ArrayLike) -> Array:\n",
        "    \"\"\"\n",
        "    Computes the log partition function (i.e. $A(\\eta)$) for an implementation\n",
        "    of ExpFam with natural parameters $\\eta$.\n",
        "\n",
        "    eta: ArrayLike, the natural parameters to evaluate under the log partition.\n",
        "\n",
        "    Returns:\n",
        "      The value of the log partition function for each observation under an\n",
        "      implementation of ExpFam.\n",
        "    \"\"\"\n",
        "    ...\n",
        "\n",
        "  def loglikelihood(self, eta: ArrayLike) -> Array:\n",
        "    \"\"\"\n",
        "    Computes the log likelihood for each observation $x$ under an implementation\n",
        "    of ExpFam with natural parameters $\\eta$.\n",
        "\n",
        "    eta: ArrayLike, the natural parameters to evaluate under the log likelihood.\n",
        "\n",
        "    Returns:\n",
        "      The log likelihood for each observation under an implementation of ExpFam.\n",
        "    \"\"\"\n",
        "\n",
        "    t_x = self.sufficient_statistics()\n",
        "    log_h_x = jnp.log(self.base_measure())\n",
        "    log_eta = self.log_partition(eta)\n",
        "    return t_x @ eta - log_eta + log_h_x\n",
        "\n",
        "  def __call__(self, eta: ArrayLike) -> Array:\n",
        "    return self.loglikelihood(eta)\n",
        "\n",
        "\n",
        "class Normal(ExpFam):\n",
        "\n",
        "  def base_measure(self) -> Array:\n",
        "    return 1. / jnp.sqrt(2 * jnp.pi)\n",
        "\n",
        "  def sufficient_statistics(self) -> Array:\n",
        "    x = self.x\n",
        "    x_sq = self.x ** 2\n",
        "    return jnp.concatenate((x[:, jnp.newaxis], x_sq[:, jnp.newaxis]), axis=1)\n",
        "\n",
        "  def log_partition(self, eta: ArrayLike) -> Array:\n",
        "    eta_1, eta_2 = eta\n",
        "    term1 = -(eta_1**2 / (4 * eta_2))\n",
        "    term2 = -0.5 * jnp.log(- 2 * eta_2)\n",
        "    return term1 + term2"
      ],
      "metadata": {
        "id": "ppu0j4ydwTnn"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Great! Having implemented our objects to perform MLE in a general setting, with a specific example of normal distributions, let's perform some sanity checks before proceeding with inference."
      ],
      "metadata": {
        "id": "If1EgDTJSFjA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import jax.random as rdm\n",
        "\n",
        "# initialize our PRNG state\n",
        "seed = 0\n",
        "key = rdm.PRNGKey(seed)\n",
        "\n",
        "# define some parameter values for N(mu, sigma2)\n",
        "mu = 5.0\n",
        "sigma_sq = 10.0\n",
        "\n",
        "# generate random data\n",
        "N = 10\n",
        "key, x_key = rdm.split(key)\n",
        "obs = mu + jnp.sqrt(sigma_sq) * rdm.normal(x_key, shape=(N,))\n",
        "\n",
        "# transform parameters to natural parameters and create some other guess at eta\n",
        "eta_true = jnp.array([mu / sigma_sq, - 1. / (2 * sigma_sq)])\n",
        "eta_guess = jnp.array([-9, -100.])\n",
        "\n",
        "# create an instance of Normal distribution using our implementation above\n",
        "model = Normal(obs)\n",
        "\n",
        "# calculate the sum of log likelihood\n",
        "# equivalent to `jnp.sum(model.loglikelihood(eta_true))`\n",
        "sum_ll_true = jnp.sum(model(eta_true))\n",
        "sum_ll_guess = jnp.sum(model(eta_guess))\n",
        "print(f\"true logl $\\ell$({eta_true}) = {sum_ll_true} | guess logl $\\ell$({eta_guess}) = {sum_ll_guess}\")\n",
        "\n",
        "# sanity check against jax loglikelihood\n",
        "import jax.scipy.stats as stats\n",
        "jax_ll_true = jnp.sum(stats.norm.logpdf(obs, mu, jnp.sqrt(sigma_sq)))\n",
        "print(f\"Our $\\ell$({eta_true}) = {sum_ll_true} | JAX logl $\\ell$({eta_true}) = {jax_ll_true}\")"
      ],
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          "text": [
            "true logl $\\ell$([ 0.5  -0.05]) = -26.96800994873047 | guess logl $\\ell$([  -9. -100.]) = -17816.912109375\n",
            "Our $\\ell$([ 0.5  -0.05]) = -26.96800994873047 | JAX logl $\\ell$([ 0.5  -0.05]) = -26.9680118560791\n"
          ]
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      "cell_type": "markdown",
      "source": [
        "## Statistical Divergences\n",
        "[Divergences](https://en.wikipedia.org/wiki/Divergence_%28statistics%29) capture a notion of \"[statistical distance](https://en.wikipedia.org/wiki/Statistical_distance)\" between parameterized distribution functions. Their full definition is beyond the scope of this course, but key properties to recall are, given distributions $q$ and $p$ over the same [sample space](https://en.wikipedia.org/wiki/Sample_space), a divergence statisfies $D(p || q) \\geq 0$ and $D(p || q) = 0$ iff $p = q$. There are many [different kinds](https://en.wikipedia.org/wiki/Divergence_%28statistics%29%23Examples) of divergences, but a very commonly used divergence is the [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence), or KL divergence.\n",
        "\n",
        "For discrete $x$ with sample space $\\mathcal{X}$, we have,\n",
        "$$\n",
        "\\begin{align*}\n",
        "D_{KL}(p || q) &= \\sum_{x \\in \\mathcal{X}} p(x) \\log \\frac{p(x)}{q(x)} = - \\sum_{x \\in \\mathcal{X}} p(x) \\log \\frac{q(x)}{p(x)} \\\\\n",
        "  &= -\\mathbb{E}_{x \\sim p}\\left[\\log \\frac{q(x)}{p(x)} \\right].\n",
        "\\end{align*}$$\n",
        "\n",
        "Fo continuous $x \\in \\mathbb{R}$, we have,\n",
        "$$\\begin{align*}\n",
        "D_{KL}(p || q) &= \\int_{-\\infty}^\\infty p(x) \\log \\frac{p(x)}{q(x)}dx = -\\int_{-\\infty}^\\infty p(x) \\log \\frac{q(x)}{p(x)}dx \\\\\n",
        "  &= -\\mathbb{E}_{x \\sim p}\\left[\\log \\frac{q(x)}{p(x)} \\right].\n",
        "\\end{align*}$$\n",
        "\n",
        "## Example: Normal Distribution\n",
        "Let $p := N(\\mu_p, \\sigma^2_p)$ and $q := N(\\mu_q, \\sigma^2_q).$ The KL divergence between $p, q$ is given by,\n",
        "$$D_{KL}(p || q) = \\frac{(\\mu_p - \\mu_q)^2}{2 \\sigma^2_q} + \\frac{1}{2}\\left(\\frac{\\sigma^2_p}{\\sigma^2_q} - 1 - \\ln \\frac{\\sigma^2_p}{\\sigma^2_q} \\right).$$\n",
        "\n",
        "Let's plot a few examples to get an intuition of how this is useful."
      ],
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    {
      "cell_type": "code",
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      "outputs": [
        {
          "output_type": "stream",
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          "text": [
            "Euclidean distance in setting 1: 25.0 and setting 2: 25.0\n",
            "KL divergence in setting 1: 8.127134323120117 and setting 2: 0.021240711212158203\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Example data\n",
        "x_values = jnp.arange(-10, 10, 0.1)\n",
        "\n",
        "mu_1 = 0.\n",
        "mu_2 = 5.\n",
        "std_1 = 0.5\n",
        "y_values11 = stats.norm.pdf(x_values, mu_1, std_1)  # N(mu_1, std_1**2)\n",
        "y_values12 = stats.norm.pdf(x_values, mu_2, std_1)  # N(mu_2, std_1**2)\n",
        "\n",
        "std_2 = 2.0\n",
        "y_values21 = stats.norm.pdf(x_values, mu_1, std_2)  # N(mu_1, std_2**2)\n",
        "y_values22 = stats.norm.pdf(x_values, mu_2, std_2)  # N(mu_2, std_2**2)\n",
        "\n",
        "# calc euclidean distances between distributions 1 and 2 in each scenario\n",
        "param_11 = jnp.array([mu_1, std_1**2])\n",
        "param_12 = jnp.array([mu_2, std_1**2])\n",
        "\n",
        "param_21 = jnp.array([mu_1, std_2**2])\n",
        "param_22 = jnp.array([mu_2, std_2**2])\n",
        "\n",
        "e_dist_1 = jnp.sum((param_11 - param_12) ** 2)\n",
        "e_dist_2 = jnp.sum((param_21 - param_22) ** 2)\n",
        "\n",
        "print(f\"Euclidean distance in setting 1: {e_dist_1} and setting 2: {e_dist_2}\")\n",
        "\n",
        "# let's code up KL divergence for scalar normals\n",
        "def kl_normal(mu1, var1, mu2, var2):\n",
        "  term1 = (mu1 - mu2) ** 2 / (2 * var2)\n",
        "  term2 = 0.5 * (var1/var2 - 1 - jnp.log(var1) + jnp.log(var2))\n",
        "  return term1 + term2\n",
        "\n",
        "# whats the KL divergence between these two scenarios?\n",
        "kl_div_1 = kl_normal(mu_1, mu_2, std_1 ** 2, std_1 ** 2)\n",
        "kl_div_2 = kl_normal(mu_1, mu_2, std_1 ** 2, std_2 ** 2)\n",
        "print(f\"KL divergence in setting 1: {kl_div_1} and setting 2: {kl_div_2}\")\n",
        "\n",
        "# Create a figure and a 1x2 grid of subplots (for horizontal alignment)\n",
        "fig, axs = plt.subplots(1, 2, figsize=(12, 4))\n",
        "\n",
        "# Plot on the first subplot\n",
        "sns.lineplot(x=x_values, y=y_values11, ax=axs[0], label=f\"N({mu_1}, {std_1**2})\")\n",
        "sns.lineplot(x=x_values, y=y_values12, ax=axs[0], label=f\"N({mu_2}, {std_1**2})\")\n",
        "axs[0].set_title(f\"Euclidean dist = {e_dist_1}\\n KL div = {kl_div_1:.3f}\")\n",
        "axs[0].set_xlabel('x')\n",
        "axs[0].set_ylabel('Likelihood')\n",
        "\n",
        "# Plot on the second subplot\n",
        "sns.lineplot(x=x_values, y=y_values21, ax=axs[1], label=f\"N({mu_1}, {std_2**2})\")\n",
        "sns.lineplot(x=x_values, y=y_values22, ax=axs[1], label=f\"N({mu_2}, {std_2**2})\")\n",
        "axs[1].set_title(f\"Euclidean dist = {e_dist_2}\\n KL div = {kl_div_2:.3f}\")\n",
        "axs[1].set_xlabel('x')\n",
        "axs[1].set_ylabel('Likelihood')\n",
        "\n",
        "# Display the plot\n",
        "plt.tight_layout()  # Adjust the layout to not overlap\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the above example, the Euclidean distance between the blue and orange distributions was the same, but the wider variance setting on the right \"feels\" like they should be more similar, given the larger overlap at relatively high density regions. This was reflected in the much lower KL divergence in the second scenario.\n",
        "\n",
        "TBD: Add information on Fisher Information, how we approximate KL div, etc."
      ],
      "metadata": {
        "id": "AzQV75s1Q2Nm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Natural Gradient Descent\n",
        "Recall under [gradient descent](https://en.wikipedia.org/wiki/Gradient_descent) we can iteratively optimize a function $f(\\theta)$ by taking steps in the steepest direction,\n",
        "$$ \\theta_{t+1} = \\theta_t - \\rho_t \\nabla f(\\theta_t).$$\n",
        "Interestingly, we can re-write this update as a *local* optimization problem,\n",
        "$$ \\theta_{t+1} = {\\arg \\min}_{\\theta} \\ \\ \\theta \\cdot \\nabla f(\\theta_t) + \\frac{1}{2\\rho_t}||\\theta - \\theta_t||^2.$$\n",
        "The intuition is that we'd like to find some $\\theta$ which finds a direction that decreases $f$ at $\\theta_t$, as rapidly as possible (i.e. $\\nabla f(\\theta_t)$ itself), while not moving too \"far\" away from $\\theta_t$  where \"far\" is captured by a [*Euclidean distance*](https://en.wikipedia.org/wiki/Euclidean_distance) (i.e. $||\\theta - \\theta_t||^2$).\n",
        "\n",
        "To see their equivalence we have,\n",
        "$$\\begin{align*}\n",
        "& \\frac{\\partial}{\\partial \\theta} \\left[\\theta \\cdot \\nabla f(\\theta_t) + \\frac{1}{2\\rho_t}||\\theta - \\theta_t||^2 \\right] \\\\\n",
        " &= \\frac{\\partial}{\\partial \\theta} [\\theta \\cdot \\nabla f(\\theta_t)] + \\frac{1}{2\\rho_t}\\frac{\\partial}{\\partial \\theta} ||\\theta - \\theta_t||^2 \\\\\n",
        "   &= \\nabla f(\\theta_t) - \\frac{(\\theta - \\theta_t)}{\\rho_t} ⇒ \\\\\n",
        "   \\theta_{t+1} &= \\theta_t - \\rho_t \\nabla f(\\theta_t).\n",
        "\\end{align*}$$\n",
        "\n",
        "We saw [above](#statistical-divergences) how Euclidean distance can lead to less meaningful measures of distance when we care about parameters underlying statistical distributions. Can we improve inference if we used a notion of *statistical distance* or (surprise) *divergence* in the above formulation?\n",
        "\n",
        "Let's replace $||\\theta - \\theta_t||^2$ with KL divergence,\n",
        "$$\\begin{align*}\n",
        "\\theta_{t+1} &= {\\arg \\min}_{\\theta} \\ \\ \\theta \\cdot \\nabla f(\\theta_t) + \\frac{1}{2\\rho_t}D_{KL}(\\theta||\\theta_t) \\\\\n",
        "  &\\approx {\\arg \\min}_{\\theta} \\ \\ \\theta \\cdot \\nabla f(\\theta_t) + \\frac{1}{2\\rho_t}(\\theta - \\theta_t)^T F(\\theta_t)(\\theta - \\theta_t) ⇒ \\\\\n",
        "\\theta_{t+1} &= \\theta_t - \\rho_t F^{-1}(\\theta_t)∇f(\\theta_t) \\\\\n",
        "  &= \\theta_t - \\rho_t \\widetilde{\\nabla} f(\\theta_t).\n",
        "\\end{align*}$$\n",
        "\n",
        "where $\\widetilde{\\nabla} f(\\theta_t)$ is the *natural* gradient, defined as $ \\widetilde{\\nabla} f(\\theta_t) := F^{-1}(\\theta_t)∇f(\\theta_t)$ and $F(\\theta_t) = \\mathbb{E}_{x \\sim p(\\theta_t)}\\left[∇\\log p(x | \\theta_t)\\nabla \\log p(x | \\theta_t)^T\\right]$ is the [Fisher Information Matrix](https://en.wikipedia.org/wiki/Fisher_information).\n",
        "\n",
        "To arrive at the approximation, we take the second-roder Taylor series of $D_{KL}$ TBD."
      ],
      "metadata": {
        "id": "9Yh-wOPnwU9m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# code for later"
      ],
      "metadata": {
        "id": "dNpPWq9oeaRX"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}