misc/kfac.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f03c2a53",
   "metadata": {},
   "source": [
    "# Laplace approximatio using KFAC approximation to posterior\n",
    "\n",
    "Based on\n",
    "https://patel-zeel.github.io/blog/posts/2022-10-18-kfac-laplace.html\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "698d14ac",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "18dce2ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "import jax.numpy as jnp\n",
    "import kfac_jax\n",
    "from jax import random as jr\n",
    "import haiku as hk\n",
    "\n",
    "from math import prod\n",
    "from functools import partial\n",
    "from time import time\n",
    "\n",
    "import blackjax\n",
    "import flax.linen as nn\n",
    "import jax\n",
    "from jax.flatten_util import ravel_pytree\n",
    "import jax.tree_util as jtu\n",
    "import jax.numpy as jnp\n",
    "# jnp.set_printoptions(linewidth=2000)\n",
    "\n",
    "import optax\n",
    "from tqdm import trange\n",
    "\n",
    "import arviz as az\n",
    "import seaborn as sns\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "jax.config.update(\"jax_enable_x64\", False)\n",
    "\n",
    "#%reload_ext watermark\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "eddf1152",
   "metadata": {},
   "outputs": [],
   "source": [
    "jitter = 1e-6\n",
    "\n",
    "def get_shapes(params):\n",
    "    return jtu.tree_map(lambda x:x.shape, params)\n",
    "\n",
    "def svd_inverse(matrix):\n",
    "    U, S, V = jnp.linalg.svd(matrix+jnp.eye(matrix.shape[0])*jitter)\n",
    "    \n",
    "    return V.T/S@U.T"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a7088897",
   "metadata": {},
   "source": [
    "# Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a1c49451",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4, 2), (4,))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2d XOR\n",
    "\n",
    "X = jnp.array([[0, 0], [0, 1], [1, 0], [1, 1]])\n",
    "y = jnp.array([0, 1, 1, 0])\n",
    "\n",
    "X.shape, y.shape"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "15909c22",
   "metadata": {},
   "source": [
    "# Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b2676b1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MLP(nn.Module):\n",
    "    features: []\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, x):\n",
    "        for n_features in self.features[:-1]:\n",
    "            x = nn.Dense(n_features, kernel_init=jax.nn.initializers.glorot_normal(), bias_init=jax.nn.initializers.normal())(x)\n",
    "            x = nn.relu(x)\n",
    "        \n",
    "        x = nn.Dense(features[-1])(x)\n",
    "        return x.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b67a242a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'params': {'Dense_0': {'bias': (2,), 'kernel': (2, 2)},\n",
       "  'Dense_1': {'bias': (1,), 'kernel': (2, 1)}}}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = [2, 1]\n",
    "key = jax.random.PRNGKey(0)\n",
    "\n",
    "model = MLP(features)\n",
    "params = model.init(key, X).unfreeze()\n",
    "\n",
    "get_shapes(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8537d6c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.00687164 -0.01380461  0.          0.        ]\n"
     ]
    }
   ],
   "source": [
    "N = X.shape[0]\n",
    "logits = model.apply(params, X)\n",
    "print(logits)\n",
    "assert logits.shape[0] == N\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "47dc68ad",
   "metadata": {},
   "source": [
    "# MAP estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9fd6eeb0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "105.03511\n"
     ]
    }
   ],
   "source": [
    "noise_var = 0.1\n",
    "\n",
    "def neg_log_joint(params):\n",
    "    y_pred = model.apply(params, X)\n",
    "    flat_params = ravel_pytree(params)[0]\n",
    "    log_prior = jax.scipy.stats.norm.logpdf(flat_params).sum()\n",
    "    log_likelihood = jax.scipy.stats.norm.logpdf(y, loc=y_pred, scale=noise_var).sum()\n",
    "    \n",
    "    return -(log_prior + log_likelihood)\n",
    "\n",
    "print(neg_log_joint(params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8ec8049a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PAtuAbuB6YGPUbCNwQ4E1xmJddwPLmqs1NCMiJakoY+5mthK4FNgMdLh7f7RpAOiY4TG3mlmvmfUODi6+Dy7NjGsuXsoT2w9w5OTpuMsREZmTgsPdzOqAnwCfcPcjudvc3QGf7nHufo+797h7T3t7e6FlzIt3vaaT0fEM//2chmZEpLQUFO5mVkE22L/n7g9Eq/eZWWe0vRPYX1iJ8Xnt8iaWNVfzs2deibsUEZE5KWS2jAH3Advc/cs5mx4CNkT3NwAP5l9evMyM91zSxRN9BxjSrBkRKSGF9NyvAD4IXGlmf4p+rgM+D7zDzLYDV0fLJes9r+liPOP8/M/9Z28sIrJIpPJ9oLs/AdgMm6/K93kXm4s661mztJ77ntjJP16+grKymXZZRGTx0BmqZ2Fm/MvbzmPngeP84SVdBlhESoPCfRbeeXEHdZUp/mvzy3GXIiIyKwr3WahJp7j5DSt4+NlX2HngeNzliIiclcJ9lm55yyoqysu46/G+uEsRETkrhfssLamv4qbLV/DA03vZO3wi7nJERP4mhfsc3PrWczGDu3+zI+5SRET+JoX7HHQ1VfMPly3jB0/uZv/Rk3GXIyIyI4X7HP3r289jbDzDvf+zM+5SRERmpHCfo3Naa7n+td189/92se+Ieu8isjgp3PPwyasvYCyT4au/eiHuUkREpqVwz8OK1ho+uH4lP3xyN9v3HY27HBGRV1G45+ljV55PbWWKz/1sK5nMtJesFxGJjcI9T821aT57zRqe6DvAt373UtzliIicQeFegJvfsIKrL+rgC794nudeORx3OSIikxTuBTAzvnjja2iureCfN/bSf1hnrorI4qBwL1BLbZpv/dPlHDs5xofu+wOH9I1NIrIIKNyLYG1XA3d/6HXsGhrh5ns384quPSMiMVO4F8mbzmvjng++jpeHRnj3fzzBb14YjLskEUkwhXsRvf3CJfz0o1fQUptmwzf/wEe+/SQvaB68iMRA4V5k5y+p4+GPvZk7rl3Dky8Ncc1Xf8u//fgZ/rR7GHfNhxeRhWGLIXB6enq8t7c37jKK7tDxUb7xWB/f+f0uRscyrGqr5W0XtHP5qhbWLK3nnNZayvWF2yKSJzN7yt17pt2mcJ9/R06e5hd/7ufhZ/t58qUhTp7OAJBOlbG8uZol9VW011fSVldJfVWK6nQ51RXZn6rofnlZduqlAWVmlJlhBmbZZQPKyozse0X2dtp2k+vPbDd1e+6tTWln0eMnbsss+wZVZq9uJyLz52+Fe2qhi0mihqoK3v/6Fbz/9SsYHcuwrf8IL+w7St/+Y+w6OMKBY6d4Zs8wg0dPMTI6Hne5RVU25c3AYPINY0Lue0Du20Hum8MZbxOzaT/H57QZXmDm58ldP7fXPeOVbIb7Rfr9hC6EXb3t6gt47yVdRX9ehfsCS6fKuGR5E5csb5p2eybjnBwb58ToOCdOj3Py9DgnRjNk3KMfgOxtJuM4kHHHHdyZbOcOjpPJRNsBjx6f247o8ZkMOc91ZjuPHp/JROsnn8ujNjntcpenaTfxXBNy/3PM/SfyzDa566dvn+uM55zj88zUnpnaF/CcZ/wmZmw/m32ZuX0I4TeT+McciqO5pmJenlfhvsiUlRk16RQ1aR0aEcmfZsuIiARI4S4iEiCFu4hIgBTuIiIBUriLiARI4S4iEiCFu4hIgBTuIiIBWhTXljGzQWBXng9vAw4UsZxSoH1OBu1zMhSyz+e4e/t0GxZFuBfCzHpnunBOqLTPyaB9Tob52mcNy4iIBEjhLiISoBDC/Z64C4iB9jkZtM/JMC/7XPJj7iIi8moh9NxFRGQKhbuISIBKOtzN7Boz+4uZ9ZnZ7XHXUyxmttzMHjOzrWb2nJndFq1vMbNHzWx7dNscrTcz+3r0e3jWzC6Ldw/yY2blZvZHM3s4Wl5lZpuj/fqhmaWj9ZXRcl+0fWWshefJzJrM7H4ze97MtpnZGxNwjD8Z/U1vMbPvm1lViMfZzL5pZvvNbEvOujkfWzPbELXfbmYb5lJDyYa7mZUD3wCuBdYCN5nZ2nirKpox4NPuvhZYD3w02rfbgU3uvhrYFC1D9newOvq5Fbhr4UsuituAbTnLXwC+4u7nA4eAW6L1twCHovVfidqVoq8Bj7j7GuASsvse7DE2s27g40CPu68DyoEPEOZx/jZwzZR1czq2ZtYC3Am8AbgcuHPiDWFWfPK7L0vrB3gj8Muc5TuAO+Kua5729UHgHcBfgM5oXSfwl+j+3cBNOe0n25XKD7As+oO/EniY7Nd/HgBSU4838EvgjdH9VNTO4t6HOe5vI7Bzat2BH+NuYDfQEh23h4G/D/U4AyuBLfkeW+Am4O6c9We0O9tPyfbc+esfyoQ90bqgRP+KXgpsBjrcvT/aNAB0RPdD+F18FfgMkImWW4Fhdx+LlnP3aXJ/o+2Ho/alZBUwCHwrGoq618xqCfgYu/te4EvAy0A/2eP2FGEf51xzPbYFHfNSDvfgmVkd8BPgE+5+JHebZ9/Kg5jHambvBva7+1Nx17KAUsBlwF3ufilwnL/+mw6EdYwBoiGF68m+sXUBtbx66CIRFuLYlnK47wWW5ywvi9YFwcwqyAb799z9gWj1PjPrjLZ3Avuj9aX+u7gCeK+ZvQT8gOzQzNeAJjNLRW1y92lyf6PtjcDBhSy4CPYAe9x9c7R8P9mwD/UYA1wN7HT3QXc/DTxA9tiHfJxzzfXYFnTMSzncnwRWR5+0p8l+MPNQzDUVhZkZcB+wzd2/nLPpIWDiE/MNZMfiJ9Z/KPrUfT1wOOffv0XP3e9w92XuvpLscfy1u98MPAbcGDWbur8Tv4cbo/Yl1cN19wFgt5ldGK26CthKoMc48jKw3sxqor/xiX0O9jhPMddj+0vgnWbWHP3X885o3ezE/aFDgR9YXAe8AOwA/j3ueoq4X28m+y/bs8Cfop/ryI43bgK2A78CWqL2Rnbm0A7gz2RnI8S+H3nu+9uBh6P75wJ/APqAHwOV0fqqaLkv2n5u3HXnua+vBXqj4/xToDn0Ywx8Dnge2AJ8F6gM8TgD3yf7ucJpsv+l3ZLPsQU+Eu1/H/DhudSgyw+IiASolIdlRERkBgp3EZEAKdxFRAKkcBcRCZDCXUQkQAp3EZEAKdxFRAL0/yTIgP7dqW3YAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "key = jax.random.PRNGKey(0)\n",
    "params = model.init(key, X).unfreeze()\n",
    "n_iters = 1000\n",
    "\n",
    "value_and_grad_fn = jax.jit(jax.value_and_grad(neg_log_joint))\n",
    "opt = optax.adam(0.01)\n",
    "state = opt.init(params)\n",
    "\n",
    "def one_step(params_and_state, xs):\n",
    "    params, state = params_and_state\n",
    "    loss, grads = value_and_grad_fn(params)\n",
    "    updates, state = opt.update(grads, state)\n",
    "    params = optax.apply_updates(params, updates)\n",
    "    return (params, state), loss\n",
    "    \n",
    "(params, state), losses = jax.lax.scan(one_step, init=(params, state), xs=None, length=n_iters)\n",
    "\n",
    "plt.plot(losses);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "abf8c635",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'params': {'Dense_0': {'bias': Array([-0.0002,  0.0003], dtype=float32), 'kernel': Array([[ 0.8275, -0.8315],\n",
      "       [-0.8277,  0.8325]], dtype=float32)}, 'Dense_1': {'bias': Array([0.0135], dtype=float32), 'kernel': Array([[1.1751],\n",
      "       [1.1685]], dtype=float32)}}}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([-2.4913e-04,  2.7019e-04,  8.2753e-01, -8.3148e-01, -8.2766e-01,\n",
       "        8.3254e-01,  1.3518e-02,  1.1751e+00,  1.1685e+00], dtype=float32)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[Array([-0.0002,  0.0003], dtype=float32),\n",
       " Array([[ 0.8275, -0.8315],\n",
       "        [-0.8277,  0.8325]], dtype=float32),\n",
       " Array([0.0135], dtype=float32),\n",
       " Array([[1.1751],\n",
       "        [1.1685]], dtype=float32)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "[{'bias': Array([-0.0002,  0.0003], dtype=float32), 'kernel': Array([[ 0.8275, -0.8315],\n",
      "       [-0.8277,  0.8325]], dtype=float32)}, {'bias': Array([0.0135], dtype=float32), 'kernel': Array([[1.1751],\n",
      "       [1.1685]], dtype=float32)}]\n",
      "2\n",
      "{'bias': Array([-0.0002,  0.0003], dtype=float32), 'kernel': Array([[ 0.8275, -0.8315],\n",
      "       [-0.8277,  0.8325]], dtype=float32)}\n",
      "{'bias': Array([0.0135], dtype=float32), 'kernel': Array([[1.1751],\n",
      "       [1.1685]], dtype=float32)}\n"
     ]
    }
   ],
   "source": [
    "\n",
    "jnp.set_printoptions(precision=4)\n",
    "\n",
    "print(params)\n",
    "\n",
    "flat_params, unravel_fn = ravel_pytree(params)\n",
    "display(flat_params)\n",
    "#print(['{:0.4f}'.format(x) for x in flat_params])\n",
    "print(len(flat_params))\n",
    "\n",
    "# get parameters for each leaf as list of matrices\n",
    "flat_params, tree_def = jtu.tree_flatten(params)\n",
    "display(flat_params)\n",
    "#print(['{:0.4f}'.format(x) for x in flat_params])\n",
    "print(len(flat_params))\n",
    "\n",
    "# get parameters for each leaf as list of dictionary\n",
    "is_leaf = lambda param: 'bias' in param\n",
    "layers, tree_def = jtu.tree_flatten(params, is_leaf=is_leaf)\n",
    "print(layers)\n",
    "print(len(layers))\n",
    "print(layers[0])\n",
    "print(layers[1])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a72e2fff",
   "metadata": {},
   "source": [
    "# Plugin prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2a026cbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.01383345, 0.98666817, 0.98563665, 0.01507111], dtype=float32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_map = model.apply(params, X)\n",
    "y_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ed2d4a94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = jnp.linspace(-0.1,1.1,100)\n",
    "X1, X2 = jnp.meshgrid(x, x)\n",
    "\n",
    "def predict_fn(x1, x2):\n",
    "    return model.apply(params, jnp.array([x1,x2]).reshape(1,2))\n",
    "\n",
    "predict_fn_vec = jax.jit(jax.vmap(jax.vmap(predict_fn)))\n",
    "\n",
    "Z = predict_fn_vec(X1, X2).squeeze()\n",
    "\n",
    "plt.contourf(X1, X2, Z)\n",
    "plt.colorbar();"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "7ba5dedd",
   "metadata": {},
   "source": [
    "# Full Hessian Laplace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "88bbcca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "flat_params, unravel_fn = ravel_pytree(params)\n",
    "\n",
    "def neg_log_joint_flat(flat_params):\n",
    "    return neg_log_joint(unravel_fn(flat_params))\n",
    "\n",
    "H = jax.hessian(neg_log_joint_flat)(flat_params)\n",
    "\n",
    "sns.heatmap(H);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9b07e522",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior_cov = svd_inverse(H)\n",
    "\n",
    "sns.heatmap(posterior_cov);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d07c67b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "class FullHessianLaplace:\n",
    "    def __init__(self, map_params, model):\n",
    "        flat_params, self.unravel_fn = ravel_pytree(map_params)\n",
    "\n",
    "        def neg_log_joint_flat(flat_params):\n",
    "            params = unravel_fn(flat_params)\n",
    "            return neg_log_joint(params)\n",
    "\n",
    "        self.H = jax.hessian(neg_log_joint_flat)(flat_params)\n",
    "        \n",
    "        self.mean = flat_params\n",
    "        self.cov = svd_inverse(self.H)\n",
    "        self.model = model\n",
    "\n",
    "    def _vectorize(self, f, seed, shape, f_kwargs={}):\n",
    "        length = prod(shape)\n",
    "        seeds = jax.random.split(seed, num=length).reshape(shape+(2,))\n",
    "        \n",
    "        sample_fn = partial(f, **f_kwargs)\n",
    "        for _ in shape:\n",
    "            sample_fn = jax.vmap(sample_fn)\n",
    "        \n",
    "        return sample_fn(seed=seeds)\n",
    "    \n",
    "    def _sample(self, seed):\n",
    "        sample = jax.random.multivariate_normal(seed, mean=self.mean, cov=self.cov)\n",
    "        return self.unravel_fn(sample)\n",
    "    \n",
    "    def sample(self, seed, shape):\n",
    "        return self._vectorize(self._sample, seed, shape)\n",
    "    \n",
    "    def _predict(self, X, seed):\n",
    "        sample = self._sample(seed)\n",
    "        return self.model.apply(sample, X)\n",
    "    \n",
    "    def predict(self, X, seed, shape):\n",
    "        return self._vectorize(self._predict, seed, shape, {'X': X})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f6f02be7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posterior = FullHessianLaplace(params, model)\n",
    "\n",
    "seed = jax.random.PRNGKey(1)\n",
    "n_samples = 100000\n",
    "y_pred_full = posterior.predict(X, seed=seed, shape=(n_samples,))\n",
    "ulim = 5\n",
    "llim = -5\n",
    "\n",
    "fig, ax = plt.subplots(2,2,figsize=(12,4))\n",
    "ax=ax.ravel()\n",
    "for i in range(len(y)):\n",
    "    az.plot_dist(y_pred_full[:, i], ax=ax[i]);\n",
    "    ax[i].grid(True)\n",
    "    ax[i].set_xticks(range(llim,ulim))\n",
    "    ax[i].set_xlim(llim, ulim)\n",
    "    ax[i].set_title(f\"X={X[i]}, y_pred_mean={y_pred_full[:, i].mean():.3f}, y_map={y_map[i]:.3f}\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ccb0f739",
   "metadata": {},
   "source": [
    "# Block diagonal approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "17c5cdaa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Array([-0.00024913,  0.00027019], dtype=float32),\n",
       " Array([[ 0.8275324 , -0.8314813 ],\n",
       "        [-0.8276633 ,  0.83254045]], dtype=float32),\n",
       " Array([0.01351773], dtype=float32),\n",
       " Array([[1.1750739],\n",
       "        [1.1685134]], dtype=float32)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyTreeDef({'params': {'Dense_0': {'bias': *, 'kernel': *}, 'Dense_1': {'bias': *, 'kernel': *}}})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flat_params, tree_def = jtu.tree_flatten(params)\n",
    "display(flat_params, tree_def)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "dc7c8593",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'bias': Array([-0.0002,  0.0003], dtype=float32),\n",
       "  'kernel': Array([[ 0.8275, -0.8315],\n",
       "         [-0.8277,  0.8325]], dtype=float32)},\n",
       " {'bias': Array([0.0135], dtype=float32),\n",
       "  'kernel': Array([[1.1751],\n",
       "         [1.1685]], dtype=float32)}]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyTreeDef({'params': {'Dense_0': *, 'Dense_1': *}})"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "is_leaf = lambda param: 'bias' in param\n",
    "layers, tree_def = jtu.tree_flatten(params, is_leaf=is_leaf)\n",
    "display(layers, tree_def)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "acc727be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Array([-2.4913e-04,  2.7019e-04,  8.2753e-01, -8.3148e-01, -8.2766e-01,\n",
       "         8.3254e-01], dtype=float32),\n",
       " Array([0.0135, 1.1751, 1.1685], dtype=float32)]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[<jax._src.util.HashablePartial at 0x7f838d56efd0>,\n",
       " <jax._src.util.HashablePartial at 0x7f838d56edc0>]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flat_params = list(map(lambda x: ravel_pytree(x)[0], layers))\n",
    "unravel_fn_list = list(map(lambda x: ravel_pytree(x)[1], layers))\n",
    "display(flat_params, unravel_fn_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2b1b5b06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Array([[139.0798,   0.    , 138.0798,   0.    ,   0.    ,   0.    ],\n",
       "        [  0.    , 410.6271,   0.    , 136.5424,   0.    , 273.0847],\n",
       "        [138.0798,   0.    , 139.0798,   0.    ,   0.    ,   0.    ],\n",
       "        [  0.    , 136.5424,   0.    , 137.5424,   0.    , 136.5424],\n",
       "        [  0.    ,   0.    ,   0.    ,   0.    ,   1.    ,   0.    ],\n",
       "        [  0.    , 273.0847,   0.    , 136.5424,   0.    , 274.0847]],      dtype=float32),\n",
       " Array([[401.    ,  82.7283,  83.441 ],\n",
       "        [ 82.7283,  69.4398,   0.    ],\n",
       "        [ 83.441 ,   0.    ,  70.3575]], dtype=float32)]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def modified_neg_log_joint_fn(flat_params):\n",
    "    layers = jtu.tree_map(lambda unravel_fn, flat_param: unravel_fn(flat_param), unravel_fn_list, flat_params)\n",
    "    params = tree_def.unflatten(layers)\n",
    "    return neg_log_joint(params)\n",
    "\n",
    "full_hessian = jax.hessian(modified_neg_log_joint_fn)(flat_params)\n",
    "\n",
    "# Pick diagonal entries from the Hessian\n",
    "useful_hessians = [full_hessian[i][i] for i in range(len(full_hessian))]\n",
    "useful_hessians"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "deca9471",
   "metadata": {},
   "outputs": [],
   "source": [
    "class KFACHessianLaplace:\n",
    "    def __init__(self, map_params, model):\n",
    "        self.model = model\n",
    "        layers, self.tree_def = jtu.tree_flatten(map_params, is_leaf=lambda x: 'bias' in x)\n",
    "        flat_layers = [ravel_pytree(layer) for layer in layers]\n",
    "        self.means = list(map(lambda x: x[0], flat_layers))\n",
    "        self.unravel_fn_list = list(map(lambda x: x[1], flat_layers))\n",
    "\n",
    "        def neg_log_joint_flat(flat_params):\n",
    "            flat_layers = [self.unravel_fn_list[i](flat_params[i]) for i in range(len(flat_params))]\n",
    "            params = self.tree_def.unflatten(flat_layers)\n",
    "            return neg_log_joint(params)\n",
    "\n",
    "        self.H = jax.hessian(neg_log_joint_flat)(self.means)\n",
    "        self.useful_H = [self.H[i][i] for i in range(len(self.H))]\n",
    "        \n",
    "        self.covs = [svd_inverse(matrix) for matrix in self.useful_H]\n",
    "        \n",
    "    def _vectorize(self, f, seed, shape, f_kwargs={}):\n",
    "        length = prod(shape)\n",
    "        seeds = jax.random.split(seed, num=length).reshape(shape+(2,))\n",
    "        \n",
    "        sample_fn = partial(f, **f_kwargs)\n",
    "        for _ in shape:\n",
    "            sample_fn = jax.vmap(sample_fn)\n",
    "        \n",
    "        return sample_fn(seed=seeds)\n",
    "    \n",
    "    def _sample_partial(self, seed, unravel_fn, mean, cov):\n",
    "        sample = jax.random.multivariate_normal(seed, mean=mean, cov=cov)\n",
    "        return unravel_fn(sample)\n",
    "    \n",
    "    def _sample(self, seed):\n",
    "        seeds = [seed for seed in jax.random.split(seed, num=len(self.means))]\n",
    "        flat_sample = jtu.tree_map(self._sample_partial, seeds, self.unravel_fn_list, self.means, self.covs)\n",
    "        sample = self.tree_def.unflatten(flat_sample)\n",
    "        return sample\n",
    "    \n",
    "    def sample(self, seed, n_samples=1):\n",
    "        return self._vectorize(self._sample, seed, shape)\n",
    "    \n",
    "    def _predict(self, X, seed):\n",
    "        sample = self._sample(seed)\n",
    "        return self.model.apply(sample, X)\n",
    "    \n",
    "    def predict(self, X, seed, shape):\n",
    "        return self._vectorize(self._predict, seed, shape, {'X': X})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "68c7fff5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kfac_posterior = KFACHessianLaplace(params, model)\n",
    "\n",
    "seed = jax.random.PRNGKey(1)\n",
    "n_samples = 1000000\n",
    "y_pred_kfac = kfac_posterior.predict(X, seed=seed, shape=(n_samples, ))\n",
    "ulim = 5\n",
    "llim = -5\n",
    "\n",
    "fig, ax = plt.subplots(2,2,figsize=(12,4))\n",
    "ax=ax.ravel()\n",
    "for i in range(len(y)):\n",
    "    az.plot_dist(y_pred_full[:, i], ax=ax[i], label='full', color='r')\n",
    "    az.plot_dist(y_pred_kfac[:, i], ax=ax[i], label='kfac', color='b')\n",
    "    ax[i].grid(True)\n",
    "    ax[i].set_xticks(range(llim,ulim))\n",
    "    ax[i].set_xlim(llim, ulim)\n",
    "    ax[i].set_title(f\"X={X[i]}, y_map={y_map[i]:.3f}\")\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "999cb2d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1296x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize=(18,5))\n",
    "sns.heatmap(posterior.cov, ax=ax[0], annot=True, fmt = '.2f')\n",
    "ax[0].set_title('Full')\n",
    "\n",
    "kfac_cov = posterior.cov * 0\n",
    "offset = 0\n",
    "for cov in kfac_posterior.covs:\n",
    "    length = cov.shape[0]\n",
    "    kfac_cov = kfac_cov.at[offset:offset+length, offset:offset+length].set(cov)\n",
    "    offset += length\n",
    "\n",
    "sns.heatmap(kfac_cov, ax=ax[1], annot=True, fmt = '.2f')\n",
    "ax[1].set_title('KFAC');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c30fbf60",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "973365f9",
   "metadata": {},
   "source": [
    "# Use KFAC-JAX library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a4ff929",
   "metadata": {},
   "outputs": [],
   "source": [
    "flat_params, unravel_fn = ravel_pytree(params)\n",
    "\n",
    "def neg_log_joint_flat(flat_params):\n",
    "    return neg_log_joint(unravel_fn(flat_params))\n",
    "\n",
    "H = jax.hessian(neg_log_joint_flat)(flat_params)\n",
    "\n",
    "sns.heatmap(H);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "4d970d86",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'params': {'Dense_0': {'bias': Array([-0.0002,  0.0003], dtype=float32), 'kernel': Array([[ 0.8275, -0.8315],\n",
      "       [-0.8277,  0.8325]], dtype=float32)}, 'Dense_1': {'bias': Array([0.0135], dtype=float32), 'kernel': Array([[1.1751],\n",
      "       [1.1685]], dtype=float32)}}}\n",
      "5.526351\n"
     ]
    }
   ],
   "source": [
    "noise_var = 0.1\n",
    "\n",
    "def neg_log_joint(params):\n",
    "    y_pred = model.apply(params, X)\n",
    "    flat_params = ravel_pytree(params)[0]\n",
    "    log_prior = jax.scipy.stats.norm.logpdf(flat_params).sum()\n",
    "    log_likelihood = jax.scipy.stats.norm.logpdf(y, loc=y_pred, scale=noise_var).sum()\n",
    "    \n",
    "    return -(log_prior + log_likelihood)\n",
    "\n",
    "print(params)\n",
    "print(neg_log_joint(params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "6dd4dfce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.526351\n"
     ]
    }
   ],
   "source": [
    "def loss_fn(params, batch):\n",
    "  del batch\n",
    "  y_pred = model.apply(params, X)\n",
    "  flat_params = ravel_pytree(params)[0]\n",
    "  log_prior = jax.scipy.stats.norm.logpdf(flat_params).sum()\n",
    "  log_likelihood = jax.scipy.stats.norm.logpdf(y, loc=y_pred, scale=noise_var).sum()\n",
    "  kfac_jax.register_squared_error_loss(y_pred, y)\n",
    "  return -(log_likelihood + log_prior)\n",
    "\n",
    "\n",
    "print(loss_fn(params, None))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f9bb6287",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'kfac_jax._src.curvature_estimator.ExplicitExactCurvature'> <kfac_jax._src.curvature_estimator.ExplicitExactCurvature object at 0x7f838d5c6d90>\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "Value <kfac_jax._src.curvature_estimator.ExplicitExactCurvature object at 0x7f838d5c6d90> with type <class 'kfac_jax._src.curvature_estimator.ExplicitExactCurvature'> is not a valid JAX type",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-51-cde8d0794627>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mestimator\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkfac_jax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mExplicitExactCurvature\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mloss_fn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mestimator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mestimator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m estimator = estimator.update_curvature_matrix_estimate(estimator, ema_old=0, ema_new=1, batch_size=0, rng=jax.random.PRNGKey(0), \n\u001b[0m\u001b[1;32m      4\u001b[0m                                                        func_args=None, pmap_axis_name=None, estimation_mode='fisher_gradients')\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mestimator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mestimator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/github/kfac-jax/kfac_jax/_src/curvature_estimator.py\u001b[0m in \u001b[0;36mupdate_curvature_matrix_estimate\u001b[0;34m(self, state, ema_old, ema_new, batch_size, rng, func_args, pmap_axis_name, estimation_mode)\u001b[0m\n\u001b[1;32m   1566\u001b[0m       )\n\u001b[1;32m   1567\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1568\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mjax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfori_loop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch_size\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msingle_state_update\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1569\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1570\u001b[0m   def update_cache(\n",
      "    \u001b[0;31m[... skipping hidden 8 frame]\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.8/site-packages/jax/_src/core.py\u001b[0m in \u001b[0;36mconcrete_aval\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m   1348\u001b[0m   \u001b[0;32mif\u001b[0m \u001b[0mhasattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'__jax_array__'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1349\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mconcrete_aval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__jax_array__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1350\u001b[0;31m   raise TypeError(f\"Value {repr(x)} with type {type(x)} is not a valid JAX \"\n\u001b[0m\u001b[1;32m   1351\u001b[0m                    \"type\")\n\u001b[1;32m   1352\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: Value <kfac_jax._src.curvature_estimator.ExplicitExactCurvature object at 0x7f838d5c6d90> with type <class 'kfac_jax._src.curvature_estimator.ExplicitExactCurvature'> is not a valid JAX type"
     ]
    }
   ],
   "source": [
    "estimator = kfac_jax.ExplicitExactCurvature(loss_fn)\n",
    "print(type(estimator), estimator)\n",
    "estimator = estimator.update_curvature_matrix_estimate(estimator, ema_old=0, ema_new=1, batch_size=0, rng=jax.random.PRNGKey(0), \n",
    "                                                       func_args=None, pmap_axis_name=None, estimation_mode='fisher_gradients')\n",
    "print(type(estimator), estimator)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e5754099",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n"
   ]
  }
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