Adversarial Training Demo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from graph_cert.certify import *\n",
    "from graph_cert.utils import *\n",
    "from graph_cert.models import PiPPNP\n",
    "from graph_cert.training import *\n",
    "from functools import partial\n",
    "\n",
    "import seaborn as sns\n",
    "import tqdm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load and preprocess the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_name = 'data/citeseer.npz'\n",
    "graph = load_dataset(file_name=file_name)\n",
    "\n",
    "adj_matrix, attr_matrix, labels = standardize(adj_matrix=graph['adj_matrix'],\n",
    "                                              attr_matrix=graph['attr_matrix'],\n",
    "                                              labels=graph['labels'])\n",
    "\n",
    "idx_train, idx_val, idx_test = split(labels, n_per_class=20, seed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup the training function with default hyper-params\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "device = 'cuda'\n",
    "alpha = 0.85\n",
    "n, d = attr_matrix.shape\n",
    "nc = labels.max()+1\n",
    "\n",
    "attr = torch.FloatTensor(attr_matrix.toarray()).to(device)\n",
    "ppr = torch.FloatTensor(propagation_matrix(adj_matrix, alpha=alpha)).to(device)\n",
    "labels = torch.LongTensor(labels).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_func = partial(train, attr=attr, ppr=ppr, labels=labels,\n",
    "                     idx_train=idx_train, idx_val=idx_val,\n",
    "                     lr=1e-2, weight_decay= 1e-4,\n",
    "                     patience=50, max_epochs=3_000, display_step=5,\n",
    "                    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train $\\pi$-PPNP using standard cross-entropy loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0: loss_train: 1.79571, loss_val: 1.79499  acc_train: 0.15000, acc_val: 0.17500 p_robust -1.00000\n",
      "Epoch    5: loss_train: 0.56064, loss_val: 1.02474  acc_train: 0.86667, acc_val: 0.65833 p_robust -1.00000\n",
      "Epoch   10: loss_train: 0.12894, loss_val: 1.08670  acc_train: 0.96667, acc_val: 0.66667 p_robust -1.00000\n",
      "Epoch   15: loss_train: 0.03541, loss_val: 1.50060  acc_train: 1.00000, acc_val: 0.65833 p_robust -1.00000\n",
      "Epoch   20: loss_train: 0.01410, loss_val: 1.86582  acc_train: 1.00000, acc_val: 0.66667 p_robust -1.00000\n",
      "Epoch   25: loss_train: 0.00669, loss_val: 2.02315  acc_train: 1.00000, acc_val: 0.65000 p_robust -1.00000\n",
      "Epoch   30: loss_train: 0.00396, loss_val: 2.06998  acc_train: 1.00000, acc_val: 0.63333 p_robust -1.00000\n",
      "Epoch   35: loss_train: 0.00285, loss_val: 2.04542  acc_train: 1.00000, acc_val: 0.64167 p_robust -1.00000\n",
      "Epoch   40: loss_train: 0.00233, loss_val: 1.96238  acc_train: 1.00000, acc_val: 0.65000 p_robust -1.00000\n",
      "Epoch   45: loss_train: 0.00216, loss_val: 1.86538  acc_train: 1.00000, acc_val: 0.65833 p_robust -1.00000\n",
      "Epoch   50: loss_train: 0.00222, loss_val: 1.76542  acc_train: 1.00000, acc_val: 0.65833 p_robust -1.00000\n",
      "Epoch   55: loss_train: 0.00245, loss_val: 1.66016  acc_train: 1.00000, acc_val: 0.66667 p_robust -1.00000\n",
      "Epoch   60: loss_train: 0.00282, loss_val: 1.56452  acc_train: 1.00000, acc_val: 0.68333 p_robust -1.00000\n"
     ]
    }
   ],
   "source": [
    "ppnp_ce = PiPPNP(n_features=d, n_classes=nc, n_hidden=[64]).to(device)\n",
    "_ = train_func(model=ppnp_ce, adver_config=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Configure the paramters for adversarial training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set the local budget proportional to the degree\n",
    "deg = adj_matrix.sum(1).A1.astype(np.int32)\n",
    "local_strength = 9\n",
    "local_budget = np.maximum(deg - 11 + local_strength, 0)\n",
    "\n",
    "fragile = get_fragile(adj=adj_matrix, threat_model='rem')\n",
    "\n",
    "adver_config = {\n",
    "    'alpha': alpha,\n",
    "    'adj_matrix': adj_matrix,\n",
    "    'fragile': fragile,\n",
    "    'local_budget': local_budget,\n",
    "    'margin': 1\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train $\\pi$-PPNP using robust cross-entropy loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0: loss_train: 1.79752, loss_val: 1.79893  acc_train: 0.16667, acc_val: 0.16667 p_robust 0.16667\n",
      "Epoch    5: loss_train: 0.73579, loss_val: 1.23677  acc_train: 0.88333, acc_val: 0.65833 p_robust 0.72500\n",
      "Epoch   10: loss_train: 0.24057, loss_val: 1.43396  acc_train: 0.95833, acc_val: 0.65833 p_robust 0.75000\n",
      "Epoch   15: loss_train: 0.10475, loss_val: 1.98628  acc_train: 0.99167, acc_val: 0.62500 p_robust 0.77500\n",
      "Epoch   20: loss_train: 0.05517, loss_val: 2.47296  acc_train: 1.00000, acc_val: 0.63333 p_robust 0.75833\n",
      "Epoch   25: loss_train: 0.03283, loss_val: 2.71785  acc_train: 1.00000, acc_val: 0.64167 p_robust 0.77083\n",
      "Epoch   30: loss_train: 0.02119, loss_val: 2.84580  acc_train: 1.00000, acc_val: 0.62500 p_robust 0.76250\n",
      "Epoch   35: loss_train: 0.01520, loss_val: 2.87234  acc_train: 1.00000, acc_val: 0.61667 p_robust 0.75833\n",
      "Epoch   40: loss_train: 0.01200, loss_val: 2.81991  acc_train: 1.00000, acc_val: 0.60833 p_robust 0.76250\n",
      "Epoch   45: loss_train: 0.01005, loss_val: 2.70644  acc_train: 1.00000, acc_val: 0.61667 p_robust 0.77083\n",
      "Epoch   50: loss_train: 0.00904, loss_val: 2.58034  acc_train: 1.00000, acc_val: 0.64167 p_robust 0.77917\n",
      "Epoch   55: loss_train: 0.00856, loss_val: 2.46319  acc_train: 1.00000, acc_val: 0.63333 p_robust 0.78333\n"
     ]
    }
   ],
   "source": [
    "adver_config['loss_type'] = 'rce'\n",
    "ppnp_rce = PiPPNP(n_features=d, n_classes=nc, n_hidden=[64]).to(device)\n",
    "_ = train_func(model=ppnp_rce, adver_config=adver_config)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train $\\pi$-PPNP using robust hinge loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0: loss_train: 6.82987, loss_val: 6.82964  acc_train: 0.16667, acc_val: 0.16667 p_robust 0.16667\n",
      "Epoch    5: loss_train: 1.19163, loss_val: 2.91158  acc_train: 0.89167, acc_val: 0.66667 p_robust 0.75000\n",
      "Epoch   10: loss_train: 0.40587, loss_val: 3.34032  acc_train: 0.95000, acc_val: 0.64167 p_robust 0.74583\n",
      "Epoch   15: loss_train: 0.18605, loss_val: 4.13616  acc_train: 1.00000, acc_val: 0.62500 p_robust 0.75417\n",
      "Epoch   20: loss_train: 0.10668, loss_val: 4.77957  acc_train: 1.00000, acc_val: 0.62500 p_robust 0.75833\n",
      "Epoch   25: loss_train: 0.06860, loss_val: 5.16008  acc_train: 1.00000, acc_val: 0.62500 p_robust 0.75000\n",
      "Epoch   30: loss_train: 0.04587, loss_val: 5.57329  acc_train: 1.00000, acc_val: 0.61667 p_robust 0.76667\n",
      "Epoch   35: loss_train: 0.03348, loss_val: 5.65594  acc_train: 1.00000, acc_val: 0.60833 p_robust 0.74583\n",
      "Epoch   40: loss_train: 0.01996, loss_val: 5.70675  acc_train: 1.00000, acc_val: 0.60833 p_robust 0.75417\n",
      "Epoch   45: loss_train: 0.01500, loss_val: 5.75718  acc_train: 1.00000, acc_val: 0.63333 p_robust 0.75833\n",
      "Epoch   50: loss_train: 0.01060, loss_val: 5.73724  acc_train: 1.00000, acc_val: 0.63333 p_robust 0.75833\n",
      "Epoch   55: loss_train: 0.00827, loss_val: 5.70730  acc_train: 1.00000, acc_val: 0.63333 p_robust 0.76250\n"
     ]
    }
   ],
   "source": [
    "adver_config['loss_type'] = 'cem'\n",
    "ppnp_cem = PiPPNP(n_features=d, n_classes=nc, n_hidden=[64]).to(device)\n",
    "_ = train_func(model=ppnp_cem, adver_config=adver_config)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the ratios of certified test nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.69198\n"
     ]
    },
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     "text": [
      "Accuracy: 0.68717\n"
     ]
    },
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     "text": [
      "Accuracy: 0.69091\n"
     ]
    },
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    {
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     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "local_strengths = [1, 3, 5, 7, 9]\n",
    "ratios_certifed = np.zeros((3, len(local_strengths)))\n",
    "\n",
    "for it, model in enumerate(tqdm.tqdm_notebook([ppnp_ce, ppnp_cem, ppnp_rce])):\n",
    "    \n",
    "    logits, weighted_logits = model(attr, ppr)\n",
    "    acc_test = accuracy(labels, weighted_logits, idx_test)\n",
    "    print(f'Accuracy: {acc_test:.5f}')\n",
    "    \n",
    "    logits = logits.detach().cpu().numpy()\n",
    "    predicted = weighted_logits.argmax(1).cpu().numpy()\n",
    "\n",
    "    for jt, local_strength in enumerate(tqdm.tqdm_notebook(local_strengths, leave=False)):\n",
    "        # set the local budget proportional to the node degree\n",
    "        local_budget = np.maximum(deg - 11 + local_strength, 0)\n",
    "\n",
    "        # precomputed the K x K perturbed graphs\n",
    "        k_squared_pageranks = k_squared_parallel(\n",
    "        adj=adj_matrix, alpha=alpha, fragile=fragile, local_budget=local_budget, logits=logits, nodes=idx_test)\n",
    "\n",
    "        # compute the exact worst-case margins for all test nodes\n",
    "        worst_margins = worst_margins_given_k_squared(\n",
    "            k_squared_pageranks=k_squared_pageranks, labels=predicted[idx_test], logits=logits)\n",
    "\n",
    "        ratios_certifed[it, jt] = (worst_margins>0).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compare different losses\n",
    "\n",
    "Note: Since GNNs are known to be senstive to choice of train/valid/test split a proper comparison should adverage of several different random splits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_context('talk')\n",
    "plt.plot(local_strengths, ratios_certifed[0], label='ce')\n",
    "plt.plot(local_strengths, ratios_certifed[1], label='cem')\n",
    "plt.plot(local_strengths, ratios_certifed[2], label='rce')\n",
    "plt.xlabel('local attack strength')\n",
    "plt.ylabel('% certified robust')\n",
    "plt.legend(title='Loss')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "pycharm": {
   "stem_cell": {
    "cell_type": "raw",
    "metadata": {
     "collapsed": false
    },
    "source": []
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}