fedavg_mnist_iid.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=#6B49F5> A Simple Implementation of FedAvg with PyTorch on IID Data </font> \n",
    "Please see https://towardsdatascience.com/federated-learning-a-simple-implementation-of-fedavg-federated-averaging-with-pytorch-90187c9c9577 for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn import tree\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "import random\n",
    "import math\n",
    "from torch.utils.tensorboard import SummaryWriter\n",
    "from matplotlib import pyplot\n",
    "\n",
    "\n",
    "from pathlib import Path\n",
    "import requests\n",
    "import pickle\n",
    "import gzip\n",
    "\n",
    "import torch\n",
    "import math\n",
    "import torch.nn.functional as F\n",
    "from torch import nn\n",
    "from torch import optim\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "from torch.utils.data import TensorDataset\n",
    "from torch.utils.data import DataLoader\n",
    "\n",
    "pd.options.display.float_format = \"{:,.4f}\".format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's download data set\n",
    "DATA_PATH = Path(\"data\")\n",
    "PATH = DATA_PATH / \"mnist\"\n",
    "# PATH = os.join.path(p1, p2)\n",
    "PATH.mkdir(parents=True, exist_ok=True)\n",
    "\n",
    "URL = \"http://deeplearning.net/data/mnist/\"\n",
    "FILENAME = \"mnist.pkl.gz\"\n",
    "\n",
    "if not (PATH / FILENAME).exists():\n",
    "        content = requests.get(URL + FILENAME).content\n",
    "        (PATH / FILENAME).open(\"wb\").write(content)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with gzip.open((PATH / FILENAME).as_posix(), \"rb\") as f:\n",
    "        ((x_train, y_train), (x_valid, y_valid), (x_test, y_test)) = pickle.load(f, encoding=\"latin-1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50000, 784), (50000,), (10000, 784), (10000,), (10000, 784), (10000,))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's see the dataset size\n",
    "x_train.shape, y_train.shape , x_valid.shape, y_valid.shape, x_test.shape, y_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 64 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = pyplot.subplots(8,8,figsize=(8,8))\n",
    "for i in range(8):\n",
    "    for j in range(8):\n",
    "        num_index = np.random.randint(len(x_train))\n",
    "        axes[i,j].imshow(x_train[num_index].reshape((28,28)), cmap=\"gray\")\n",
    "        axes[i,j].axis(\"off\")\n",
    "pyplot.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Let's check how many of each tag are**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 >> train: 4932 , valid: 991 , test: 980 , total: 6903\n",
      "1 >> train: 5678 , valid: 1064 , test: 1135 , total: 7877\n",
      "2 >> train: 4968 , valid: 990 , test: 1032 , total: 6990\n",
      "3 >> train: 5101 , valid: 1030 , test: 1010 , total: 7141\n",
      "4 >> train: 4859 , valid: 983 , test: 982 , total: 6824\n",
      "5 >> train: 4506 , valid: 915 , test: 892 , total: 6313\n",
      "6 >> train: 4951 , valid: 967 , test: 958 , total: 6876\n",
      "7 >> train: 5175 , valid: 1090 , test: 1028 , total: 7293\n",
      "8 >> train: 4842 , valid: 1009 , test: 974 , total: 6825\n",
      "9 >> train: 4988 , valid: 961 , test: 1009 , total: 6958\n",
      "y_train_total= 50000\n",
      "y_valid_total= 10000\n",
      "y_test_total= 10000\n",
      "total= 70000\n"
     ]
    }
   ],
   "source": [
    "# Let's check how many of each tag are.\n",
    "y_train_total=0\n",
    "y_valid_total=0\n",
    "y_test_total=0\n",
    "total=0\n",
    "for i in range(10):\n",
    "    print(i,\">> train:\", sum(y_train==i), \", valid:\", sum(y_valid==i), \n",
    "          \", test:\", sum(y_test==i), \", total:\", sum(y_train==i)+sum(y_valid==i)+sum(y_test==i) )\n",
    "    y_train_total=y_train_total + sum(y_train==i)\n",
    "    y_valid_total=y_valid_total + sum(y_valid==i)\n",
    "    y_test_total=y_test_total + sum(y_test==i)\n",
    "    total=total+sum(y_train==i)+sum(y_valid==i)+sum(y_test==i)\n",
    "    \n",
    "print(\"y_train_total=\", y_train_total) \n",
    "print(\"y_valid_total=\", y_valid_total) \n",
    "print(\"y_test_total=\", y_test_total)\n",
    "print(\"total=\", total)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_and_shuffle_labels(y_data, seed, amount):\n",
    "    y_data=pd.DataFrame(y_data,columns=[\"labels\"])\n",
    "    y_data[\"i\"]=np.arange(len(y_data))\n",
    "    label_dict = dict()\n",
    "    for i in range(10):\n",
    "        var_name=\"label\" + str(i)\n",
    "        label_info=y_data[y_data[\"labels\"]==i]\n",
    "        np.random.seed(seed)\n",
    "        label_info=np.random.permutation(label_info)\n",
    "        label_info=label_info[0:amount]\n",
    "        label_info=pd.DataFrame(label_info, columns=[\"labels\",\"i\"])\n",
    "        label_dict.update({var_name: label_info })\n",
    "    return label_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_iid_subsamples_indices(label_dict, number_of_samples, amount):\n",
    "    sample_dict= dict()\n",
    "    batch_size=int(math.floor(amount/number_of_samples))\n",
    "    for i in range(number_of_samples):\n",
    "        sample_name=\"sample\"+str(i)\n",
    "        dumb=pd.DataFrame()\n",
    "        for j in range(10):\n",
    "            label_name=str(\"label\")+str(j)\n",
    "            a=label_dict[label_name][i*batch_size:(i+1)*batch_size]\n",
    "            dumb=pd.concat([dumb,a], axis=0)\n",
    "        dumb.reset_index(drop=True, inplace=True)    \n",
    "        sample_dict.update({sample_name: dumb}) \n",
    "    return sample_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_iid_subsamples(sample_dict, x_data, y_data, x_name, y_name):\n",
    "    x_data_dict= dict()\n",
    "    y_data_dict= dict()\n",
    "    \n",
    "    for i in range(len(sample_dict)):  ### len(sample_dict)= number of samples\n",
    "        xname= x_name+str(i)\n",
    "        yname= y_name+str(i)\n",
    "        sample_name=\"sample\"+str(i)\n",
    "        \n",
    "        indices=np.sort(np.array(sample_dict[sample_name][\"i\"]))\n",
    "        \n",
    "        x_info= x_data[indices,:]\n",
    "        x_data_dict.update({xname : x_info})\n",
    "        \n",
    "        y_info= y_data[indices]\n",
    "        y_data_dict.update({yname : y_info})\n",
    "        \n",
    "    return x_data_dict, y_data_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------\n",
    "### <span style=\"background-color:#F087F9\"> Classification Model </span> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Net2nn(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net2nn, self).__init__()\n",
    "        self.fc1=nn.Linear(784,200)\n",
    "        self.fc2=nn.Linear(200,200)\n",
    "        self.fc3=nn.Linear(200,10)\n",
    "        \n",
    "    def forward(self,x):\n",
    "        x=F.relu(self.fc1(x))\n",
    "        x=F.relu(self.fc2(x))\n",
    "        x=self.fc3(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class WrappedDataLoader:\n",
    "    def __init__(self, dl, func):\n",
    "        self.dl = dl\n",
    "        self.func = func\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.dl)\n",
    "\n",
    "    def __iter__(self):\n",
    "        batches = iter(self.dl)\n",
    "        for b in batches:\n",
    "            yield (self.func(*b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(model, train_loader, criterion, optimizer):\n",
    "    model.train()\n",
    "    train_loss = 0.0\n",
    "    correct = 0\n",
    "\n",
    "    for data, target in train_loader:\n",
    "        output = model(data)\n",
    "        loss = criterion(output, target)\n",
    "        optimizer.zero_grad()\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        train_loss += loss.item()\n",
    "        prediction = output.argmax(dim=1, keepdim=True)\n",
    "        correct += prediction.eq(target.view_as(prediction)).sum().item()\n",
    "        \n",
    "\n",
    "    return train_loss / len(train_loader), correct/len(train_loader.dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def validation(model, test_loader, criterion):\n",
    "    model.eval()\n",
    "    test_loss = 0.0\n",
    "    correct = 0\n",
    "    with torch.no_grad():\n",
    "        for data, target in test_loader:\n",
    "            output = model(data)\n",
    "            \n",
    "            test_loss += criterion(output, target).item()\n",
    "            prediction = output.argmax(dim=1, keepdim=True)\n",
    "            correct += prediction.eq(target.view_as(prediction)).sum().item()\n",
    "\n",
    "    test_loss /= len(test_loader)\n",
    "    correct /= len(test_loader.dataset)\n",
    "\n",
    "    return (test_loss, correct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------------------------------\n",
    "### <span style=\"background-color:#F087F9\"> Functions for Federated Averaging </span> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_model_optimizer_criterion_dict(number_of_samples):\n",
    "    model_dict = dict()\n",
    "    optimizer_dict= dict()\n",
    "    criterion_dict = dict()\n",
    "    \n",
    "    for i in range(number_of_samples):\n",
    "        model_name=\"model\"+str(i)\n",
    "        model_info=Net2nn()\n",
    "        model_dict.update({model_name : model_info })\n",
    "        \n",
    "        optimizer_name=\"optimizer\"+str(i)\n",
    "        optimizer_info = torch.optim.SGD(model_info.parameters(), lr=learning_rate, momentum=momentum)\n",
    "        optimizer_dict.update({optimizer_name : optimizer_info })\n",
    "        \n",
    "        criterion_name = \"criterion\"+str(i)\n",
    "        criterion_info = nn.CrossEntropyLoss()\n",
    "        criterion_dict.update({criterion_name : criterion_info})\n",
    "        \n",
    "    return model_dict, optimizer_dict, criterion_dict "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_averaged_weights(model_dict, number_of_samples):\n",
    "   \n",
    "    fc1_mean_weight = torch.zeros(size=model_dict[name_of_models[0]].fc1.weight.shape)\n",
    "    fc1_mean_bias = torch.zeros(size=model_dict[name_of_models[0]].fc1.bias.shape)\n",
    "    \n",
    "    fc2_mean_weight = torch.zeros(size=model_dict[name_of_models[0]].fc2.weight.shape)\n",
    "    fc2_mean_bias = torch.zeros(size=model_dict[name_of_models[0]].fc2.bias.shape)\n",
    "    \n",
    "    fc3_mean_weight = torch.zeros(size=model_dict[name_of_models[0]].fc3.weight.shape)\n",
    "    fc3_mean_bias = torch.zeros(size=model_dict[name_of_models[0]].fc3.bias.shape)\n",
    "    \n",
    "    with torch.no_grad():\n",
    "    \n",
    "    \n",
    "        for i in range(number_of_samples):\n",
    "            fc1_mean_weight += model_dict[name_of_models[i]].fc1.weight.data.clone()\n",
    "            fc1_mean_bias += model_dict[name_of_models[i]].fc1.bias.data.clone()\n",
    "        \n",
    "            fc2_mean_weight += model_dict[name_of_models[i]].fc2.weight.data.clone()\n",
    "            fc2_mean_bias += model_dict[name_of_models[i]].fc2.bias.data.clone()\n",
    "        \n",
    "            fc3_mean_weight += model_dict[name_of_models[i]].fc3.weight.data.clone()\n",
    "            fc3_mean_bias += model_dict[name_of_models[i]].fc3.bias.data.clone()\n",
    "\n",
    "        \n",
    "        fc1_mean_weight =fc1_mean_weight/number_of_samples\n",
    "        fc1_mean_bias = fc1_mean_bias/ number_of_samples\n",
    "    \n",
    "        fc2_mean_weight =fc2_mean_weight/number_of_samples\n",
    "        fc2_mean_bias = fc2_mean_bias/ number_of_samples\n",
    "    \n",
    "        fc3_mean_weight =fc3_mean_weight/number_of_samples\n",
    "        fc3_mean_bias = fc3_mean_bias/ number_of_samples\n",
    "    \n",
    "    return fc1_mean_weight, fc1_mean_bias, fc2_mean_weight, fc2_mean_bias, fc3_mean_weight, fc3_mean_bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def set_averaged_weights_as_main_model_weights_and_update_main_model(main_model,model_dict, number_of_samples):\n",
    "    fc1_mean_weight, fc1_mean_bias, fc2_mean_weight, fc2_mean_bias, fc3_mean_weight, fc3_mean_bias = get_averaged_weights(model_dict, number_of_samples=number_of_samples)\n",
    "    with torch.no_grad():\n",
    "        main_model.fc1.weight.data = fc1_mean_weight.data.clone()\n",
    "        main_model.fc2.weight.data = fc2_mean_weight.data.clone()\n",
    "        main_model.fc3.weight.data = fc3_mean_weight.data.clone()\n",
    "\n",
    "        main_model.fc1.bias.data = fc1_mean_bias.data.clone()\n",
    "        main_model.fc2.bias.data = fc2_mean_bias.data.clone()\n",
    "        main_model.fc3.bias.data = fc3_mean_bias.data.clone() \n",
    "    return main_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare_local_and_merged_model_performance(number_of_samples):\n",
    "    accuracy_table=pd.DataFrame(data=np.zeros((number_of_samples,3)), columns=[\"sample\", \"local_ind_model\", \"merged_main_model\"])\n",
    "    for i in range (number_of_samples):\n",
    "    \n",
    "        test_ds = TensorDataset(x_test_dict[name_of_x_test_sets[i]], y_test_dict[name_of_y_test_sets[i]])\n",
    "        test_dl = DataLoader(test_ds, batch_size=batch_size * 2)\n",
    "    \n",
    "        model=model_dict[name_of_models[i]]\n",
    "        criterion=criterion_dict[name_of_criterions[i]]\n",
    "        optimizer=optimizer_dict[name_of_optimizers[i]]\n",
    "    \n",
    "        individual_loss, individual_accuracy = validation(model, test_dl, criterion)\n",
    "        main_loss, main_accuracy =validation(main_model, test_dl, main_criterion )\n",
    "    \n",
    "        accuracy_table.loc[i, \"sample\"]=\"sample \"+str(i)\n",
    "        accuracy_table.loc[i, \"local_ind_model\"] = individual_accuracy\n",
    "        accuracy_table.loc[i, \"merged_main_model\"] = main_accuracy\n",
    "\n",
    "    return accuracy_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def send_main_model_to_nodes_and_update_model_dict(main_model, model_dict, number_of_samples):\n",
    "    with torch.no_grad():\n",
    "        for i in range(number_of_samples):\n",
    "\n",
    "            model_dict[name_of_models[i]].fc1.weight.data =main_model.fc1.weight.data.clone()\n",
    "            model_dict[name_of_models[i]].fc2.weight.data =main_model.fc2.weight.data.clone()\n",
    "            model_dict[name_of_models[i]].fc3.weight.data =main_model.fc3.weight.data.clone() \n",
    "            \n",
    "            model_dict[name_of_models[i]].fc1.bias.data =main_model.fc1.bias.data.clone()\n",
    "            model_dict[name_of_models[i]].fc2.bias.data =main_model.fc2.bias.data.clone()\n",
    "            model_dict[name_of_models[i]].fc3.bias.data =main_model.fc3.bias.data.clone() \n",
    "    \n",
    "    return model_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def start_train_end_node_process(number_of_samples):\n",
    "    for i in range (number_of_samples): \n",
    "\n",
    "        train_ds = TensorDataset(x_train_dict[name_of_x_train_sets[i]], y_train_dict[name_of_y_train_sets[i]])\n",
    "        train_dl = DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "#         valid_ds = TensorDataset(x_valid_dict[name_of_x_valid_sets[i]], y_valid_dict[name_of_y_valid_sets[i]])\n",
    "#         valid_dl = DataLoader(valid_ds, batch_size=batch_size * 2)\n",
    "        \n",
    "        test_ds = TensorDataset(x_test_dict[name_of_x_test_sets[i]], y_test_dict[name_of_y_test_sets[i]])\n",
    "        test_dl = DataLoader(test_ds, batch_size= batch_size * 2)\n",
    "    \n",
    "        model=model_dict[name_of_models[i]]\n",
    "        criterion=criterion_dict[name_of_criterions[i]]\n",
    "        optimizer=optimizer_dict[name_of_optimizers[i]]\n",
    "    \n",
    "        print(\"Subset\" ,i)\n",
    "        for epoch in range(numEpoch):        \n",
    "            train_loss, train_accuracy = train(model, train_dl, criterion, optimizer)\n",
    "#             valid_loss, valid_accuracy = validation(model, valid_dl, criterion)\n",
    "            test_loss, test_accuracy = validation(model, test_dl, criterion)\n",
    "    \n",
    "            print(\"epoch: {:3.0f}\".format(epoch+1) + \" | train accuracy: {:7.5f}\".format(train_accuracy) + \" | test accuracy: {:7.5f}\".format(test_accuracy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def start_train_end_node_process_without_print(number_of_samples):\n",
    "    for i in range (number_of_samples): \n",
    "\n",
    "        train_ds = TensorDataset(x_train_dict[name_of_x_train_sets[i]], y_train_dict[name_of_y_train_sets[i]])\n",
    "        train_dl = DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "        test_ds = TensorDataset(x_test_dict[name_of_x_test_sets[i]], y_test_dict[name_of_y_test_sets[i]])\n",
    "        test_dl = DataLoader(test_ds, batch_size= batch_size * 2)\n",
    "    \n",
    "        model=model_dict[name_of_models[i]]\n",
    "        criterion=criterion_dict[name_of_criterions[i]]\n",
    "        optimizer=optimizer_dict[name_of_optimizers[i]]\n",
    "    \n",
    "        for epoch in range(numEpoch):        \n",
    "            train_loss, train_accuracy = train(model, train_dl, criterion, optimizer)\n",
    "            test_loss, test_accuracy = validation(model, test_dl, criterion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def start_train_end_node_process_print_some(number_of_samples, print_amount):\n",
    "    for i in range (number_of_samples): \n",
    "\n",
    "        train_ds = TensorDataset(x_train_dict[name_of_x_train_sets[i]], y_train_dict[name_of_y_train_sets[i]])\n",
    "        train_dl = DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "        test_ds = TensorDataset(x_test_dict[name_of_x_test_sets[i]], y_test_dict[name_of_y_test_sets[i]])\n",
    "        test_dl = DataLoader(test_ds, batch_size= batch_size * 2)\n",
    "    \n",
    "        model=model_dict[name_of_models[i]]\n",
    "        criterion=criterion_dict[name_of_criterions[i]]\n",
    "        optimizer=optimizer_dict[name_of_optimizers[i]]\n",
    "    \n",
    "        if i<print_amount:\n",
    "            print(\"Subset\" ,i)\n",
    "            \n",
    "        for epoch in range(numEpoch):\n",
    "        \n",
    "            train_loss, train_accuracy = train(model, train_dl, criterion, optimizer)\n",
    "            test_loss, test_accuracy = validation(model, test_dl, criterion)\n",
    "            \n",
    "            if i<print_amount:        \n",
    "                print(\"epoch: {:3.0f}\".format(epoch+1) + \" | train accuracy: {:7.5f}\".format(train_accuracy) + \" | test accuracy: {:7.5f}\".format(test_accuracy))    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train, y_train, x_valid, y_valid,x_test, y_test = map(torch.tensor, (x_train, y_train, x_valid, y_valid, x_test, y_test))\n",
    "number_of_samples=100\n",
    "learning_rate = 0.01\n",
    "numEpoch = 10\n",
    "batch_size = 32\n",
    "momentum = 0.9\n",
    "\n",
    "train_amount=4500\n",
    "valid_amount=900\n",
    "test_amount=900\n",
    "print_amount=3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------------\n",
    "\n",
    "### <span style=\"background-color:#F087F9\"> Let's examine what would the performance of the centralized model be if the data were not distributed to nodes at all? </span>   \n",
    "\n",
    "The model used in this example is very simple, different things can be done to improve model performance, such as using more complex models, increasing epoch or hyperparameter tuning. However, the purpose here is to compare the performance of the main model that is formed by combining the parameters of the local models trained on their own data with a centralized model that trained on all training data. In this way, we can gain insight into the capacity of federated learning.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "centralized_model = Net2nn()\n",
    "centralized_optimizer = torch.optim.SGD(centralized_model.parameters(), lr=0.01, momentum=0.9)\n",
    "centralized_criterion = nn.CrossEntropyLoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_ds = TensorDataset(x_train, y_train)\n",
    "train_dl = DataLoader(train_ds, batch_size=batch_size, shuffle=True)\n",
    "\n",
    "valid_ds = TensorDataset(x_valid, y_valid)\n",
    "valid_dl = DataLoader(valid_ds, batch_size=batch_size * 2)\n",
    "\n",
    "test_ds = TensorDataset(x_test, y_test)\n",
    "test_dl = DataLoader(test_ds, batch_size=batch_size * 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------ Centralized Model ------\n",
      "epoch:   1 | train accuracy:  0.8725 | test accuracy:  0.9479\n",
      "epoch:   2 | train accuracy:  0.9572 | test accuracy:  0.9663\n",
      "epoch:   3 | train accuracy:  0.9710 | test accuracy:  0.9713\n",
      "epoch:   4 | train accuracy:  0.9780 | test accuracy:  0.9715\n",
      "epoch:   5 | train accuracy:  0.9833 | test accuracy:  0.9725\n",
      "epoch:   6 | train accuracy:  0.9864 | test accuracy:  0.9780\n",
      "epoch:   7 | train accuracy:  0.9900 | test accuracy:  0.9762\n",
      "epoch:   8 | train accuracy:  0.9923 | test accuracy:  0.9811\n",
      "epoch:   9 | train accuracy:  0.9933 | test accuracy:  0.9791\n",
      "epoch:  10 | train accuracy:  0.9950 | test accuracy:  0.9779\n",
      "------ Training finished ------\n"
     ]
    }
   ],
   "source": [
    "print(\"------ Centralized Model ------\")\n",
    "for epoch in range(numEpoch):\n",
    "    central_train_loss, central_train_accuracy = train(centralized_model, train_dl, centralized_criterion, centralized_optimizer)\n",
    "    central_test_loss, central_test_accuracy = validation(centralized_model, test_dl, centralized_criterion)\n",
    "    \n",
    "    print(\"epoch: {:3.0f}\".format(epoch+1) + \" | train accuracy: {:7.4f}\".format(central_train_accuracy) + \" | test accuracy: {:7.4f}\".format(central_test_accuracy))\n",
    "\n",
    "print(\"------ Training finished ------\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "----------------\n",
    "-----------------\n",
    "**Data is distributed to nodes**\n",
    "\n",
    "<!-- ### <span style=\"background-color:#F087F9\"> Datanın nodelara dağıtılması </span>    -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "label_dict_train=split_and_shuffle_labels(y_data=y_train, seed=1, amount=train_amount) \n",
    "sample_dict_train=get_iid_subsamples_indices(label_dict=label_dict_train, number_of_samples=number_of_samples, amount=train_amount)\n",
    "x_train_dict, y_train_dict = create_iid_subsamples(sample_dict=sample_dict_train, x_data=x_train, y_data=y_train, x_name=\"x_train\", y_name=\"y_train\")\n",
    "\n",
    "\n",
    "label_dict_valid = split_and_shuffle_labels(y_data=y_valid, seed=1, amount=train_amount) \n",
    "sample_dict_valid = get_iid_subsamples_indices(label_dict=label_dict_valid, number_of_samples=number_of_samples, amount=valid_amount)\n",
    "x_valid_dict, y_valid_dict = create_iid_subsamples(sample_dict=sample_dict_valid, x_data=x_valid, y_data=y_valid, x_name=\"x_valid\", y_name=\"y_valid\")\n",
    "\n",
    "label_dict_test = split_and_shuffle_labels(y_data=y_test, seed=1, amount=test_amount) \n",
    "sample_dict_test = get_iid_subsamples_indices(label_dict=label_dict_test, number_of_samples=number_of_samples, amount=test_amount)\n",
    "x_test_dict, y_test_dict = create_iid_subsamples(sample_dict=sample_dict_test, x_data=x_test, y_data=y_test, x_name=\"x_test\", y_name=\"y_test\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([450, 784]) torch.Size([450])\n",
      "torch.Size([90, 784]) torch.Size([90])\n",
      "torch.Size([90, 784]) torch.Size([90])\n",
      "tensor(1)\n"
     ]
    },
    {
     "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": [
    "print(x_train_dict[\"x_train1\"].shape, y_train_dict[\"y_train1\"].shape)\n",
    "print(x_valid_dict[\"x_valid1\"].shape, y_valid_dict[\"y_valid1\"].shape) \n",
    "print(x_test_dict[\"x_test1\"].shape, y_test_dict[\"y_test1\"].shape)\n",
    "\n",
    "num_index = np.random.randint(test_amount/number_of_samples*10)\n",
    "pyplot.imshow(x_test_dict[\"x_test0\"][num_index].reshape((28,28)), cmap=\"gray\")\n",
    "print(y_test_dict[\"y_test0\"][num_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Main model is created**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "main_model = Net2nn()\n",
    "main_optimizer = torch.optim.SGD(main_model.parameters(), lr=learning_rate, momentum=0.9)\n",
    "main_criterion = nn.CrossEntropyLoss()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Models,optimizers and loss functions in nodes are defined**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_dict, optimizer_dict, criterion_dict = create_model_optimizer_criterion_dict(number_of_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Keys of dicts are being made iterable**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "name_of_x_train_sets=list(x_train_dict.keys())\n",
    "name_of_y_train_sets=list(y_train_dict.keys())\n",
    "name_of_x_valid_sets=list(x_valid_dict.keys())\n",
    "name_of_y_valid_sets=list(y_valid_dict.keys())\n",
    "name_of_x_test_sets=list(x_test_dict.keys())\n",
    "name_of_y_test_sets=list(y_test_dict.keys())\n",
    "\n",
    "name_of_models=list(model_dict.keys())\n",
    "name_of_optimizers=list(optimizer_dict.keys())\n",
    "name_of_criterions=list(criterion_dict.keys())\n",
    "\n",
    "# print(name_of_x_train_sets)\n",
    "# print(name_of_y_train_sets)\n",
    "# print(name_of_x_valid_sets)\n",
    "# print(name_of_y_valid_sets)\n",
    "# print(name_of_x_test_sets)\n",
    "# print(name_of_y_test_sets)\n",
    "# print(\"\\n ------------\")\n",
    "# print(name_of_models)\n",
    "# print(name_of_optimizers)\n",
    "# print(name_of_criterions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.0107,  0.0547,  0.0518, -0.0648, -0.0447]],\n",
      "       grad_fn=<SliceBackward>)\n",
      "tensor([[ 0.0618,  0.0372,  0.0352, -0.0636,  0.0521]],\n",
      "       grad_fn=<SliceBackward>)\n"
     ]
    }
   ],
   "source": [
    "print(main_model.fc2.weight[0:1,0:5])\n",
    "print(model_dict[\"model1\"].fc2.weight[0:1,0:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Parameters of main model are sent to nodes**  \n",
    "Since the parameters of the main model and parameters of all local models in the nodes are randomly initialized, all these parameters will be different from each other. For this reason, the main model sends its parameters to the nodes before the training of local models in the nodes begins. You can check the weights below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_dict=send_main_model_to_nodes_and_update_model_dict(main_model, model_dict, number_of_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.0107,  0.0547,  0.0518, -0.0648, -0.0447]],\n",
      "       grad_fn=<SliceBackward>)\n",
      "tensor([[-0.0107,  0.0547,  0.0518, -0.0648, -0.0447]],\n",
      "       grad_fn=<SliceBackward>)\n"
     ]
    }
   ],
   "source": [
    "print(main_model.fc2.weight[0:1,0:5])\n",
    "print(model_dict[\"model1\"].fc2.weight[0:1,0:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Models in the nodes are trained**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subset 0\n",
      "epoch:   1 | train accuracy: 0.13778 | test accuracy: 0.17778\n",
      "epoch:   2 | train accuracy: 0.29333 | test accuracy: 0.28889\n",
      "epoch:   3 | train accuracy: 0.39778 | test accuracy: 0.44444\n",
      "epoch:   4 | train accuracy: 0.54444 | test accuracy: 0.54444\n",
      "epoch:   5 | train accuracy: 0.55111 | test accuracy: 0.60000\n",
      "epoch:   6 | train accuracy: 0.66667 | test accuracy: 0.73333\n",
      "epoch:   7 | train accuracy: 0.75333 | test accuracy: 0.78889\n",
      "epoch:   8 | train accuracy: 0.78222 | test accuracy: 0.75556\n",
      "epoch:   9 | train accuracy: 0.83111 | test accuracy: 0.76667\n",
      "epoch:  10 | train accuracy: 0.86000 | test accuracy: 0.81111\n",
      "Subset 1\n",
      "epoch:   1 | train accuracy: 0.12222 | test accuracy: 0.20000\n",
      "epoch:   2 | train accuracy: 0.29111 | test accuracy: 0.31111\n",
      "epoch:   3 | train accuracy: 0.35333 | test accuracy: 0.43333\n",
      "epoch:   4 | train accuracy: 0.42667 | test accuracy: 0.46667\n",
      "epoch:   5 | train accuracy: 0.52444 | test accuracy: 0.63333\n",
      "epoch:   6 | train accuracy: 0.66444 | test accuracy: 0.72222\n",
      "epoch:   7 | train accuracy: 0.69333 | test accuracy: 0.65556\n",
      "epoch:   8 | train accuracy: 0.73556 | test accuracy: 0.73333\n",
      "epoch:   9 | train accuracy: 0.77333 | test accuracy: 0.78889\n",
      "epoch:  10 | train accuracy: 0.82889 | test accuracy: 0.76667\n",
      "Subset 2\n",
      "epoch:   1 | train accuracy: 0.13556 | test accuracy: 0.18889\n",
      "epoch:   2 | train accuracy: 0.18889 | test accuracy: 0.26667\n",
      "epoch:   3 | train accuracy: 0.26000 | test accuracy: 0.31111\n",
      "epoch:   4 | train accuracy: 0.42222 | test accuracy: 0.58889\n",
      "epoch:   5 | train accuracy: 0.67556 | test accuracy: 0.66667\n",
      "epoch:   6 | train accuracy: 0.68444 | test accuracy: 0.74444\n",
      "epoch:   7 | train accuracy: 0.77778 | test accuracy: 0.70000\n",
      "epoch:   8 | train accuracy: 0.77333 | test accuracy: 0.71111\n",
      "epoch:   9 | train accuracy: 0.79556 | test accuracy: 0.73333\n",
      "epoch:  10 | train accuracy: 0.88000 | test accuracy: 0.71111\n"
     ]
    }
   ],
   "source": [
    "# start_train_end_node_process()\n",
    "start_train_end_node_process_print_some(number_of_samples, print_amount)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.0107,  0.0547,  0.0518, -0.0648, -0.0447], grad_fn=<SliceBackward>)\n",
      "tensor([-0.0107,  0.0631,  0.0521, -0.0655, -0.0570], grad_fn=<SliceBackward>)\n"
     ]
    }
   ],
   "source": [
    "## As you can see, wieghts of local models are updated after training process\n",
    "print(main_model.fc2.weight[0,0:5])\n",
    "print(model_dict[\"model1\"].fc2.weight[0,0:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's compare the performance of federated main model, individual local models and centralized model  \n",
    "\n",
    "**Federated main model vs individual local models before 1st iteration (on distributed test set)**  \n",
    "Since main model is randomly initialized and no action taken on it yet, its performance is very poor. Please before_acc_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "before_acc_table=compare_local_and_merged_model_performance(number_of_samples=number_of_samples)\n",
    "before_test_loss, before_test_accuracy = validation(main_model, test_dl, main_criterion)\n",
    "\n",
    "main_model= set_averaged_weights_as_main_model_weights_and_update_main_model(main_model,model_dict, number_of_samples) \n",
    "\n",
    "after_acc_table=compare_local_and_merged_model_performance(number_of_samples=number_of_samples)\n",
    "after_test_loss, after_test_accuracy = validation(main_model, test_dl, main_criterion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Federated main model vs individual local models before FedAvg first iteration\n"
     ]
    },
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sample</th>\n",
       "      <th>local_ind_model</th>\n",
       "      <th>merged_main_model</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>sample 0</td>\n",
       "      <td>0.8111</td>\n",
       "      <td>0.0889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>sample 1</td>\n",
       "      <td>0.7667</td>\n",
       "      <td>0.1222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>sample 2</td>\n",
       "      <td>0.7111</td>\n",
       "      <td>0.1556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>sample 3</td>\n",
       "      <td>0.8111</td>\n",
       "      <td>0.1222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>sample 4</td>\n",
       "      <td>0.7222</td>\n",
       "      <td>0.1222</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sample  local_ind_model  merged_main_model\n",
       "0  sample 0           0.8111             0.0889\n",
       "1  sample 1           0.7667             0.1222\n",
       "2  sample 2           0.7111             0.1556\n",
       "3  sample 3           0.8111             0.1222\n",
       "4  sample 4           0.7222             0.1222"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Federated main model vs individual local models before FedAvg first iteration\")\n",
    "before_acc_table.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Federated main model vs individual local models after FedAvg first iteration\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sample</th>\n",
       "      <th>local_ind_model</th>\n",
       "      <th>merged_main_model</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>sample 0</td>\n",
       "      <td>0.8111</td>\n",
       "      <td>0.9000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>sample 1</td>\n",
       "      <td>0.7667</td>\n",
       "      <td>0.8222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>sample 2</td>\n",
       "      <td>0.7111</td>\n",
       "      <td>0.7889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>sample 3</td>\n",
       "      <td>0.8111</td>\n",
       "      <td>0.8556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>sample 4</td>\n",
       "      <td>0.7222</td>\n",
       "      <td>0.8667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sample  local_ind_model  merged_main_model\n",
       "0  sample 0           0.8111             0.9000\n",
       "1  sample 1           0.7667             0.8222\n",
       "2  sample 2           0.7111             0.7889\n",
       "3  sample 3           0.8111             0.8556\n",
       "4  sample 4           0.7222             0.8667"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Federated main model vs individual local models after FedAvg first iteration\")\n",
    "after_acc_table.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Federated main model vs centralized model before 1st iteration (on all test data)**  \n",
    "Please be aware that the centralized model gets approximately %98 accuracy on all test data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before 1st iteration main model accuracy on all test data:  0.1152\n",
      "After 1st iteration main model accuracy on all test data:  0.8556\n",
      "Centralized model accuracy on all test data:  0.9779\n"
     ]
    }
   ],
   "source": [
    "print(\"Before 1st iteration main model accuracy on all test data: {:7.4f}\".format(before_test_accuracy))\n",
    "print(\"After 1st iteration main model accuracy on all test data: {:7.4f}\".format(after_test_accuracy))\n",
    "print(\"Centralized model accuracy on all test data: {:7.4f}\".format(central_test_accuracy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a single iteration, we can send the weights of the main model back to the nodes and repeat the above steps.\n",
    "Now let's check how the performance of the main model improves when we repeat the iteration 10 more times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 2 : main_model accuracy on all test data:  0.8973\n",
      "Iteration 3 : main_model accuracy on all test data:  0.9098\n",
      "Iteration 4 : main_model accuracy on all test data:  0.9173\n",
      "Iteration 5 : main_model accuracy on all test data:  0.9231\n",
      "Iteration 6 : main_model accuracy on all test data:  0.9295\n",
      "Iteration 7 : main_model accuracy on all test data:  0.9348\n",
      "Iteration 8 : main_model accuracy on all test data:  0.9370\n",
      "Iteration 9 : main_model accuracy on all test data:  0.9393\n",
      "Iteration 10 : main_model accuracy on all test data:  0.9427\n",
      "Iteration 11 : main_model accuracy on all test data:  0.9441\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    model_dict=send_main_model_to_nodes_and_update_model_dict(main_model, model_dict, number_of_samples)\n",
    "    start_train_end_node_process_without_print(number_of_samples)\n",
    "    main_model= set_averaged_weights_as_main_model_weights_and_update_main_model(main_model,model_dict, number_of_samples) \n",
    "    test_loss, test_accuracy = validation(main_model, test_dl, main_criterion)\n",
    "    print(\"Iteration\", str(i+2), \": main_model accuracy on all test data: {:7.4f}\".format(test_accuracy))   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The accuracy of the centralized model was calculated as approximately 98%. The accuracy of the main model obtained by FedAvg method started from 85% and improved to 94%. In this case, we can say that although the main model obtained by FedAvg method was trained without seeing the data, its performance cannot be underestimated."
   ]
  }
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