sghmc.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import multivariate_normal\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import torch.optim as optim\n",
    "import torch.utils.data as data\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noise_var = 0.1\n",
    "num_data = 50\n",
    "num_features = 2\n",
    "prior_var = 1.\n",
    "\n",
    "X = np.random.randn(num_data, num_features)\n",
    "w_true = np.random.randn(num_features, 1) * np.sqrt(noise_var)\n",
    "noise = np.random.randn(num_data, 1) * np.sqrt(noise_var)\n",
    "y = X.dot(w_true) + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w_grid_x = np.linspace(-1, 1, num=100)\n",
    "w_grid_y = np.linspace(-1, 1, num=100)\n",
    "w_grid_x, w_grid_y = np.meshgrid(w_grid_x, w_grid_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w_grid_x = w_grid_x.reshape(-1)[:, None]\n",
    "w_grid_y = w_grid_y.reshape(-1)[:, None]\n",
    "w_grid = np.hstack([w_grid_x, w_grid_y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prior: $p(w) = \\mathcal{N}(0, I)$. Likelihood: $p(y \\vert w) = \\mathcal{N}(0, 0.1 \\cdot I)$\n",
    "\n",
    "Posterior $p(w \\vert y) \\propto p(w) p(y \\vert w)$.\n",
    "\n",
    "### True posterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# prior parameters\n",
    "S0 = np.eye(num_features) * prior_var\n",
    "m0 = np.zeros([num_features, 1])\n",
    "\n",
    "beta = 1 / noise_var\n",
    "\n",
    "# posterior parameters\n",
    "S0_inv = np.linalg.inv(S0)\n",
    "Sn_inv = S0_inv + beta * X.T.dot(X)\n",
    "Sn = np.linalg.inv(Sn_inv)\n",
    "\n",
    "\n",
    "mn = Sn.dot(S0_inv.dot(m0) + beta * X.T.dot(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 739,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_posterior = multivariate_normal(mean=mn[:, 0], cov=Sn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1098,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w_samples = np.random.multivariate_normal(mn[:, 0], Sn, size=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1099,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x127d30390>]"
      ]
     },
     "execution_count": 1099,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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YphTDcWB3uLwbOJ6z7/XjohiMGY+HxcVimJ+vf/pJlf5LvNK1be3nSdSpzdblmTbHRVaf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1282aa160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(w_samples[:, 0], w_samples[:, 1], 'bo')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SGHMC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 896,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class RegDataset(data.Dataset):\n",
    "    \n",
    "    def __init__(self, X, y):\n",
    "        self.X = torch.from_numpy(X).float()\n",
    "        self.y = torch.from_numpy(y).float()\n",
    "        \n",
    "    def __len__(self):\n",
    "        return self.X.size()[0]\n",
    "    \n",
    "    def __getitem__(self, index):\n",
    "        return self.X[index], self.y[index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1048,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dataset = RegDataset(X, y)\n",
    "dataloader = data.DataLoader(dataset, batch_size=10, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1049,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SGHMC:\n",
    "    \n",
    "    def __init__(self, var, alpha, eta, log_density, num_data):\n",
    "        \"\"\"\n",
    "        Stochastic Gradient Monte Carlo sampler.\n",
    "        \n",
    "        Args:\n",
    "            var: `Variable` corresponding to the variable that is sampled\n",
    "            alpha: momentum parameter\n",
    "            eta: learning rate parameter\n",
    "            log_density: function computing log_density for a given sample\n",
    "                and batch of data\n",
    "        \"\"\"\n",
    "        self.var = var\n",
    "        self.alpha = alpha\n",
    "        self.eta = eta\n",
    "        self.log_density = log_density\n",
    "        self.dataloader = dataloader\n",
    "        self.optimizer = optim.SGD([self.var], lr=1, momentum=(1 - self.alpha))\n",
    "        self.num_data = num_data\n",
    "    \n",
    "    def _noise(self):\n",
    "        std = np.sqrt(2 * self.alpha * self.eta)\n",
    "        n = Variable(torch.normal(0, std= std * torch.ones(self.var.size())))\n",
    "        return torch.sum(n * self.var)\n",
    "        \n",
    "    def sample(self, x_batch, y_batch):\n",
    "        loss = self.log_density(self.var, x_batch, y_batch) * self.eta\n",
    "        loss += self._noise() / self.num_data\n",
    "        loss.backward()\n",
    "        self.optimizer.step()\n",
    "        self.var.grad.data.zero_()\n",
    "#         print(self.var.grad)\n",
    "        return self.var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1050,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class BayesianLinearRegression:\n",
    "\n",
    "    def __init__(self, prior_std, noise_std, num_data):\n",
    "        self.prior_std = prior_std\n",
    "        self.noise_std = noise_std\n",
    "        self.num_data = num_data\n",
    "    \n",
    "    def log_prior(self, w):\n",
    "        return - torch.sum(w**2 / (2 * self.prior_std**2))\n",
    "\n",
    "    def log_posterior_density(self, w, X_batch, y_batch):\n",
    "        Xv = Variable(X_batch)\n",
    "        yv = Variable(y_batch)[:, 0]\n",
    "        preds = torch.matmul(Xv, w)\n",
    "        loss = - torch.mean((preds - yv)**2 /(2 * self.noise_std**2))\n",
    "        loss += self.log_prior(w)/ self.num_data\n",
    "        return -loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1129,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = torch.from_numpy(np.random.multivariate_normal(m0[:, 0], S0)).float()\n",
    "w_v = Variable(w, requires_grad=True)\n",
    "bayes_reg = BayesianLinearRegression(np.sqrt(prior_var), np.sqrt(noise_var), X.shape[0])\n",
    "sghmc = SGHMC(w_v, .01, 5e-3, bayes_reg.log_posterior_density, X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "100\n",
      "200\n",
      "300\n",
      "400\n",
      "500\n",
      "600\n",
      "700\n",
      "800\n",
      "900\n",
      "1000\n",
      "1100\n",
      "1200\n",
      "1300\n",
      "1400\n",
      "1500\n",
      "1600\n",
      "1700\n",
      "1800\n",
      "1900\n",
      "2000\n",
      "2100\n",
      "2200\n",
      "2300\n",
      "2400\n",
      "2500\n",
      "2600\n",
      "2700\n",
      "2800\n",
      "2900\n",
      "3000\n",
      "3100\n",
      "3200\n",
      "3300\n",
      "3400\n",
      "3500\n",
      "3600\n",
      "3700\n",
      "3800\n",
      "3900\n",
      "4000\n",
      "4100\n",
      "4200\n",
      "4300\n",
      "4400\n",
      "4500\n",
      "4600\n",
      "4700\n",
      "4800\n",
      "4900\n",
      "5000\n",
      "5100\n",
      "5200\n",
      "5300\n",
      "5400\n",
      "5500\n",
      "5600\n",
      "5700\n",
      "5800\n",
      "5900\n",
      "6000\n",
      "6100\n",
      "6200\n",
      "6300\n",
      "6400\n",
      "6500\n",
      "6600\n",
      "6700\n",
      "6800\n",
      "6900\n",
      "7000\n",
      "7100\n",
      "7200\n",
      "7300\n",
      "7400\n",
      "7500\n",
      "7600\n",
      "7700\n",
      "7800\n",
      "7900\n",
      "8000\n",
      "8100\n",
      "8200\n",
      "8300\n",
      "8400\n",
      "8500\n",
      "8600\n",
      "8700\n",
      "8800\n",
      "8900\n",
      "9000\n",
      "9100\n",
      "9200\n",
      "9300\n",
      "9400\n",
      "9500\n",
      "9600\n",
      "9700\n",
      "9800\n",
      "9900\n"
     ]
    }
   ],
   "source": [
    "samples = []\n",
    "for epoch in range(10000):\n",
    "    for i, data_ in enumerate(dataloader, 0):\n",
    "        x_batch, y_batch = data_\n",
    "        w_sample = sghmc.sample(x_batch, y_batch)\n",
    "        samples.append(np.copy(w_sample.data.numpy()))\n",
    "    if not(epoch % 100):\n",
    "        print(epoch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50000, 2)"
      ]
     },
     "execution_count": 1132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = np.vstack(samples)\n",
    "samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1292edf98>]"
      ]
     },
     "execution_count": 1133,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cAXAgfX8AwBmPfb4L4Kb0/ecA3BZ63r74KEIXMDH5Klx2T5uDW6c+7urci7bD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\nEOKEioIQQogTKgpCCCFO/h+CGGAq2m9riQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x129314668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_from=45000\n",
    "plus = 5000\n",
    "plt.plot(samples[start_from:start_from+plus, 0], samples[start_from:start_from+plus, 1], 'bo')\n",
    "plt.plot(mn[0] ,mn[1], 'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12941b518>]"
      ]
     },
     "execution_count": 1134,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HjplnNrWvz0DXiVbplUTPdR4Tje/8G1skX/LdGh9fazaN6uVjtlIfQ8ulzYoh\nT3RCHXZM2zl19rNK0xJ1RNKexU7HLztAUmyNdZ5Jna5JoHkn07UdVQwNkDeSoY4Zky4FoDmTVNos\nttQxSee1T5K7PNcV6a/Zy2XwVQwSlO0vZmdnzdLSUtPVWMOWLelpiKOVq8qWL1sH6E2aZEUpSpFn\nP0qrHfd7iARNuw+dTrBcbtXvYhsRkceMMbNZ5dT5XCF5IxlsC+6srHQ77PLginrydebpOg9KFhMT\nsG1b9ectEgyRFr2UphTGx9Of7V/9KlieNG+04CCjiqFCbBELtv1RhFJa2OmJE3DTTdmRFLZzpkVp\n+EZUnHee/+JByvDR6QTrMC8v+5XP09EoEvXjUiadzup7cM89cOGFa8ucOROE0drem6HEx97UNhkU\nH0OEyyba6VQ3A3NhIZ8T+rzzVm22utiPCgQ5t6qI+BkbWxs9Fz2bVSW5i84VZ1h8CTZQ53MzFMmZ\nUiRiqGjkUtr6DK7rz8+7s8GqDJ/YGuJOx/7sp70X8fDVMonw8mQrHtQZzb6oYugjiqyXkKeHkxXZ\nkXUdjWZSiUvVve4qGmvf5XAHNQeSL76KQX0MLWDPnnSb/siIPR2Gry02ithYWQleg5UVuOuu4O/0\ndOB0c9mAjVm7iLoy3GzcmL6/6KzgKtJP7N3r5zx2+eCUGD7ao20yaCMGY4JefLK3Mz6eL+lYGrp6\nm0rVUqXfy/WMFl3NcJAmpFUNOmLoLx58cO2+06fLR0toLiSlCLaRKgQjyKxnMk8knS1s++TJfCHb\nc3PdCft0FFCcdU1XQAlwDafn5oo95IuLwYt59myxOq1bB299q5qShpGXXrJPlhSBv/1b+7HJCWcr\nK8FnSH+Oo3233db9rJ044T5OqRGfYUXbZBBNSVVHS5TJZR9d1ze5WFEZGdG1INookRM5T3hzfKnZ\nPM+yz0I8wxIx1AvoVVQSsBE4QLCK2wFgQ0qZGYI1nx8HngFuiX13FcEqbsvAn0GQpsMlg6gYqo6W\nKOpbyMpXoxlZB1/m51f/93mOi5aa9Y1a8u10DMscg17gqxiq8DHsAg4ZY7YSLPO5K6XMceAaY8yV\nwG8Bu0Tk4vC7vwB+H9gayocrqFPfUXW0RF7fgu81i5qllPYzOgrz83Dnnav7ohxbPkRmIN8MAL4L\n8QzNGggtogrFsB3YH27vBz6WLGCMOW2MeSP8uD66rohsBi4wxvwg1Gb3px0/LFTpPMvzMs3M2K+Z\nDHdVBpPtv0/hAAARY0lEQVSZGXjzzWDFtbjTOC2HUBa+qxT6dF6GOV9Ro/gMK1wCvBrblvjnRLnL\ngCeBU8Bnwn2zwMFYmfcC37EcvxNYApamp6drGGQNFr5pCLLMVRruOvjiSl0xMRGYlnwnOUYmx/ia\n0Lb02FlmydHRbrOWUh6q9DEAB4GnU2R7UhEAr2Sc62LgUeCiPIohLoPoY7BRJjbblYbA93y6wM/g\nSvIZcC1WU2T2e7LTUSSQIVJMOj+hGipVDM4TwGFgc7i9GTjsccw9wPVh+f8T2/8J4MtZxw+LYmjD\n9H0dMQyuJKmjExCPKMpaJc02giiTR0npxlcxVOFjeADYEW7vAL6dLCAil4rI+eH2BuC3QwVyHPiV\niLxbRAT4VNrxw0qac+7UqWB/r7BNPiqDpvRuHhG49dZuf4It1UUWLgd13I9gWyTq3LlVScOY7s+9\nfgeGkSoUwxeAD4jIEeD94WdEZFZE7g7L/CPghyLyBPA3wH8yxjwVfncrcDdBuOqzwF9VUKeBoEgO\nmTwzTn2IoqVs+ZRE8p/z9OmgfqogekPa/8iY1ZxZxgR/f/1rGBsrdt6snF6Li/ZnJSqTJ2BCZ/TX\njM+wom0yLKakvJPe6jQ9uWLTi6bljtuPmzarqATS6dhNOlFa7ej/Hv/OtR6D61mOnh/b82t77nTS\nWzHQXEn9j2/YX0Sdpqe8q9P5cOpUkAvq6FFYWMg3+li3zp3PRynGyy/D/v3pz93v/u7qZ2O6vz99\nGi64wD4Px9bDN2a1TNpcnltu0SU3G8FHe7RN2jhiqCuzY57zupyHZevmGo24Ila2bXNHosRntaYt\nImST0dH2ryrnk+6j01kbdZOWUbdqyeqJp63hkVUn1wzlMilfepk1ddAztKIL9fSOJqOHfOLCs6I6\nfF8GWzlXY+FjJrLFuUex8E038EVlZMT9fXz+gCusuNPJPlcehWBr6F3PrO//0fWcNh1hl0U/1LEs\nqhh6SFPLBfrEhfv0DMu+DFU0WK5r9nouhcjaiYB1SVqDPz6+OjmsSsUY5TKKPz9ZHYL48ptZ9yzr\nmWlrbzzrNw6SP0MVQw9paoHxrLhw18MevchVZLSsqvGyXbOXzulIQc3PV9dLb4skFUMc26glj0mr\nH/HtXA0Kqhh6SFMjBh+F5Fq43df2n0Ydpg7bNetM/R2X0dH6U403KXnu78REPoXfr73qsiayfkMV\nQw9pyjbpo5CKvvR57cXj4+VNPlnXjBRRXY1mVId+9msUub9lR2T9bIfPep76+beloYqhxzRhP/VV\nSGl1c70QTSXW65d1rJu+ftWNd15lG81naJuvoAhZvoV+/m1pqGIYEooqJJd/os7EerZjXfbvJPPz\nzTewbR1VrFuXvn/btvzPQpq5cdB60MMQiRRHFYPipMwLkachGRvrjrBJm3uQ90Vsqsfe6XSH1fZi\nWdKRkWoipKKOQ1oHwvUstDWSqEqG4TdGqGJQMin6QhRpSGwO3Xhj60uVfoY853LdvyrnGiQlSh1S\n9TnzzmUZpgZ0UFHFoNRK3kaiysitqkYM0UIwPhFIaTOC4xPw6p5rUYdTPM+9HzaTy6CiikEpTJU9\nw6zJQ2khlFnXz3Ke+0p07WRjb1vlrskw1mjeSZXXzxOf31RItlItvopBk+gpXSTXeF5ZCT4XSd8d\nP5eNZBK+tOvffDNs2rSaShyC78qSlgBwago+/en0ZHC+i9fXwfT02iRznc7a1OUTE7Bt22qa9NHR\n4DfZzulLkRTwSh/joz3aJoM+YmjSlttLk0+aKcLHTOSah+GbLyr63Om400XHqdtcZDt/vD5pye18\nfANlzUA6YhgM6IUpCdgIHACOhH83pJSZAX4MPA48A9wS++4RgqVBHw/l7T7XHWTF0LQtt8r0HlnZ\nXss0vrZQSltyuG3bshefz2rw6oyGSq5NEdU1y4Hv+2yU7Ww0/Vwq1dArxXAHsCvc3gXcnlJmHFgf\nbk8BR4GLzapimM173UFWDE33zPJcP6uxKfJbfBvfyOaelt8nPpqI0lrntc3bfB8+5xkZcSuh8XF3\nT992X5t+NjRyqf/plWI4DGwOtzcTrOPsKt8BjqlisNNUQr6IPLOps8oVmZmd5vzNo6jK5vzJamx9\no5KSGVKj7azG0vYbXOGqbUnypqOK9tMrxfBqbFvinxPlLgOeBE4Bn4ntfwR4KjQjfQ4Qn+sOsmJo\nuldojF+vz7eePhFGWZPifH0AVZl6Rkb8G/I898IH27myzHJtoA3PruKmMsUAHASeTpHtSUUAvJJx\nrouBR4GLws+XhH/fAvw18CnHsTuBJWBpenq65tvXHP3S66pqZOObCNDHPFGXczjr/vfKL2OTIpME\n66Dp0a6STStNSWG5e4DrU/b/a+DPfa47yCMGY/rDTltV77DKxiRPqo68UsQv0svJe23oPOiIof34\nKoay8xgeAHaE2zuAbycLiMilInJ+uL0B+G3gsIisE5FN4f4x4CPhSGTgWVwM4vGjuPzkHIG5OTh6\nFM6dC/5Gi6W3iT17qlmk3RZLb9vvune2Ou3dG8T/T07mq1scV7x+VffCdi6R7ONOnQrmWTRJlfdB\naRgf7WETAmfyIYJw1YPAxnD/LHB3uP0BAv/CE+HfneH+SeCxcN8zwF5g1Oe6/Txi6BdTkQ9VjGzy\n3A9fh7erTkVzDmX1euuYLe5an7mtJpt+GO0OM2hKjHaiw+21+DYmVd27Iqklmm7g4veoiuVYleHE\nVzFoSoweM0ypBbJMZhG+prOq7t3cHFxzTfe+9evt5TudfOY839+dh/g92r+/GZNNHb9LaSk+2qNt\noiOG9hJPmpd0LJc1mdnunc/iQnFs5qRt28qb+XplKuy1yWaQTKDDDGpKaieD/IL5mGjKKEDX+fPc\nQ5spJlIwZRrcQVX8g/q7hg1fxSBB2f5idnbWLC0tNV2NwiwuBhEkx44F0Td79rQz8igvW7a4M6lC\nEGFz7lzxaywuwo4dcPbs2u9mZgJzSxauKJ+yr8PISPo5yv7uphnU3zVsiMhjxpjZrHLqY2iAfghH\nLYKPrT9Pquc05ubsDZGvryFKSe27P8LHxp43/LZfaOvvUr9HPahiUCojq5GoykFappFaXITzz0//\nbudO93E+61QMaix/G39XlWuHKAl87E1tk372MQwyaT6AyAFdpYO0qJ/G5qMQCRzSLqrMOtuvtO13\nqd8jP6iPQWmCXvlPilzH5gPx8U2ojb196P8kP74+BlUMytBQpiEpo1SUetD/SX7U+awoCcr4Jtpo\nYx929H9SH6oYlKGhTEMyNxck4puZCUYYMzPB50GJKOtH9H9SH2pKUoaKQZ1Doig++JqS1vWiMorS\nFubmVBEoShZqSlIURVG6UMWgKIqidFFaMYjIRhE5ICJHwr8bHGUvEJHnReTPY/uuEpGnRGRZRP5M\nxGe9KkVRFKUuqhgx7AIOGWO2EqzmtstR9j8C/yux7y+A3we2hvLhCuqkKIqiFKQKxbAd2B9u7wc+\nllZIRK4CLgL+OrZvM3CBMeYH4XTt+23HK4qiKL2hCsVwkTHmeLj9c4LGvwsRGQH+M/CHia8uAZ6P\nfX4+3KcoiqI0hFe4qogcBH4j5avd8Q/GGCMiaRMjbgUeNMY8X9SFICI7gZ0A003n+lUURRlgvBSD\nMeb9tu9E5BcistkYczw0Df0ypdg1wHtF5FZgChgXkZPAXuDSWLlLgRcsddgH7INggptPvRVFUZT8\nVGFKegDYEW7vAL6dLGCMmTPGTBtjthCYk+43xuwKTVC/EpF3h9FIn0o7XlEURekdVSiGLwAfEJEj\nwPvDz4jIrIjc7XH8rcDdwDLwLPBXFdRJURRFKYjmSlIURRkSNO22oiiKUghVDIqiKEoXqhgUpSUs\nLgarko2MBH91UXulKTTttqK0gMVF2LkTTp0KPq+sBJ9B04QrvUdHDIrSAnbvXlUKEadOBfsVpdeo\nYlCUFnDsWL79ilInqhgUpQXYsrxo9helCVQxKEoL2LMHJia6901MBPsVpdeoYlCUFjA3B/v2wcwM\niAR/9+1Tx7PSDBqVpCgtYW5OFYHSDnTEoCiKonShikFRFEXpQhWDoiiK0oUqBkVRFKULVQyKoihK\nF325HoOIvAi8BrzUdF0sbKKddWtrvUDrVpS21q2t9YLhrtuMMeZtWYX6UjEAiMiSz4ITTdDWurW1\nXqB1K0pb69bWeoHWzQc1JSmKoihdqGJQFEVRuuhnxbCv6Qo4aGvd2lov0LoVpa11a2u9QOuWSd/6\nGBRFUZR66OcRg6IoilIDrVYMIrJRRA6IyJHw74aUMleKyPdF5BkReVJEPh777j4ReU5EHg/lyhbV\n7XIR+aGILIvI10VkvFf1Cst9V0ReFZHvJPY3es8y6lbLPctZtx1hmSMisiO2/xERORy7b28vWZ8P\nh+dbFpFdKd+vD+/BcnhPtsS++2y4/7CIfKhMPaqsm4hsEZHXY/forgbq9i9E5Mci8qaIXJ/4LvV/\n24J6nY3dsweqrJcVY0xrBbgD2BVu7wJuTynzTmBruH0xcBy4MPx8H3B9S+v2DeCGcPsuYL5X9Qq/\n2wZ8FPhOYn+j9yyjbrXcsxz/z43AT8O/G8LtDeF3jwCzFdVlFHgWuAIYB54A3pUocytwV7h9A/D1\ncPtdYfn1wOXheUYrvE9l6rYFeLqOZytH3bYA/wS4P/6cu/63TdYr/O5kXffMJq0eMQDbgf3h9n7g\nY8kCxpi/N8YcCbf/L/BLIHMCR5N1ExEB3gd8y3V8XfUK63MI+HVF1/SlcN1qvme+dfsQcMAY87Ix\n5hXgAPDhCusQcTWwbIz5qTHmNPC1sH62+n4L2Bbeo+3A14wxbxhjngOWw/O1oW51k1k3Y8xRY8yT\nwLnEsXX+b8vUqxHarhguMsYcD7d/DlzkKiwiVxNo5Gdju/eEZpwvicj6ltStA7xqjHkz/Pp54JIm\n6mWhFfcsQZ33zLdulwA/i31O1uHecLj/uZINYdZ1usqE9+QfCO6Rz7FlKFM3gMtF5H+LyN+IyHsr\nrJdv3eo4tu5znyciSyLyAxGpsjNkpfGFekTkIPAbKV/tjn8wxhgRsYZQichm4KvADmNMpHU/S/CS\njxOEgf0H4PNN161s56mqelloxT2rg5rrNmeMeUFE3gL8V+CTBGYBZZXjwLQx5oSIXAX8dxH5TWPM\nr5quWMuZCZ+tK4CHReQpY8yzmUeVoHHFYIx5v+07EfmFiGw2xhwPG9dfWspdAPwPYLcx5gexc0c9\nwDdE5F7gD1tStxPAhSKyLuxRXQq80Mt6Oc7d+D2zUOqeVVS3F4BrY58vJfAtYIx5Ifz7axH5SwLz\nQVHF8AJwWeI6yd8alXleRNYBbyW4Rz7HlqFw3UxgMH8DwBjzmIg8S+CHW+ph3VzHXps49pFKalXy\nfxJ7tn4qIo8A/5Ruq0jltN2U9AAQRQfsAL6dLCBBZMp/A+43xnwr8d3m8K8Q2IyfbkPdwhfkfwLX\nu46vq14umr5nNmq+Z751ewj4oIhskCBq6YPAQyKyTkQ2AYjIGPARyt23HwFbJYjCGidw4CajUeL1\nvR54OLxHDwA3hJFBlwNbgUdL1KWyuonI20RkFCDs/W4lcPL2sm42Uv+3TdcrrM/6cHsT8B7gJxXV\ny06vvd15hMAueQg4AhwENob7Z4G7w+0bgTPA4zG5MvzuYeApgpd0AZhqUd2uIHhhl4FvAut7Va/w\n8/eAF4HXCWyeH2rDPcuoWy33LGfdbg6vvwzcFO6bBB4DngSeAfZSMhIIuA74e4Ke4e5w3+eB3wm3\nzwvvwXJ4T66IHbs7PO4w8C9reC8L1Q34V+H9eRz4MfDRBur2z8Jn6jWCEdYzrv9t0/UC/nn4Pj4R\n/v101fcsTXTms6IoitJF201JiqIoSo9RxaAoiqJ0oYpBURRF6UIVg6IoitKFKgZFURSlC1UMiqIo\nSheqGBRFUZQuVDEoiqIoXfw/+DLFqmmRkU8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12941b588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "freq = 10\n",
    "new_samples = []\n",
    "for i in range(int(samples.shape[0] / freq))[100:]:#[400:]:\n",
    "    new_samples.append(samples[i * freq][None, :])\n",
    "new_samples = np.vstack(new_samples)\n",
    "plt.plot(new_samples[:, 0], new_samples[:, 1], 'bo')\n",
    "plt.plot(mn[0] ,mn[1], 'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1295a0b38>]"
      ]
     },
     "execution_count": 1137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1295a0ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "start_from=0\n",
    "plus = 100\n",
    "plt.plot(samples[start_from:start_from+plus, 0], samples[start_from:start_from+plus, 1], 'bo')\n",
    "plt.plot(mn[0] ,mn[1], 'ro')"
   ]
  }
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