autograd_test.ipynb

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      "[-1.14993102  0.69084953  0.68523832]\n",
      "(-2.7430635540781623e-10, -2.5915536383536164e-10, -4.730811298259141e-10)\n"
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   "source": [
    "austria = pd.read_csv('http://dl.dropbox.com/u/8649795/AT_Austria.csv')\n",
    "austria = austria[austria['Origin'] != austria['Destination']]\n",
    "f = np.reshape(austria['Data'].values, (-1,1))\n",
    "o = austria['Origin'].values\n",
    "d = austria['Destination'].values\n",
    "dij = np.reshape(austria['Dij'].values, (-1,1))\n",
    "o_vars = np.reshape(austria['Oi2007'].values, (-1,1))\n",
    "d_vars = np.reshape(austria['Dj2007'].values, (-1,1))\n",
    "dij = np.reshape(austria['Dij'].values, (-1,1))\n",
    "o_vars = np.reshape(austria['Oi2007'].values, (-1,1))\n",
    "d_vars = np.reshape(austria['Dj2007'].values, (-1,1))\n",
    "\n",
    "def newton(f, x0):\n",
    "    # wrap scipy.optimize.newton with our automatic derivatives\n",
    "    params = scipy.optimize.fsolve(f, x0)\n",
    "    return params\n",
    "\n",
    "def poiss_loglike(mu, sig, ep, x, inputs):\n",
    "    a,b,c = inputs[:,0], inputs[:,1], inputs[:,2]\n",
    "    predict = sig*a + ep*b + mu*c\n",
    "    predict = np.reshape(predict, (-1,1))\n",
    "    return -np.sum(x*np.log(predict)-predict)\n",
    "\n",
    "#def loglike(mu, k, x, inputs):\n",
    "    #return np.sum(poiss_loglike(mu, k, x, inputs))\n",
    "\n",
    "\n",
    "def fit_maxlike(x, inputs, mu_guess, o_guess, d_guess):\n",
    "    prime = lambda p: multigrad(poiss_loglike, argnums=[0,1,2])(p[0], p[1], p[2], x, inputs)\n",
    "    params = newton(prime, (mu_guess, o_guess, d_guess))\n",
    "    return params\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    \n",
    "    x=np.log(f)\n",
    "    inputs = np.hstack((np.log(o_vars), np.log(d_vars), np.log(dij)))\n",
    "    params = fit_maxlike(x, inputs, mu_guess=0.0, o_guess=1.0, d_guess=1.0)\n",
    "    print(params)\n",
    "    \n",
    "    prime = lambda p: multigrad(poiss_loglike, argnums=[0,1,2])(p[0], p[1], p[2], x, inputs)\n",
    "    print(prime(params))\n",
    "\n",
    "\n"
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