basic_saga.ipynb

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     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
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   "source": [
    "%pylab inline"
   ]
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   "source": [
    "# suppose we want to minimize the quadratic loss function\n",
    "# 1/n ||A x - b||^2\n",
    "n_samples, n_features = 100, 10\n",
    "A = np.random.randn(n_samples, n_features)\n",
    "b = np.random.randn(n_samples)\n",
    "def partial_grad(x):\n",
    "    i = np.random.randint(n_samples)\n",
    "    return i, A[i] * (A[i].dot(x) - b[i])\n",
    "\n",
    "def saga(pg, x, step_size, n_samples, max_iter=n_samples * 1000):\n",
    "    memory_gradients = np.zeros((n_samples, n_features))\n",
    "    for _ in range(max_iter):\n",
    "        i, cur_grad = pg(x)\n",
    "        x -= step_size * (cur_grad - memory_gradients[i] + memory_gradients.mean(0))\n",
    "        memory_gradients[i] = cur_grad\n",
    "    return x\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.082629  ,  0.07154017,  0.15254069, -0.03220931, -0.03776542,\n",
       "       -0.09992818,  0.03298484,  0.11354239,  0.09035411, -0.13045454])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "saga(partial_grad, np.zeros(n_features), 0.01, n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.082629  ,  0.07154017,  0.15254069, -0.03220931, -0.03776542,\n",
       "       -0.09992818,  0.03298484,  0.11354239,  0.09035411, -0.13045454])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sanity check, to see if solutions coincide\n",
    "from scipy import linalg\n",
    "linalg.lstsq(A, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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