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    "# Introduction to keras\n",
    "\n",
    "This is a short introductive tutorial for [keras](http://keras.io). Keras is a high-level interface for machine learning with **neural networks**.\n",
    "\n",
    "In order to introduce and illustrate the principle of neural networks, we will consider the well-known classification problem of **iris species**."
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    "## Classification of iris species\n",
    "\n",
    "*Iris setosa*, *Iris versicolor* and *Iris virginica* are closely-related species. They differ by the **size** of their petal and sepal.\n",
    "\n",
    "![flowers](./images/flowers.png)\n",
    "\n",
    "For instance the dataset below list the **height** and **width** of the petals of different specimens, and **whether** these specimens belong to the species *setosa*. "
   ]
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   "source": [
    "import pandas as pd\n",
    "df = pd.read_csv('./data/setosa/train.csv')\n",
    "df.head(6)"
   ]
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   "source": [
    "### Problem statement\n",
    "\n",
    "Based on this dataset, and given the petal height and width of a **new specimen**, we would like to predict the **probability** that this specimen belongs to the species setosa.\n",
    "![Model](./images/Model_Schematic.png)"
   ]
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    "## Using neural networks for this problem\n",
    "\n",
    "### General structure of fully-connected neural networks\n",
    "\n",
    "Neural networks are an extremeley versatile machine learning technique. \n",
    "\n",
    "They consist in stacking individual units (a.k.a. *artificial neurons*) that :\n",
    "- perform a **weighted sum** of their inputs ($\\,S = \\sum_i w_i x_i + w_0\\,$)\n",
    "- apply a **non-linear function** to this sum ($\\,y = f(S)\\,$) and return it as output\n",
    "\n",
    "![neural_nets](./images/Schematic_neural_net.png)\n",
    "\n",
    "- The number of units and layers are ** *arbitrarily* chosen** by the user.\n",
    "- The non-linear function $f$ are ** *arbitrarily* chosen** by the user (typical example include the sigmoid function or the `tanh` function).\n",
    "- The values of the weights are **determined by an algorithm**, so as to produce the right output on a known dataset.\n",
    "\n",
    "**Training the network consists in finding the right values for the weights $w_i$.**"
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    "### Using a neural network for the classification of Iris setosa\n",
    "\n",
    "In order to solve the problem of classification for *Iris setosa*, we will start with the simplest kind of neural network: a **single layer** network. \n",
    "\n",
    "For the non-linear function, we will choose the **sigmoid** function, since its output is between 0 and 1 and can thus easily be interpreted as a probability.\n",
    "\n",
    "![single_layer](./images/single_layer.png)\n",
    "\n",
    "With this model, we have: $ p_{setosa} = f( w_0 + w_1\\times height + w_2 \\times width )$, and training the model consists in finding $w_1$ and $w_2$."
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   "source": [
    "### Next steps in this tutorial\n",
    "\n",
    "We will first build a neural network by hand [here](./Single_layer_by_hand.ipynb), before using `keras` to automate the process."
   ]
  }
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