{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Data Analysis and Machine Learning Applications for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Material for a* [*University of Illinois*](http://illinois.edu) *course offered by the* [*Physics Department*](https://physics.illinois.edu). *This content is maintained on* [*GitHub*](https://github.com/illinois-mla) *and is distributed under a* [*BSD3 license*](https://opensource.org/licenses/BSD-3-Clause).\n", "\n", "[Table of contents](Contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np\n", "import pandas as pd\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.collections" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import scipy.signal" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "from sklearn import model_selection" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import tensorflow as tf" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from mls import locate_data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Neural Network Architectures for Deep Learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We previously took a bottom-up look at how a neural network is composed of basic building blocks. Now, we take a top-down look at some of the novel network architectures that are enabling the current [deep-learning revolution](https://www.techrepublic.com/article/the-deep-learning-revolution-how-understanding-the-brain-will-let-us-supercharge-ai/):\n", " - Convolutional networks\n", " - Unsupervised learning networks\n", " - Recurrent networks\n", " - Reinforcement learning\n", " \n", "We conclude with some reflections on where \"deep learning\" is headed.\n", "\n", "The examples below use higher-level tensorflow APIs than we have seen before, so we start with a brief introduction to them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### High-Level Tensorflow APIs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our earlier examples, we built our networks using [low-level tensorflow primitives](https://www.tensorflow.org/programmers_guide/low_level_intro). For more complex networks composed of standard building blocks, there are convenient higher-level application programming interfaces (APIs) that abstract aways the low-level graphs and sessions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Reading Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [tf.data API](https://www.tensorflow.org/programmers_guide/datasets) handles data used to train and test a network, replacing the low-level placeholders we used earlier. For a small dataset that fits in memory, use:\n", "```\n", "dataset = tf.data.Dataset.from_tensor_slices((dict(X), y))\n", "```\n", "\n", "Creating a Dataset adds nodes to a graph so you should normally wrap your code to create a Dataset in a function that tensorflow will call in the appropriate context. For example, to split the 300 `circles` samples above into train (200) and test (100) datasets:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "X = pd.read_hdf(locate_data('circles_data.hf5'))\n", "y = pd.read_hdf(locate_data('circles_targets.hf5'))\n", "X_train, X_test, y_train, y_test = model_selection.train_test_split(\n", " X, y, test_size=100, random_state=123)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def get_train_data(batch_size=50):\n", " dataset = tf.data.Dataset.from_tensor_slices((dict(X_train), y_train))\n", " return dataset.shuffle(len(X_train)).repeat().batch(batch_size)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def get_test_data(batch_size=50):\n", " dataset = tf.data.Dataset.from_tensor_slices((dict(X_test), y_test))\n", " return dataset.batch(batch_size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While `from_tensor_slices` is convenient, it is not very efficient since the whole dataset is added to the graph with constant nodes (and potentially copied multiple times). Alternatively, convert your data to tensorflow's [binary file format](https://www.tensorflow.org/api_guides/python/python_io) so it can be read as a [TFRecordDataset](https://www.tensorflow.org/api_docs/python/tf/data/TFRecordDataset)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Building a Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [tf.estimator API](https://www.tensorflow.org/programmers_guide/estimators) builds and runs a graph for training, evaluation and prediction. This API generates a lot of INFO log messages, which can be suppressed using:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "tf.logging.set_verbosity(tf.logging.WARN)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First specify the names and types (but not values) of the features that feed the network's input layer:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "inputs = [tf.feature_column.numeric_column(key=key) for key in X]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, build the network graph. There are [pre-made estimators](https://www.tensorflow.org/programmers_guide/estimators#pre-made_estimators) for standard architectures that are easy to use. For example, to recreate our earlier architecture of a single 4-node hidden layer with sigmoid activation:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "config = tf.estimator.RunConfig(\n", " model_dir='tfs/circle',\n", " tf_random_seed=123\n", ")" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "classifier = tf.estimator.DNNClassifier(\n", " config=config,\n", " feature_columns=inputs,\n", " hidden_units=[4],\n", " activation_fn=tf.sigmoid,\n", " n_classes=2\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are only a limited number of pre-defined models available so you often have to build a [custom estimator](https://www.tensorflow.org/get_started/custom_estimators) using the intermediate-level [layers API](https://www.tensorflow.org/api_docs/python/tf/layers). See convolutional-network example below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Training a Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An estimator remembers any previous training (using files saved to its `model_dir`) so if you really want to start from scratch you will need to clear this history:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "!rm -rf tfs/circle/*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `train` method runs a specified number of steps (each learning from one batch of training data):" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow/python/framework/op_def_library.py:263: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Colocations handled automatically by placer.\n", "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow/python/feature_column/feature_column_v2.py:2703: to_float (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use tf.cast instead.\n" ] } ], "source": [ "classifier.train(input_fn=get_train_data, steps=5000);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After training, you can list the model parameters and access their values:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['dnn/hiddenlayer_0/bias',\n", " 'dnn/hiddenlayer_0/bias/t_0/Adagrad',\n", " 'dnn/hiddenlayer_0/kernel',\n", " 'dnn/hiddenlayer_0/kernel/t_0/Adagrad',\n", " 'dnn/logits/bias',\n", " 'dnn/logits/bias/t_0/Adagrad',\n", " 'dnn/logits/kernel',\n", " 'dnn/logits/kernel/t_0/Adagrad',\n", " 'global_step']" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "classifier.get_variable_names()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.78543633, 3.8394272 , 3.5696874 , -3.0604234 ],\n", " [ 4.556375 , 0.05935226, -2.6338506 , -2.281971 ]],\n", " dtype=float32)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "classifier.get_variable_value('dnn/hiddenlayer_0/kernel')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Testing a Model" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow/python/ops/metrics_impl.py:2002: div (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Deprecated in favor of operator or tf.math.divide.\n", "WARNING:tensorflow:Trapezoidal rule is known to produce incorrect PR-AUCs; please switch to \"careful_interpolation\" instead.\n", "WARNING:tensorflow:Trapezoidal rule is known to produce incorrect PR-AUCs; please switch to \"careful_interpolation\" instead.\n", "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow/python/training/saver.py:1266: checkpoint_exists (from tensorflow.python.training.checkpoint_management) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use standard file APIs to check for files with this prefix.\n" ] } ], "source": [ "results = classifier.evaluate(input_fn=get_test_data)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'accuracy': 1.0,\n", " 'accuracy_baseline': 0.53,\n", " 'auc': 1.0,\n", " 'auc_precision_recall': 1.0,\n", " 'average_loss': 0.10397522,\n", " 'label/mean': 0.53,\n", " 'loss': 5.198761,\n", " 'precision': 1.0,\n", " 'prediction/mean': 0.52295226,\n", " 'recall': 1.0,\n", " 'global_step': 5000}" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Convolutional Networks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **Convolutional Neural Network (CNN)** is a special architecture that:\n", " - Assumes that input features measure some property on a grid. The grid is usually spatial or temporal, but this is not required. For example, a 1D spectrum or time series, a 2D monochrome image, or a 3D stack of 2D images in different filters (RGB, etc).\n", " - Performs translation-invariant learning efficiently. For example, identifying a galaxy wherever it appears in an image, or a transient pulse wherever it appears in a time series. The main efficiency is a much reduced number of parameters compared to the number of input features, relative to the dense fully connected networks we have seen so far.\n", " \n", "As we saw in the previous lecture, Neural Networks receive an input (a single vector), and transform it through a series of hidden layers. Each hidden layer is made up of a set of neurons, where each neuron is fully connected to all neurons in the previous layer, and where neurons in a single layer function completely independently and do not share any connections. The last fully-connected layer is called the “output layer” and in classification settings it represents the class scores.\n", "\n", "The fully-connected, feed-forward neural networks we have studied thus far do not scale well to large image data. For example, a modest 200$\\times$200$\\times$3 (x-pixels, y-pixels, 3 colors) image would lead to neurons that have 200$\\times$200$\\times$3 = 120,000 weights. Moreover, we would almost certainly want to have several such neurons, so the parameters would add up quickly! Clearly, this full connectivity is wasteful and the huge number of parameters would quickly lead to overfitting.\n", "\n", "Convolutional Neural Networks take advantage of the fact that the input consists of images and they constrain the architecture in a more sensible way to reduce the number of parameters. In particular, unlike a regular Neural Network, the layers of a CNN have neurons arranged in 3 dimensions: width, height, depth. (Note that the word depth here refers to the third dimension of an activation volume, not to the depth of a full Neural Network, which can refer to the total number of layers in a network.) The neurons in a CNN layer will only be connected to a small region of the layer before it, instead of all of the neurons in a fully-connected manner. \n", "\n", "A CNN is made up of layers of different types (convolutions, pooling, fully-connected), in general. Every layer has a simple API: It transforms an input 3D volume to an output 3D volume with some differentiable function that may or may not have parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use the following problem to motivate and demonstration a CNN:\n", " - The input data consists of triplets of digitized waveforms.\n", " - Each waveform has a slowly varying level with some narrow pulses superimposed.\n", " - Each triplet has a single pulse that is synchronized (coincident) in all three waveforms.\n", " - Waveforms also contain a random number of unsynchronized \"background\" pulses.\n", " - Synchronized and unsynchronized pulses can overlap in time and between traces.\n", " \n", "The goal is to identify the location of the synchronized pulses in each triplet. This is a simplified version of a common task in data acquisition trigger systems and transient analysis pipelines." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def generate(N=10000, ntrace=3, nt=100, nbg=1., A=5., nsmooth=3, T=1., seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " t_grid = np.linspace(0., T, nt)\n", " # Generate the smooth background shapes as superpositions of random cosines.\n", " wlen = 2 * T * gen.lognormal(mean=0., sigma=0.2, size=(nsmooth, N, ntrace, 1))\n", " phase = gen.uniform(size=wlen.shape)\n", " X = np.cos(2 * np.pi * (t_grid + phase * wlen) / wlen).sum(axis=0)\n", " # Superimpose short pulses.\n", " sigma = 0.02 * T\n", " tsig = T * gen.uniform(0.05, 0.95, size=N)\n", " y = np.empty(N, dtype=int)\n", " nbg = gen.poisson(lam=nbg, size=(N, ntrace))\n", " for i in range(N):\n", " # Add a coincident pulse to all traces.\n", " xsig = A * np.exp(-0.5 * (t_grid - tsig[i]) ** 2 / sigma ** 2)\n", " y[i] = np.argmax(xsig)\n", " X[i] += xsig\n", " # Add non-coincident background pulses to each trace.\n", " for j in range(ntrace):\n", " if nbg[i, j] > 0:\n", " t0 = T * gen.uniform(size=(nbg[i, j], 1))\n", " X[i, j] += (A * np.exp(-0.5 * (t_grid - t0) ** 2 / sigma ** 2)).sum(axis=0)\n", " return X.astype(np.float32), y\n", " \n", "X, y = generate()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_traces(X, y):\n", " Nsample, Ntrace, D = X.shape\n", " _, ax = plt.subplots(Nsample, 1, figsize=(9, 1.5 * Nsample))\n", " t = np.linspace(0., 1., 100)\n", " dt = t[1] - t[0]\n", " for i in range(Nsample):\n", " for j in range(Ntrace):\n", " ax[i].plot(t, X[i, j], lw=1)\n", " ax[i].axvline(t[y[i]], c='k', ls=':')\n", " ax[i].set_yticks([])\n", " ax[i].set_xticks([])\n", " ax[i].set_xlim(-0.5 * dt, 1 + 0.5 * dt)\n", " plt.subplots_adjust(left=0.01, right=0.99, bottom=0.01, top=0.99, hspace=0.1)\n", " \n", "plot_traces(X[:5], y[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The derivative of $f(x)$ can be approximated as\n", "\n", "$$ \\Large\n", "f'(x) \\simeq \\frac{f(x + \\delta) - f(x - \\delta)}{2\\delta}\n", "$$\n", "\n", "for small $\\delta$. We can use this approximation to convert an array of $f(n \\Delta x)$ values into an array of estimated $f'(n \\Delta x)$ values using:\n", "```\n", "K = np.array([-1, 0, +1]) / ( 2 * dx)\n", "fp[0] = K.dot(f[[0,1,2]])\n", "fp[1] = K.dot(f[[1,2,3]])\n", "...\n", "fp[N-2] = K.dot(f[[N-3,N-2,N-1]]\n", "```\n", "The numpy [convolve function](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.convolve.html) automates this process of sliding an arbitrary kernel $K$ along an input array like this. The result only estimates a first (or higher-order) derivative when the kernel contains [special values](https://en.wikipedia.org/wiki/Finite_difference_coefficient) (and you should normally use the numpy [gradient function](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.gradient.html) for this), but any convolution is a valid and potentially useful transformation.\n", "\n", "A clarifying word about terminology: In the context of convolutional networks, kernal is a simple group of weights shared all over the input space that is engineered to determine what specific features are to be detected. The kernel is also sometimes referred to as a \"feature map\" or \"filter\" in this context. \n", "\n", "See for example the application of a kernel in convolution over a simple black-and-white image:\n", "[here](https://i.stack.imgur.com/9Iu89.gif).\n", "\n", "\n", "The kernel needs to completely overlap the input array it is being convolved with, which means that the output array is smaller and offset. Alternatively, you can pad the input array with zeros to extend the output array. There are three different conventions for handling these edge effects via the `mode` parameter to `np.convolve`:\n", " - **valid**: no zero padding, so output length is $N - K + 1$ and offset is $(K-1)/2$.\n", " - **same**: apply zero padding and trim so output length equals input length $N$, and offset is zero.\n", " - **full**: apply zero padding without trimming, so output length is $N + K - 1$ and offset is $-(K-1)/2$.\n", "\n", "(Here $N$ and $K$ are the input and kernel lengths, respectively).\n", "\n", "We can use a convolution to identify features in our input data:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def plot_convolved(x, kernel, smax=50):\n", " t = np.arange(len(x))\n", " plt.plot(t, x, lw=1, c='gray')\n", " z = np.convolve(x, kernel, mode='same')\n", " for sel, c in zip(((z > 0), (z < 0)), 'rb'):\n", " plt.scatter(t[sel], x[sel], c=c, s=smax * np.abs(z[sel]), lw=0)\n", " plt.gca()\n", " plt.grid(False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's pick out regions of large positive (red) or negative slope (notice how the edge padding causes some artifacts):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_convolved(X[1, 1], [0.5,0,-0.5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also pick out regions of large curvature (using the finite-difference coefficients for a second derivative):" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_convolved(X[1, 1], [1.,-2.,1.])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can apply both of these convolutions to transform our input data to a new representation that highlights regions of large first or second derivative. Use a tanh activation to accentuate the effect:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def apply_convolutions(X, *kernels):\n", " N1, N2, D = X.shape\n", " out = []\n", " for i in range(N1):\n", " sample = []\n", " for j in range(N2):\n", " for K in kernels:\n", " sample.append(np.tanh(np.convolve(X[i, j], K, mode='valid')))\n", " out.append(sample)\n", " return np.asarray(out)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "out = apply_convolutions(X, [0.5,0,-0.5], [1.,-2.,1.])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting array can be viewed as a synthetic image and offers an easy way to visually identify individual narrow peaks and their correlations between traces:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_synthetic(Z):\n", " _, ax = plt.subplots(len(Z), 1, figsize=(9, len(Z)))\n", " for i, z in enumerate(Z):\n", " ax[i].imshow(z, aspect='auto', origin='upper', interpolation='none',\n", " cmap='coolwarm', vmin=-1, vmax=+1);\n", " ax[i].grid(False)\n", " ax[i].axis('off')\n", " plt.subplots_adjust(left=0.01, right=0.99, bottom=0.01, top=0.99, hspace=0.1)\n", " \n", "plot_synthetic(out[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The patterns that identify individual and coincident peaks are all translation invariant so can be identified in this array using a new convolution, but now in the 2D space of these synthetic images.\n", "\n", "Since matrix convolution is a linear operation, it is a special case of our general neural network unit,\n", "\n", "$$ \\Large\n", "\\mathbf{f}(\\mathbf{x}) = W\\mathbf{x} + \\mathbf{b} \\; ,\n", "$$\n", "\n", "but with the matrix $W$ now having many repeated elements so its effective number of dimensions is greatly reduced in typical applications.\n", "\n", "A **convolutional layer** takes an arbitrary input array and applies a number of filters with the same shape in parallel. By default, the filter kernels march with single-element steps through the input array, but you can also specify larger **stride vector**.\n", "\n", "In the general case, the input array, kernels and stride vector are all multidimensional, but with the same dimension. Tensorflow provides convenience functions for 1D, 2D and 3D convolutional layers, for example:\n", "```\n", "hidden = tf.layers.Conv2D(\n", " filters=3, kernel_size=[4, 5], strides=[2, 1],\n", " padding='same', activation=tf.nn.relu)\n", "```\n", "Note that `padding` specifies how edges effects are handled, but only `same` and `valid` are supported (and `valid` is the default). You can also implement higher-dimensional convolutional layers using the lower-level APIs.\n", "\n", "A **convolutional neural network (CNN)** is a network containing convolutional layers. A typical architecture starts with convolutional layers, processing the input, then finishes with some fully connected dense layers to calculate the output. Since one of the goals of a CNN is reduce the number of parameters, a CNN often also incorporates [pooling layers](https://en.wikipedia.org/wiki/Convolutional_neural_network#Pooling_layer) to reduce the size of the array fed to to later layers by \"downsampling\" (typically using a maximum or mean value). See [these Stanford CS231n notes](http://cs231n.github.io/convolutional-networks/) for more details in the context of image classification." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def pulse_model(features, labels, mode, params):\n", " \"\"\"Build a graph to TRAIN/TEST/PREDICT a pulse coincidence detection model.\n", " \"\"\"\n", " D = params['time_steps']\n", " M = params['number_of_traces']\n", " n1 = params['conv1_width']\n", " n2 = params['conv2_width']\n", " eta = params['learning_rate']\n", " assert n1 % 2 == 1 and n2 % 2 == 1\n", "\n", " # Build the input layer.\n", " inputs = tf.reshape(features['X'], [-1, M, D, 1])\n", " # Add the first convolutional layer.\n", " conv1 = tf.layers.conv2d(\n", " inputs=inputs, filters=2, kernel_size=[1, n1],\n", " padding='same', activation=tf.tanh, name='conv1')\n", " # Add the second convolutional (and output) layer.\n", " logits = tf.layers.conv2d(\n", " inputs=conv1, filters=1, kernel_size=[M, n2],\n", " padding='valid', activation=None, name='conv2')\n", " # Flatten the outputs.\n", " logits = tf.reshape(logits, [-1, D - n2 + 1])\n", "\n", " # Calculate the offset between input labels and the output-layer node index\n", " # that is introduced by using padding='valid' for the output layer below.\n", " offset = (n2 - 1) // 2\n", " \n", " # Calculate the network's predicted best label.\n", " predicted_labels = tf.argmax(logits, axis=1) + offset\n", "\n", " # Calculate the network's predicted probability of each label.\n", " probs = tf.nn.softmax(logits)\n", " \n", " # Calculate the network's predicted mean label.\n", " bins = tf.range(0., D - n2 + 1., dtype=np.float32) + offset\n", " mean_labels = tf.reduce_sum(bins * probs, axis=-1)\n", "\n", " # Return predicted labels and probabilities in PREDICT mode.\n", " if mode == tf.estimator.ModeKeys.PREDICT:\n", " return tf.estimator.EstimatorSpec(mode, predictions={\n", " 'label': predicted_labels,\n", " 'probs': tf.nn.softmax(logits)\n", " })\n", " \n", " # Calculate the loss for TRAIN and EVAL modes. We need to offset the labels\n", " # used here so they correspond to output-layer node indices.\n", " loss = tf.losses.sparse_softmax_cross_entropy(labels=labels - offset, logits=logits)\n", " \n", " # Compute evaluation metrics.\n", " if mode == tf.estimator.ModeKeys.EVAL:\n", " accuracy = tf.metrics.accuracy(labels=labels, predictions=predicted_labels)\n", " rmse = tf.metrics.root_mean_squared_error(\n", " labels=tf.cast(labels, np.float32), predictions=mean_labels)\n", " return tf.estimator.EstimatorSpec(\n", " mode, loss=loss, eval_metric_ops={'accuracy': accuracy, 'rmse': rmse})\n", " \n", " # Create optimizer.\n", " assert mode == tf.estimator.ModeKeys.TRAIN\n", " optimizer = tf.train.AdamOptimizer(learning_rate=eta)\n", " step = optimizer.minimize(loss, global_step=tf.train.get_global_step())\n", " return tf.estimator.EstimatorSpec(mode, loss=loss, train_op=step)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "tf.logging.set_verbosity(tf.logging.WARN)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "!rm -rf tfs/pulses" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "config = tf.estimator.RunConfig(\n", " model_dir='tfs/pulses',\n", " tf_random_seed=123\n", ")" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "pulse = tf.estimator.Estimator(\n", " config=config,\n", " model_fn=pulse_model,\n", " params = dict(\n", " time_steps=100,\n", " number_of_traces=3,\n", " conv1_width=3,\n", " conv2_width=7,\n", " learning_rate=0.01))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "X_train, X_test, y_train, y_test = model_selection.train_test_split(\n", " X, y, test_size=0.4, random_state=123)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow_estimator/python/estimator/inputs/queues/feeding_queue_runner.py:62: QueueRunner.__init__ (from tensorflow.python.training.queue_runner_impl) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "To construct input pipelines, use the `tf.data` module.\n", "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow_estimator/python/estimator/inputs/queues/feeding_functions.py:500: add_queue_runner (from tensorflow.python.training.queue_runner_impl) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "To construct input pipelines, use the `tf.data` module.\n", "WARNING:tensorflow:From :16: conv2d (from tensorflow.python.layers.convolutional) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use keras.layers.conv2d instead.\n", "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow/python/training/monitored_session.py:809: start_queue_runners (from tensorflow.python.training.queue_runner_impl) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "To construct input pipelines, use the `tf.data` module.\n" ] } ], "source": [ "pulse.train(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': X_train}, y=y_train,\n", " batch_size=500, num_epochs=None, shuffle=True),\n", " steps=500);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the kernels learned during training with the derivative kernels we used above. We find that they are qualitatively similar:\n", " - The \"odd\" kernel correlates most strongly with a rising slope, so approximately measures $+f'(t)$.\n", " - The \"even\" kernel correlates most strongly with a local maximum, so approximately measures $-f''(t)$.\n", " - The odd-numbered rows of the image are correlated with the odd kernel, and correlate with a pulse that rises (red) on the left and falls on the right (blue).\n", " - The even-numbered rows of the image are correlated with the even kernel, and correlate with a pulse that peaks (dark red) at the center.\n", " \n", "Note that nothing in the network architecture requires that the three traces be processed the same way in the second convolutional layer (right-hand image), and we do find some variations. A more detailed analysis of these weights would take into account the additional bias parameters and the influence of the activations." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_kernels():\n", " M = pulse.params['number_of_traces']\n", " n1 = pulse.params['conv1_width']\n", " n2 = pulse.params['conv2_width']\n", " K1 = pulse.get_variable_value('conv1/kernel')\n", " K2 = pulse.get_variable_value('conv2/kernel')\n", " assert K1.shape == (1, n1, 1, 2)\n", " assert K2.shape == (M, n2, 2, 1)\n", " _, ax = plt.subplots(1, 2, figsize=(10, 3))\n", " # Plot the two 1D kernels used in the first layer.\n", " dt = np.arange(n1) - 0.5 * (n1 - 1)\n", " ax[0].plot(dt, K1[0, :, 0, 0], 'o:', label='even')\n", " ax[0].plot(dt, K1[0, :, 0, 1], 'o:', label='odd')\n", " ax[0].legend(fontsize='x-large')\n", " # Assemble an image of the second-layer kernel that can be compared with plot_synthetic().\n", " K2img = np.empty((M, 2, n2))\n", " K2img[:, 0] = K2[:, :, 0, 0]\n", " K2img[:, 1] = K2[:, :, 1, 0]\n", " vlim = np.max(np.abs(K2))\n", " ax[1].imshow(K2img.reshape(2 * M, n2), aspect='auto', origin='upper',\n", " interpolation='none', cmap='coolwarm', vmin=-vlim, vmax=+vlim)\n", " ax[1].axis('off')\n", " ax[1].grid(False)\n", " plt.tight_layout()\n", " \n", "plot_kernels()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evaluate how well the trained network performs on the test data:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "scrolled": false }, "outputs": [], "source": [ "results = pulse.evaluate(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': X_test}, y=y_test,\n", " num_epochs=1, shuffle=False))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We find that about 95% of test samples are classified \"correctly\", defined as the network predicting the bin containing the the coincidence maximum exactly. However, The RMS error between the predicted and true bins is only 0.4 bins, indicating that the network usually predicts a neighboring bin in the 5% of \"incorrect\" test cases." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'accuracy': 0.94875,\n", " 'loss': 0.15017106,\n", " 'rmse': 0.40454262,\n", " 'global_step': 500}" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, compare the predicted (gray histogram) and true (dotted line) coincidence locations for a few test samples:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_predictions(X, y):\n", " # Calculate predicted labels and PDFs over labels.\n", " predictions = pulse.predict(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': X}, y=None, num_epochs=1, shuffle=False)) \n", " Nsample, Ntrace, D = X.shape\n", " t = np.linspace(0., 1., 100)\n", " dt = t[1] - t[0]\n", " bins = np.linspace(-0.5 * dt, 1 + 0.5 * dt, len(t) + 1)\n", " probs = np.zeros(D)\n", " # Plot input data, truth, and predictions.\n", " _, ax = plt.subplots(Nsample, 1, figsize=(9, 1.5 * Nsample))\n", " for i, pred in enumerate(predictions):\n", " label = pred['label']\n", " # Plot the input traces.\n", " for x in X[i]:\n", " ax[i].plot(t, x, lw=1)\n", " # Indicate the true coincidence position.\n", " ax[i].axvline(t[y[i]], c='k', ls=':')\n", " # Indicate the predicted probability distribution.\n", " n2 = D - len(pred['probs']) + 1\n", " offset = (n2 - 1) // 2\n", " probs[offset:-offset] = pred['probs']\n", " rhs = ax[i].twinx()\n", " rhs.hist(t, weights=probs, bins=bins, histtype='stepfilled', alpha=0.25, color='k')\n", " rhs.set_ylim(0., 1.)\n", " rhs.set_xlim(bins[0], bins[-1])\n", " rhs.set_yticks([])\n", " ax[i].set_xticks([])\n", " ax[i].set_yticks([])\n", " ax[i].grid(False)\n", " ax[i].set_xlim(bins[0], bins[-1])\n", " plt.subplots_adjust(left=0.01, right=0.99, bottom=0.01, top=0.99, hspace=0.1)\n", " \n", "plot_predictions(X_test[:5], y_test[:5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that our loss function does not know that consecutive labels are close and being off by one is almost as good as getting the right label. We could change this by treating this as a regression problem, but a nice feature of our multi-category approach is that we can predict a a full probability density over labels (the gray histograms above) which is often useful." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Networks for Unsupervised Learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Neural networks are usually used for supervised learning since their learning is accomplished by optimizing a loss function that compares the network's outputs with some target values. However, it is possible to perform unsupervised learning if we can somehow use the same data for both the input values and the target output values. This requires that the network have the same number of input and output nodes, and effectively means that we are asking it to learn the identify function, which does not sound obviously useful.\n", "\n", "Suppose we have a single hidden layer with the same number of nodes as the input and output layers, then all the network has to do is pass each input value through to the output, which does not require any training at all! However, if the hidden layer has fewer nodes then we are asking the network to solve a more interesting problem: how can the input dataset be encoded and then decoded. This is the same **dimensionality reduction** problem we discussed [earlier](Dimensionality.ipynb), and is known as an **autoencoder network** since it learns to encode itself:\n", "\n", "![AutoEncoder architecture](img/DeepLearning/AutoEncoder.png)\n", "\n", "The network can be thought of as the combination of separate encoder and decoder networks, with the encoder feeding its output latent variables $\\mathbf{z}$ into the decoder. Although the architecture looks symmetric, the encoder and decoder will generally learn different parameters because of the asymmetry introduced by nonlinear activations. These is a high-level design pattern and the internal architectures of the encoder and decoder networks should be customized for the type of data being encoded (and typically combined convolutional and dense layers).\n", "\n", "See this [blog post](http://kvfrans.com/variational-autoencoders-explained/) for an example based on decoding handwritten digits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Autoencoder Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Re-use the spectral data for an example. Recall that there are only 200 samples in 500 dimensions:" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "X = pd.read_hdf(locate_data('spectra_data.hf5')).values" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in (0, 6, 7):\n", " plt.plot(X[i], '.', ms=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The tensorflow layers API initializes parameters assuming that inputs are roughly normalized:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "X0 = np.mean(X, axis=0)\n", "Xmax = np.max(np.abs(X - X0))\n", "Xn = (X - X0) / Xmax\n", "original = lambda x: Xmax * x + X0\n", "assert np.allclose(X, original(Xn))" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in (0, 6, 7):\n", " plt.plot(Xn[i], '.', ms=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Tensorflow does not provide a premade autoencoder so we build a custom estimator using the intermediate-level layers API:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "def autoencoder_model(features, labels, mode, params):\n", " \"\"\"Build a graph to TRAIN/TEST/PREDICT an autoencoder model.\n", " \"\"\"\n", " D = params['dimension']\n", " C = params['n_components']\n", " eta = params['learning_rate']\n", "\n", " # Build the input layer.\n", " inputs = tf.reshape(features['X'], [-1, D])\n", " # Add encoder hidden layers with softsign activations.\n", " encoded = inputs\n", " for units in params['hidden_units']:\n", " encoded = tf.layers.dense(inputs=encoded, units=units, activation=tf.nn.softsign)\n", " # Add the final encoder layer with linear activation.\n", " latent = tf.layers.dense(inputs=encoded, units=C, activation=None)\n", " # Add decoder hidden layers with softsign activations.\n", " decoded = latent\n", " for units in params['hidden_units'][::-1]:\n", " decoded = tf.layers.dense(inputs=decoded, units=units, activation=tf.nn.softsign)\n", " # The final decoder layer has linear activation.\n", " outputs = tf.layers.dense(inputs=decoded, units=D, activation=None)\n", " \n", " # Return predicted labels and probabilities in PREDICT mode.\n", " if mode == tf.estimator.ModeKeys.PREDICT:\n", " return tf.estimator.EstimatorSpec(mode, predictions={\n", " 'latent': latent, 'output': outputs})\n", " \n", " # Calculate the loss for TRAIN and EVAL modes.\n", " loss = tf.nn.l2_loss(outputs - inputs)\n", " \n", " # Compute evaluation metrics.\n", " if mode == tf.estimator.ModeKeys.EVAL:\n", " return tf.estimator.EstimatorSpec(mode, loss=loss)\n", " \n", " # Create optimizer.\n", " optimizer = tf.train.AdamOptimizer(learning_rate=eta)\n", " step = optimizer.minimize(loss, global_step=tf.train.get_global_step())\n", " return tf.estimator.EstimatorSpec(mode, loss=loss, train_op=step)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The subsequent steps are similar to the previous examples:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "tf.logging.set_verbosity(tf.logging.WARN)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "!rm -rf tfs/autoenc" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "config = tf.estimator.RunConfig(\n", " model_dir='tfs/autoenc',\n", " tf_random_seed=123\n", ")" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "autoenc = tf.estimator.Estimator(\n", " config=config,\n", " model_fn=autoencoder_model,\n", " params = dict(\n", " dimension=500,\n", " hidden_units=[4],\n", " n_components=2,\n", " learning_rate=0.01))" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:From :13: dense (from tensorflow.python.layers.core) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use keras.layers.dense instead.\n" ] } ], "source": [ "autoenc.train(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': Xn}, y=None,\n", " batch_size=200, num_epochs=None, shuffle=True),\n", " steps=1000);" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_reconstructed(Xn, model):\n", " predictions = model.predict(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': Xn}, y=None, num_epochs=1, shuffle=False))\n", " N, D = Xn.shape\n", " fig = plt.figure(figsize=(8.5, 4))\n", " for i, pred in enumerate(predictions):\n", " Xr = original(pred['output'])\n", " plt.plot(original(Xn[i]), '.', ms=5)\n", " plt.plot(Xr, 'k-', lw=1, alpha=0.5)\n", " plt.xlim(-0.5, D+0.5)\n", " plt.xlabel('Feature #')\n", " plt.ylabel('Normalized Feature Value')\n", " \n", "plot_reconstructed(Xn[[0, 6, 7]], model=autoenc)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_latent(Xn, model):\n", " predictions = model.predict(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': Xn}, y=None, num_epochs=1, shuffle=False))\n", " latent = []\n", " for pred in predictions:\n", " latent.append(pred['latent'])\n", " df = pd.DataFrame(latent)\n", " sns.pairplot(df)\n", " return df\n", " \n", "latent = plot_latent(Xn, model=autoenc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Variational Autoencoder" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A further refinement on the autoencoder idea is to learn a posterior probability distribution in the latent variable space, instead of simply mapping each input to its corresponding point in the latent variable space. This is easier than it sounds if we assume that the posterior for each individual sample is described by an (uncorrelated) multi-variate Gaussian.\n", "\n", "In practice, we simply need to learn how to transform each input to a corresponding vector of means $\\mathbf{\\mu}$ and sigmas $\\mathbf{\\sigma}$ in the latent variable space, effectively doubling the the number of output values for the encoder network, now re-interpreted as a posterior inference network. Since this first stage is effectively a variational model of the posterior, learning its parameters is equivalent to performing a variational inference and we call this approach a **variational autoencoder (VAE)**.\n", "\n", "The decoder network is also re-interpreted as a probabilistic generator of realistic (smoothed) data. It is a generator rather than a decoder since it is no longer directly connected to the inputs. After training, it can be useful as a standalone simulator of realistic inputs.\n", "\n", "Finally we need a prior which we take to be a unit (multivariate) Gaussian in the latent-variable space. This is an arbitrary choice, but some choice is necessary in order to setup the balance between the influence of each input against some prior that is a key feature of Bayesian learning. In effect, we are reversing the way we usually build a model, which is to specify the parameters then ask what their prior should be. Instead, we are specifying the prior and then learning a (latent) parameter space that can explain the data with this prior.\n", "\n", "![Variational autoencoder architecture](img/DeepLearning/VariationalAutoEncoder.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a bit more detail, the upper network implements a variational model $Q(z;X,\\Theta)$ for the posterior probability density $P(X\\mid z)$ of a single sample $X$, parameterized by its weights and biases in $\\Theta$. Specifically, $Q$ is a multivariate Gaussian in $z$ with parameters $\\mu_z(X, \\Theta)$ and $\\sigma_z(X, \\Theta)$ output by the upper network.\n", "\n", "The lower network generates $X$ from $z$ and the the part of the loss function that compares its output against the input plays the role of the negative-log likelihood $-\\log P(X\\mid z)$ of a single sample $X$.\n", "\n", "Recall that in variational inference, we minimize the negative **evidence lower bound (ELBO)**:\n", "\n", "$$ \\Large\n", "-\\int d z\\, Q(z; X,\\Theta) \\log P(X\\mid z) + \\text{KL}(Q\\parallel P)\n", "= \\langle -\\log P(X\\mid z)\\rangle_{z\\sim Q} + \\text{KL}(Q\\parallel P)\n", "\\; ,\n", "$$\n", "\n", "where $P$ is the prior on $z$. Since both $Q$ and $P$ are (multivariate) Gaussians, we can evaluate their KL divergence analytically, as\n", "\n", "$$ \\Large\n", "\\text{KL}(Q\\parallel P) = \\frac{1}{2} \\sum_{i=1}^C\\,\n", "\\left[ \\mu_{z,i}^2 + \\sigma_{z,i}^2 - \\log \\sigma_{z,i}^2 - 1 \\right]\n", "$$\n", "\n", "where $C$ is the dimension of the latent space. Therefore the total loss function we want to optimize combines the likelihood, which compares the input with the generated output, and a KL divergence term. If we assume that the data samples have Gaussian homoscedastic noise with variance $\\sigma_x^2$, then the first term in the negative ELBO is\n", "\n", "$$ \\Large\n", "-\\log P(X\\mid z) = \\frac{1}{2\\sigma_x^2} \\left| \\mathbf{X}_{out} - \\mathbf{X}_{in}\\right|^2 + \\text{constant} \\; .\n", "$$\n", "\n", "Note that is almost the $L_2$ loss, but since we are combining it with the KL term, we must keep track of the $\\sigma_x^{-2}$ scaling. With this choice of noise model, $\\sigma_x$ is a hyperparameter but other noise models (e.g., Poisson errors) would not need any hyperparameter. After normalization, the uncertainties in this dataset correspond to $\\sigma_x \\simeq 0.017$.\n", "\n", "Finally, training the overall network accomplishes two goals in parallel:\n", " - Find a latent space where a unit Gaussian prior can explain the training data.\n", " - Perform variational inference to find the best $Q(z; X, \\Theta)$ that approximates the posteriors $P(z\\mid X)$ for each training sample.\n", "\n", "See this [tutorial](https://arxiv.org/abs/1606.05908) for more details on the probabilistic background of VAE." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our custom estimator to implement a VAE shares most of its code with the earlier autoencoder:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "def variational_autoencoder_model(features, labels, mode, params):\n", " \"\"\"Build a graph to TRAIN/TEST/PREDICT a variational autoencoder model.\n", " \"\"\"\n", " D = params['dimension']\n", " C = params['n_components']\n", " eta = params['learning_rate']\n", " sigx = params['noise_sigma']\n", "\n", " # Build the input layer.\n", " inputs = tf.reshape(features['X'], [-1, D])\n", " # Add encoder hidden layers with softsign activations.\n", " encoded = inputs\n", " for units in params['hidden_units']:\n", " encoded = tf.layers.dense(inputs=encoded, units=units, activation=tf.nn.softsign)\n", "\n", " # Add the final encoder layer with linear activation.\n", " # Estimate the posterior mean and t=log(sigma) in the latent space.\n", " latent_mu = tf.layers.dense(inputs=encoded, units=C, activation=None)\n", " latent_t = tf.layers.dense(inputs=encoded, units=C, activation=None)\n", " \n", " # Draw random samples from the encoded posterior.\n", " sigma = tf.exp(latent_t)\n", " latent = latent_mu + sigma * tf.random_normal(tf.shape(sigma))\n", " \n", " # Add decoder hidden layers with softsign activations.\n", " decoded = latent\n", " for units in params['hidden_units'][::-1]:\n", " decoded = tf.layers.dense(inputs=decoded, units=units, activation=tf.nn.softsign)\n", " # The final decoder layer has linear activation.\n", " outputs = tf.layers.dense(inputs=decoded, units=D, activation=None)\n", " \n", " # Return predicted labels and probabilities in PREDICT mode.\n", " if mode == tf.estimator.ModeKeys.PREDICT:\n", " return tf.estimator.EstimatorSpec(mode, predictions={\n", " 'mean': latent_mu,\n", " 'sigma': sigma,\n", " 'latent': latent,\n", " 'output': outputs})\n", " \n", " # Calculate the loss for TRAIN and EVAL modes.\n", " decoder_loss = tf.reduce_sum((outputs - inputs) ** 2, axis=1) / (2 * sigx)\n", " kl_loss = 0.5 * tf.reduce_sum(latent_mu ** 2 + sigma ** 2 - 2 * latent_t - 1, axis=1)\n", " loss = tf.reduce_mean(decoder_loss + kl_loss)\n", " \n", " # Compute evaluation metrics.\n", " if mode == tf.estimator.ModeKeys.EVAL:\n", " return tf.estimator.EstimatorSpec(mode, loss=loss)\n", " \n", " # Create optimizer.\n", " optimizer = tf.train.AdamOptimizer(learning_rate=eta)\n", " step = optimizer.minimize(loss, global_step=tf.train.get_global_step())\n", " return tf.estimator.EstimatorSpec(mode, loss=loss, train_op=step)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "tf.logging.set_verbosity(tf.logging.WARN)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "!rm -rf tfs/vae" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "config = tf.estimator.RunConfig(\n", " model_dir='tfs/vae',\n", " tf_random_seed=123\n", ")" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "vae = tf.estimator.Estimator(\n", " config=config,\n", " model_fn=variational_autoencoder_model,\n", " params = dict(\n", " dimension=500,\n", " hidden_units=[],\n", " n_components=2,\n", " noise_sigma=0.015,\n", " learning_rate=0.001))" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING:tensorflow:From /Users/msn/anaconda3/envs/iDAMLA/lib/python3.6/site-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use tf.cast instead.\n" ] } ], "source": [ "vae.train(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': Xn}, y=None,\n", " batch_size=250, num_epochs=None, shuffle=True),\n", " steps=10000);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plots below summarize the trained network's predictions. The left plot shows random samples drawn from the posteriors of individual samples and the right plot shows the distribution of the training data in the latent space. A few samples are highlighted in red in both plots: ellipses in the right-hand plot show each sample's posterior compared with the prior (dotted red circle)." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_predicted(Xn, model=vae, nsamples=5, nsig=2.45):\n", " predictions = model.predict(\n", " input_fn=tf.estimator.inputs.numpy_input_fn(\n", " x={'X': Xn}, y=None, num_epochs=1, shuffle=False))\n", " N, D = Xn.shape\n", " mean, sigma, z = [], [], []\n", " _, ax = plt.subplots(1, 2, figsize=(12, 6)) \n", " for i, pred in enumerate(predictions):\n", " Xr = original(pred['output'])\n", " if i < nsamples:\n", " ax[0].plot(Xr, 'r-', lw=1, alpha=0.5, zorder=10)\n", " else:\n", " ax[0].plot(Xr, 'k-', lw=4, alpha=0.02)\n", " mean.append(pred['mean'])\n", " sigma.append(pred['sigma'])\n", " z.append(pred['latent'])\n", " ax[0].set_xlim(-0.5, D+0.5)\n", " ax[0].set_xlabel('Feature #')\n", " ax[0].set_ylabel('Feature Value')\n", " mean = np.array(mean)\n", " sigma = np.array(sigma)\n", " z = np.array(z)\n", " ax[1].scatter(z[:, 0], z[:, 1], s=10, lw=0)\n", " ax[1].add_artist(plt.Circle([0,0], nsig, ls=':', fc='none', ec='r', lw=1))\n", " mu = mean[:nsamples]\n", " ax[1].scatter(mu[:, 0], mu[:, 1], s=25, marker='+', color='r') \n", " widths = nsig * sigma[:nsamples, 0]\n", " heights = nsig * sigma[:nsamples, 1]\n", " angles = np.zeros_like(widths)\n", " ax[1].add_collection(matplotlib.collections.EllipseCollection(\n", " widths, heights, angles, units='xy', offsets=mu, linewidths=1,\n", " transOffset=ax[1].transData, facecolors='none', edgecolors='r'))\n", " ax[1].set_xlabel('Latent variable $z_1$')\n", " ax[1].set_ylabel('Latent variable $z_2$')\n", " \n", "plot_predicted(Xn)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Generative-Adversarial Network" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Building on the theme of a probabilistic generator, we can set up an \"arms race\" between two networks:\n", " - A generator that learns to synthesize realistic data.\n", " - An adversary that learns to discriminate between real and generated data.\n", " \n", "This is the central idea of a **generative-adversarial network (GAN)**, which is a [recent idea](https://arxiv.org/abs/1406.2661) (2014):\n", "\n", "![Generative adversarial network](img/DeepLearning/GAN.png)\n", "\n", "Each training step now has several parts:\n", " - Generate some random data.\n", " - Test how well the discriminator identifies the generated data as a fake.\n", " - Feed the same discriminator some real data.\n", " - Test how well the discriminator identifies the real data as real.\n", "\n", "Optimizing the loss function then simultaneously improves the generator and the discriminator. The usual goal of training a GAN is to obtain a useful generator of realistic data.\n", "\n", "See this [blog post](http://kvfrans.com/generative-adversial-networks-explained/) for an example based on image generation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Recurrent Networks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All the architectures we have seen so far are **feed-foward** networks, with input data always from left (input layer) to right (output layer). A **recurrent neural network (RNN)** adds links that feed back into a previous layer. This simple modification adds significant complexity but also expressive power (comparable to the electronics revolution associated with the idea of transistor feedback).\n", "\n", "Architectures with feedback are still maturing but some useful building blocks have emerged, such as the [long short-term memory unit](https://en.wikipedia.org/wiki/Long_short-term_memory), which allows a network to remember some internal state but also forget it based on new input.\n", "\n", "Some practical considerations for RNN designs:\n", " - The order of training data is now significant and defines a \"model time\", but the network can be reset whenever needed.\n", " - Input data can be packaged into variable-length messages that generate variable (and different) length output messages. This is exactly what language translation needs.\n", " - Optimization of the weights using gradients is still possible but requires \"unrolling\" the network by cloning it enough times to process the longest allowed messages.\n", " \n", "A feed-foward network implements a universal approximating function. Since the internal state of an RNN acts like local variables, you can think of an RNN as a universal approximating program.\n", "\n", "See this [blog post](http://karpathy.github.io/2015/05/21/rnn-effectiveness/) for an example based on natural language synthesis." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reinforcement Learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The architectures we have seen so far all have target output values associated with each input sample, which are necessary to update the network parameters during the learning (loss optimization) phase:\n", "\n", "![Sample learning](img/DeepLearning/SampleLearning.png)\n", "\n", "\n", "However, we can relax this requirement of being able to calculate a loss after each new input as long as we eventually get some feedback on how well our input-to-output mapping is doing. This is the key idea of **reinforcement learning (RL)**:\n", "\n", "![Reinforcement learning](img/DeepLearning/ReinforcementLearning.png)\n", "\n", "A RL network watches some external \"reality\" (which is often simulated) and learns a policy for how to take actions. A sequence of actions eventually leads to some feedback, which is then used to take a single step in optimizing the policy network's parameters:\n", "\n", "![Policy network](img/DeepLearning/PolicyNetwork.png)\n", "\n", "See this [blog post](http://karpathy.github.io/2016/05/31/rl/) for an example based on image generation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deep Learning Outlook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The depth of \"deep learning\" comes primarily from network architectures that stack many layers. In another sense, deep learning is very shallow since it often performs well using little to no specific knowledge about the problem it is solving, using generic building blocks.\n", "\n", "The field of modern deep learning [started around 2012](https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) when the architectures described above were first used successfully, and the necessary large-scale computing and datasets were available. Massive neural networks are now the state of the art for many benchmark problems, including image classification, speech recognition and language translation.\n", "\n", "However, less than a decade into the field, there are signs that deep learning is reaching its limits. Some of the pioneers are focusing on new directions such as [capsule networks](https://arxiv.org/abs/1710.09829) and [causal inference](https://arxiv.org/abs/1801.04016). Others are taking a [critical look](https://arxiv.org/abs/1801.00631) at the current state of the field:\n", " - Deep learning does not use data efficiently.\n", " - Deep learning does not integrate prior knowledge.\n", " - Deep learning often give correct answers but without associated uncertainties.\n", " - Deep learning applications are hard to interpret and transfer to related problems.\n", " - Deep learning is excellent at learning stable input-output mappings but does not cope well with varying conditions.\n", " - Deep learning cannot distinguish between correlation and causation.\n", " \n", "These are mostly concerns for the future of neural networks as a general model for artificial intelligence, but they also limit the potential of scientific applications.\n", "\n", "However, there are many challenges in scientific data analysis and interpretation that could benefit from deep learning approaches, so I encourage you to follow the field and experiment. Through this course, you now have a pretty solid foundation in data science and machine learning to further your studies toward more advanced and current topics!" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }