{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Overview\n", "\n", "This project is about the Bayesian approach to machine learning. More specifically we go through the Bayesian formulation of regression and neural networks for classification. We apply these methods to data from simulations of the 1 and 2 dimensional Ising models in similar style as Mehta et al. [4].\n", "\n", "This text is split up into 4 parts.\n", "\n", "- Part 1 - General intro to Bayesian statistics\n", "- Part 2 - Bayesian regression\n", "- Part 3 - Bayesian Convolutional Neural Network\n", "- Part 4 - Using Bayesian reasoning on the probability of life\n", "\n", "The Python code for part 2 is written from scratch in raw NumPy, while the code for part 3 uses the TensorFlow Probability library." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 1 - Bayesian statistics\n", "\n", "Bayesian statistics is an alternative approach to the more common classical (frequentist) school of thought in statistics. It differs in the way that it views probability as our subjective uncertainty about the world, instead of as there being something inherently random in nature.\n", "\n", "\n", "The most noticable difference in Bayesian statistics is probably the use of a __prior__, which is a way of incorporating the prior knowledge one often has about the problem into the inference. In Bayesian machine learning, using various priors are in many cases mathematically equivalent to specific regularization schemes that one often sees in classical machine learning.\n", "\n", "\n", "A very useful property of Bayesian inference is that we don't just get point estimates of our model parameters, but we will instead get a full distribution of our probability estimate in parameter space. This means that we can get knowledge about how points in the neighbourhood of our best estimate compares. This has the useful property of leting us define __credible intervals__, which we will see in part 2, but it can in addition be used to do probabilistic estimation, which we will see in part 3. The Bayesian approach also solutions for some of the inherent pathologies that exist in classical statistics -- so it can for example do inference from a one-off event, which we will see in part 4." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Derivation of Bayes theorem\n", "\n", "Everything starts with Bayes theorem.\n", "\n", "We have two parameters $A$ and $B$. \n", "For any two values we have $p(A,B)$ as the probability that both of those values are the true values of A and B.\n", "\n", "\n", "We start with the intuitive statement $$p(A,B) = p(A|B)p(B).$$\n", "\n", "\n", "Then since $p(A,B) = p(B,A)$ it must follow that\n", "\n", "$$p(A|B)p(B) = p(B|A)p(A),$$\n", "\n", "which leads to Bayes theorem\n", "\n", "$${p(A|B) = \\frac{p(B|A)p(A)}{p(B)}},$$\n", "\n", "\n", "Usually written as \n", " \n", "\n", "$$\\boxed{p(A|B) \\propto p(B|A)p(A)}$$\n", " \n", "$p(B)$ is as a normalization constant making sure that $\\int_A p(A'|B)dA' = 1$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian Inference\n", "\n", "Say we have a dataset $D = \\{d_1, d_2, .., d_N\\}$ that are measurements of value $y$ that is a function of a parameter vector $\\vec{x}$. In other words $d_i = y(\\vec{x}_i | \\boldsymbol{\\theta})$.\n", "\n", "$D$ and $X=[\\vec{x}_1, \\vec{x}_2, .., \\vec{x}_N ]^T$ are known, and we want to find the function $y$, meaning we need to find its parameters $\\boldsymbol{\\theta}$ (if the shape/form of $y$ is assumed, otherwise we'd need to find the shape as well). \n", "\n", "Any parameter configuration $\\boldsymbol{\\theta}$ is a unique hypothesis for the model.\n", "For any given $\\boldsymbol{\\theta}$, we want to know the probability of that hypothesis being true from the data, described as\n", "\n", "$$\n", "p(\\boldsymbol{\\theta}|D).\n", "$$\n", "\n", "We can then use Bayes theorem to get\n", "$$ \n", "\\boxed{\n", "p(\\boldsymbol{\\theta}|D) \\propto {p(D|\\boldsymbol{\\theta})p(\\boldsymbol{\\theta})}\n", "}.$$\n", "\n", "The factor $p(D|\\boldsymbol{\\theta})$ is called the __likelihood function__ and describes the probability of getting the data $D$ if the given hypothesis $\\boldsymbol{\\theta}$ is true. The factor $p(\\boldsymbol{\\theta})$ is called the __prior distribution__ for the hypothesis, meaning the probability distribution for various hypotheses $\\boldsymbol{\\theta}$ being true prior to seeing the data. If we have the likelihood and the prior, then we can create $p(\\boldsymbol{\\theta}|D)$ which is known as the __posterior distribution__.\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 2 - Bayesian Regression on the 1D Ising model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The 1D ising model (with noise)\n", "\n", "We randomly generate $N$ states of the 1D ising model (meaning N 1D vectors consisting of -1s and 1s) and calculate their energies using the following Hamiltonian:\n", "$$\n", "H[\\vec{S^i}] = J\\sum_{j=1}^L [S_j^i S_{j+1}^i + S_{j+1}^i S_j^i] + \\epsilon\n", "$$\n", "Where $S_j^i$ is the j'th element of the i'th state $\\vec{S^i}$. We set the value $J=-0.5$. The max energy is 40 so $\\epsilon \\sim \\mathcal{N}(0,2.5)$ seems like a good choice.\n", "\n", "We will then try to see if we can re-extract this Hamiltonian from the data using Bayesian Linear regression." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import scipy.sparse as sp\n", "np.random.seed(13)\n", "\n", "import warnings\n", "# Comment this to turn on warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "### define Ising model aprams\n", "# system size\n", "L=40\n", "\n", "# create 10000 random Ising states\n", "states=np.random.choice([-1, 1], size=(1400,L))\n", "\n", "def ising_energies(states_, plot_true=False):\n", " \"\"\"\n", " This function calculates the energies of the states in the nn Ising Hamiltonian\n", " \"\"\"\n", " L = states.shape[1]\n", " J = np.zeros((L, L),)\n", " for i in range(L): \n", " J[i,(i+1)%L]=-0.5 # interaction between nearest-neighbors\n", " J[(i+1)%L,i]=-0.5\n", " # compute energies\n", " E = np.einsum('...i,ij,...j->...',states_,J,states_)\n", " \n", " if plot_true:\n", " import matplotlib.pyplot as plt\n", " %matplotlib inline\n", " import seaborn as sns\n", "\n", " sns.heatmap(J)\n", " plt.title(\"True Hamiltonian\")\n", " plt.show()\n", " return E\n", "\n", "# calculate Ising energies\n", "energies=ising_energies(states,plot_true=True)\n", "\n", "# Adding noise:\n", "noise_variance = 2.5\n", "energies += np.random.normal(0,scale=np.sqrt(noise_variance), size=energies.shape)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Remapping data for regression\n", "\n", "We pretend that we're ignorant about the Hamiltonian used to generate the above data. That means that the values aren't the only unknowns, but the shape of it as well. So we need to consider the __all-to-all Hamiltonian__\n", "\n", "$$\n", "H_{model}[\\vec{S^i}] = \\sum_{j=1}^L\\sum_{k=1}^L J_{jk}S_j^iS_{k}^i\n", "$$\n", "\n", "We see that the actual Hamiltonian we used above is just a special case of this, with $J_{jk} =-0.5 \\cdot \\delta_{j,k-1}$.\n", "\n", "\n", "\n", "Taking the outer product\n", "\n", "$\\vec{{x}} \\rightarrow \\phi(\\vec{{x}})=\\vec{{x}}\\otimes \\vec{{x}}$\n", "\n", "then we make the vector $\\phi(\\vec{x})$ one-dimensional.\n", "But we'll just write $\\phi(\\vec{x})$ as $\\vec{x}$ for simplicity." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "new_states = np.einsum('bi,bo->bio',states,states)\n", "new_states = new_states.reshape(new_states.shape[0],-1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Getting the posterior\n", "We want the posterior \n", "$$ p(\\boldsymbol{\\theta}|D) \\propto {p(D|\\boldsymbol{\\theta})p(\\boldsymbol{\\theta})}.$$\n", "\n", "We need to specify the likelihood and the prior. This is of course problem dependent.\n", "\n", "\n", "In regular regression, one is only interested in the value for $\\boldsymbol{\\theta}$ that maximizes the probability of getting the obtained data, i.e.\n", "\n", "$$\n", "\\hat{\\boldsymbol{\\theta}} = \\underset{\\boldsymbol{\\theta}}{\\text{argmax}} p(D|\\boldsymbol{\\theta})\n", "$$\n", "\n", "$\\hat{\\boldsymbol{\\theta}}$ is known as the MLE (maximum likelihood estimate). But this is just a point estimate and gives no information about the robustness of the estimate, i.e. how much the probability changes by moving to other points that are close to $\\hat{\\boldsymbol{\\theta}}$ in parameter space.\n", "\n", "This is something we can get with Bayesian linear regression.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Choosing the Likelihood\n", "It is common to make the assumption that the data is __iid__ (identically and independently distributed), which it is in our case.\n", "\n", "The likelihood can then be modelled as \n", "$$\n", "p(D|\\boldsymbol{\\theta}) = p(d_1|\\boldsymbol{\\theta})p(d_2|\\boldsymbol{\\theta})..p(d_N|\\boldsymbol{\\theta})\n", "$$\n", "where \n", "$$\n", "\\begin{align}\n", "p(d_i|\\boldsymbol{\\theta}) & = \\mathcal{N}(\\vec{w}^T\\vec{x}_i, \\sigma^2) \\\\ \n", " & \\propto \\exp \\Big(-\\dfrac{1}{2\\sigma^2} (d_i-\\vec{w}^T\\vec{x}_i)^2\\Big)\n", "\\end{align}\n", "$$\n", "\n", "Where $\\boldsymbol{\\theta} = \\{\\vec{w}, \\sigma^2\\}$. \n", "The product $\\vec{w}^T \\vec{x}$ is just some weighing of the input parameters.\n", "The Gaussian is commonly used because this is the probability distribution with the highest entropy for iids. In other words, if the data is iid, the Gaussian is the _most probable way for the data to be distributed_. Here we assume that the noise variation $\\sigma^2$ does not change with $\\vec{x}$, which is not always a correct assumption.\n", "\n", "\n", "The full likelihood is then\n", "$$\n", "\\begin{align}\n", "p(D|\\boldsymbol{\\theta}) &\\propto \\exp \\Big[-\\sum_i^N \\dfrac{1}{\\sigma^2} (d_i-\\vec{w}^T\\vec{x}_i)^2\\Big]\\\\\n", "& = \\exp \\Big[ - \\dfrac{1}{2\\sigma^2}(\\vec{y}-X\\vec{w})^T(\\vec{y}-X\\vec{w}) \\Big]\n", "\\end{align}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Choosing the Prior\n", "We need to decide a shape for our prior \n", "$$\n", "p(\\boldsymbol{\\theta}) = p(\\vec{w},\\sigma^2).\n", "$$\n", "\n", "Since our data is actually deterministic, $\\sigma^2$ is actually zero, but for now we will assume that $\\sigma^2$ is known and a small number.\n", "\n", "Our prior to find is therefore just \n", "$$\n", "p(\\boldsymbol{\\theta}) = p(\\vec{w}).$$\n", "\n", "\n", "A common choice is the zero mean Gaussian. \n", "This gives a higher prior probaility to functions with small, even parameters, i.e. smoother / less complex functions. \n", "This in a way captures the ide of Occam's Razor that we should prefer the simplest hypothesis that explains the data (although other zero zentered, symmetric distributions would do this as well).\n", "\n", "It also makes it easier mathematically to pick a Gaussian when the likelihood is Gaussian as well (called conjugate prior). Therefore\n", "\n", "$$\n", "\\begin{align}\n", "p(\\vec{w}) &= \\mathcal{N}(\\vec{w} | \\vec{w}_0, V_0)\\\\\n", "& \\propto \\exp \\Big[ - \\frac{1}{2}(\\vec{w}- \\vec{w}_0)^T V_0^{-1} (\\vec{w}- \\vec{w}_0) \\Big]\n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The Posterior\n", "The posterior is then\n", "$$\n", "\\begin{align}\n", "p(\\vec{w}|D) & \\propto {p(D|\\vec{w})p(\\vec{w})} \\\\\n", " & \\propto \\exp \\Big[ -\\dfrac{1}{2\\sigma^2}(\\vec{y}-X\\vec{w})^T(\\vec{y}-X\\vec{w}) - \\frac{1}{2}(\\vec{w}- \\vec{w}_0)^T V_0^{-1} (\\vec{w}- \\vec{w}_0) \\Big]\n", "\\end{align}\n", "$$\n", "\n", "By doing some algebra this can be rewritten as a multivariate normal distribution (MVN)\n", "\n", "\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "p(\\vec{w}|D) = \\mathcal{N}(\\vec{w}|\\vec{w}_N, V_N)\n", "\\end{align}},\n", "$$\n", "where\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "\\vec{w}_N &= V_N V_0^{-1} + \\frac{1}{\\sigma^2}V_N X^T \\vec{y}, \\\\\n", "V_N^{-1} &= V_0^{-1} + \\frac{1}{\\sigma^2}X^TX,\\\\\n", "V_N &= \\sigma^2(\\sigma^2V_0^{-1} + X^T X)^{-1} \n", "\\end{align}}.\n", "$$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The Posterior when $\\vec{w}_0=\\vec{0}$ and $V_0 = \\tau^2I$\n", "The prior is then\n", "$$\n", "\\begin{align}\n", "p(\\vec{w}) &= \\prod_j^M \\mathcal{N}(w_j | 0, \\tau^2)\\\\\n", "& \\propto \\exp \\Big(- \\frac{1}{2\\tau^2}\\sum_j^M {w_j^2} \\Big)\n", "\\end{align}\n", "$$\n", "where $1/\\tau^2$ controls the strength of the prior.\n", "\n", "\n", "We now have\n", "$$\n", "\\begin{align}\n", "p(\\vec{w}|D) & \\propto {p(D|\\vec{w})p(\\vec{w})} \\\\\n", " & \\propto \\exp (- \\Big( \\sum_i^N \\dfrac{1}{\\sigma^2} (d_i-\\vec{w}^T\\vec{x}_i)^2 +\\sum_j^M w_j^2 / \\tau^2\\Big) )\n", "\\end{align}\n", "$$\n", "The MAP estimate is the value of $\\vec{w}$ that maximizes $p(\\vec{w}|D)$, which means the value that minimizes the exponent, i.e.\n", "\n", "$$\n", "\\begin{align}\n", "\\vec{w}_{MAP} & = \\underset{\\vec{w}}{\\text{argmin}} \\sum_i^N \\dfrac{1}{\\sigma^2} (d_i-\\vec{w}^T\\vec{x}_i)^2 +\\sum_j^M w_j^2 / \\tau^2 \\\\\n", "\\end{align}\n", "$$\n", "\n", "where $\\vec{y}$ is the vector containing the data $D$. We can see that this is equivalent to regular regression with L2 regularization.\n", "This has an analytical solution, which we can find by rewriting to matrix formulation\n", "\n", "$$\n", "\\vec{w}_{MAP} = \\underset{\\vec{w}}{\\text{argmin}} \\ (\\vec{y}-X\\vec{w})^T(\\vec{y}-X\\vec{w}) + \\lambda \\vec{w}^T\\vec{w}\n", "$$\n", "\n", "and we can then differentiate the right side with respect to $\\vec{w}$ and set equal to zero to find the solution as\n", "\n", "$$\n", "\\boxed{\\vec{w}_{MAP} = (\\lambda I_M + {X}^T{X})^{-1}{X}^T\\vec{y}}\n", "$$\n", "\n", "which is regular ridge regression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Reminder: $\\sigma^2$ is assumed" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import time\n", "from sys import exit\n", "t0 = time.time()\n", "\n", "\n", "n = new_states.shape[0] # number of data\n", "D = new_states.shape[1] # data dimension\n", "\n", "# Prior:\n", "variance = 2.5\n", "w0 = np.zeros(D)\n", "tau = 1 # 1 means unitary gaussian, determines the strength of the prior\n", "V0 = tau**2*np.identity(D) # precision matrix of prior\n", "V0_inv = np.linalg.inv(V0)\n", "\n", "mean_x = np.mean(new_states,axis=0,keepdims=True)\n", "\n", "X = new_states #- mean_x # data matrix with data as rows, centered\n", "\n", "\n", "y = energies - np.mean(energies)\n", "\n", "\n", "VN_inv = V0_inv + np.dot(X.T,X) / variance\n", "VN = np.linalg.inv(VN_inv)\n", "\n", "wN = np.dot(np.dot(VN,V0_inv),w0) + np.dot(np.dot(VN,X.T),y) / variance\n", "t1 = time.time()-t0\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reshape and plot $\\vec{w}_{MAP}$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import seaborn as sns\n", "\n", "sns.heatmap(wN.reshape(L,L))\n", "plt.title(\"Estimated Hamiltonian\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Gir mening at den fordeler verdiene i w sånn, fordi 0.5^2 + 0.5^2 er mindre enn 1^2 + 1^2 \n", "\n", "Det at Lasso er mer riktig er ikke fordi den henter det ut fra dataen, men pga. prioren.\n", "\n", "Men er variansen 0 her egentlig?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Posterior Distribution\n", "\n", "Since we now have the full posterior $P(\\vec{w}|D)$, we can see how the probability changes as we move in parameter space away from the MAP estimate, i.e. how confident we would be in points near $\\vec{w}_{MAP}$. We only show the posterior for four of the parameters.\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dw = 0.001\n", "w_range = np.arange(-1.,1., dw)\n", "\n", "#print(w_range)\n", "def Pw(index1,index2):\n", " \n", " index = index1*L + index2\n", " vec = wN.copy()\n", " \n", " logs = np.zeros(len(w_range))\n", " for k in range(len(w_range)):\n", " w = w_range[k]\n", " vec[index] = w\n", " logs[k] = -0.5 * np.dot(np.dot((vec - wN).T, VN_inv),vec - wN)\n", " \n", " logs -= np.max(logs)\n", " P = np.exp(logs)\n", " return P \n", "\n", "def plot_w_distribution(ax, index1,index2,show=False,grid=True):\n", " P = Pw(index1,index2)\n", " ax.plot(w_range,P, label=\"$P(w_{%.i,%.i}|D)$\" % (index1,index2))\n", " ax.legend()\n", " ax.grid() if grid else None\n", " if show:\n", " plt.show()\n", "\n", "fig, axes = plt.subplots(2,2,sharex=False, sharey=True)\n", "fig.set_size_inches(18.5*0.75, 10.5*0.7)\n", "plot_w_distribution(axes[0,0], 0,0)\n", "plot_w_distribution(axes[0,1],0,1)\n", "plot_w_distribution(axes[1,0],1,0)\n", "plot_w_distribution(axes[1,1],1,1)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Credible Intervals\n", "\n", "We will show the 95 % HDI (Highest Density Interval) which means the region that contains 95 % of the probability mass where all points in the region are higher than the ones outside. \n", "This area is not necessarily contiguous if the PDF is multimodal. But since the posterior here is gaussian, the HDI is the same as the central interval.\n", "\n", "The algorithm used to find the HDI region can be easily derived by thinking of it as turning the curve upside down and filling it with water drop by drop." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def credible_interval(ax, index1, index2):\n", " P_ = Pw(index1,index2)\n", " # normalize\n", " P_normed = P_ / np.sum(P_)\n", " \n", " ############################\n", " # Water filling algorithm: #\n", " ############################\n", " #points = np.zeros_like(P_normed, dtype=np.int)\n", " points_taken= []\n", " points = []\n", " done = False\n", " t = 0\n", " while not done:\n", " best=0\n", " bestindex=0\n", " for i in range(len(P_normed)-1):\n", " if i not in points_taken:\n", " val = P_normed[i]\n", " if val > best:\n", " best = val\n", " bestindex = i\n", " points_taken.append(bestindex)\n", " points.append(best)\n", " if np.sum(points) >= 0.95:\n", " done=True\n", " \n", " points_taken = np.array(points_taken, dtype=np.int)\n", " argsorted = np.argsort(points_taken)\n", "\n", " points_taken = points_taken[argsorted]\n", " \n", " \n", " plot_w_distribution(ax, index1,index2,show=False,grid=False)\n", " first_lastw = [w_range[points_taken[0]], w_range[points_taken[-1]]]\n", " first_lastP = [P_[points_taken[0]], P_[points_taken[-1]]]\n", "\n", " \n", " fill = np.zeros(len(points_taken)+2)\n", " fill[1:-1] = P_[points_taken]\n", " \n", " w_range_fill = np.zeros_like(fill)\n", " w_range_fill[1:-1] = w_range[points_taken]\n", " w_range_fill[0] = w_range_fill[1]\n", " w_range_fill[-1] = w_range_fill[-2]\n", " \n", " ax.fill(w_range_fill,fill,facecolor=\"red\",alpha=0.5)\n", " \n", " line = [P_[points_taken[0]],P_[points_taken[-1]]] \n", " line = np.ones(2)*P_[points_taken[0]] # looks better, but not actually totally correct\n", " ax.plot(first_lastw,line, \"k\", alpha=0.5)\n", "\n", " \n", "fig, axes = plt.subplots(2,2,sharex=False, sharey=True)\n", "fig.set_size_inches(18.5*0.75, 10.5*0.75)\n", "credible_interval(axes[0,0], 0,0)\n", "credible_interval(axes[0,1],0,1)\n", "credible_interval(axes[1,0],1,0)\n", "credible_interval(axes[1,1],1,1)\n", "plt.suptitle(\"95 % Credible Interval\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Test data\n", "\n", "We can evaluate the performance by calculationg the __coefficient of determination__, given by\n", "\n", "$$\n", "\\begin{align}\n", "R^2 &= \\big(1-\\frac{u}{v}\\big),\\\\\n", "u &= \\big(y_{\\text{predicted}} - y_{\\text{true}}\\big)^2 \\\\\n", "v &= \\big(y_{\\text{predicted}} - \\langle y_{\\text{true}}\\rangle\\big)^2\n", "\\end{align}\n", "$$\n", "\n", "The best possible score is then $R^2=1$, but it can also be negative. A constant model that always predicts the expected value of $y$, $ \\langle y_{\\text{true}}\\rangle$, disregarding the input features, would get a $R^2$ score of 0 [4]." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.92679016596241\n" ] } ], "source": [ "test_states=np.random.choice([-1, 1], size=(1000,L))\n", "# calculate Ising test energies\n", "test_energies=ising_energies(test_states)\n", "\n", "# remapping states:\n", "test_states = np.einsum('bi,bo->bio',test_states,test_states)\n", "test_states = test_states.reshape(test_states.shape[0],-1)\n", "\n", "predicted_energies = np.dot(test_states, wN)\n", "\n", "\n", "### R^2 - coefficient of determination\n", "y_true_avg = np.mean(test_energies)\n", "residuals = predicted_energies - test_energies\n", "u = np.dot(residuals,residuals)\n", "v = test_energies - y_true_avg\n", "v = np.dot(v,v)\n", "\n", "R_squared = 1 - u/v\n", "\n", "print(R_squared)\n" ] }, { "attachments": { "bayescnn.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# Part 3 - Bayesian Neural Networks\n", "### The Essence\n", "A general classical neural network is a function on the form\n", "\n", "\\begin{equation}\n", " \\mathcal{F}(\\boldsymbol{x}) = g_L(\\boldsymbol{W}^L \\ g_{L-1}(\\boldsymbol{W}^{L-1} \\dots g_1(\\boldsymbol{W}^1\\boldsymbol{x}) \\dots )),\n", " \\label{eq_dnn}\n", "\\end{equation}\n", "\n", "where the weights are elements in the matrices $\\boldsymbol{W}^l$ and $g_l: \\mathbb{R}^k \\rightarrow \\mathbb{R}^k$ are activation functions. For any arbitrary architecture we denote the total number of parameters in such a network by $N$.\n", "\n", "In a Bayesian Neural Network with the same architecture, the number of parameters is instead $2N$. Instead of the parameters (weights) being a point estimate, each weight $w_{ij}$ in the classical neural net is instead switched out with two parameters $\\mu_{ij}$ and $\\sigma_{ij}$ which are the mean and standard deviation in a normal distribution. When we do a forward pass and need the weight, we just sample it from this distribution, i.e.\n", "\n", "$$\n", "w_{ij} \\sim \\mathcal{N}(\\mu_{ij}, \\sigma_{ij}^2)\n", "$$\n", "\n", "where the trainable parameters are now $\\theta = \\{ \\mu, \\sigma^2 \\}$\n", "\n", "\n", "The full posterior is in other words not just useful for finding credible intervals, but for sampling! It gives us only twice the number of parameters for in principle an infinite ensemble of networks.\n", "\n", "The figure below is an illustration of the difference between a frequentist and a Bayesian CNN. \n", "\n", "![bayescnn.png](attachment:bayescnn.png)\n", "Source: Shridhar et al. [1].\n", "\n", "### The Math \n", "We want to find the posterior\n", "$$\n", "p(\\theta|D) = \\frac{p(D|\\theta)p(\\theta)}{p(D)}\n", "$$\n", "\n", "so that we can use this to do inference \n", "$$\n", "p(y^*|x^*,D) = \\int p(y^*|x^*,\\theta)p(\\theta|D)d\\theta.\n", "$$\n", "\n", "This can be understood as checking how much we believe test data $x^*$ is in class $y^*$ for all possible hypothesises $\\theta$ while weighing for how much we believe in each $\\theta$, based on the data.\n", "\n", "\n", "Let our Neural Network model be an approximation $q$ to the true posterior $p$.\n", "\n", "$$\n", "q_\\theta(w|D) \\approx p(w|D)\n", "$$\n", "\n", "and then minimize the Kullback-Leibler (KL) divergence between the two distributions\n", "\n", "\n", "$$\n", "\\theta_{opt} = \\underset{\\theta}{\\text{argmin}} \\ \\text{KL} \\ \\big[q_\\theta(w|D)||p(w|D)\\big].\n", "$$\n", "\n", "The KL divergence is a measure of how close two distributions are to each other, and is defined as\n", "\n", "$$\n", "\\text{KL} \\ \\big[q_\\theta(w|D)||p(w|D)\\big] = \\int q_\\theta(w|D) \\log \\frac{q_\\theta(w|D)}{p(w|D)}dw.\n", "$$\n", "\n", "This can also be seen as the expectation value of $\\log \\frac{q_\\theta(w|D)}{p(w|D)}$ with respect to $q_\\theta(w|D)$, i.e.\n", "\n", "$$\n", "\\text{KL} \\ \\big[q_\\theta(w|D)||p(w|D)\\big] = \\mathbb{E}_{q_\\theta(w|D)}\\big[\\log \\frac{q_\\theta(w|D)}{p(w|D)}\\big].\n", "$$\n", "\n", "\n", "This can be approximated as a discrete sum\n", "\n", "$$\n", "\\mathbb{E}_{q_\\theta(w|D)}\\big[\\log \\frac{q_\\theta(w|D)}{p(w|D)}\\big] \\approx \\frac{1}{m}\\sum_i^m \\log \\frac{q_\\theta(w^i|D)}{p(w^{i}|D)}.\n", "$$\n", "\n", "We then substitute $p(w^i|D) = \\frac{p(D|w^)p(w^i)}{p(D)}$ and use the rule for the logarithm of fractions $\\log \\frac{a}{b} = \\log a - \\log b$ so that we get\n", "\n", "$$\n", "\\mathbb{E}_{q_\\theta(w|D)}\\big[\\log \\frac{q_\\theta(w|D)}{p(w|D)}\\big] \\approx \\frac{1}{m}\\sum_i^m \\log {q_\\theta(w^i|D)} - \\log p(w^i) - \\log p(D|w^i) + \\log p(D)\n", "$$\n", "\n", "This is a tractable objective function that can be minimized with respect to $\\theta = (\\mu, \\sigma^2)$ by variational methods, Monte Carlo, evolutionary algorithms etc. The term $\\log p(D)$ is just a constant, so we can remove that. \n", "\n", "The optimum can now be found as\n", "\n", "$$\n", "\\boxed{\n", "\\begin{align}\n", "\\theta_{opt} & = \\underset{\\theta}{\\text{argmin}} \\frac{1}{m}\\sum_i^m \\log {q_\\theta(w^i|D)} - \\log p(w^i) - \\log p(D|w^i) \\\\\n", "& = \\underset{\\theta}{\\text{argmin}} \\ \\text{KL} \\ \\big[q_\\theta(w|D)||p(w)\\big] - \\mathbb{E}_{q_\\theta(w|D)}[\\log p(D|w^i)] \\\\\n", "\\end{align}}\n", "$$\n", "\n", "by sampling $w^i$ from $q_\\theta(w|D)$. This is also known as the __evidence lower bound__ (ELBO)." ] }, { "attachments": { "states.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Training a Bayesian Convolutional Neural Net on the 2D Ising model\n", "\n", "The 2D Ising model undergoes a phase transition around a critical temperature $T_c$ where it switches from the disordered to the ordered state. The idea is to train a classifier on states that we know are ordered or disordered, and then after use that classifier on states from the transition state / critical region.\n", "\n", "![states.png](attachment:states.png)\n", "Source: Mehta et al. [4] \n", "\n", "The following code trains a Bayesian Neural Network to classify states of the 2 dimensional Ising model by minimizing the ELBO, using a minimizing scheme called Flipout [1]. The architecture is LeNet-5 [3]. \n", "\n", "It is written using TensorFlow Probability, a library built on TensorFlow for doing probabilistic machine learning." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "W0816 18:16:38.151205 140047177033536 :403] Warning: deleting old log directory at /tmp/bayesian_neural_network/\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "(20000, 40, 40, 1)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "W0816 18:16:45.300953 140047177033536 deprecation.py:323] From :236: DatasetV1.output_types (from tensorflow.python.data.ops.dataset_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use `tf.compat.v1.data.get_output_types(dataset)`.\n", "W0816 18:16:45.301640 140047177033536 deprecation.py:323] From :236: DatasetV1.output_shapes (from tensorflow.python.data.ops.dataset_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use `tf.compat.v1.data.get_output_shapes(dataset)`.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Step: 0 Loss: 137.559 Accuracy: 0.508\n", "Step: 100 Loss: 129.428 Accuracy: 0.955\n", "Step: 200 Loss: 124.614 Accuracy: 0.975\n", "Step: 300 Loss: 119.730 Accuracy: 0.983\n", " ... Held-out nats: -0.004\n", "saved /tmp/bayesian_neural_network/step00399_weights.png\n", "saved /tmp/bayesian_neural_network/step00399_pred.png\n", "saved /tmp/bayesian_neural_network/step00399_test_pred.png\n", "Step: 400 Loss: 114.894 Accuracy: 0.987\n", "Step: 500 Loss: 109.927 Accuracy: 0.989\n", "Step: 600 Loss: 105.041 Accuracy: 0.991\n", "Step: 700 Loss: 100.179 Accuracy: 0.992\n", " ... Held-out nats: -0.001\n", "saved /tmp/bayesian_neural_network/step00799_weights.png\n", "saved /tmp/bayesian_neural_network/step00799_pred.png\n", "saved /tmp/bayesian_neural_network/step00799_test_pred.png\n", "Step: 800 Loss: 95.349 Accuracy: 0.993\n", "Step: 900 Loss: 90.562 Accuracy: 0.994\n", "Step: 1000 Loss: 85.854 Accuracy: 0.994\n", "Step: 1100 Loss: 81.265 Accuracy: 0.994\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step01199_weights.png\n", "saved /tmp/bayesian_neural_network/step01199_pred.png\n", "saved /tmp/bayesian_neural_network/step01199_test_pred.png\n", "Step: 1200 Loss: 76.613 Accuracy: 0.995\n", "Step: 1300 Loss: 72.092 Accuracy: 0.995\n", "Step: 1400 Loss: 67.628 Accuracy: 0.995\n", "Step: 1500 Loss: 63.252 Accuracy: 0.996\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step01599_weights.png\n", "saved /tmp/bayesian_neural_network/step01599_pred.png\n", "saved /tmp/bayesian_neural_network/step01599_test_pred.png\n", "Step: 1600 Loss: 58.971 Accuracy: 0.996\n", "Step: 1700 Loss: 54.797 Accuracy: 0.996\n", "Step: 1800 Loss: 50.719 Accuracy: 0.996\n", "Step: 1900 Loss: 46.775 Accuracy: 0.996\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step01999_weights.png\n", "saved /tmp/bayesian_neural_network/step01999_pred.png\n", "saved /tmp/bayesian_neural_network/step01999_test_pred.png\n", "Step: 2000 Loss: 42.951 Accuracy: 0.997\n", "Step: 2100 Loss: 39.284 Accuracy: 0.997\n", "Step: 2200 Loss: 35.774 Accuracy: 0.997\n", "Step: 2300 Loss: 32.496 Accuracy: 0.997\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step02399_weights.png\n", "saved /tmp/bayesian_neural_network/step02399_pred.png\n", "saved /tmp/bayesian_neural_network/step02399_test_pred.png\n", "Step: 2400 Loss: 29.387 Accuracy: 0.997\n", "Step: 2500 Loss: 26.434 Accuracy: 0.997\n", "Step: 2600 Loss: 23.643 Accuracy: 0.997\n", "Step: 2700 Loss: 21.023 Accuracy: 0.997\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step02799_weights.png\n", "saved /tmp/bayesian_neural_network/step02799_pred.png\n", "saved /tmp/bayesian_neural_network/step02799_test_pred.png\n", "Step: 2800 Loss: 18.600 Accuracy: 0.997\n", "Step: 2900 Loss: 16.375 Accuracy: 0.998\n", "Step: 3000 Loss: 14.435 Accuracy: 0.998\n", "Step: 3100 Loss: 12.780 Accuracy: 0.997\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step03199_weights.png\n", "saved /tmp/bayesian_neural_network/step03199_pred.png\n", "saved /tmp/bayesian_neural_network/step03199_test_pred.png\n", "Step: 3200 Loss: 11.394 Accuracy: 0.998\n", "Step: 3300 Loss: 10.121 Accuracy: 0.998\n", "Step: 3400 Loss: 8.961 Accuracy: 0.998\n", "Step: 3500 Loss: 7.911 Accuracy: 0.998\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step03599_weights.png\n", "saved /tmp/bayesian_neural_network/step03599_pred.png\n", "saved /tmp/bayesian_neural_network/step03599_test_pred.png\n", "Step: 3600 Loss: 6.966 Accuracy: 0.998\n", "Step: 3700 Loss: 6.122 Accuracy: 0.998\n", "Step: 3800 Loss: 5.373 Accuracy: 0.998\n", "Step: 3900 Loss: 4.718 Accuracy: 0.998\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step03999_weights.png\n", "saved /tmp/bayesian_neural_network/step03999_pred.png\n", "saved /tmp/bayesian_neural_network/step03999_test_pred.png\n", "Step: 4000 Loss: 4.154 Accuracy: 0.998\n", "Step: 4100 Loss: 3.666 Accuracy: 0.998\n", "Step: 4200 Loss: 3.266 Accuracy: 0.998\n", "Step: 4300 Loss: 2.917 Accuracy: 0.998\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step04399_weights.png\n", "saved /tmp/bayesian_neural_network/step04399_pred.png\n", "saved /tmp/bayesian_neural_network/step04399_test_pred.png\n", "Step: 4400 Loss: 2.624 Accuracy: 0.998\n", "Step: 4500 Loss: 2.372 Accuracy: 0.998\n", "Step: 4600 Loss: 2.153 Accuracy: 0.998\n", "Step: 4700 Loss: 1.963 Accuracy: 0.998\n", " ... Held-out nats: -0.000\n", "saved /tmp/bayesian_neural_network/step04799_weights.png\n", "saved /tmp/bayesian_neural_network/step04799_pred.png\n", "saved /tmp/bayesian_neural_network/step04799_test_pred.png\n", "Step: 4800 Loss: 1.797 Accuracy: 0.998\n", "Step: 4900 Loss: 1.674 Accuracy: 0.998\n", "Step: 5000 Loss: 1.562 Accuracy: 0.998\n", "Step: 5100 Loss: 1.463 Accuracy: 0.998\n" ] } ], "source": [ "\"\"\"Trains a Bayesian neural network to classify data from the 2D Ising model.\n", "The architecture is LeNet-5 [1].\n", "#### References\n", "[1]: Yann LeCun, Leon Bottou, Yoshua Bengio, and Patrick Haffner.\n", " Gradient-based learning applied to document recognition.\n", " _Proceedings of the IEEE_, 1998.\n", " http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf\n", "\"\"\"\n", "\n", "from __future__ import absolute_import\n", "from __future__ import division\n", "from __future__ import print_function\n", "\n", "import os\n", "import warnings\n", "\n", "# Dependency imports\n", "from absl import flags\n", "import matplotlib\n", "matplotlib.use(\"Agg\")\n", "from matplotlib import figure # pylint: disable=g-import-not-at-top\n", "from matplotlib.backends import backend_agg\n", "import numpy as np\n", "import tensorflow as tf\n", "import tensorflow_probability as tfp\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "from tensorflow.contrib.learn.python.learn.datasets import mnist\n", "\n", "\n", "\n", "# TODO(b/78137893): Integration tests currently fail with seaborn imports.\n", "warnings.simplefilter(action=\"ignore\")\n", "\n", "try:\n", " import seaborn as sns # pylint: disable=g-import-not-at-top\n", " HAS_SEABORN = True\n", "except ImportError:\n", " HAS_SEABORN = False\n", "\n", "tfd = tfp.distributions\n", "\n", "ISING = True\n", "\n", "IMAGE_SHAPE = [40,40,1] if ISING else [28, 28, 1] \n", "\n", "flags.DEFINE_float(\"learning_rate\",\n", " default=0.001,\n", " help=\"Initial learning rate.\")\n", "flags.DEFINE_integer(\"max_steps\",\n", " default=6000,\n", " help=\"Number of training steps to run.\")\n", "flags.DEFINE_integer(\"batch_size\",\n", " default=128,\n", " help=\"Batch size.\")\n", "flags.DEFINE_string(\"data_dir\",\n", " default=os.path.join(os.getenv(\"TEST_TMPDIR\", \"/tmp\"),\n", " \"bayesian_neural_network/data\"),\n", " help=\"Directory where data is stored (if using real data).\")\n", "flags.DEFINE_string(\n", " \"model_dir\",\n", " default=os.path.join(os.getenv(\"TEST_TMPDIR\", \"/tmp\"),\n", " \"bayesian_neural_network/\"),\n", " help=\"Directory to put the model's fit.\")\n", "flags.DEFINE_integer(\"viz_steps\",\n", " default=400,\n", " help=\"Frequency at which save visualizations.\")\n", "flags.DEFINE_integer(\"num_monte_carlo\",\n", " default=10,\n", " help=\"Network draws to compute predictive probabilities.\")\n", "flags.DEFINE_bool(\"fake_data\",\n", " default=None,\n", " help=\"If true, uses fake data. Defaults to real data.\")\n", "\n", "FLAGS = flags.FLAGS\n", "\n", "def plot_weight_posteriors(names, qm_vals, qs_vals, fname):\n", " \"\"\"Save a PNG plot with histograms of weight means and stddevs.\n", " Args:\n", " names: A Python `iterable` of `str` variable names.\n", " qm_vals: A Python `iterable`, the same length as `names`,\n", " whose elements are Numpy `array`s, of any shape, containing\n", " posterior means of weight varibles.\n", " qs_vals: A Python `iterable`, the same length as `names`,\n", " whose elements are Numpy `array`s, of any shape, containing\n", " posterior standard deviations of weight varibles.\n", " fname: Python `str` filename to save the plot to.\n", " \"\"\"\n", " fig = figure.Figure(figsize=(6, 3))\n", " canvas = backend_agg.FigureCanvasAgg(fig)\n", "\n", " ax = fig.add_subplot(1, 2, 1)\n", " for n, qm in zip(names, qm_vals):\n", " sns.distplot(qm.flatten(), ax=ax, label=n)\n", " ax.set_title(\"weight means\")\n", " ax.set_xlim([-1.5, 1.5])\n", " ax.legend()\n", "\n", " ax = fig.add_subplot(1, 2, 2)\n", " for n, qs in zip(names, qs_vals):\n", " sns.distplot(qs.flatten(), ax=ax)\n", " ax.set_title(\"weight stddevs\")\n", " ax.set_xlim([0, 1.])\n", "\n", " fig.tight_layout()\n", " \n", " canvas.print_figure(fname, format=\"png\")\n", " print(\"saved {}\".format(fname))\n", "\n", "\n", "def plot_heldout_prediction(input_vals, label_vals, probs,\n", " fname, n=10, title=\"\"):\n", " \"\"\"Save a PNG plot visualizing posterior uncertainty on heldout data.\n", " Args:\n", " input_vals: A `float`-like Numpy `array` of shape\n", " `[num_heldout] + IMAGE_SHAPE`, containing heldout input images.\n", " probs: A `float`-like Numpy array of shape `[num_monte_carlo,\n", " num_heldout, num_classes]` containing Monte Carlo samples of\n", " class probabilities for each heldout sample.\n", " fname: Python `str` filename to save the plot to.\n", " n: Python `int` number of datapoints to vizualize.\n", " title: Python `str` title for the plot.\n", " \"\"\"\n", " fig = figure.Figure(figsize=(9, 3*n))\n", " canvas = backend_agg.FigureCanvasAgg(fig)\n", " indices = np.random.randint(low=0,high=input_vals.shape[0],size=n)\n", " for i in range(n):\n", " ax = fig.add_subplot(n, 3, 3*i + 1)\n", " ax.imshow(input_vals[indices[i], :].reshape(IMAGE_SHAPE[:-1]), interpolation=\"None\")\n", "\n", " ax = fig.add_subplot(n, 3, 3*i + 2)\n", " for prob_sample in probs:\n", " sns.barplot(np.arange(2) if ISING else np.arange(10), prob_sample[indices[i], :], alpha=0.5 if ISING else 0.1, ax=ax)\n", " ax.set_ylim([0, 1])\n", " ax.set_title(\"posterior samples\")\n", "\n", " ax = fig.add_subplot(n, 3, 3*i + 3)\n", " sns.barplot(np.arange(2) if ISING else np.arange(10), np.mean(probs[:, indices[i], :], axis=0), ax=ax)\n", " ax.set_ylim([0, 1])\n", " ax.set_title(\"predictive probs, correct=%.i\" % label_vals[indices[i]] )\n", " \n", " fig.suptitle(title)\n", " fig.tight_layout()\n", "\n", " canvas.print_figure(fname, format=\"png\")\n", " print(\"saved {}\".format(fname))\n", "\n", "\n", "\n", "def plot_test_prediction(input_vals, probs,\n", " fname, n=10, title=\"\"):\n", " \"\"\"Save a PNG plot visualizing posterior uncertainty on heldout data.\n", " Args:\n", " input_vals: A `float`-like Numpy `array` of shape\n", " `[num_heldout] + IMAGE_SHAPE`, containing heldout input images.\n", " probs: A `float`-like Numpy array of shape `[num_monte_carlo,\n", " num_heldout, num_classes]` containing Monte Carlo samples of\n", " class probabilities for each heldout sample.\n", " fname: Python `str` filename to save the plot to.\n", " n: Python `int` number of datapoints to vizualize.\n", " title: Python `str` title for the plot.\n", " \"\"\"\n", " fig = figure.Figure(figsize=(9, 3*n))\n", " canvas = backend_agg.FigureCanvasAgg(fig)\n", " indices = np.random.randint(low=0,high=input_vals.shape[0],size=n)\n", " for i in range(n):\n", " ax = fig.add_subplot(n, 3, 3*i + 1)\n", " ax.imshow(input_vals[indices[i], :].reshape(IMAGE_SHAPE[:-1]), interpolation=\"None\")\n", "\n", " ax = fig.add_subplot(n, 3, 3*i + 2)\n", " for prob_sample in probs:\n", " sns.barplot(np.arange(2) if ISING else np.arange(10), prob_sample[indices[i], :], alpha=0.5 if ISING else 0.1, ax=ax)\n", " ax.set_ylim([0, 1])\n", " ax.set_title(\"posterior samples\")\n", "\n", " ax = fig.add_subplot(n, 3, 3*i + 3)\n", " sns.barplot(np.arange(2) if ISING else np.arange(10), np.mean(probs[:, indices[i], :], axis=0), ax=ax)\n", " ax.set_ylim([0, 1])\n", " ax.set_title(\"predictive probs, test set\")\n", " \n", " fig.suptitle(title)\n", " fig.tight_layout()\n", "\n", " canvas.print_figure(fname, format=\"png\")\n", " print(\"saved {}\".format(fname))\n", "\n", "def build_input_pipeline(mnist_data, batch_size, heldout_size):\n", " \"\"\"Build an Iterator switching between train and heldout data.\"\"\"\n", "\n", " # Build an iterator over training batches.\n", " training_dataset = tf.data.Dataset.from_tensor_slices(\n", " (mnist_data.train.images, np.int32(mnist_data.train.labels)))\n", "\n", " print(mnist_data.train.images.shape)\n", " training_batches = training_dataset.shuffle(\n", " 50000, reshuffle_each_iteration=True).repeat().batch(batch_size)\n", " training_iterator = tf.compat.v1.data.make_one_shot_iterator(training_batches)\n", "\n", " # Build a iterator over the heldout set with batch_size=heldout_size,\n", " # i.e., return the entire heldout set as a constant.\n", " heldout_dataset = tf.data.Dataset.from_tensor_slices(\n", " (mnist_data.validation.images,\n", " np.int32(mnist_data.validation.labels)))\n", " heldout_frozen = (heldout_dataset.take(heldout_size).\n", " repeat().batch(heldout_size))\n", " heldout_iterator = tf.compat.v1.data.make_one_shot_iterator(heldout_frozen)\n", "\n", "\n", " test_dataset = tf.data.Dataset.from_tensor_slices(\n", " (mnist_data.test.images,\n", " np.int32(mnist_data.test.labels)))\n", " test_frozen = (test_dataset.take(heldout_size).\n", " repeat().batch(heldout_size))\n", " test_iterator = tf.compat.v1.data.make_one_shot_iterator(test_frozen)\n", "\n", "\n", " # Combine these into a feedable iterator that can switch between training\n", " # and validation inputs.\n", " handle = tf.compat.v1.placeholder(tf.string, shape=[])\n", " feedable_iterator = tf.compat.v1.data.Iterator.from_string_handle(\n", " handle, training_batches.output_types, training_batches.output_shapes)\n", " images, labels = feedable_iterator.get_next()\n", "\n", " return images, labels, handle, training_iterator, heldout_iterator, test_iterator\n", "\n", "\n", "def test_data_pipeline(mnist_data, batch_size):\n", " \"\"\"Build an Iterator switching between train and heldout data.\"\"\"\n", "\n", "\n", " # Build a iterator over the heldout set with batch_size=heldout_size,\n", " # i.e., return the entire heldout set as a constant.\n", " heldout_dataset = tf.data.Dataset.from_tensor_slices(\n", " (mnist_data.test.images))\n", " heldout_frozen = (heldout_dataset.take(batch_size).\n", " repeat().batch(batch_size))\n", " test_iterator = tf.compat.v1.data.make_one_shot_iterator(heldout_frozen)\n", "\n", " # Combine these into a feedable iterator that can switch between training\n", " # and test inputs.\n", " handle = tf.compat.v1.placeholder(tf.string, shape=[])\n", " feedable_iterator = tf.compat.v1.data.Iterator.from_string_handle(\n", " handle, heldout_dataset.output_types, heldout_dataset.output_shapes)\n", " images = feedable_iterator.get_next()\n", "\n", " return images, handle, test_iterator\n", "\n", "\n", "def Get_ising_data():\n", " import pickle\n", " \n", " def read_t(t,root=\"/home/samknu/MyRepos/MLProjectIsingModel/data/IsingData/\"):\n", " data = pickle.load(open(root+'Ising2DFM_reSample_L40_T=%.2f.pkl'%t,'rb'))\n", " return np.unpackbits(data).astype(int).reshape(-1,1600)\n", " \n", " temperatures = np.arange(0.25, 4., step=0.25)\n", " \n", " ordered = np.zeros(shape=(np.sum(temperatures<2.0),10000,1600))\n", " disordered = np.zeros(shape=(np.sum(temperatures>2.5),10000,1600))\n", " critical = np.zeros(shape=(np.sum((temperatures>=2.0)*(temperatures<=2.5)),10000,1600))\n", " \n", " ordered_index = 0\n", " disordered_index = 0\n", " crit_index = 0\n", " for i in range(len(temperatures)):\n", " T = temperatures[i]\n", " if T < 2.0:\n", " ordered[ordered_index] = read_t(T)\n", " ordered_index += 1\n", " elif T > 2.5:\n", " disordered[disordered_index] = read_t(T)\n", " disordered_index += 1\n", " else:\n", " critical[crit_index] = read_t(T)\n", " crit_index += 1\n", "\n", " ordered = ordered.reshape(-1,1600) # 70000\n", " disordered = disordered.reshape(-1,1600) # 50000\n", " critical = critical.reshape(-1,1600) # 30000\n", "\n", " # Shuffling before separating into training, validation and test set\n", " np.random.shuffle(ordered)\n", " np.random.shuffle(disordered)\n", " np.random.shuffle(critical)\n", "\n", " training_data = np.zeros((6000*12,1600))\n", " validation_data = np.zeros((2000*12,1600))\n", " test_data = np.zeros((2000*12 + 10000*3,1600))\n", "\n", " training_data[:round(0.6*70000)] = ordered[:round(0.6*70000)]\n", " training_data[round(0.6*70000):] = disordered[:round(0.6*50000)]\n", "\n", " validation_data[:round(0.2*70000)] = ordered[round(0.6*70000):round(0.6*70000)+round(0.2*70000)]\n", " validation_data[round(0.2*70000):] = disordered[round(0.6*50000):round(0.6*50000)+round(0.2*50000)]\n", "\n", " test_data[:round(0.2*70000)] = ordered[round(0.6*70000)+round(0.2*70000):round(0.6*70000)+2*round(0.2*70000)]\n", " test_data[round(0.2*70000):round(0.2*70000)+round(0.2*50000)] = disordered[round(0.6*50000)+round(0.2*50000):round(0.6*50000)+2*round(0.2*50000)]\n", " test_data[round(0.2*70000)+round(0.2*50000):] = critical\n", "\n", " training_labels = np.zeros(6000*12)\n", " training_labels[round(0.6*70000):] = np.ones(round(0.6*50000))\n", "\n", " validation_labels = np.zeros(2000*12)\n", " validation_labels[round(0.2*70000):] = np.ones(round(0.2*50000))\n", "\n", " # Class 0 is ordered, class 1 is disordered\n", "\n", " ############################################################\n", " # Reshaping since we want them as matrices for convolution #\n", " ############################################################\n", " training_data = training_data.reshape(-1,40,40)\n", " training_data = training_data[:,:,:,np.newaxis]\n", "\n", " validation_data = validation_data.reshape(-1,40,40)\n", " validation_data = validation_data[:,:,:,np.newaxis]\n", " \n", " test_data = test_data.reshape(-1,40,40)\n", " test_data = test_data[:,:,:,np.newaxis]\n", " \n", "\n", " del ordered\n", " del disordered\n", " del critical\n", " del temperatures\n", "\n", " \n", " #############################\n", " # Shuffling data and labels #\n", " #############################\n", " indices = np.random.permutation(np.arange(training_data.shape[0]))\n", " training_data = training_data[indices]\n", " training_labels = training_labels[indices]\n", " \n", " indices = np.random.permutation(np.arange(validation_data.shape[0]))\n", " validation_data = validation_data[indices]\n", " validation_labels = validation_labels[indices]\n", " \n", " indices = np.random.permutation(np.arange(test_data.shape[0]))\n", " test_data = test_data[indices]\n", " #test_labels = test_labels[indices]\n", " \n", " cut_train = 20000 \n", " cut_val = 5000\n", " cut_test = 1000\n", " training_data = training_data[:cut_train]\n", " training_labels = training_labels[:cut_train]\n", "\n", " validation_data = validation_data[:cut_val]\n", " validation_labels = validation_labels[:cut_val]\n", " \n", " test_data = test_data[:cut_test]\n", "\n", " class Dummy(object):\n", " pass\n", " ising_data = Dummy()\n", " ising_data.train=Dummy()\n", " ising_data.train.images = training_data\n", " ising_data.train.labels = training_labels\n", " ising_data.train.num_examples = training_data.shape[0]\n", "\n", " ising_data.validation=Dummy()\n", " ising_data.validation.images = validation_data\n", " ising_data.validation.labels = validation_labels\n", " ising_data.validation.num_examples = validation_data.shape[0]\n", "\n", "\n", " ising_data.test=Dummy()\n", " ising_data.test.images = test_data\n", " ising_data.test.labels = np.zeros(test_data.shape[0]) # dummy labels\n", " ising_data.test.num_examples = test_data.shape[0]\n", "\n", " return ising_data\n", "\n", "\n", "def main(argv):\n", " del argv # unused\n", "\n", " if tf.io.gfile.exists(FLAGS.model_dir):\n", " tf.compat.v1.logging.warning(\n", " \"Warning: deleting old log directory at {}\".format(FLAGS.model_dir))\n", " tf.io.gfile.rmtree(FLAGS.model_dir)\n", " tf.io.gfile.makedirs(FLAGS.model_dir)\n", "\n", "\n", "\n", " if ISING:\n", " the_data = Get_ising_data()\n", " else:\n", " the_data = mnist.read_data_sets(FLAGS.data_dir, reshape=False)\n", "\n", " \n", " (images, labels, handle, training_iterator, heldout_iterator, test_iterator) = build_input_pipeline(\n", " the_data, FLAGS.batch_size, the_data.validation.num_examples) \n", "\n", "\n", " # Build a Bayesian LeNet5 network. We use the Flipout Monte Carlo estimator\n", " # for the convolution and fully-connected layers: this enables lower\n", " # variance stochastic gradients than naive reparameterization.\n", " with tf.compat.v1.name_scope(\"bayesian_neural_net\", values=[images]):\n", " neural_net = tf.keras.Sequential([\n", " tfp.layers.Convolution2DFlipout(6,\n", " kernel_size=5,\n", " padding=\"SAME\",\n", " activation=tf.nn.relu),\n", " tf.keras.layers.MaxPooling2D(pool_size=[2, 2],\n", " strides=[2, 2],\n", " padding=\"SAME\"),\n", " tfp.layers.Convolution2DFlipout(16,\n", " kernel_size=5,\n", " padding=\"SAME\",\n", " activation=tf.nn.relu),\n", " tf.keras.layers.MaxPooling2D(pool_size=[2, 2],\n", " strides=[2, 2],\n", " padding=\"SAME\"),\n", " tfp.layers.Convolution2DFlipout(120,\n", " kernel_size=5,\n", " padding=\"SAME\",\n", " activation=tf.nn.relu),\n", " tf.keras.layers.Flatten(),\n", " tfp.layers.DenseFlipout(84, activation=tf.nn.relu),\n", " tfp.layers.DenseFlipout(2) if ISING else tfp.layers.DenseFlipout(10)\n", " ])\n", " \n", " logits = neural_net(images)\n", " labels_distribution = tfd.Categorical(logits=logits)\n", "\n", " # Compute the -ELBO as the loss, averaged over the batch size.\n", " neg_log_likelihood = -tf.reduce_mean(\n", " input_tensor=labels_distribution.log_prob(labels))\n", " kl = sum(neural_net.losses) / the_data.train.num_examples # 72000 is the size of the training set\n", " elbo_loss = neg_log_likelihood + kl\n", "\n", " # Build metrics for validation. Predictions are formed from a single forward\n", " # pass of the probabilistic layers. They are cheap but noisy predictions.\n", " predictions = tf.argmax(input=logits, axis=1)\n", " accuracy, accuracy_update_op = tf.compat.v1.metrics.accuracy(\n", " labels=labels, predictions=predictions)\n", "\n", " # Extract weight posterior statistics for layers with weight distributions\n", " # for later visualization.\n", " names = []\n", " qmeans = []\n", " qstds = []\n", " for i, layer in enumerate(neural_net.layers):\n", " try:\n", " q = layer.kernel_posterior\n", " except AttributeError:\n", " continue\n", " names.append(\"Layer {}\".format(i))\n", " qmeans.append(q.mean())\n", " qstds.append(q.stddev())\n", "\n", "\n", " with tf.compat.v1.name_scope(\"train\"):\n", " optimizer = tf.compat.v1.train.AdamOptimizer(\n", " learning_rate=FLAGS.learning_rate)\n", " train_op = optimizer.minimize(elbo_loss)\n", "\n", " init_op = tf.group(tf.compat.v1.global_variables_initializer(),\n", " tf.compat.v1.local_variables_initializer())\n", "\n", " with tf.compat.v1.Session() as sess:\n", " sess.run(init_op)\n", "\n", " # Run the training loop.\n", " train_handle = sess.run(training_iterator.string_handle())\n", " heldout_handle = sess.run(heldout_iterator.string_handle())\n", " test_handle = sess.run(test_iterator.string_handle())\n", " \n", " for step in range(FLAGS.max_steps):\n", " #for step in range(0):\n", " _ = sess.run([train_op, accuracy_update_op],\n", " feed_dict={handle: train_handle})\n", " if step % 100 == 0:\n", " loss_value, accuracy_value = sess.run(\n", " [elbo_loss, accuracy], feed_dict={handle: train_handle})\n", " print(\"Step: {:>3d} Loss: {:.3f} Accuracy: {:.3f}\".format(\n", " step, loss_value, accuracy_value))\n", "\n", " if (step+1) % FLAGS.viz_steps == 0:\n", " # Compute log prob of heldout set by averaging draws from the model:\n", " # p(heldout | train) = int_model p(heldout|model) p(model|train)\n", " # ~= 1/n * sum_{i=1}^n p(heldout | model_i)\n", " # where model_i is a draw from the posterior p(model|train).\n", " probs = np.asarray([sess.run((labels_distribution.probs),\n", " feed_dict={handle: heldout_handle})\n", " for _ in range(FLAGS.num_monte_carlo)])\n", " mean_probs = np.mean(probs, axis=0)\n", "\n", " image_vals, label_vals = sess.run((images, labels),\n", " feed_dict={handle: heldout_handle})\n", " \n", " \n", " probs_test = np.asarray([sess.run((labels_distribution.probs),\n", " feed_dict={handle: test_handle})\n", " for _ in range(FLAGS.num_monte_carlo)])\n", " mean_probs_test = np.mean(probs_test, axis=0)\n", " image_vals_test = sess.run((images),\n", " feed_dict={handle: test_handle})\n", "\n", " heldout_lp = np.mean(np.log(mean_probs[np.arange(mean_probs.shape[0]),\n", " label_vals.flatten()]))\n", " \n", " print(\" ... Held-out nats: {:.3f}\".format(heldout_lp))\n", "\n", " qm_vals, qs_vals = sess.run((qmeans, qstds))\n", "\n", " if HAS_SEABORN:\n", " plot_weight_posteriors(names, qm_vals, qs_vals,\n", " fname=os.path.join(\n", " FLAGS.model_dir,\n", " \"step{:05d}_weights.png\".format(step)))\n", "\n", " plot_heldout_prediction(image_vals, label_vals, probs,\n", " fname=os.path.join(\n", " FLAGS.model_dir,\n", " \"step{:05d}_pred.png\".format(step)),\n", " title=\"mean heldout logprob {:.2f}\"\n", " .format(heldout_lp))\n", "\n", " plot_test_prediction(image_vals_test, probs_test,\n", " fname=os.path.join(\n", " FLAGS.model_dir,\n", " \"step{:05d}_test_pred.png\".format(step)))\n", "\n", "\n", "if __name__ == \"__main__\":\n", " \n", " tf.compat.v1.app.run() # this thing will run the main(argv) function with sys.argv as argument" ] }, { "attachments": { "step00399_weights.png": { "image/png": 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" }, "step04399_test_pred.png": { "image/png": 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" }, "step04799_test_pred.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Weights near the beginning:\n", "![step00399_weights.png](attachment:step00399_weights.png)\n", "Weights near the end:\n", "![step03999_weights.png](attachment:step03999_weights.png)\n", "\n", "### Classification on the unseen data:\n", "(The data includes both ordered and disordered in addition to the critical state)\n", "\n", "Class 0 = ordered, Class 1 = disordered\n", "![step04399_test_pred.png](attachment:step04399_test_pred.png)\n", "\n", "![step04799_test_pred.png](attachment:step04799_test_pred.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Part 4 - Bayesian Reasoning on the Probability of Life\n", "\n", "A frequentist will claim that we cannot say anything about the probability that life can arise, because we have only observed a single example of it. Here I will give a Bayesian explanation of why this intuition is wrong.\n", "\n", "In Bayesian logic we can use other types of information about life on Earth to do inference -- in this case the datapoint that life on Earth seems to have appeared very shortly after the planet cooled down enough to allow for complex molecules to exist. The reasoning goes like this:\n", "\n", "Let us say that we _initially_ only know two facts:\n", " 1. Life exist on Earth \n", " 2. We also have a modern understanding of biology, meaning that we know that life is essentially an extension of thermodynamics, but we have no information about the actual probability of life to spontaneously appear\n", "\n", "\n", "We now ask ourselves if we can say something about the probability of life to occur or not. To simplify the analysis we assume a binary hypothesis space $\\theta$ where \n", "\n", "\n", "$$\n", " \\theta = 0 \\ \\text{is the hypothesis that life has a} \\textbf{ low } \\text{probability of occurring}\\\\\n", " \\theta = 1 \\ \\text{is the hypothesis that life has a} \\textbf{ high } \\text{probability of occurring}. \n", "$$\n", "\n", "\n", "The question is then which of these hypotheses is true. Since we are initially completely ignorant, meaning we have no reason to believe either hypothesis more than the other, we start with a uniform prior, i.e.\n", "\n", "$$\n", "p(\\theta=0) = 0.5\n", "$$\n", "and\n", "$$\n", "p(\\theta=1) = 0.5 .\n", "$$\n", "\n", "\n", "Let us then assume that we observe a datapoint \n", "$$D = \\{\\textrm{Life appeared shortly after it was possible}\\}.$$ \n", "\n", "Using Bayes theorem we can then write our two posterior estimates as\n", "\n", "$$\n", "p(\\theta=0|D) = \\frac{p(D|\\theta=0)p(\\theta=0)}{p(D)}\n", "$$\n", "and\n", "$$\n", "p(\\theta=1|D) = \\frac{p(D|\\theta=1)p(\\theta=1)}{p(D)}\n", "$$\n", "\n", "\n", "The denominators are the same in both cases, and since the priors are $p(\\theta=0)=p(\\theta=1)$ we see that the only factors that differ between the two posterior hypotheses are $p(D|\\theta=1)$ and $p(D|\\theta=0)$ (this factor is called the likelihood).\n", "\n", "Further it must be true that $p(D|\\theta=1)>p(D|\\theta=0)$, since observing datapoint $D$ is more probable if $\\theta=1$ than if $\\theta=0$, so it follows that\n", "\n", "$$\n", "p(\\theta=1|D) > p(\\theta=0|D). \n", "$$\n", "\n", "So we conclude that our posterior, based on this single datapoint $D$, says that we should give a higher probability estimate that $\\theta=1$ is true. In other words, we should lend more credence to the hypothesis that life has a high probability of occurring.\n", "\n", "We could also do this analysis with a continuous hypothesis space. Our prior would then not be uniform, but would fall to zero towards the right end, because we know that if life were extremely, extremely probable we would have seen it arise in experiments, which we have not." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "\n", "[1] Shridhar et al. Uncertainty Estimations by Softplus normalization in Bayesian Convolutional Neural Networks with Variational Inference https://arxiv.org/pdf/1806.05978.pdf\n", "\n", "[2] Wen et al. Flipout: Efficient pseudo independent weight perturbations on mini-batches https://arxiv.org/pdf/1803.04386.pdf\n", "\n", "[3] LeCun et al. Gradient-Based Learning Applied to Document Recognition http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf\n", "\n", "[4] Mehta et al. A high-bias, low-variance introduction to Machine Learning for physisits https://arxiv.org/pdf/1803.08823.pdf, https://physics.bu.edu/~pankajm/MLnotebooks.html\n", "\n", "[5] Book: Machine Learning: A Probabilistic Perspective by Kevin P. Murphy\n" ] } ], "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 2 }