{ "cells": [ { "cell_type": "code", "execution_count": 6, "id": "0484b0fd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Normnalized IDIF_mean: [0. 0. 0. 0. 0.55 1. 0.99 0.38 0.18 0.17 0.17 0.11 0.09 0.07\n", " 0.05 0.04 0.04 0.04 0.04 0.04 0.04]\n", "The shape of IDIF_Brain: (21,)\n" ] } ], "source": [ "#import libraries\n", "import tensorflow_probability as tfp\n", "import tensorflow as tf\n", "from scipy import integrate\n", "import pandas as pd\n", "import numpy as np\n", "from numpy import asarray\n", "tfd = tfp.distributions\n", "\n", "\n", "# The joint_model function takes parameters 1/λz, and μ_(x), σ_x and sets up a joint distribution using TFP’s \n", "# JointDistributionCoroutine. Within this function, an exponential distribution\n", "# for the latent variable IDIF-Mean and a normal distribution for the observed variable TAC are defined.\n", "\n", "def joint_model(alpha_0, mu_g, sigma, n_samples): \n", " \n", " Z = yield tfd.JointDistributionCoroutine.Root(\n", " tfd.Exponential(\n", " rate=alpha_0,\n", " force_probs_to_zero_outside_support=True,\n", " name=\"mu\",\n", " )\n", " )\n", " X = yield tfd.Normal(\n", " loc=mu_g,\n", " scale=sigma, name=\"X\"\n", " )\n", "\n", "\n", "\n", "# Data from Matlab file is loaded into three separate arrays: \n", "# mu_prior, mu_gray, and sigma_gray, \n", "# which represent prior mean, means of gray matter, and standard deviations of gray matter, respectively. \n", "data = pd.read_csv(\"VI_data_pXX.csv\",usecols=range(1,22))\n", "\n", "#Read prior (IDIF-Mean), mu and sigma (gray_TAC).csv\n", "data = np.array(data)\n", "mu_prior, mu_gray, sigma_gray = data[0, :], data[1, :], data[2, :]\n", "\n", "print('Normnalized IDIF_mean:',mu_prior)\n", "#print(mu_gray)\n", "#print(sigma_gray)\n", "\n", "\n", "#An empty list mu_surrogate is initialized to store the surrogate posterior values.\n", "mu_surrogate =list()\n", "N=1000\n", "\n", "# A loop iterates over 21 elements representing time steps, where for each iteration, \n", "# corresponding values from mu_prior, mu_gray, and sigma_gray are selected.\n", "for t in range(21):\n", " mu_prior_i = mu_prior[t]\n", " mu_gray_i = mu_gray[t]\n", " sigma_gray_i = sigma_gray[t]\n", " \n", " \n", " #A normal distribution is created for the observed data, and N samples are drawn to form the dataset. \n", " #The log-probability function joint_pdf_fixed_to_data is created to calculate the log probability of \n", " #the joint model given the dataset.\n", " \n", " # Sample from the observed data distribution\n", " X=tfp.distributions.Normal(loc=mu_gray_i, scale=sigma_gray_i)\n", " dataset = X.sample(N)\n", " \n", " # Define the joint distribution model\n", " joint_pdf = tfd.JointDistributionCoroutine(\n", " lambda : joint_model(mu_prior_i,mu_gray_i, sigma_gray_i, N)\n", " )\n", "\n", " # Define the log-probability function for the dataset\n", " joint_pdf_fixed_to_data = lambda Z: joint_pdf.log_prob(Z, dataset)\n", "\n", " #A surrogate posterior distribution is defined as an exponential distribution taking the mu_s, \n", " #which is the prior mean (using IDIF-Mean).\n", " \n", " # Define the surrogate posterior distribution\n", " mu_s = tf.Variable(mu_prior_i, name=\"mu_surrogate\")\n", "\n", " surrogate_posterior = tfp.distributions.Exponential(\n", " mu_s,\n", " force_probs_to_zero_outside_support=True,\n", " name=\"surrogate_posterior\"\n", " )\n", "\n", " #An Adam optimizer with a learning rate of 0.01 is set up to minimize the loss, \n", " #defined as the negative Evidence Lower Bound (ELBO). \n", " #The optimization loop runs for 1000 steps, updating mu_s\n", " #The surrogate posterior values are stored after completing the loop for all time steps.\n", " \n", " # Fit the surrogate posterior using variational inference\n", " mvn_loss = tfp.vi.fit_surrogate_posterior(target_log_prob_fn=joint_pdf_fixed_to_data,\n", " surrogate_posterior=surrogate_posterior,\n", " optimizer=tf.optimizers.Adam(0.01), \n", " num_steps=1000,sample_size=1)\n", " \n", " \n", " \n", " mu_surrogate.append(mu_s)\n", " \n", "mu_surr= asarray(mu_surrogate)\n", "\n", "print('The shape of IDIF_Brain:',mu_surr.shape)\n", "np.savetxt(\"VI_data_gen_pXX.csv\", mu_surr, delimiter=',')" ] }, { "cell_type": "code", "execution_count": 12, "id": "c5084cd7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Normnalized IDIF_Brain: [[0. ]\n", " [0. ]\n", " [0. ]\n", " [0.581 ]\n", " [0.977 ]\n", " [1.03 ]\n", " [0.442 ]\n", " [0.207 ]\n", " [0.198 ]\n", " [0.142 ]\n", " [0.0647]\n", " [0.0785]\n", " [0.0919]\n", " [0.0487]\n", " [0.0455]\n", " [0.0432]\n", " [0.0398]\n", " [0.0338]\n", " [0.0339]\n", " [0.0357]]\n" ] } ], "source": [ "#Load and verify the IDIF_Brain\n", "IDIF_Brain = pd.read_csv(\"VI_data_gen_pxx.csv\")\n", "\n", "IDIF_Brain = np.array(IDIF_Brain)\n", "\n", "print('Normnalized IDIF_Brain:',IDIF_Brain)" ] }, { "cell_type": "code", "execution_count": 16, "id": "1f7f85ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.5.3\n" ] } ], "source": [ "#TF version\n", "import tensorflow as tf\n", "print(tf. __version__)" ] }, { "cell_type": "code", "execution_count": null, "id": "1f8a55f2", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 5 }