{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian-Linear Hidden Markov Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook shows an example of training and inspecting a Gaussian-Linear Hidden Markov Model (GLHMM). This model is fit to two sets of timeseries, such as a neuroimaging/electrophysiological recording and a corresponding behavioural or other physiological timeseries. If you want to model just one set of timeseries, you can e.g., use the [*Standard Gaussian HMM*](./GaussianHMM_example.ipynb). If you are new to the HMM or the GLHMM toolbox, we recommend starting there for a thorough introduction.\n", "\n", "**Note:** Due to rendering issues when viewing this notebook through github, internal links, like the table of contents, may not work correctly. To ensure that the notebook renders correctly, you can view it through [this link](https://nbviewer.org/github/vidaurre/glhmm/blob/main/docs/notebooks/GLHMM_example.ipynb).\n", "\n", "Authors: Christine Ahrends " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outline\n", "1. [Background](#background)\n", "2. [Example: Modelling time-varying interaction between brain and physiological data](#example-modelling)\n", " * [Preparation](#preparation)\n", " * [Load data](#load-data)\n", " * [Initialise and train a GLHMM](#initialise-glhmm)\n", " * [Inspect model](#inspect-model)\n", " * [Interaction between brain and physiological measures](#interaction)\n", " * [State means and covariances](#state-means-covariances)\n", " * [Dynamics: Transition probabilities and Viterbi path](#dynamics)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background \n", "The GLHMM is a generalization of the HMM, introduced in [Vidaurre et al., 2023](https://arxiv.org/abs/2312.07151). \n", "We here assume that the observations *Y* at time point *t* were generated by a Gaussian distribution with parameters $\\mu$ and $\\Sigma$ (similar to the standard Gaussian HMM), as well as regression coefficients $\\beta$ that relate the second set of variables *X* to *Y*. When state *k* is active at time point *t*, the GLHMM thus assumes that the timeseries *Y* follows the following distribution:\n", "$$Y_t\\sim N(\\mu^k+X_t\\beta^k,\\Sigma^k)$$\n", "Compared to the standard Gaussian HMM, the GLHMM thus adds the $X_t\\beta^k$ term, which allows modelling the relationship to a second set of variables.\n", "\n", "The remaining HMM parameters are essentially the same as in the standard HMM, i.e. the transition probabilities $\\theta$:\n", "$$P(s_t=k|s_{t-1}=l)=\\theta_{k,l}$$\n", "the initial state probabilities $\\pi$:\n", "$$P(s_t=k)=\\pi_k$$\n", "as well as the posterior estimates for both X and Y:\n", "$$\\gamma_{t,k}:=P(s_t=k|s_{>t},s_{t},s_{\n", "We will now go through an example illustrating how to fit and inspect a GLHMM. The example uses simulated data that can be found in the `example_data` folder. The data were generated to resemble one set of fMRI timeseries and two corresponding non-brain physiological (e.g., heart rate and respiration) timeseries. Our goal is to estimate time-varying amplitude and functional connectivity (FC) within the fMRI recordings and temporal changes in the relationship between the fMRI and the physiological data. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Preparation \n", "If you dont have the **GLHMM-package** installed, then run the following command in your terminal:\n", "\n", "```pip install glhmm```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then need to import the relevant modules:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sb\n", "from glhmm import glhmm, preproc, utils, graphics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load and prepare data \n", "Example data for this tutorial are available for download from the OSF. This notebook will fetch the relevant data from the OSF project page using the osfclient package. If you prefer, you can also directly download the files from the [OSF project page](https://osf.io/8qcyj/?view_only=119c38072a724e0091db5ba377935666) and skip the next two cells. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# checks if osfclient is installed and otherwise installs it using pip install\n", "# skip this if you have manually downloaded the data\n", "import sys\n", "import pip\n", "\n", "def install(package):\n", " pip.main(['install', package])\n", "\n", "try:\n", " import osfclient\n", "except ImportError:\n", " print('osfclient is not installed, installing it now')\n", " install('osfclient')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "usage: osf fetch [-h] [-f] [-U] remote [local]\n", "osf fetch: error: Local file ./example_data/data.csv already exists, not overwriting.\n", "100%|████████████████████████████████████| 496k/496k [00:00<00:00, 2.43Mbytes/s]\n", "usage: osf fetch [-h] [-f] [-U] remote [local]\n", "osf fetch: error: Local file ./example_data/T.csv already exists, not overwriting.\n" ] } ], "source": [ "! osf -p 8qcyj fetch GLHMM/data.csv ./example_data/data.csv\n", "! osf -p 8qcyj fetch GLHMM/dataX.csv ./example_data/dataX.csv\n", "! osf -p 8qcyj fetch GLHMM/T.csv ./example_data/T.csv" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The GLHMM requires two inputs: a timeseries `Y`and a second timeseries `X`. When running the model on a concatenated timeseries, e.g., a group of subjects or several scanning sessions, you also need to provide the `indices` indicating where each subject/session in the concatenated timeseries `Y` starts and ends. Loading data and data formats are explained in more detail in the [Standard Gaussian HMM tutorial](./GaussianHMM_example.ipynb).\n", "\n", "Synthetic data for this example should now be in the `glhmm/docs/notebooks/example_data` folder. The file `data.csv` contains synthetic data for the first set of timeseries `Y`. This is the brain data, containing fMRI recordings from 20 subjects with 1,000 timepoints each, concatenated along the first dimension, and 50 brain areas. The file `dataX.csv` contains the corresponding physiological measures, heart rate and respiration. The sessions have the same duration as the brain data, i.e., there are 20 concatenated subjects with 1,000 timepoints each, but only 2 variables (heart rate and respiration). The file `T.csv` specifies the beginning and end of each subject's session (same for `X` and `Y`). " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "brain_data = pd.read_csv('./example_data/data.csv', header=None).to_numpy()\n", "phys_data = pd.read_csv('./example_data/dataX.csv', header=None).to_numpy()\n", "T_t = pd.read_csv('./example_data/T.csv', header=None).to_numpy()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**NOTE: It is important to standardise your timeseries and, if necessary, apply other kinds of preprocessing before fitting the model.**\\\n", "This will be done separately for each session/subject as specified in the indices. The data provided here are already close to standardised (so the code below will not do much). " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "brain_data,_ = preproc.preprocess_data(brain_data, T_t)\n", "phys_data,_ = preproc.preprocess_data(phys_data, T_t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initialise and train a GLHMM \n", "We first initialise the glhmm object, which we here call `brainphys_glhmm`. By specifying the parameters of the glhmm object, we define which type of model we want to fit and how states should be defined. In the case of the GLHMM, we need to set the `model_beta` parameter to indicate that we wish to model an interaction between two sets of variables. There are two options for modelling the interaction: global, meaning we estimate regression coefficients that are static over the timeseries in which case `model_beta='shared'`, or state-dependent, meaning we estimate regression coefficients that vary over time in which case `model_beta='state'`. In this example, we want to model the time-varying interaction between the brain data and the physiological data, so we set `model_beta='state'`. For the other parameters, we here want to use the same set-up as in the [standard Gaussian HMM](./GaussianHMM_example.ipynb), i.e., each state will be defined in terms of mean and covariance. That means, we will also estimate the time-varying amplitude and functional connectivity in the brain timeseries. We model 4 states by setting the parameter `K=4`, which you can compare to the states from the standard Gaussian HMM." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "brainphys_glhmm = glhmm.glhmm(model_beta='state', K=4, covtype='full')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check the hyperparameters of the object to make sure the model is defined as we planned:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'K': 4, 'covtype': 'full', 'model_mean': 'state', 'model_beta': 'state', 'dirichlet_diag': 10, 'connectivity': None, 'Pstructure': array([[ True, True, True, True],\n", " [ True, True, True, True],\n", " [ True, True, True, True],\n", " [ True, True, True, True]]), 'Pistructure': array([ True, True, True, True])}\n" ] } ], "source": [ "print(brainphys_glhmm.hyperparameters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then train the model. To model the interaction, we need to train the GLHMM using both the brain data and the physiological data. The \"main\" timeseries we are looking to model, i.e., the data for which we also want to estimate mean and covariance, is `Y`, so in this case `Y=brain_data`. The secondary timeseries from which we model only the interaction with the main timeseries is called `X` so `X=phys_data`. When fitting the model to a group of subjects or sessions, we also need to specify the indices of the start and end of each session (here called `T_t`). Note that the indices are shared for `X` and `Y`, so the beginning and end of the sessions in `X` and `Y` need to correspond. During training, the output will usually show the progress in model fit at each iteration. This can be quite long, so we have here suppressed it for displaying purposes. You can remove the first line (`%%capture`) to show it." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "%%capture\n", "np.random.seed(123)\n", "brainphys_glhmm.train(X=phys_data, Y=brain_data, indices=T_t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inspect model " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Interaction between brain and physiological measures \n", "Let's start by retrieving the parameters describing the interaction, i.e., the $\\beta$ values, between the two sets of timeseries: the brain data and the physiological data (heart rate & respiration). The beta-values can be obtained from the trained model using the `get_betas()` function (or alternatively `get_beta(k)` to obtain only the beta-values for state `k`):" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "K = brainphys_glhmm.hyperparameters[\"K\"] # the number of states\n", "q = brain_data.shape[1] # the number of parcels/channels\n", "state_betas = np.zeros(shape=(2,q,K))\n", "state_betas = brainphys_glhmm.get_betas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we here defined $\\beta$ to be time-varying, i.e., state-dependent, we have a matrix describing the interaction between each of the 50 brain regions and the 2 physiological measures for each of the 4 states:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cmap = \"coolwarm\"\n", "ytick =[\"Heart rate\", \"Respiration\"]\n", "for k in range(K):\n", " plt.subplot(2,2,k+1)\n", " plt.imshow(state_betas[:,:,k], cmap=cmap,aspect='auto', interpolation='none')\n", " plt.colorbar()\n", " plt.ylabel('Physiological data')\n", " plt.yticks(np.arange(2), ytick)\n", " plt.xlabel('Brain area')\n", " plt.title(f\"Betas for state #{k+1}\")\n", "plt.subplots_adjust(hspace=0.5, wspace=1)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### State means and covariances \n", "We have defined the model so that each state also has a mean (amplitude) and covariance (functional connectivity), as in the [Standard Gaussian HMM](./GaussianHMM_example.ipynb). We can retrieve them by using the `get_mean` and `get_covariance_matrix` functions:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "state_means = np.zeros(shape=(q, K))\n", "for k in range(K):\n", " state_means[:,k] = brainphys_glhmm.get_mean(k) # the state means in the shape (no. features, no. states)\n", "state_FC = np.zeros(shape=(q, q, K))\n", "for k in range(K):\n", " state_FC[:,:,k] = brainphys_glhmm.get_covariance_matrix(k=k) # the state covariance matrices in the shape (no. features, no. features, no. states)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And plot them:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(state_means,cmap=cmap, interpolation=\"none\")\n", "plt.colorbar(label='Activation Level') # Label for color bar\n", "plt.title(\"State mean activation\")\n", "plt.xticks(np.arange(K), np.arange(1,K+1))\n", "plt.gca().set_xlabel('State')\n", "plt.gca().set_ylabel('Brain region')\n", "plt.tight_layout() # Adjust layout for better spacing\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for k in range(K):\n", " plt.subplot(2,2,k+1)\n", " plt.imshow(state_FC[:,:,k], cmap=cmap, interpolation=\"none\")\n", " plt.xlabel('Brain region')\n", " plt.ylabel('Brain region')\n", " plt.colorbar()\n", " plt.title(\"State covariance\\nstate #%s\" % (k+1))\n", "plt.subplots_adjust(hspace=0.7, wspace=0.8)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Dynamics: Transition probabilities and Viterbi path \n", "We can also look at the transition probabilities and the Viterbi path to understand the temporal sequence in which the states occur. See [Standard Gaussian HMM](./GaussianHMM_example.ipynb) for a detailed explanation. The transition probabilities with and without self-transitions:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TP = brainphys_glhmm.P.copy() # the transition probability matrix\n", "\n", "# Plot Transition Probabilities\n", "plt.figure(figsize=(7, 4))\n", "\n", "# Plot 1: Full Transition Probabilities\n", "plt.subplot(1, 2, 1)\n", "plt.imshow(TP, cmap=cmap, interpolation='nearest') # Improved color mapping\n", "plt.title('Transition Probabilities')\n", "plt.xlabel('To State')\n", "plt.ylabel('From State')\n", "plt.colorbar(fraction=0.046, pad=0.04)\n", "\n", "# Plot 2: Transition Probabilities without Self-Transitions\n", "TP_noself = TP - np.diag(np.diag(TP)) # Remove self-transitions\n", "TP_noself2 = TP_noself / TP_noself.sum(axis=1, keepdims=True) # Normalize probabilities\n", "plt.subplot(1, 2, 2)\n", "plt.imshow(TP_noself2, cmap=cmap, interpolation='nearest') # Improved color mapping\n", "plt.title('Transition Probabilities\\nwithout Self-Transitions')\n", "plt.xlabel('To State')\n", "plt.ylabel('From State')\n", "plt.colorbar(fraction=0.046, pad=0.04)\n", "\n", "plt.tight_layout() # Adjust layout for better spacing\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the Viterbi path:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "vpath = brainphys_glhmm.decode(X=phys_data, Y=brain_data, indices=T_t, viterbi=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And plot the Viterbi path (see also `graphics` module):" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphics.plot_vpath(vpath, title=\"Viterbi path\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, let's have a look at the first 1000 timepoints from one subject to get a feeling for the rate at which states switch over the scanning session. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_subject = 0\n", "graphics.plot_vpath(vpath[T_t[num_subject,0]:T_t[num_subject,1],:], title=\"Viterbi path\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As for the standard HMM, there is a range of useful summary metrics that you can compute to describe the obtained patterns. Have a look at the [Standard Gaussian HMM tutorial](./GaussianHMM_example.ipynb) to see how to obtain them from your trained model. These can be used, e.g., for statistical testing (see [Statistical testing tutorial](./Testing_across_subjects.ipynb)) or prediction/machine learning (see [Prediction tutorial](./Prediction_tutorial.ipynb)). " ] } ], "metadata": { "kernelspec": { "display_name": "glhmm", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 2 }