.. BayesML documentation master file, created by sphinx-quickstart on Mon Feb 21 21:21:00 2022. You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. .. Document Author Yuta Nakahara Shota Saito .. image:: ./logos/BayesML_logo.svg :class: only-light .. image:: ./logos/BayesML_logo_reverse.svg :class: only-dark Your First Library for Bayesian Machine Learning ================================================ BayesML contributes to wide society through promoting education, research, and application of machine learning based on Bayesian statistics and Bayesian decision theory. Characteristics --------------- * **Easy-to-use:** * You can use pre-defined Bayesian statistical models by simply importing it. You don't need to define models yourself like PyMC or Stan. * **Bayesian Decision Theoretic API:** * BayesML's API corresponds to the structure of decision-making based on Bayesian decision theory. Bayesian decision theory is a unified framework for handling various decision-making processes, such as parameter estimation and prediction of new data. Therefore, BayesML enables intuitive operations for a wider range of decision-making compared to the fit-predict type API adopted in libraries like scikit-learn. Moreover, many of our models also implement fit-predict functions. * **Model Visualization Functions:** * All packages have methods to visualize the probabilistic data generative model, generated data from that model, and the posterior distribution learned from the data in 2~3 dimensional space. Thus, you can effectively understand the characteristics of probabilistic data generative models and algorithms through the generation of synthetic data and learning from them. * **Fast Algorithms Using Conjugate Prior Distributions:** * Many of our learning algorithms adopt exact calculation methods or variational Bayesian methods that effectively use the conjugacy between probabilistic data generative models and prior distributions. Therefore, they are much faster than general-purpose MCMC methods and are also suitable for online learning. Although some algorithms adopt MCMC methods, but they use MCMC methods specialized for each model, taking advantage of conjugacy. News ---- * Our algorithm for the meta-tree model has been accepted to AISTATS 2025! For more details, please see the links below. * `Paper `__ * `Code Example `__ Installation ------------ Please use the following command to install BayesML. .. code-block:: bash pip install bayesml The following are required. * Python (>= 3.10) * NumPy (>= 1.20) * SciPy (>= 1.7) * MatplotLib (>= 3.5) * Scikit-learn (>= 1.1) Tutorial -------- Each model in BayesML has two classes. One is ``GenModel``, which can be used for parameter generation from prior or posterior distributions, and data generation. The other is ``LearnModel``, which can be used for estimating posterior distributions from data and calculating predictive distributions. Each has an API that aligns with Bayesian decision theory. Let's look at how to use each with the ``linearregression`` model as an example. Synthetic Data Generation with ``GenModel`` ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ First, let's import the library. .. code-block:: python import numpy as np from bayesml import linearregression Next, we create an instance of the probabilistic data generative model. Here, we specify the dimension of the regression coefficients (including the constant term) as ``c_degree=2`` as a constant of the model, and we specify the regression coefficients as ``theta_vec = np.array([1,1])`` and the precision (inverse of variance) of the noise term as ``tau = 10`` as parameters. .. code-block:: python gen_model = linearregression.GenModel( c_degree = 2, # degree theta_vec = np.array([1,1]), # coefficients tau = 10, # noise precision ) You can visualize the characteristics of the created model by the following method. .. code-block:: python gen_model.visualize_model() Output: | theta_vec: | [1. 1.] | tau: | 10.0 .. image:: ./images/README_LR1.png To generate a sample and save it to variables ``x`` and ``y``, we use the following method: .. code-block:: python x,y = gen_model.gen_sample(sample_size=100) Let's also generate test data for later use. .. code-block:: python x_test,y_test = gen_model.gen_sample(sample_size=100) Learning and Decision Making with ``LearnModel`` ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Let's use ``LearnModel`` to learn a model from the data we just generated. Of course, the data that can be used with ``LearnModel`` is not limited to data generated from ``GenModel``. You can analyze various real-world data. First, let's create an instance of the learning model. Here, we only specify the degree ``c_degree = 2`` as a constant of the model, but you can also specify hyperparameters for the prior distribution. .. code-block:: python learn_model = linearregression.LearnModel( c_degree = 2, # degree ) A method for visualizing the posterior distribution of parameters is implemented in ``LearnModel``. If you visualize the posterior distribution at this point, the prior distribution will be displayed since learning from data has not yet been performed. .. code-block:: python learn_model.visualize_posterior() Output: .. image:: ./images/README_LR2.png To update the posterior distribution through learning from data, we use the following method. .. code-block:: python learn_model.update_posterior(x,y) If you visualize the updated posterior distribution, you can see that the density of the posterior distribution has moved closer to the true parameters used to generate ``x`` and ``y``. .. code-block:: python learn_model.visualize_posterior() Output: .. image:: ./images/README_LR3.png To make decisions such as parameter estimation and prediction of new data based on the learned model, we proceed as follows. For parameter estimation, we use the ``estimate_params`` method. By specifying the ``loss`` option as ``squared``, you can obtain an estimate that minimizes the Bayes risk function based on the squared error loss function. The resulting value is the expected value of the posterior distribution. .. code-block:: python learn_model.estimate_params(loss="squared",dict_out=True) Output: | {'theta_vec': array([0.99846525, 0.96263024]), 'tau': 6.9036925167513195} If you specify the ``loss`` option as ``abs``, you can obtain an estimate that minimizes the Bayes risk function based on the absolute error loss function. The resulting value is the median of the posterior distribution, which is why the estimated value of ``tau`` differs from the previous one. .. code-block:: python learn_model.estimate_params(loss="abs",dict_out=True) Output: | {'theta_vec': array([0.99846525, 0.96263024]), 'tau': 6.858623148933392} To predict new data, we first use the following method to calculate the predictive distribution for new explanatory variables. .. code-block:: python learn_model.calc_pred_dist(x_test) Next, we use the ``make_prediction`` method to obtain predicted values. Similar to parameter estimation, you can specify the loss function using the ``loss`` option. (In this example, the same predicted values will be returned whether you assume squared error loss or absolute error loss since the posterior predictive distribution is symmetrical.) .. code-block:: python y_pred = learn_model.make_prediction(loss="squared") Let's calculate the mean squared error. .. code-block:: python mse = np.sum((y_test - y_pred)**2) / len(y_test) print(f"MSE: {mse}") Output: | MSE: 0.09020880284291456 Taking into account that the precision (inverse of variance) of the noise term used for data generation was 10, we can see that the predictions are achieved with sufficient accuracy. Sampling from Posterior Distribution Using ``GenModel`` ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ``GenModel`` can also be used to sample parameters from the posterior distribution learned by ``LearnModel``, or to sample new data from the posterior predictive distribution. First, the hyperparameters of the posterior distribution learned by ``LearnModel`` can be obtained as follows. .. code-block:: python hn_params = learn_model.get_hn_params() print(hn_params) Output: | {'hn_mu_vec': array([0.99846525, 0.96263024]), 'hn_lambda_mat': array([[ 99.87503339, 5.96145913], [ 5.96145913, 101. ]]), 'hn_alpha': 51.0, 'hn_beta': 7.387351026461872} By passing these to ``GenModel``, you can sample parameters from the posterior distribution. We create a new ``GenModel`` instance for parameter sampling and pass the hyperparameters through the ``set_h_params`` method. (In the example below, we are unpacking the values of the dictionary ``hn_params`` using ``*`` for ``hn_params.values()``. This is a Python feature, not a BayesML functionality.) .. code-block:: python posterior_gen_model = linearregression.GenModel( c_degree = 2, # degree ) posterior_gen_model.set_h_params(*hn_params.values()) We use the ``gen_params`` method to generate parameters and the ``get_params`` method to retrieve the generated parameters. If you want to perform multiple samplings, please repeat the following in a ``for`` loop. .. code-block:: python posterior_gen_model.gen_params() print(posterior_gen_model.get_params()) Output: | {'theta_vec': array([1.00935782, 0.93804208]), 'tau': 5.50775630793475} To sample new data from the posterior predictive distribution, we generate data after sampling parameters. When we generated the synthetic data, we did not provide explanatory variables as arguments to ``gen_sample`` (see [here](#synthetic-data-generation-with-genmodel)), but you can also specify them explicitly as follows. .. code-block:: python posterior_gen_model.gen_params() _,y_new = posterior_gen_model.gen_sample(x=x_test[:10]) print(f"y_new: {y_new}") Output: | y_new: [-0.49532975 2.03473075 1.13758759 -0.46735058 -0.71902336 -0.09288005 0.89463227 2.07886012 2.81211771 1.60020635] Package list ------------ The following packages are currently available. In this library, a probabilistic data generative model, prior distribution, posterior distribution (or approximate posterior distribution), and predictive distribution (or approximate predictive distribution) are collectively called a model. * :doc:`bayesml` * :doc:`bayesml.autoregressive` * :doc:`bayesml.bernoulli` * :doc:`bayesml.categorical` * :doc:`bayesml.contexttree` * :doc:`bayesml.exponential` * :doc:`bayesml.gaussianmixture` * :doc:`bayesml.hiddenmarkovnormal` * :doc:`bayesml.linearregression` * :doc:`bayesml.sparselinearregression` * :doc:`bayesml.logisticregression` * :doc:`bayesml.linearregressionmixture` * :doc:`bayesml.metatree` * :doc:`bayesml.multivariate_normal` * :doc:`bayesml.normal` * :doc:`bayesml.poisson` In the future, we will add packages to deal with more complicated hierarchical models. Citation -------- When you use BayesML for your academic work, please provide the following bibliographic reference. Plain text .. code-block:: Y. Nakahara, N. Ichijo, K. Shimada, Y. Iikubo, S. Saito, K. Kazama, T. Matsushima, BayesML Developers, ``BayesML,'' Python package version 0.5.1, 2026. [Online] https://github.com/bayesml/BayesML BibTeX .. code-block:: bibtex @misc{bayesml, author = {Nakahara, Yuta and Ichijo, Naoki and Shimada, Koshi and Iikubo, Yuji and Saito, Shota and Kazama, Koki and Matsushima, Toshiyasu and {BayesML Developers}}, title = {{BayesML}}, howpublished = {Python package version 0.5.1}, note = {\url{https://github.com/bayesml/BayesML}}, year = {2026} } Star Us on GitHub ----------------- .. include:: _star.rst Contents -------- .. toctree:: :maxdepth: 1 bayesml examples developers Indices ======= * :ref:`genindex` * :ref:`modindex` * :ref:`search`