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ProbFlow is a Python package for building probabilistic Bayesian models with TensorFlow or PyTorch, performing stochastic variational inference with those models, and evaluating the models’ inferences. It provides both high-level Modules for building Bayesian neural networks, as well as low-level Parameters and Distributions for constructing custom Bayesian models.

It’s very much still a work in progress.

Getting Started

ProbFlow allows you to quickly and painlessly less painfully build, fit, and evaluate custom Bayesian models (or ready-made ones!) which run on top of either TensorFlow and TensorFlow Probability or PyTorch.

With ProbFlow, the core building blocks of a Bayesian model are parameters and probability distributions (and, of course, the input data). Parameters define how the independent variables (the features) predict the probability distribution of the dependent variables (the target).

For example, a simple Bayesian linear regression

\[y \sim \text{Normal}(w x + b, \sigma)\]

can be built by creating a ProbFlow Model. This is just a class which inherits Model (or ContinuousModel or CategoricalModel depending on the target type). The __init__ method sets up the parameters, and the __call__ method performs a forward pass of the model, returning the predicted probability distribution of the target:

import probflow as pf
import tensorflow as tf

class LinearRegression(pf.ContinuousModel):

    def __init__(self):
        self.weight = pf.Parameter(name='weight')
        self.bias = pf.Parameter(name='bias')
        self.std = pf.ScaleParameter(name='sigma')

    def __call__(self, x):
        return pf.Normal(x*self.weight()+self.bias(), self.std())

model = LinearRegression()

Then, the model can be fit using stochastic variational inference, in one line:

# x and y are Numpy arrays or pandas DataFrame/Series, y)

You can generate predictions for new data:

# x_test is a Numpy array or pandas DataFrame
>>> model.predict(x_test)

Compute probabilistic predictions for new data, with 95% confidence intervals:

model.pred_dist_plot(x_test, ci=0.95)

Evaluate your model’s performance using various metrics:

>>> model.metric('mse', x_test, y_test)

Inspect the posterior distributions of your fit model’s parameters, with 95% confidence intervals:


Investigate how well your model is capturing uncertainty by examining how accurate its predictive intervals are:

>>> model.pred_dist_coverage(ci=0.95)

and diagnose where your model is having problems capturing uncertainty:


ProbFlow also provides more complex modules, such as those required for building Bayesian neural networks. Also, you can mix ProbFlow with TensorFlow (or PyTorch!) code. For example, even a somewhat complex multi-layer Bayesian neural network like this:


Can be built and fit with ProbFlow in only a few lines:

class DensityNetwork(pf.ContinuousModel):

    def __init__(self, units, head_units):
        self.core = pf.DenseNetwork(units)
        self.mean = pf.DenseNetwork(head_units)
        self.std  = pf.DenseNetwork(head_units)

    def __call__(self, x):
        z = tf.nn.relu(self.core(x))
        return pf.Normal(self.mean(z), tf.exp(self.std(z)))

# Create the model
model = DensityNetwork([x.shape[1], 256, 128], [128, 64, 32, 1])

# Fit it!, y)

For convenience, ProbFlow also includes several pre-built models for standard tasks (such as linear regressions, logistic regressions, and multi-layer dense neural networks). For example, the above linear regression example could have been done with much less work by using ProbFlow’s ready-made LinearRegression model:

model = pf.LinearRegression(x.shape[1]), y)

And a multi-layer Bayesian neural net can be made easily using ProbFlow’s ready-made DenseRegression model:

model = pf.DenseRegression([x.shape[1], 128, 64, 1]), y)

Using parameters and distributions as simple building blocks, ProbFlow allows for the painless creation of more complicated Bayesian models like generalized linear models, deep time-to-event models, neural matrix factorization models, and Gaussian mixture models. You can even mix probabilistic and non-probabilistic models! Take a look at the Examples and the User Guide for more!


If you already have your desired backend installed (i.e. Tensorflow/TFP or PyTorch), then you can just do:

pip install probflow

Or, to install both ProbFlow and a specific backend,

pip install probflow[tensorflow]


Post bug reports, feature requests, and tutorial requests in GitHub issues.


Pull requests are totally welcome! Any contribution would be appreciated, from things as minor as pointing out typos to things as major as writing new applications and distributions. For info on how to set up a development environment and run the tests, see the Developer Guide.

Why the name, ProbFlow?

Because it’s a package for probabilistic modeling, and it was built on TensorFlow. ¯\_(ツ)_/¯