# ProbFlow¶

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.

**Git repository:**http://github.com/brendanhasz/probflow**Documentation:**http://probflow.readthedocs.io**Bug reports:**http://github.com/brendanhasz/probflow/issues

## 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

can be built by creating a ProbFlow Model:

```
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()
```

```
import probflow as pf
import torch
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):
x = torch.tensor(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
model.fit(x, y)
```

You can generate predictions for new data:

```
# x_test is a Numpy array or pandas DataFrame
>>> model.predict(x_test)
[0.983]
```

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)
0.217
```

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

```
model.posterior_plot(ci=0.95)
```

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

```
>>> model.pred_dist_coverage(ci=0.95)
0.903
```

and diagnose *where* your model is having problems capturing uncertainty:

```
model.coverage_by(ci=0.95)
```

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):
x = self.core(x)
return pf.Normal(self.mean(x), tf.exp(self.std(x)))
# Create the model
model = DensityNetwork([x.shape[1], 256, 128], [128, 64, 32, 1])
# Fit it!
model.fit(x, y)
```

```
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):
x = self.core(x)
return pf.Normal(self.mean(x), torch.exp(self.std(x)))
# Create the model
model = DensityNetwork([x.shape[1], 256, 128], [128, 64, 32, 1])
# Fit it!
model.fit(x, 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])
model.fit(x, 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])
model.fit(x, 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. Take a look at the Examples and the User Guide for more!

## Installation¶

Before installing ProbFlow, you’ll first need to install either PyTorch, or TensorFlow 2.0 and TensorFlow Probability.

```
pip install tensorflow==2.0.0 tensorflow-probability==0.8.0
```

```
pip install tensorflow-gpu==2.0.0 tensorflow-probability==0.8.0
```

```
pip install torch
```

Then, you can install ProbFlow itself:

```
pip install probflow
```

## Support¶

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

## Contributing¶

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.

## Why the name, ProbFlow?¶

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