This is a PyTorch implementation of planar and radial flows as described in Variational Inference with Normalizing Flows (authors: Danilo Jimenez Rezende, Shakir Mohamed)
Parameters are trained with plain MLE rather than variational inference. This is made possible by explicitly inverting the flows using closed-form inverse functions. To that end, h(x)=tanh(x) is replaced with h(x)=1/(1+|x|) with no change to the paper's reparametrization trick.
| Radial flows |
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| Radial flows |
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| Planar flows |
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Invertibility makes it easy to compute the likelihood of arbitrary data points. Caveat: vanilla radial and planar flows are transformations from Rd to Rd (d: input dimension) that don't scale well to high dimensions. See Sylvester Normalizing Flows to overcome this limitation.
| dataset | IForest precision@k | Anoflows precision@k | dimensions |
|---|---|---|---|
| banknote | 86.3% | 99.4% | 4 |
| forest covtype | 5.1% | 1.3% | 10 (continuous features only) |
| gamma telescope | 58.9% | 59.2% | 10 |
| mammographic | 75.6% | 76.7% | 4 |
| occupancy | 90.1% | 84.9% | 5 |
| shuttle | 63.3% | 70.5% | 8 |
| wine quality | 17.1% | 11.6% | 11 |
| avg | 56.63% | 57.66% |
HPO disabled.
Look at the YAML files in benchmarks/ for details about datasets and benchmark setup.
Run cd benchmarks && python3 eval.py <dataset>.yml to reproduce the benchmarks.
- 15 planar flows: 447,201 rows / second
- 15 radial flows: 295,458 rows / second
- Isolation Forest: 44,735 rows / second
- python >= 3.5 (tested: 3.6.7)
- torch >= 1.0 (tested: 1.0.1.post2)
- numpy >= 1.14 (tested: 1.16.2)
- tqdm >= 4.26, not mandatory but recommended (tested: 4.31.1)
- scikit-learn >= 0.20.3, only for benchmarks (tested: 0.20.3)
- pandas >= 0.23, only for benchmarks (tested: 0.24.1)
python3 setup.py install --user
or
sudo python3 setup.py install
If that went well, open up a Python shell and verify the install:
from anoflows.hpo import find_best_flows