https://github.com/raphaelsty/abayes
Autoregressive Bayesian linear model
https://github.com/raphaelsty/abayes
autoregressive bayes bayesian bayesian-inference linear-regression machine-learning online
Last synced: 7 months ago
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Autoregressive Bayesian linear model
- Host: GitHub
- URL: https://github.com/raphaelsty/abayes
- Owner: raphaelsty
- License: mit
- Created: 2020-09-08T17:07:06.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2020-09-10T01:15:52.000Z (over 5 years ago)
- Last Synced: 2025-10-08T19:23:54.383Z (7 months ago)
- Topics: autoregressive, bayes, bayesian, bayesian-inference, linear-regression, machine-learning, online
- Language: Python
- Homepage:
- Size: 177 KB
- Stars: 21
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
Online autoregressive bayesian linear regression
This minimalist tool is dedicated to the bayesian linear regression implemented by **[Max Halford](https://github.com/MaxHalford)** in his blog post **[Bayesian linear regression for practitioners](https://maxhalford.github.io/blog/bayesian-linear-regression/)**. I slightly modified the code to obtain an autoregressive version of the original model.
**For the time being, the model will systematically assume that the residues follow a normal distribution. It will be necessary to wait for the next updates of the library to include new distributions.**
Bayesian linear regression has many advantages. It allows to measure the **uncertainty** of the model and to build **confidence intervals**. The simplicity of this model and its ability to answer "I don't know" makes it practical and adapted to many **concrete problems**.
Its online autoregressive counterpart is a nice tool for the toolbox of programmers, hackers and practitioners.
#### Installation:
```
pip install git+https://github.com/raphaelsty/abayes
```
#### Example:
Let's try to predict my ice cream consumption. I have created a dummy dataset where I record my ice cream consumption for each month of the year and for 3 years.
```python3
from abayes import dataset
df = dataset.LoadIceCream()
df.head()
```
We initialise the auto-regressive model with a periodicity of 24. We will use the years n-1 and n-2 to predict my ice consumption in year n.
```python3
from abayes import linear
model = linear.AbayesLr(
p = 24,
alpha = 0.3,
beta = 1.,
)
model.learn(df['y'].values)
forecast = model.forecast(12)
lower_bound, upper_bound = model.forecast_interval(12, alpha = 0.90)
```
plot
```python3
import matplotlib.pyplot as plt
%config InlineBackend.figure_format = 'retina'
range_train = range(len(df['y']))
range_forecast = range(len(df['y']), len(df['y']) + len(forecast))
fig, ax = plt.subplots(figsize=(15, 6))
ax.plot(range_train, df['y'], color='deepskyblue', label ='train')
ax.plot(range_forecast, forecast, color='red', linestyle='--', label ='forecast')
ax.fill_between(
x = range_forecast,
y1 = lower_bound,
y2 = upper_bound,
alpha = 0.1,
color = 'red',
label = 'confidence'
)
plt.xticks(
range(len(df['y']) + len(forecast)),
df['time'].tolist() + [f"2020/{'%02d' % i}" for i in range(1, 13)],
rotation='vertical'
)
ax.set_title('Quantity of ice cream')
ax.set_xlabel('Period')
ax.set_ylabel('Quantity')
ax.legend()
plt.show()
```
**The model can also learn by mini-batch.**
```python3
import numpy as np
from abayes import linear
model = linear.AbayesLr(
p = 24,
alpha = 0.3,
beta = 1,
)
for time, y in enumerate(df['y'].values):
# Online autoregressive model needs to store enough data to make a prediction (> period).
if time > 24:
lower_bound, upper_bound = model.forecast_interval(1, alpha = 0.9)
y_pred = model.forecast(1)
print('\n')
print(f'time: {time}')
print(f'\t y: {y}')
print(f'\t Most likely value: {y_pred[0]:6f}')
print(f'\t Confidence interval: [{lower_bound[0]:6f} ; {upper_bound[0]:6f}]')
model.learn(np.array([y]))
```
```
time: 25
y: 46
Most likely value: 16.066921
Confidence interval: [-231.651593 ; 263.785435]
time: 26
y: 27
Most likely value: 50.016886
Confidence interval: [-179.828306 ; 279.862078]
time: 27
y: 30
Most likely value: 16.442225
Confidence interval: [-214.224545 ; 247.108994]
time: 28
y: 101
Most likely value: 21.766659
Confidence interval: [-205.891318 ; 249.424635]
time: 29
y: 135
Most likely value: 106.731389
Confidence interval: [-124.906692 ; 338.369470]
time: 30
y: 250
Most likely value: 143.074596
Confidence interval: [-75.066693 ; 361.215885]
time: 31
y: 210
Most likely value: 231.908803
Confidence interval: [38.905614 ; 424.911993]
time: 32
y: 127
Most likely value: 165.226916
Confidence interval: [-17.324602 ; 347.778435]
time: 33
y: 50
Most likely value: 78.684325
Confidence interval: [-75.679416 ; 233.048066]
time: 34
y: 14
Most likely value: -14.522046
Confidence interval: [-157.498855 ; 128.454763]
time: 35
y: 56
Most likely value: 52.063575
Confidence interval: [-50.776582 ; 154.903732]
```
#### License
This project is free and open-source software licensed under the MIT license.