https://github.com/florents-tselai/vasco
vasco: Discover hidden patterns in your Postgres data
https://github.com/florents-tselai/vasco
correlation-coefficient maximal-information-coefficient postgres postgresql-extension similarity vector-similarity vectors
Last synced: 8 months ago
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vasco: Discover hidden patterns in your Postgres data
- Host: GitHub
- URL: https://github.com/florents-tselai/vasco
- Owner: Florents-Tselai
- License: gpl-3.0
- Created: 2023-08-14T08:21:04.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-07-08T07:18:45.000Z (over 1 year ago)
- Last Synced: 2024-07-08T09:21:59.428Z (over 1 year ago)
- Topics: correlation-coefficient, maximal-information-coefficient, postgres, postgresql-extension, similarity, vector-similarity, vectors
- Language: C
- Homepage:
- Size: 5.28 MB
- Stars: 26
- Watchers: 5
- Forks: 2
- Open Issues: 9
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# vasco: Maximal Information Coefficient (MIC) Extension for Postgres
[](https://github.com/Florents-Tselai/vasco/actions/workflows/build.yml)
**vasco** is a Postgres extension that helps you discover hidden
correlations in your data.
It is based on the [MIC](https://en.wikipedia.org/wiki/Maximal_information_coefficient) and
the [MINE family of statistics](http://www.exploredata.net).
Consider the following table for example:
```tsql
CREATE TABLE vasco_data
AS (SELECT RANDOM() AS rand_x,
RANDOM() AS rand_y,
x AS x,
x AS ident,
4 * pow(x, 3) + pow(x, 2) - 4 * x AS cubic,
COS(12 * PI() + x * (1 + x)) AS periodic
FROM GENERATE_SERIES(0, 1, 0.001) x);
```
With vasco you can compute the MIC score between any pair of columns.
Strongly-correlated variables will get a score closer to 1.
```tsql
SELECT MIC(x, ident),
MIC(x, rand_x),
MIC(x, cubic),
MIC(x, periodic)
FROM vasco_data;
```
```
mic | mic | mic | mic | mic
-----+-------------------+-------------------+-----+-----
1 | 0.150372685226294 | 0.129610387112352 | 1 | 1
(1 row)
```
To get a convenient correlation matrix between all column pairs, you can
```tsql
SELECT vasco_corr_matrix('vasco_data', 'mic_vasco_data')
```
This will create a `mic_vasco_data` that looks like this.
```tsql
col | cubic | ident | periodic | rand_x | rand_y | x
----------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------
cubic | 1 | 0.999999280092894 | 0.999999280092894 | 0.128758229244777 | 0.133036207766184 | 0.999999280092894
ident | 0.999999280092894 | 1 | 1 | 0.150372685226294 | 0.141592810546451 | 1
periodic | 0.999999280092894 | 1 | 1 | 0.150233087894353 | 0.140555864286285 | 1
rand_x | 0.128758229244777 | 0.150372685226294 | 0.150233087894353 | 1 | 0.129610387112352 | 0.150372685226294
rand_y | 0.133036207766184 | 0.141592810546451 | 0.140555864286285 | 0.129610387112352 | 1 | 0.141592810546451
x | 0.999999280092894 | 1 | 1 | 0.150372685226294 | 0.141592810546451 | 1
(6 rows)
```
## Usage
Let's start by populating Postgres with some stock price data for the S&P 500.
```shell
psql -f demo/stocks.sql postgres
```
A `v_sample` view that contains daily closing prices for FAANG and a few other tickers is now available.
We want to explore which of these stock prices are correlated and how strong that correlation is.
### Correlation Pairs
The **Maximal Information Coefficient (MIC)** measures how strong is the
association between a pair of variables (columns).
For our example, we can compute this by using the `mic(x,y)` aggregate function for each pair of stocks we're interested
in.
Let's pick some arbitrary pairs and compute the MIC for them.
```sql
select mic(aapl, nflx) as aapl_nfxl,
mic(aapl, googl) as aapl_googl,
mic(aapl, ba) as aapl_ba,
mic(ba, pg) as ba_pg,
mic(pg, gm) as pg_gm
from v_sample
```
| aapl_nfxl | aapl_googl | aapl_ba | ba_pg | pg_gm |
|:----------|:-----------|:--------|:------|:------|
| 0.51 | 0.80 | 0.55 | 0.48 | 0.32 |
We can see that Apple's stock price is strongly correlated with Google's,
while with Netflix's, not so much.
The correlation strength between Procter & Gamble (PG) is not really associated
with Boeing's (BA) price.
### Exploring a table
To exhaustively explore the correlations between all stock pairs in a relation we can do it in one go:
```sql
select vasco_corr_matrix('v_faang', 'mic_v_faang')
```
This will compute the MIC for all column pairs in `v_faang` and store
the correlation matrix as a new table `mic_v_faang`.
| col | aapl | meta | amzn | googl | nflx |
|-------|------|------|------|-------|------|
| aapl | 1.00 | 0.63 | 0.51 | 0.81 | 0.52 |
| meta | 0.63 | 1.00 | 0.72 | 0.64 | 0.80 |
| amzn | 0.51 | 0.72 | 1.00 | 0.58 | 0.80 |
| googl | 0.81 | 0.64 | 0.58 | 1.00 | 0.47 |
| nflx | 0.52 | 0.80 | 0.80 | 0.47 | 1.00 |
Here's a plot of this correlation matrix as a heatmap
### Additional Metrics: Exploring the association
No algorithm can magically detect the function of the relationship
between two variables, but MINE statistics can shed some light into the
nature of that relationship.
| Metric | SQL Function | Interpretation |
|-------------------------------------------------|----------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------|
| Maximum Asymmetry Score (MAS) | `SELECT mas(X, Y)` | measures how much the relationship deviates from monotonicity |
| Maximum Edge Value (MEV) | `SELECT mev(X, Y)` | measures the degree to which the dataset appears to be sampled from a continuous function. |
| Minimum Cell Number (MCN) | `SELECT mcn(X, Y`) | measures the complexity of the association. |
| Minimum Cell Number General (MCNG) | `SELECT mcn_general(X, Y)` | returns the MCN with `eps = 1 - MIC` |
| Total Information Coefficient (TIC) | `SELECT tic(X, Y)` | returns the total information coefficient |
| Generalized Mean Information Coefficient (GMIC) | `SELECT gmic(X, Y)` | generalization of MIC, which incorporates a tuning parameter that can be used to modify the complexity of the association favored by the measure [Luedtke2013] |
### Choosing an estimator
There have been proposed a number of algorithms to estimate the MIC.
Currently, in **vasco**, you can choose between `ApproxMIC` from
Reshef2011 or `MIC_e` from Reshef2016 .
``` sql
SET vasco.mic_estimator = ApproxMIC
SET vasco.mic_estimator = MIC_e
```
### Configuration parameters
The following MINE parameters can be set via GUC.
- `vasco.mine_c`
- `vasco.mine_alpha`
- `vasco.mic_estimator`
- `vasco.mine_mcn_eps`
- `vasco.mine_tic_norm`
- `vasco.mine_gmic_p`
## Installation
``` bash
cd /tmp
git clone git@github.com:Florents-Tselai/vasco.git
cd vasco
make all
make install # may need sudo
```
Then in a Postgres session run
``` tsql
CREATE EXTENSION vasco
```
## Next Steps
- Try out ChiMIC [Chen2013] and BackMIC
- Currently `M` is re-computed every time a function score is called.
That\'s a huge waste of resources. Caching `M` or sharing it between
runs should be the first optimization to be done.
- A potential next step would be continuously updating the CM as
columns are updated (think a trigger or bgw process).
- Make an extension for SQLite and DuckDB as well
- Build convenience functions to create variable pairs and explore
tables in one pass.
## Thanks
For MINE statistics, **vasco** currently uses the implementation
provided by Albanese2013 via the [minepy](https://github.com/minepy/minepy) package.
Alternative implementations are coming up.
## References
- **Albanese2013**: Albanese, D., Filosi, M., Visintainer, R., Riccadonna, S., Jurman, G., & Furlanello, C. (2013). Minerva and minepy: a C engine for the MINE suite and its R, Python and MATLAB wrappers. Bioinformatics, 29(3), 407-408.
- **Albanese2018**: Davide Albanese, Samantha Riccadonna, Claudio Donati, Pietro Franceschi; A practical tool for Maximal Information Coefficient analysis, GigaScience, giy032, [https://doi.org/10.1093/gigascience/giy032](https://doi.org/10.1093/gigascience/giy032)
- **Cao2021**: Cao, D., Chen, Y., Chen, J., Zhang, H., & Yuan, Z. (2021). An improved algorithm for the maximal information coefficient and its application. Royal Society open science, 8(2), 201424. [PDF](https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.201424) [GitHub](https://github.com/Caodan82/BackMIC)
- **Chen2013**: Chen Y, Zeng Y, Luo F, Yuan Z. 2016 A new algorithm to optimize maximal information coefficient. PLoS ONE 11, e0157567. [doi:10.1371/journal.pone.0157567](https://doi.org/10.1371/journal.pone.0157567) [GitHub](https://github.com/chenyuan0510/Chi-MIC)
- **Ge2016**: Ge, R., Zhou, M., Luo, Y. et al. McTwo: a two-step feature selection algorithm based on maximal information coefficient. BMC Bioinformatics 17, 142 (2016). [https://doi.org/10.1186/s12859-016-0990-0](https://doi.org/10.1186/s12859-016-0990-0)
- **Luedtke2013**: Luedtke A., Tran L. The Generalized Mean Information Coefficient. [https://doi.org/10.48550/arXiv.1308.5712](https://doi.org/10.48550/arXiv.1308.5712)
- **Matejka2017**: J. Matejka and G. Fitzmaurice. Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing. ACM SIGCHI Conference on Human Factors in Computing Systems, 2017.
- **Reshef2011**: Reshef, D. N., Reshef, Y. A., Finucane, H. K., Grossman, S. R., McVean, G., Turnbaugh, P. J., ... & Sabeti, P. C. (2011). Detecting novel associations in large data sets. Science, 334(6062), 1518-1524.
- **Reshef2016**: Yakir A. Reshef, David N. Reshef, Hilary K. Finucane, Pardis C. Sabeti, and Michael Mitzenmacher. Measuring Dependence Powerfully and Equitably. Journal of Machine Learning Research, 2016. [PDF](https://jmlr.csail.mit.edu/papers/volume17/15-308/15-308.pdf)
- **Shao2021**: Shao, F. & Liu, H. (2021). The Theoretical and Experimental Analysis of the Maximal Information Coefficient Approximate Algorithm. Journal of Systems Science and Information, 9(1), 95-104. [https://doi.org/10.21078/JSSI-2021-095-10](https://doi.org/10.21078/JSSI-2021-095-10)
- **Xu2016**: Xu, Z., Xuan, J., Liu, J., & Cui, X. (2016, March). MICHAC: Defect prediction via feature selection based on maximal information coefficient with hierarchical agglomerative clustering. In 2016 IEEE 23rd International Conference on Software Analysis, Evolution, and Reengineering (SANER) (Vol. 1, pp. 370-381). IEEE. [http://cstar.whu.edu.cn/paper/saner_16.pdf](http://cstar.whu.edu.cn/paper/saner_16.pdf)
- **Zhang2014**: Zhang Y, Jia S, Huang H, Qiu J, Zhou C. 2014 A novel algorithm for the precise calculation of the maximal information coefficient. Sci. Rep.-UK 4, 6662. [doi:10.1038/srep06662](https://doi.org/10.1038/srep06662) [http://lxy.depart.hebust.edu.cn/SGMIC/SGMIC.htm](http://lxy.depart.hebust.edu.cn/SGMIC/SGMIC.htm)