precise 0.3.13

Online covariance and precision estimation

precise

A collection of autonomous incremental estimators for covariance, precision, correlation and associated quantities.

TLDR: "Just a pile of functions that forecast covariance in online fashion"

The running_empirical_covariance colab notebook illustrates the style. To see all the other online methods of covariance estimation supplied here, run the cov skaters manifest notebook. Or to look at Elo ratings, run the elo_ratings_and_urls.

Install

pip install precise 

Covariance skaters

Similar in style to skaters used in the timemachines package, this package may be thought of as a collection of covariance prediction functions taking one vector at a time, and also the prior state, and spitting out a prediction mean vector x, a prediction covariance x_cov, and a posterior state whose interpretation is the responsibility of the skater, not the caller.

This mildly unusual convention requires the caller to maintain state from one call to the next:

from precise.skatertools.syntheticdata.miscellaneous import create_correlated_dataset
from precise.skaters.covariance.runemmp import run_emp_pcov_d0 # <-- Running empirical population covariance
from pprint import pprint

if __name__=='__main__':
    ys = create_correlated_dataset(n=500)
    s = {}
    for y in ys:
        x, x_cov, s = run_emp_pcov_d0(s=s, y=y)
    pprint(x_cov)

See /examples_basic_usage.

See the timemachines faq for justification of this style.

Skater Elo ratings

As noted, see the elo_ratings_and_urls.

Browsing for skaters

You can hunt for skaters other than run_emp_pcov_d0 in precise/skaters/covariance. There are some location utilities in precise/whereami.

Examples of interpretation:

Skater name	Location	Meaning
buf_huber_pcov_d1_a1_b2_n50	skaters/covariance/bufhuber	Applies an approach that exploits Huber pseudo-means to a buffer of data of length 50 in need of differencing once, with generalized Huber loss parameters a=1, b=2.
buf_sk_ld_pcov_d0_n100	skaters/covariance/bufsk	Applies sk-learn's implementation of Ledoit-Wolf to stationary buffered data of length 100
ewa_pm_emp_scov_r01	skaters/covariance/ewapartial	Performs an incremental, recency-weighted sample covariance estimate that exploits partial moments. Uses a memory parameter r=0.01

Reading skater names

Broad calculation style categories

Shorthand	Interpretation	Incremental ?
buf	Performs classical batch calculation on a fixed window of data each time	No
win	Performs incremental fixed window calculation.	Yes
run	Running calculation weighing all observations equally	Yes
ewa	Running calculation weighing recent observations more	Yes

Methodology hints (can be combined)

Shorthand	Inspiration
emp	"Empirical" (not shrunk or augmented)
lz	Le-Zhong variable-by-variable updating
lw	Ledoit-Wolf
pm	Partial moments
huber	Generalized Huber pseudo-mean
oas	Oracle approximating shrinkage.
gl	Graphical Lasso
mcd	Minimum covariance determinant

Intended main target (more than one may be produced in the state)

Shorthand	Intent
scov	Sample covariance
pcov	Population covariance
spre	Inverse of sample covariance
ppre	Inverse of population covariance

Differencing hints:

Shorthand	Intent
d0	For use on stationary, ideally IID data
d1	For use on data that is iid after taking one difference

Portfolio & mixture of experts

See the portfolio directories in skaters. Work in progress.

Stand-alone utilities

1. The covariance/statefunctions are illustrated by the example running_oas_covariance.
2. State covariatnce/statemutations do things like ensuring both covariance and precision matrices exist in the state. Or for instance: s = both_cov(s) ensures both sample and population covariances are present.
3. Some /covariance/datascatterfunctions
4. The /covariance/datacovfunctions take data and produce covariance functions.
5. The /covariance/covfunctions manipulate 2d cov arrays.

Miscellaneous

• Here is some related, and potentially related, literature.
• This is a piece of the microprediction project, should you ever care to cite the same. The uses include mixtures of experts models for time-series analysis, buried in timemachines somewhere.
• If you just want univariate calculations, and don't want numpy as a dependency, there is momentum. However if you want univariate forecasts of the variance of something, as distinct from mere online calculations of the same, I would suggest checking the time-series elo ratings and the "special" category in particular.
• The name of this package refers to precision matrices, not numerical precision. This isn't a source of high precision covariance calculations per se. The intent is more in forecasting future realized covariance. Perhaps I'll include some more numerically stable methods from this survey to make the name more fitting. Pull requests are welcome!
• The intent is that methods are parameter free. However some not-quite autonomous methods admit a few parameters (the factories). A few might even use just one additional scalar parameter r with a space-filling curve convention - somewhat akin to the tuning of skaters explained here in the timemachines package).