EwaPrecision¶

Exponentially weighted precision (inverse covariance) matrix.

The recency-weighted analogue of EmpiricalPrecision. It maintains the inverse of an exponentially weighted second-moment matrix online via a forgetting-factor Sherman-Morrison update (the recursive-least-squares trick), and applies the mean centering on read. It is genuinely online: the per-step cost is O(d^2) and the matrix is never explicitly inverted.

When to use it. Several methods need the precision matrix rather than the covariance: the Mahalanobis distance (anomaly detection), the Gaussian log-likelihood, and the weights of a Gaussian graphical model. Use this when those quantities must track a non-stationary stream, where inverting a stale covariance would lag. Like EmpiricalPrecision, the result is not guaranteed identical to inverting the matching covariance (there is a decaying identity prior), but the difference shrinks as observations accumulate. Requires 0 < fading_factor < 1.

Parameters¶

• fading_factor

  Type → float

  Default → 0.5

  Recency weight of the most recent observation. The effective memory is roughly 1 / fading_factor observations.

Attributes¶

• matrix

Examples¶

from river import covariance, datasets

tickers = ["AAPL", "JPM", "XOM"]
prec = covariance.EwaPrecision(fading_factor=0.02)
for x, _ in datasets.SP500Stocks():
    prec.update({t: x[t] for t in tickers})
prec

       AAPL     JPM      XOM
AAPL    0.676   -0.241   -0.169
 JPM   -0.241    1.105   -0.498
 XOM   -0.169   -0.498    0.934

Up to the decaying prior, this approximates the inverse of the matching EwaCovariance:

import numpy as np
cov = covariance.EwaCovariance(fading_factor=0.02)
for x, _ in datasets.SP500Stocks():
    cov.update({t: x[t] for t in tickers})
S = np.array([[cov[i, j] for j in tickers] for i in tickers])
P = np.array([[prec[i, j] for j in tickers] for i in tickers])
bool(np.allclose(P @ S, np.eye(3), atol=1e-6))

True

Methods¶

References¶

• Online Estimation of the Inverse Covariance Matrix - Markus Thill

• Recursive least squares filter