Implementation:Online ml River Stats Var

Knowledge Sources	Online_ml_River
Domains	Online_Learning, Statistics
Last Updated	2026-02-08 16:00 GMT

Overview

Var computes the running variance of a data stream using Welford's algorithm.

Description

This statistic calculates variance incrementally as data arrives, maintaining numerical stability through Welford's method. Variance measures the spread of data around its mean. The implementation supports weighted observations, includes a revert method for rolling windows, and provides batch update capabilities. The ddof parameter controls degrees of freedom correction, with ddof=1 giving the sample variance (unbiased estimator).

Usage

Use Var when you need to measure the variability or spread of streaming data. Common applications include monitoring data quality, detecting anomalies, statistical process control, understanding feature distributions, normalization (standardization requires mean and standard deviation), and as a building block for computing standard deviation, standard error, and other higher-order statistics.

Code Reference

Source Location

• Repository: Online_ml_River
• File: river/stats/var.py

Signature

class Var(stats.base.Univariate):
    def __init__(self, ddof=1) -> None:
        self.ddof = ddof
        self.mean = stats.Mean()
        self._S = 0

Import

from river import stats

I/O Contract

Inputs

Name	Type	Required	Description
x	numbers.Number	Yes	Value to update the statistic with
w	float	No	Weight for the observation (default: 1.0)
ddof	int	Yes (init)	Delta Degrees of Freedom (default: 1 for sample variance)

Outputs

Name	Type	Description
get()	float	Current variance (0.0 if n <= ddof)

Usage Examples

from river import stats

# Basic running variance
X = [3, 5, 4, 7, 10, 12]
var = stats.Var()

for x in X:
    var.update(x)
    print(f"Value: {x}, Variance: {var.get():.6f}")

# Output:
# Value: 3, Variance: 0.000000
# Value: 5, Variance: 2.000000
# Value: 4, Variance: 1.000000
# Value: 7, Variance: 2.916666
# Value: 10, Variance: 7.700000
# Value: 12, Variance: 12.566666

# Rolling variance
from river import utils

X = [1, 4, 2, -4, -8, 0]
rvar = utils.Rolling(stats.Var(ddof=1), window_size=3)

for x in X:
    rvar.update(x)
    print(f"Value: {x}, Rolling Var: {rvar.get():.6f}")

# Output:
# Value: 1, Rolling Var: 0.000000
# Value: 4, Rolling Var: 4.500000
# Value: 2, Rolling Var: 2.333333
# Value: -4, Rolling Var: 17.333333
# Value: -8, Rolling Var: 25.333333
# Value: 0, Rolling Var: 16.000000

# Computing standard deviation from variance
import math

variance = stats.Var()
data = [2, 4, 4, 4, 5, 5, 7, 9]

for x in data:
    variance.update(x)

print(f"Variance: {variance.get():.4f}")
print(f"Std Dev: {math.sqrt(variance.get()):.4f}")

# Monitoring data variability
quality_var = stats.Var()

# Normal operation
for x in [10.1, 10.2, 9.9, 10.0, 10.1]:
    quality_var.update(x)

print(f"Normal operation variance: {quality_var.get():.4f}")

# With anomaly
quality_var.update(15.0)
print(f"With anomaly variance: {quality_var.get():.4f}")

# Weighted variance
weighted_var = stats.Var()
weighted_var.update(10, w=1.0)
weighted_var.update(20, w=2.0)
weighted_var.update(30, w=3.0)
print(f"Weighted variance: {weighted_var.get():.4f}")

# Population vs sample variance
pop_var = stats.Var(ddof=0)  # Population variance
sample_var = stats.Var(ddof=1)  # Sample variance

data = [1, 2, 3, 4, 5]
for x in data:
    pop_var.update(x)
    sample_var.update(x)

print(f"Population variance: {pop_var.get():.4f}")
print(f"Sample variance: {sample_var.get():.4f}")

Related Pages

• Environment:Online_ml_River_Python_Runtime_Environment