# Why ML models fail in production: Model Drift

Author

Murat Koptur

Published

September 4, 2022

# Introduction

Model drift is a huge problem for machine learning models in production. Model drift reveals itself as a significant increase in error rates for models. To reduce risk, it is essential to track model performance and detect concept drift.

Assume that, given a set of features $$X$$ and a target variable $$y$$, we are trying to predict the target variable. Then, model drift can occur as following:

• If $$P(y|X)$$ conditional distribution changes over time, this is called concept drift;
• if $$P(y)$$ distribution changes over time, this is called label drift;
• if $$P(X)$$ distribution changes over time, this is called data drift.

We’ve said that “changes over time”, this change can occur at different shapes:

1. Sudden drift: Change occurs in a short period of time.
3. Incremental drift: Change occurs incrementally.
4. Reoccurring drifts: Some time after a change occurs, the old distribution comes again. # Methods for detecting model drift

## Kolmogorov-Smirnov (KS) Test & Chi-squared Test

These sets used for compare two statistical distributions. We can apply these tests to compare distributions of training data and post-training data.

## Population Stability Index (PSI)

PSI is a measure for determining how much a population shifted over time.

## Drift Detection Method / Early Drift Detection Method

Drift Detection Method (DDM) uses a binomial distribution to describe the behavior of a random variable that gives the number of classification errors. If the distribution of the samples is stationary, probability of misclassification will decrease as sample size increases. If the error rate of the learning algorithm increases significantly, it suggests changes in the distribution of classes, and thus providing the signal to update the model $$^5$$.

Early Drift Detection Method (EDDM) is a modification of DDM and improves the detection in presence of gradual concept drift $$^5$$.

## Page-Hinkley method

This change detection method works by computing the observed values and their mean up to the current moment $$^6$$.

ADWIN (ADaptive WINdowing) is a popular drift detection method with mathematical guarantees. ADWIN efficiently keeps a variable-length window of recent items; such that it holds that there has no been change in the data distribution. This window is further divided into two sub-windows $$(W_0, W_1)$$ used to determine if a change has happened. ADWIN compares the average of $$W_0$$ and $$W_1$$ to confirm that they correspond to the same distribution. Concept drift is detected if the distribution equality no longer holds. Upon detecting a drift, $$W_0$$ is replaced by $$W_1$$ and a new $$W_0$$ is initialized. ADWIN uses a significance value $$\delta\in(0,1)$$ to determine if the two sub-windows correspond to the same distribution $$^8$$.

# Examples

Let’s generate example data:

• Sudden drift:

n=2000
mu1=3
sigma1=2
mu2=8
sigma2=1

data_sudden = np.random.rand(n) * sigma1 + mu1
data_sudden[1000:] = np.random.randn(1000) * sigma2 + mu2

label = ['Old'] * 2000
label[1000:] = ['New'] * 1000

px.line(data_sudden, title='Sudden Drift', color=label)

n=2000
mu1=3
sigma1=2
mu2=8
sigma2=1

data_gradual = np.random.rand(n) * sigma1 + mu1
data_gradual[1000:1500] = np.random.choice([mu1, mu2], size=500) + np.random.randn(500)
data_gradual[1500:] = np.random.randn(500) * sigma2 + mu2

label = ['Old'] * 2000
label[1000:1500] = ['Switching btw. old & new'] * 500
label[1500:] = ['New'] * 500

px.line(data_gradual, title='Gradual Drift', color=label)
• Incremental drift:

n=2000
mu1=3
sigma1=2
mu2=8
sigma2=1

data_incremental = np.random.rand(n) * sigma1 + mu1
data_incremental[1000:1500] = np.linspace(4, 8, 500) + np.random.randn(500)
data_incremental[1500:] = np.random.randn(500) * sigma2 + mu2

label = ['Old'] * 2000
label[1000:1500] = ['Transition'] * 500
label[1500:] = ['New'] * 500

px.line(data_incremental, title='Incremental Drift', color=label)
• Reoccurring drift:

n=2000
mu1=3
sigma1=2
mu2=8
sigma2=1

data_reoccurring = np.random.rand(n) * sigma1 + mu1
data_reoccurring[1000:1500] = np.random.randn(500) * sigma2 + mu2
data_reoccurring[1500:] = np.random.rand(500) * sigma1 + mu1

label = ['Old'] * 2000
label[1000:1500] = ['New'] * 500
label[1500:] = ['Old '] * 500

px.line(data_reoccurring, title='Reoccurring Drift', color=label)

Let’s apply ADWIN method to each series:

• Sudden drift

from skmultiflow.drift_detection.adwin import ADWIN

for i in range(2000):
print('Change detected in data: ' + str(data_sudden[i]) + ' - at index: ' + str(i))
Change detected in data: 8.092633344755715 - at index: 1023
Change detected in data: 9.929671318625031 - at index: 1055
Change detected in data: 9.487942606466301 - at index: 1087

Sudden drift was first detected at index 1023, so the method lagged 23 observations.

adwin = ADWIN()
for i in range(2000):
print('Change detected in data: ' + str(data_gradual[i]) + ' - at index: ' + str(i))
Change detected in data: 3.7276303613439605 - at index: 1087
Change detected in data: 3.5763573220924223 - at index: 1119
Change detected in data: 4.187222721823322 - at index: 1151
Change detected in data: 7.472834846368913 - at index: 1183
Change detected in data: 7.910709686691047 - at index: 1279
Change detected in data: 6.861296525734318 - at index: 1663
Change detected in data: 6.278295128233516 - at index: 1727
Change detected in data: 5.99610175295946 - at index: 1791

Gradual drift was first detected at index 1087, so the method lagged 87 observations. After the index 1500, the method gave 3 misalerts.

• Incremental drift

adwin = ADWIN()
for i in range(2000):
print('Change detected in data: ' + str(data_incremental[i]) + ' - at index: ' + str(i))
Change detected in data: 5.230485716995449 - at index: 1151
Change detected in data: 7.135720345796623 - at index: 1183
Change detected in data: 6.408763400413527 - at index: 1215
Change detected in data: 6.121233942647503 - at index: 1247
Change detected in data: 5.2509644445949215 - at index: 1279
Change detected in data: 7.032973666011305 - at index: 1311
Change detected in data: 6.825815433971569 - at index: 1343
Change detected in data: 7.094917550861222 - at index: 1375
Change detected in data: 6.021976471064258 - at index: 1407
Change detected in data: 7.563053572886224 - at index: 1471
Change detected in data: 9.326706248481413 - at index: 1503
Change detected in data: 7.410570560565155 - at index: 1535
Change detected in data: 8.318959498454486 - at index: 1567
Change detected in data: 8.425934499842729 - at index: 1599
Change detected in data: 7.461700640162903 - at index: 1791

Incremental drift was first detected at index 1151, so the method lagged 151 observations. After the index 1500, the method gave 4 misalerts.

• Reoccurring drift

adwin = ADWIN()
for i in range(2000):
print('Change detected in data: ' + str(data_reoccurring[i]) + ' - at index: ' + str(i))
Change detected in data: 7.817990447479633 - at index: 1023
Change detected in data: 8.162873100846571 - at index: 1055
Change detected in data: 7.732247538441721 - at index: 1087
Change detected in data: 3.798546626428176 - at index: 1535
Change detected in data: 3.978688037122022 - at index: 1567
Change detected in data: 3.0069507591156173 - at index: 1599
Change detected in data: 3.7546042052686808 - at index: 1631
Change detected in data: 4.746055229599389 - at index: 1663

As seen from the results, sudden changes can be detected early but it can be a challenge that detect gradual and incremental drifts.

## Solutions to model drift

1. Discard the old data and retrain the model blindly without detecting any concept drift periodically.
2. Weight the all data inversly propotional to the age of data, then train the model.
3. Use online (incremental) learning. As the new data arrives, retrain the existing model.

Full source code: https://github.com/mrtkp9993/MyDsProjects/tree/main/ConceptDrift