# Explainability and Interpretability in Concept and Data Drift: A Systematic Literature Review
## 2 Background: Drift Phenomena and Explainable/Interpretable AI
### Drift Overview
#### 2.2.2 Concept Drift  
As shown in Figure 2, the blue points, time \(t_{0}\), lie roughly on an increasing linear trend: larger input values map to proportionally larger outputs. By time \(t_{1}\) (orange points), the input distribution is essentially unchanged; the cloud spans the same range on the x-axis, but the relationship between \(X\) and \(Y\) has rotated into a curved, non-linear shape. Formally,  
\[P_{t_{0}}(X)\ \approx\ P_{t_{1}}(X)\qquad\text{while}\qquad P_{t_{0}}(Y\mid X)\ \
eq\ P_{t_{1}}(Y\mid X).\]  
This is the hallmark of concept drift: the true decision surface moves even though the feature space the model sees stays put. A classifier or regressor trained on the blue relationship will project a straight decision boundary or regression line; when confronted with the orange regime, it will systematically mis-predict, for instance, by over-estimating outputs around \(X\approx 0\) and under-estimating them for larger \(|X|\).  
The concept drift literature distinguishes four temporal profiles, each posing different monitoring and adaptation requirements.  
Figure 1: Data drift scenario.  
Figure 2: Concept drift scenario.  
* **Sudden drift**: The relationship between inputs and outputs changes instantaneously at a specific point in time, as shown in Figure 3. The data overview panel demonstrates two distinct regimes: an initial positive linear relationship, in blue, abruptly replaced by a negative linear relationship, in orange, after the change point. This discontinuity is quantitatively confirmed in the parameter evolution panel, where the slope coefficient m exhibits a step change from 2.0 to \(-1.0\) at time index 500, with no transitional states.
* **Gradual drift**: Both old and new concepts coexist during an extended transition period. Figure 4 shows four phases: an initial positive linear relationship (in blue) progressively gives way to a negative relationship (in orange) through intermediate mixed states (in green). Quantitatively, the slope coefficient linearly decreases from 2.0 to \(-1.0\) between time indices 300 and 700, confirming a smooth transition without abrupt changes.
* **Incremental drift**: The relationship between inputs and outputs undergoes continuous, stepwise evolution rather than an abrupt change or extended coexistence. As shown in Figure 5, the initial positive linear relationship (blue points) progresses through intermediate states (green points) to a final negative relationship (orange points), with each step showing a slight rotation of the regression line. This continuous transformation is quantitatively confirmed in the parameter evolution panel, where the slope coefficient linearly decreases from 2.0 to \(-1.0\) across the entire time period without plateaus or abrupt jumps.  
Figure 3: Sudden concept drift.  
Figure 4: Gradual concept drift.  
Figure 5: Incremental concept drift.  
* **Recurrent drift**: The system alternates periodically between distinct concepts, creating a cyclical pattern of change. Two stable relationships repeatedly alternate, as is visible in Figure 6: Concept A maintains a positive linear relationship (blue points), while Concept B follows a negative relationship (orange points). The parameter evolution panel confirms this periodicity through a square-wave pattern, where the slope coefficient alternates precisely between 2.0 and \(-\)1.0 every 250 time steps. This recurrent mechanism is clearly visible in both the full-period visualizations and in the square-wave slope pattern.