Machine learning in concept drift detection using statistical measures

Figures & data

Table 1. Summarizing the key differences between concept drift and data drift.

Feature	Concept drift	Data drift
Definition	Changes in the underlying relationship between the input data and the target variable	Changes in the distribution of the input data
Cause	External factors such as changes in the user population, changes in the environment, or changes in the underlying technology	Internal factors such as changes in the data collection process, changes in the way that data is preprocessed, or changes in the underlying data source
Impact	The model’s predictions become less accurate over time	The model’s predictions become less accurate over time
Detection	More difficult to detect	Easier to detect
Mitigation	Retrain the model with new data	Apply data drift detection and correction techniques

Figure 1. The diagram of block PCDD.

Table 2. Nonstandard abbreviations and acronyms.

$M_{v1},M_{v2}$	The average values in the respective vectors $v1,v2$ are highlighted
S	Size
$T$	Training data
V	Vector
$\mathrm{c\tau }$	Current time
$\mathrm{p\tau }$	Previous time
$c_i$	Classifier
$v_1,v_2$	Values of vectors
$A\left(v_1\right),A\left(v_2\right)$	Aggregate values of $v1,v2$
$\mathrm{pr}$	Previous element cumulative ratio
$e_j$	Element
$C{R}_{v_1},C{R}_{v_2}$	Cumulative ratio in vector$v_1,v_2$
$i$	Index
$\mathrm{AD}$	Exact distance
$\mathrm{rs}$	Record Set
$t_j$	Transaction record
$\mathrm{dsrt}$	Distribution similarity ratio threshold
$\mathrm{rsr}$	Record-level similarity ratio
$\mathrm{rsrt}$	Record-level similarity ratio threshold
DDAL	Drift Detection Method Based on Active Learning

Figure 2. The differentiation of the drift detection rates between PCDD and DDAL.

Figure 3. The differentiation of the rates of drift detection error between PCDD and DDAL.

Table 3. The detection rates of concept drift were observed from PCDD and DDAL.

Fold ID		1	2	3	4	5
Sudden drift detection rate	DDAL	0.935	0.821	0.9	0.833	0.83
	PCDD	0.984	0.964	0.95	0.952	0.964
Gradual drift detection rate	DDAL	0.823	0.857	0.756	0.841	0.855
	PCDD	0.952	0.946	0.951	0.977	0.962
Recursive drift detection rate	DDAL	0.839	0.839	0.816	0.864	0.909
	PCDD	0.968	0.982	0.947	0.955	0.964

Table 4. The observed rates of drift detection error from both PCDD and DDAL.

Fold ID		1	2	3	4	5
Sudden drift detection error rate	DDAL	0.065	0.179	0.1	0.167	0.17
	PCDD	0.016	0.036	0.05	0.048	0.036
Gradual drift detection error rate	DDAL	0.177	0.143	0.244	0.159	0.145
	PCDD	0.048	0.054	0.049	0.023	0.038
Recursive drift detection error rate	DDAL	0.161	0.161	0.184	0.136	0.091
	PCDD	0.032	0.018	0.053	0.045	0.036

Table 5. t-Test and Wilcoxon rank-sum test results, alongside corresponding probability values (p-values).

t-Value	z-Value	w-Value
9.6981	−3.4163	0
p-Value	p-Value	p-Value
<.00001	.0006	<.01