---
title: "Drift Detection with datadriftR"
output:
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 2
vignette: >
  %\VignetteIndexEntry{Drift Detection with datadriftR}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 4,
  message = FALSE,
  warning = FALSE
)

library(datadriftR)
```

# Introduction {#intro}

In production, the data generating process rarely stays still. Seasonality, product changes, user behavior, and policy updates can shift the distribution of your features—and sometimes even change the relationship between features and the target.

**Example (concept drift):** You train a model to predict whether electricity prices will go up based on demand and price signals. After a market reform, the same demand level can imply a different price movement. In practice this often shows up as a rising error rate or shifting model outputs.

**datadriftR** helps you detect these shifts early in streaming settings, so you can trigger investigation, retraining, or alerts.

# Drift Taxonomy {#drift-taxonomy}

Many “drift” problems are forms of **dataset shift**:

$$P_{train}(X, Y) \neq P_{prod}(X, Y)$$

What changed?

- **Covariate shift:** $P(X)$ changes while $P(Y|X)$ stays roughly the same.
- **Concept drift:** $P(Y|X)$ changes (the mapping from inputs to outputs changes).

# Drift Patterns {#drift-patterns}

Drift can also differ by **how it unfolds over time**:

- **Abrupt:** change happens at once (deployments, outages, policy changes)
- **Gradual:** mixture of old/new concepts (slow adoption, rollout)
- **Incremental:** continuously moving distribution (wear-and-tear, trend)
- **Recurring:** seasonal or cyclical patterns (day/night, weekdays, holidays)

```{r drift-types-viz, fig.height=5, fig.cap="Common drift patterns", echo=FALSE}
set.seed(42)
n <- 400
par(mfrow = c(2, 2), mar = c(4, 4, 3, 1))

# Abrupt
plot(c(rnorm(200, 0, 1), rnorm(200, 3, 1)), type = "l", col = "#457B9D",
     main = "Abrupt Drift", xlab = "Time", ylab = "Value")
abline(v = 200, col = "#E63946", lty = 2, lwd = 2)

# Gradual
gradual <- sapply(1:n, function(i) rnorm(1, mean = min(3, max(0, (i-150)/80)), sd = 1))
plot(gradual, type = "l", col = "#457B9D",
     main = "Gradual Drift", xlab = "Time", ylab = "Value")
rect(150, -4, 230, 6, col = rgb(0.9, 0.2, 0.2, 0.15), border = NA)

# Incremental
plot(rnorm(n, mean = (1:n)/100, sd = 1), type = "l", col = "#457B9D",
     main = "Incremental Drift", xlab = "Time", ylab = "Value")

# Recurring
plot(sin((1:n)/25) * 2 + rnorm(n, 0, 0.3), type = "l", col = "#457B9D",
     main = "Recurring Drift", xlab = "Time", ylab = "Value")
par(mfrow = c(1, 1))
```

# Available Methods {#available-methods}

| Method | What you feed |
|:-------|:-------------|
| **DDM, EDDM, HDDM-A/W** | Binary (0/1) error stream |
| **KSWIN, ADWIN, Page-Hinkley, KL Divergence** | Numeric stream (or rolling window/batches) |
| **ProfileDifference** | Two profiles (e.g., PDPs) |

---

# Quick Start {#quick-start}

Quick start with `detect_drift()`:

```{r quick-start}
set.seed(1)
x <- c(rnorm(300, 0, 1), rnorm(200, 3, 1))

detect_drift(x, method = "page_hinkley", delta = 0.05, threshold = 50)
```

---

# Part 1: Error-Rate Detectors (Binary Stream) {#error-rate-detectors}

These methods monitor a stream of **prediction errors**:

```r
error_stream <- as.integer(y_pred != y_true)
```

They work well when you can observe labels reasonably quickly (or with a known delay).

## Simulating Model Errors

```{r error-rate-setup}
set.seed(123)

n_good <- 500
n_bad <- 500
error_stream <- c(
  rbinom(n_good, 1, prob = 0.05),
  rbinom(n_bad, 1, prob = 0.30)
)
true_drift_error <- n_good + 1
```

## Comparing All Error-Rate Methods

```{r error-methods-comparison}
error_methods <- c("ddm", "eddm", "hddm_a", "hddm_w")

first_index <- function(res, type) {
  idx <- res$index[res$type == type]
  if (length(idx) == 0) NA_integer_ else idx[1]
}

error_results <- do.call(rbind, lapply(error_methods, function(m) {
  res <- detect_drift(error_stream, method = m, include_warnings = TRUE)
  warning_idx <- first_index(res, "warning")
  drift_idx <- first_index(res, "drift")
  data.frame(
    Method = gsub("_", "-", toupper(m)),
    Warning = warning_idx,
    Drift = drift_idx,
    DriftDelay = if (!is.na(drift_idx)) drift_idx - true_drift_error else NA,
    stringsAsFactors = FALSE
  )
}))

error_results
```

```{r error-rate-plot, fig.height=4, echo=FALSE}
window <- 50
error_rate <- sapply(seq_along(error_stream), function(i) {
  mean(error_stream[max(1, i-window+1):i])
})

plot(error_rate, type = "l", col = "gray50", lwd = 2,
     xlab = "Observation", ylab = paste0("Error Rate (", window, "-obs window)"),
     main = "Error-Rate Method Comparison")
abline(v = true_drift_error, col = "black", lty = 2, lwd = 2)

colors <- c("#E63946", "#F4A261", "#2A9D8F", "#9B5DE5")
for (i in seq_len(nrow(error_results))) {
  if (!is.na(error_results$Warning[i])) {
    abline(v = error_results$Warning[i], col = colors[i], lwd = 2, lty = 3)
  }
  if (!is.na(error_results$Drift[i])) {
    abline(v = error_results$Drift[i], col = colors[i], lwd = 2)
  }
}

legend("topleft", c("True drift", error_results$Method),
       col = c("black", colors),
       lty = c(2, rep(1, nrow(error_results))),
       lwd = 2, cex = 0.8)
legend("bottomright", c("Warning", "Drift"),
       lty = c(3, 1), col = "gray30", lwd = 2, bty = "n", cex = 0.8)
```

## Online Processing (Streaming)

```{r online-error-rate}
ddm <- DDM$new()
drifts <- c()

for (i in seq_along(error_stream)) {
  ddm$add_element(error_stream[i])
  if (ddm$change_detected) {
    drifts <- c(drifts, i)
    ddm$reset()
  }
}

data.frame(Method = "DDM", True = true_drift_error, Detected = drifts)
```

The loop above is the “low-level” way to run a detector. For convenience, `detect_drift()` provides the same idea as a single function call:

```{r online-error-rate-detect-drift}
ddm_res <- detect_drift(error_stream, method = "ddm", include_warnings = FALSE)
ddm_res
```

---

# Part 2: Continuous-Stream Detectors (Numeric Data) {#continuous-streams}

These methods work with **any numeric stream**—sensor readings, feature values, model predictions.

## Simulating Sensor Data

```{r continuous-setup}
set.seed(456)

n_normal <- 300
n_faulty <- 200
sensor_stream <- c(
  rnorm(n_normal, mean = 20, sd = 1),
  rnorm(n_faulty, mean = 28, sd = 2)
)
true_drift_sensor <- n_normal + 1
```

## Comparing All Distribution Methods

```{r dist-methods-comparison}
dist_methods <- c("kswin", "adwin", "page_hinkley")

dist_results <- do.call(rbind, lapply(dist_methods, function(m) {
  res <- detect_drift(sensor_stream, method = m)
  data.frame(
    Method = gsub("_", "-", toupper(m)),
    Detected = if (nrow(res) > 0) res$index[1] else NA,
    Delay = if (nrow(res) > 0) res$index[1] - true_drift_sensor else NA,
    stringsAsFactors = FALSE
  )
}))

dist_results
```

```{r dist-plot, fig.height=4, echo=FALSE}
plot(sensor_stream, type = "l", col = "gray50",
     xlab = "Time", ylab = "Temperature (°C)",
     main = "Distribution Method Comparison")
abline(v = true_drift_sensor, col = "black", lty = 2, lwd = 2)

colors <- c("#E63946", "#2A9D8F", "#9B5DE5")
for (i in seq_along(dist_results$Detected)) {
  if (!is.na(dist_results$Detected[i])) abline(v = dist_results$Detected[i], col = colors[i], lwd = 2)
}

legend("topleft", c("True drift", dist_results$Method),
       col = c("black", colors), lty = c(2, rep(1, 3)), lwd = 2, cex = 0.8)
```

---

# Part 3: KL Divergence {#kl-divergence}

Sometimes you want to compare recent values to a reference window (latency, transaction amount, sensor readings, model scores).

`KLDivergence` is a simple histogram-based implementation of Kullback–Leibler divergence. When the divergence crosses a threshold, it flags drift.

```{r kld-setup}
set.seed(789)

n_ref <- 400
n_shift <- 400
latency_ms <- c(
  rlnorm(n_ref, meanlog = log(100), sdlog = 0.25),
  rlnorm(n_shift, meanlog = log(180), sdlog = 0.30)
)
true_drift_kld <- n_ref + 1
```

```{r kld-detect}
window <- 200
kld <- KLDivergence$new(bins = 30, drift_level = 0.15)
kld$set_initial_distribution(latency_ms[1:window])

kl <- rep(NA_real_, length(latency_ms))
for (t in (window + 1):length(latency_ms)) {
  current <- latency_ms[(t - window + 1):t]
  kld$add_distribution(current)
  kl[t] <- kld$get_kl_result()
}

detected_kld <- which(kl > kld$drift_level)[1]
data.frame(True = true_drift_kld, Detected = detected_kld, Threshold = kld$drift_level)
```

```{r kld-plot, fig.height=4, echo=FALSE}
plot(kl, type = "l", col = "gray50", lwd = 2,
     xlab = "Time", ylab = "KL divergence",
     main = "KL Divergence vs. Reference Window")
abline(v = true_drift_kld, col = "black", lty = 2, lwd = 2)
abline(h = kld$drift_level, col = "#9B5DE5", lty = 2, lwd = 2)
if (!is.na(detected_kld)) abline(v = detected_kld, col = "#E63946", lwd = 2)

legend("topright",
       c("True drift", "Detected", "Threshold"),
       col = c("black", "#E63946", "#9B5DE5"),
       lty = c(2, 1, 2),
       lwd = 2,
       cex = 0.8)
```

---

# Part 4: ProfileDifference (Model Behavior) {#model-behavior}

Partial Dependence Profiles (PDPs) show how a model's prediction changes with a feature. When concept drift occurs, the **relationship between features and target** changes—PDPs capture this.

## Available Methods

| Method | Description |
|:-------|:------------|
| **pdi** | Profile Disparity Index - compares derivative signs |
| **L2** | L2 norm between profiles |
| **L2_derivative** | L2 norm of profile derivatives |

## Example: Electricity Prices (elec2)

The `elec2` dataset from the `dynaTree` package is a classic benchmark for concept drift—Australian electricity prices where market dynamics changed over time. This section requires the optional packages `dynaTree` and `ranger`. For readability we rename `x1..x4`/`y`, and for speed we train on a small subset from each time period.

```{r elec2-setup, eval=requireNamespace("dynaTree", quietly = TRUE) && requireNamespace("ranger", quietly = TRUE)}
library(dynaTree)
library(ranger)

elec2_env <- new.env(parent = emptyenv())
data("elec2", package = "dynaTree", envir = elec2_env)
elec2_df <- get("elec2", envir = elec2_env)
stopifnot(is.data.frame(elec2_df))

names(elec2_df) <- c("nswprice", "nswdemand", "vicprice", "vicdemand", "class_raw")
elec2_df$class <- factor(elec2_df$class_raw, levels = c(1, 2), labels = c("DOWN", "UP"))
elec2_df$class_raw <- NULL

split_idx <- floor(nrow(elec2_df) / 2)
period1_data <- elec2_df[1:split_idx, ]
period2_data <- elec2_df[(split_idx + 1):nrow(elec2_df), ]

n_train <- min(2000, nrow(period1_data), nrow(period2_data))
period1_train <- period1_data[1:n_train, ]
period2_train <- period2_data[1:n_train, ]

rf1 <- ranger(class ~ nswprice + nswdemand + vicprice + vicdemand,
	             data = period1_train, probability = TRUE, num.trees = 200, seed = 1)
rf2 <- ranger(class ~ nswprice + nswdemand + vicprice + vicdemand,
	             data = period2_train, probability = TRUE, num.trees = 200, seed = 1)

compute_pdp_rf <- function(model, data, var, grid) {
  preds <- sapply(grid, function(val) {
    newdata <- data
    newdata[[var]] <- val
    mean(predict(model, newdata)$predictions[, "UP"])
  })
  list(x = grid, y = preds)
}

demand_grid <- seq(min(elec2_df$nswdemand), max(elec2_df$nswdemand), length.out = 50)
pdp1 <- compute_pdp_rf(rf1, period1_train, "nswdemand", demand_grid)
pdp2 <- compute_pdp_rf(rf2, period2_train, "nswdemand", demand_grid)
```

```{r elec2-plot, fig.height=4, eval=requireNamespace("dynaTree", quietly = TRUE) && requireNamespace("ranger", quietly = TRUE), echo=FALSE}
plot(pdp1$x, pdp1$y, type = "l", lwd = 2, col = "#2A9D8F",
     xlab = "NSW Demand", ylab = "P(Price UP)",
     main = "PDP Drift: NSW Demand Effect on Price",
     ylim = range(c(pdp1$y, pdp2$y)))
lines(pdp2$x, pdp2$y, lwd = 2, col = "#E63946")
legend("topright", c("Period 1", "Period 2"), col = c("#2A9D8F", "#E63946"), lwd = 2)
```

## Comparing All Methods

```{r elec2-methods, eval=requireNamespace("dynaTree", quietly = TRUE) && requireNamespace("ranger", quietly = TRUE)}
# PDI (Profile Disparity Index)
pd_pdi <- ProfileDifference$new(method = "pdi", deriv = "gold")
pd_pdi$set_profiles(pdp1, pdp2)
res_pdi <- pd_pdi$calculate_difference()

# L2 norm
pd_l2 <- ProfileDifference$new(method = "L2")
pd_l2$set_profiles(pdp1, pdp2)
res_l2 <- pd_l2$calculate_difference()

# L2 derivative
pd_l2d <- ProfileDifference$new(method = "L2_derivative")
pd_l2d$set_profiles(pdp1, pdp2)
res_l2d <- pd_l2d$calculate_difference()

data.frame(
  Method = c("PDI", "L2", "L2_derivative"),
  Distance = round(c(res_pdi$distance, res_l2$distance, res_l2d$distance), 4)
)
```

Higher distance indicates the model learned different demand-price relationships in each period—concept drift detected.

---

# Quick Reference {#quick-reference}

| What you monitor | Typical signal | Recommended |
|:----------------|:---------------|:------------|
| Binary error stream | Sudden or gradual accuracy drop | DDM, EDDM, HDDM-A/W |
| Numeric stream | Feature/sensor/score distribution shift | KSWIN, ADWIN, Page-Hinkley |
| Reference vs. current batch | Periodic samples (e.g., daily latency) | KLDivergence |
| Model behavior profiles | PDP/feature effect changes | ProfileDifference |

---

# References

The drift detection methods implemented in **datadriftR** are based on established algorithms from the streaming machine learning literature. For Python implementations, see:

- **River** ([riverml.xyz](https://riverml.xyz/)): Online machine learning library with drift detectors
- **scikit-multiflow** ([scikit-multiflow.github.io](https://scikit-multiflow.github.io/)): Stream learning framework

**Source code**: [github.com/ugurdar/datadriftR](https://github.com/ugurdar/datadriftR)
