Package {rupturesRcpp}

Exact Dynamic Programming (Dynp)

Description

An R6 class implementing exact dynamic programming for offline change-point detection.

Details

Dynp finds the segmentation that globally minimises the total cost for a specified number of change-points – unlike PELT (exact for a penalty, not a change-point count) and binSeg (greedy at each split, not guaranteed globally optimal for a fixed count), Dynp is exact for whatever nBkps is requested. The price is complexity: building the full table costs O(\text{nBkpsMax} \cdot M^2) where M is the number of ⁠(minSize, jump)⁠-admissible grid points (M \approx n/\text{jump} in the worst case), versus PELT's near-linear pruning or binSeg's O(n \log n)-ish greedy search. ⁠$fit()⁠ computes the exact minimal cost for every change-point count from 0 to nBkpsMax in one pass (see ⁠$costPath()⁠). Dynp is therefore useful when an exact fixed-number-of-change-points solution is required, particularly when using custom cost functions for which PELT pruning cannot be guaranteed.

Dynp requires a R6 object of class costFunc, exactly as PELT/binSeg/Window do – see costFunc for the supported cost functions ("L1", "L2", "SIGMA", "VAR", "LinearL2", "LinearSIGMA", "LinearL1", "Custom").

Some examples are provided below. See the package website for detailed usage!

Methods

$new()

Initialises a Dynp object.

$describe()

Describes the Dynp object.

$fit()

Constructs a Dynp module in ⁠C++⁠.

$eval()

Evaluates the cost of a segment.

$predict()

Returns the exact optimal breakpoints, for a given pen or nBkps.

$segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

$costPath()

Returns the exact minimal cost for every change-point count up to nBkpsMax.

$getHistory()

Same data as ⁠$costPath()⁠, as a k/cost data.frame (same shape as binSeg/Window's ⁠$getHistory()⁠, minus added_bkp – see its own docs for why).

$plotElbow()

Plots the elbow curve (Total Cost vs. Number of Change-Points).

$plot()

Plots change-point segmentation in ggplot style.

$clone()

Clones the R6 object.

Active bindings

Methods

Public methods

• Dynp$new()

• Dynp$describe()

• Dynp$fit()

• Dynp$eval()

• Dynp$predict()

• Dynp$segments()

• Dynp$costPath()

• Dynp$getHistory()

• Dynp$plotElbow()

• Dynp$plot()

• Dynp$clone()

Method new()

Initialises a Dynp object.

Usage

Dynp$new(minSize, jump, nBkpsMax, costFunc)

Arguments

Returns

Invisibly returns NULL.

Method describe()

Describes a Dynp object.

Usage

Dynp$describe(printConfig = FALSE)

Arguments

Returns

Invisibly returns a list storing at least the following fields:

minSize

Minimum allowed segment length.

jump

Search grid step size.

nBkpsMax

The user-set nBkpsMax (possibly NULL).

resolvedNBkpsMax

The nBkpsMax actually used by the last ⁠$fit()⁠ (NULL if not fitted).

costFunc

The costFunc object.

fitted

Whether or not ⁠$fit()⁠ has been run.

tsMat

Time series matrix.

covariates

Covariate matrix (if exists).

n

Number of observations.

p

Number of features.

Method fit()

Constructs a ⁠C++⁠ module for Dynp and builds the exact DP table.

Usage

Dynp$fit(tsMat = NULL, covariates = NULL)

Arguments

Details

This method constructs a ⁠C++⁠ Dynp module and sets private$.fitted to TRUE, enabling the use of ⁠$predict()⁠, ⁠$costPath()⁠ and ⁠$eval()⁠. If ⁠$nBkpsMax⁠ is NULL, it is resolved here to min(20, floor(n / minSize) - 1) (with a message); if set higher than floor(n / minSize) - 1, it is capped to that (with a warning).

Returns

Invisibly returns NULL.

Method eval()

Evaluate the cost of the segment (a,b]

Usage

Dynp$eval(a, b)

Arguments

Returns

The segment cost. See costFunc for the cost formulas.

Method predict()

Returns the exact optimal breakpoints, either under a linear penalty or for a specified number of change-points.

Usage

Dynp$predict(pen = 0, nBkps = NULL)

Arguments

Details

With nBkps = k, this returns the segmentation into exactly k change-points that globally minimises the total cost – exact, unlike binSeg$predict() for the same k. With pen, this instead minimises the penalised cost over every change-point count the DP table covers, matching how PELT/binSeg/Window already select a count from a penalty.

Both the DP table (via ⁠$fit()⁠) and the traceback here only depend on minSize/jump admissible positions, so ⁠$predict()⁠ itself is cheap (O(nBkps)) regardless of which mode is used – the cost was already paid in ⁠$fit()⁠.

Temporary segment end-points are saved to private$.tmpEndPoints after ⁠$predict()⁠, enabling users to call ⁠$plot()⁠ without specifying endpoints manually.

Returns

An integer vector of regime end-points. By design, the last element is the number of observations.

Method segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

Usage

Dynp$segments()

Details

Let 0 = c_0 < c_1 < \dots < c_{k+1} = n be the end-points from the latest ⁠$predict()⁠. Segment i is (c_{i-1}, c_i], Cost is c_{(c_{i-1}, c_i]} and Params is its minimiser. The costs sum to ⁠$costPath()[k + 1]⁠, the exact minimal total cost for k change-points. With nBkps, k is the requested count (capped at the resolved nBkpsMax). With pen, k is the count, from 0 up to the resolved nBkpsMax, that minimises the total cost plus pen times k.

Temporary end-points are cleared by ⁠$fit()⁠, so ⁠$predict()⁠ must be run again after modifying the object via its active bindings.

Returns

A list with one element per segment (Start, End]. Each element is a list with:

Start

Start index of the segment (exclusive, 0-based), same convention as ⁠$eval()⁠.

End

End index of the segment (inclusive).

Cost

The segment cost, as returned by ⁠$eval(Start, End)⁠.

Params

A named list of the segment parameter estimates, e.g. list(mean = ...) for "L2". See costFactory for the fields returned by each cost function.

Method costPath()

Returns the exact minimal cost for every change-point count the DP table covers.

Usage

Dynp$costPath()

Details

This is the data behind the "elbow method" for choosing the number of change-points: plot it (see ⁠$getHistory()⁠/⁠$plotElbow()⁠) and look for where the marginal decrease in cost flattens out. It comes for free out of ⁠$fit()⁠ – no extra computation is triggered here.

Returns

A numeric vector of length resolvedNBkpsMax + 1: element k+1 is the exact minimal total cost of segmenting the series into exactly k change-points, for ⁠k = 0, ..., resolvedNBkpsMax⁠. Inf at position k+1 means no valid segmentation with exactly k change-points exists given minSize/jump (only possible when jump is large relative to minSize).

Method getHistory()

Retrieves the exact minimal cost for every change-point count the DP table covers, as a data.frame (same shape as binSeg/Window's ⁠$getHistory()⁠, minus added_bkp).

Usage

Dynp$getHistory()

Details

Unlike binSeg/Window, there is no added_bkp column here: binSeg and Window each build a single nested sequence of change-points, where every k's answer is the previous k-1's answer plus one more point, so "the breakpoint added at this step" is well-defined. Dynp's per-k solutions are each independently exact and need not be nested at all – the optimal segmentation for k change-points can differ completely from the one for k-1. Use ⁠$predict(nBkps = k)⁠ to get the full breakpoint set for a given k.

Returns

A data.frame with two columns:

k

The number of change-points, from 0 to the resolved nBkpsMax.

cost

The exact minimal total cost of segmenting the series into exactly k change-points (see ⁠$costPath()⁠).

Method plotElbow()

Plots the elbow curve (Total Cost vs. Number of Change-Points).

Usage

Dynp$plotElbow(maxK = NULL)

Arguments

Returns

A ggplot object.

Method plot()

Plots change-point segmentation

Usage

Dynp$plot(
  d = 1L,
  endPts,
  dimNames,
  main,
  xlab,
  tsWidth = 0.25,
  tsCol = "#5B9BD5",
  bgCol = c("#A3C4F3", "#FBB1BD"),
  bgAlpha = 0.5,
  ncol = 1L
)

Arguments

Details

Plots change-point segmentation results. Based on ggplot2. Multiple plots can easily be horizontally and vertically stacked using patchwork's operators / and |, respectively.

Returns

An object of classes gg and ggplot.

Method clone()

The objects of this class are cloneable with this method.

Usage

Dynp$clone(deep = FALSE)

Arguments

Author(s)

Minh Long Nguyen edelweiss611428@gmail.com
Toby Dylan Hocking toby.hocking@r-project.org
Charles Truong ctruong@ens-paris-saclay.fr
Huy Nhat Minh Nguyen sleepysnorlax0115@gmail.com

References

Truong, C., Oudre, L., & Vayatis, N. (2020). Selective review of offline change point detection methods. Signal Processing, 167, 107299.

Examples

## L2 example
set.seed(1121)
signals = as.matrix(c(rnorm(100,0,1),
                     rnorm(100,5,1)))
# Default L2 cost function; nBkpsMax left NULL -> resolved to min(20, maximum feasible value)
DynpObj = Dynp$new(minSize = 1L, jump = 1L)
DynpObj$fit(signals)
DynpObj$predict(nBkps = 1)
DynpObj$plot()

# Same result, reached via a penalty instead of an explicit count
DynpObj$predict(pen = 100)

# The exact cost of every change-point count from 0 to nBkpsMax -- elbow-method data
DynpObj$getHistory()
DynpObj$plotElbow()

Pruned Exact Linear Time (PELT)

Description

An R6 class implementing the PELT algorithm for offline change-point detection.

Details

PELT (Pruned Exact Linear Time) is an efficient algorithm for change point detection that prunes the search space to achieve optimal segmentation in linear time under certain conditions.

PELT requires a R6 object of class costFunc, which can be created via costFunc$new(). Currently, the following cost functions are supported:

• "L1" and "L2" for (independent) piecewise Gaussian process with constant variance

• "SIGMA": for (independent) piecewise Gaussian process with varying variance

• "VAR": for piecewise Gaussian vector-regressive process with constant noise variance

• "LinearL2": for piecewise linear regression process with constant noise variance

• "LinearSIGMA": for piecewise linear regression process with varying noise covariance

• "LinearL1": for piecewise linear regression process under L1 (least absolute deviations) loss

See ⁠$eval()⁠ method for more details on computation of cost.

Some examples are provided below. See the package website for detailed usage!

Methods

$new()

Initialises a PELT object.

$describe()

Describes the PELT object.

$fit()

Constructs a PELT module in ⁠C++⁠.

$eval()

Evaluates the cost of a segment.

$predict()

Performs PELT given a linear penalty value.

$segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

$plot()

Plots change-point segmentation in ggplot style.

$clone()

Clones the R6 object.

Active bindings

Methods

Public methods

• PELT$new()

• PELT$describe()

• PELT$fit()

• PELT$eval()

• PELT$predict()

• PELT$segments()

• PELT$plot()

• PELT$clone()

Method new()

Initialises a PELT object.

Usage

PELT$new(minSize, jump, costFunc)

Arguments

Returns

Invisibly returns NULL.

Method describe()

Describes a PELT object.

Usage

PELT$describe(printConfig = FALSE)

Arguments

Returns

Invisibly returns a list storing at least the following fields:

minSize

Minimum allowed segment length.

jump

Search grid step size.

costFunc

The costFunc object.

fitted

Whether or not ⁠$fit()⁠ has been run.

tsMat

Time series matrix.

covariates

Covariate matrix (if exists).

n

Number of observations.

p

Number of features.

Method fit()

Constructs a ⁠C++⁠ module for PELT.

Usage

PELT$fit(tsMat = NULL, covariates = NULL)

Arguments

Details

This method constructs a ⁠C++⁠ PELT module and sets private$.fitted to TRUE, enabling the use of ⁠$predict()⁠ and ⁠$eval()⁠.

Returns

Invisibly returns NULL.

Method eval()

Evaluate the cost of the segment (a,b]

Usage

PELT$eval(a, b)

Arguments

Details

The segment cost is evaluated as follows:

• L1 cost function:

  c_{L_1}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \tilde{y}_{(a+1)...b} \|_1

  where \tilde{y}_{(a+1)...b} is the coordinate-wise median of the segment. If a \ge b - 1, return 0.

• L2 cost function:

  c_{L_2}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \bar{y}_{(a+1)...b} \|_2^2

  where \bar{y}_{(a+1)...b} is the empirical mean of the segment. If a \ge b - 1, return 0.

• SIGMA cost function:

  c_{\Sigma}(y_{(a+1)...b}) := (b - a)\log \det \hat{\Sigma}_{(a+1)...b}

  where \hat{\Sigma}_{(a+1)...b} is the empirical covariance matrix of the segment without Bessel's correction. Here, if addSmallDiag = TRUE, a small bias epsilon is added to the diagonal of estimated covariance matrices to improve numerical stability.
  
  By default, addSmallDiag = TRUE and epsilon = 1e-6. In case addSmallDiag = TRUE, if the covariance matrix is numerically singular (its log-determinant cannot be computed) or its log-determinant is smaller than the lower bound p*log(epsilon), return (b - a)*p*log(epsilon), otherwise, output an error message.

• VAR(r) cost function:

  c_{\mathrm{VAR}}(y_{(a+1)...b}) := \sum_{t = \max(a, r)+1}^{b} \left\| y_t - \hat c - \sum_{j=1}^r \hat A_j y_{t-j} \right\|_2^2

  where \hat c and \hat A_j are the OLS estimates of the intercept and VAR coefficients on the segment. The lagged values y_{t-j} may come from before a+1, so only the first r observations of the whole series lack a full set of lags. If the system is singular, an approximate (minimum-norm) least-squares solve is used. If b-a < p*r+1 (i.e., not enough observations), or a > n-r (where n is the time series length), return 0.

"LinearL2" for piecewise linear regression process with constant noise variance

c_{\text{LinearL2}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_2^2

where \hat{\beta} are OLS estimates on segment (a+1):b. If segment is shorter than the minimum number of points needed for OLS, return 0.

• "LinearSIGMA" for piecewise linear regression process with varying noise covariance

  c_{\text{LinearSIGMA}}(y_{(a+1):b}) := (b-a)\log \det \hat\Sigma_{(a+1):b}

  where \hat\Sigma_{(a+1):b} is the empirical covariance matrix of OLS residuals y - X\hat{\beta} on segment (a+1):b, divided by b-a with no degrees-of-freedom correction for the fitted coefficients, and otherwise estimated the same way as in the SIGMA cost function.

• "LinearL1" for piecewise linear regression process under L1 (least absolute deviations) loss

  c_{\text{LinearL1}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_1

  where \hat{\beta} is fit column-by-column via IRLS on segment (a+1):b, iterated until convergence (tol) or maxIter. Unlike the other regression costs, this has no O(1)-per-segment closed form.

Returns

The segment cost.

Method predict()

Performs PELT given a linear penalty value.

Usage

PELT$predict(pen = 0)

Arguments

Details

The PELT algorithm detects multiple change-points by finding the set of break-points that globally minimises a penalised cost function. PELT uses dynamic programming combined with a pruning rule to reduce the number of candidate change-points, achieving efficient computation.

Let [c_1, \dots, c_k, c_{k+1}] denote the set of segment end-points with 0 = c_0 < c_1 < c_2 < \dots < c_k < c_{k+1} = n, where k is the number of detected change-points and n is the total number of data points. Let c_{(c_{i-1}, c_i]} be the cost of segment (c_{i-1}, c_i]. The total penalised cost is

\text{TotalCost} = \sum_{i=1}^{k+1} c_{(c_{i-1}, c_i]} + \lambda \cdot k,

where \lambda is a linear penalty applied per change-point. PELT finds the set of endpoints that minimises this cost exactly.

The pruning step eliminates candidate change-points that cannot lead to an optimal solution, allowing PELT to run in linear time with respect to the number of data points.

Temporary segment end-points are saved to private$.tmpEndPoints after ⁠$predict()⁠, enabling users to call ⁠$plot()⁠ without specifying endpoints manually.

Returns

An integer vector of regime end-points. By design, the last element is the number of observations.

Method segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

Usage

PELT$segments()

Details

Let 0 = c_0 < c_1 < \dots < c_{k+1} = n be the end-points from the latest ⁠$predict(pen)⁠. Segment i is (c_{i-1}, c_i], Cost is c_{(c_{i-1}, c_i]} and Params is its minimiser. The costs therefore sum to the optimal total penalised cost minus \lambda \cdot k.

Temporary end-points are cleared by ⁠$fit()⁠, so ⁠$predict()⁠ must be run again after modifying the object via its active bindings.

Returns

A list with one element per segment (Start, End]. Each element is a list with:

Start

Start index of the segment (exclusive, 0-based), same convention as ⁠$eval()⁠.

End

End index of the segment (inclusive).

Cost

The segment cost, as returned by ⁠$eval(Start, End)⁠.

Params

A named list of the segment parameter estimates, e.g. list(mean = ...) for "L2". See costFactory for the fields returned by each cost function.

Method plot()

Plots change-point segmentation

Usage

PELT$plot(
  d = 1L,
  endPts,
  dimNames,
  main,
  xlab,
  tsWidth = 0.25,
  tsCol = "#5B9BD5",
  bgCol = c("#A3C4F3", "#FBB1BD"),
  bgAlpha = 0.5,
  ncol = 1L
)

Arguments

Details

Plots change-point segmentation results. Based on ggplot2. Multiple plots can easily be horizontally and vertically stacked using patchwork's operators / and |, respectively.

Returns

An object of classes gg and ggplot.

Method clone()

The objects of this class are cloneable with this method.

Usage

PELT$clone(deep = FALSE)

Arguments

Author(s)

Minh Long Nguyen edelweiss611428@gmail.com
Toby Dylan Hocking toby.hocking@r-project.org
Charles Truong ctruong@ens-paris-saclay.fr
Huy Nhat Minh Nguyen sleepysnorlax0115@gmail.com

References

Truong, C., Oudre, L., & Vayatis, N. (2020). Selective review of offline change point detection methods. Signal Processing, 167, 107299.

Killick, R., Fearnhead, P., & Eckley, I. A. (2012). Optimal detection of change points with a linear computational cost. Journal of the American Statistical Association, 107(500), 1590-1598.

Examples

## L2 example
set.seed(1121)
signals = as.matrix(c(rnorm(100,0,1),
                     rnorm(100,5,1)))
# Default L2 cost function
PELTObj = PELT$new(minSize = 1L, jump = 1L)
PELTObj$fit(signals)
PELTObj$predict(pen = 100)
PELTObj$plot()

## SIGMA example
set.seed(111)
signals = as.matrix(c(rnorm(100,-5,1),
                      rnorm(100,-5,10),
                      rnorm(100,-5,1)))
# L2 cost function
PELTObj = PELT$new(minSize = 1L, jump = 1L)
PELTObj$fit(signals)
# We choose pen = 50.
PELTObj$predict(pen = 50)
PELTObj$plot()

# The standard L2 cost function is not suitable.
# Use the SIGMA cost function.
PELTObj$costFunc = costFunc$new(costFunc = "SIGMA")
PELTObj$predict(pen = 50)
PELTObj$plot()

Slicing Window (Window)

Description

An R6 class implementing slicing window for offline change-point detection.

Details

Slicing window is a scalable, linear-time change-point detection algorithm that selects breakpoints based on local gains computed over sliding windows.

Currently supports the following cost functions:

• "L1" and "L2" for (independent) piecewise Gaussian process with constant variance

• "SIGMA": for (independent) piecewise Gaussian process with varying variance

• "VAR": for piecewise Gaussian vector-regressive process with constant noise variance

• "LinearL2": for piecewise linear regression process with constant noise variance

• "LinearSIGMA": for piecewise linear regression process with varying noise covariance

• "LinearL1": for piecewise linear regression process under L1 (least absolute deviations) loss

Window requires a R6 object of class costFunc, which can be created via costFunc$new(). Currently, the following cost functions are supported:

• "L1" and "L2" for (independent) piecewise Gaussian process with constant variance

• "SIGMA": for (independent) piecewise Gaussian process with varying variance

• "VAR": for piecewise Gaussian vector-regressive process with constant noise variance

• "LinearL2": for piecewise linear regression process with constant noise variance

• "LinearSIGMA": for piecewise linear regression process with varying noise covariance

• "LinearL1": for piecewise linear regression process under L1 (least absolute deviations) loss

See ⁠$eval()⁠ method for more details on computation of cost.

Some examples are provided below. See the package website for detailed usage!

Methods

$new()

Initialises a Window object.

$describe()

Describes the Window object.

$fit()

Constructs a Window module in ⁠C++⁠.

$eval()

Evaluates the cost of a segment.

$predict()

Performs Window given a linear penalty value.

$segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

$getHistory()

Retrieves the full cost history and sequentially added breakpoints.

$plotElbow()

Plots the elbow curve (Total Cost vs. Number of Change-Points).

$plot()

Plots change-point segmentation in ggplot style.

$clone()

Clones the R6 object.

Active bindings

Methods

Public methods

• Window$new()

• Window$describe()

• Window$fit()

• Window$eval()

• Window$predict()

• Window$segments()

• Window$getHistory()

• Window$plotElbow()

• Window$plot()

• Window$clone()

Method new()

Initialises a Window object.

Usage

Window$new(minSize, jump, radius, costFunc)

Arguments

Returns

Invisibly returns NULL.

Method describe()

Describes a Window object.

Usage

Window$describe(printConfig = FALSE)

Arguments

Returns

Invisibly returns a list storing at least the following fields:

minSize

Minimum allowed segment length.

jump

Search grid step size.

radius

Radius of each sliding window.

costFunc

The costFunc object.

fitted

Whether or not ⁠$fit()⁠ has been run.

tsMat

Time series matrix.

covariates

Covariate matrix (if exists).

n

Number of observations.

p

Number of features.

Method fit()

Constructs a ⁠C++⁠ module for Window.

Usage

Window$fit(tsMat = NULL, covariates = NULL)

Arguments

Details

This method constructs a ⁠C++⁠ Window module and sets private$.fitted to TRUE, enabling the use of ⁠$predict()⁠ and ⁠$eval()⁠. Some precomputations are performed to allow ⁠$predict()⁠ to run in linear time with respect to the number of local change-points (see ⁠$predict()⁠ for more details).

Returns

Invisibly returns NULL.

Method eval()

Evaluate the cost of the segment (a,b]

Usage

Window$eval(a, b)

Arguments

Details

The segment cost is evaluated as follows:

• L1 cost function:

  c_{L_1}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \tilde{y}_{(a+1)...b} \|_1

  where \tilde{y}_{(a+1)...b} is the coordinate-wise median of the segment. If a \ge b - 1, return 0.

• L2 cost function:

  c_{L_2}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \bar{y}_{(a+1)...b} \|_2^2

  where \bar{y}_{(a+1)...b} is the empirical mean of the segment. If a \ge b - 1, return 0.

• SIGMA cost function:

  c_{\Sigma}(y_{(a+1)...b}) := (b - a)\log \det \hat{\Sigma}_{(a+1)...b}

  where \hat{\Sigma}_{(a+1)...b} is the empirical covariance matrix of the segment without Bessel's correction. Here, if addSmallDiag = TRUE, a small bias epsilon is added to the diagonal of estimated covariance matrices to improve numerical stability.
  
  By default, addSmallDiag = TRUE and epsilon = 1e-6. In case addSmallDiag = TRUE, if the covariance matrix is numerically singular (its log-determinant cannot be computed) or its log-determinant is smaller than the lower bound p*log(epsilon), return (b - a)*p*log(epsilon), otherwise, output an error message.

• VAR(r) cost function:

  c_{\mathrm{VAR}}(y_{(a+1)...b}) := \sum_{t = \max(a, r)+1}^{b} \left\| y_t - \hat c - \sum_{j=1}^r \hat A_j y_{t-j} \right\|_2^2

  where \hat c and \hat A_j are the OLS estimates of the intercept and VAR coefficients on the segment. The lagged values y_{t-j} may come from before a+1, so only the first r observations of the whole series lack a full set of lags. If the system is singular, an approximate (minimum-norm) least-squares solve is used. If b-a < p*r+1 (i.e., not enough observations), or a > n-r (where n is the time series length), return 0.

• "LinearL2" for piecewise linear regression process with constant noise variance

  c_{\text{LinearL2}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_2^2

  where \hat{\beta} are OLS estimates on segment (a+1):b. If segment is shorter than the minimum number of points needed for OLS, return 0.

• "LinearSIGMA" for piecewise linear regression process with varying noise covariance

  c_{\text{LinearSIGMA}}(y_{(a+1):b}) := (b-a)\log \det \hat\Sigma_{(a+1):b}

  where \hat\Sigma_{(a+1):b} is the empirical covariance matrix of OLS residuals y - X\hat{\beta} on segment (a+1):b, divided by b-a with no degrees-of-freedom correction for the fitted coefficients, and otherwise estimated the same way as in the SIGMA cost function.

• "LinearL1" for piecewise linear regression process under L1 (least absolute deviations) loss

  c_{\text{LinearL1}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_1

  where \hat{\beta} is fit column-by-column via IRLS on segment (a+1):b, iterated until convergence (tol) or maxIter. Unlike the other regression costs, this has no O(1)-per-segment closed form.

Returns

The segment cost.

Method predict()

Performs Window given a linear penalty value, or a target number of change-points.

Usage

Window$predict(pen = 0, nBkps = NULL)

Arguments

Details

The algorithm scans the data with a fixed-size window to detect candidate local change-points (lcps) if the gains of its k_\text{thresh} neighbors to the left and right are all smaller than its gain, where k_\text{thresh} is defined as

k_\text{thresh} = \max \left( \left\lfloor \frac{\max(2\text{radius}, 2 \cdot \text{minSize})}{2 \cdot \text{jump}} \right\rfloor, 1 \right)

After candidate local change-points and computing the local gains, the algorithm selects the "optimal" set of break-points given the linear penalty threshold. Let G_i denote the local gain for candidate change-point i, for i = 1, \dots, n_\text{lcps}. The local gains are ordered such that G_1 \ge G_2 \ge \dots \ge G_{n_\text{lcps}}. Note that it is possible that no local change-points are detected, for example if the window size is too large.

The total cost for the selected k change-points is then calculated as

\text{TotalCost} = - \sum_{i=1}^{k} G_i + \lambda \cdot k,

where \lambda is a linear penalty applied per change-point. We then optimise over k = 1, \dots, n_\text{lcps} to minimise the penalised cost function. k = 0 is not a candidate, so at least one change-point is returned whenever a local change-point exists, however large the penalty.

This approach allows detecting multiple change-points in a time series while controlling model complexity through the linear penalty threshold.

In our implementation, scanning the data to detect candidate local change-points and computing their corresponding local gains is already performed in ⁠$fit()⁠. Therefore, ⁠$predict()⁠ runs in linear time with respect to the number of local change-points.

Temporary segment end-points are saved to private$.tmpEndPoints after ⁠$predict()⁠, enabling users to call ⁠$plot()⁠ without specifying endpoints manually.

Returns

An integer vector of regime end-points. By design, the last element is the number of observations.

Method segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

Usage

Window$segments()

Details

Let 0 = c_0 < c_1 < \dots < c_{k+1} = n be the end-points from the latest ⁠$predict()⁠, called with either pen or nBkps. Segment i is (c_{i-1}, c_i], Cost is c_{(c_{i-1}, c_i]} and Params is its minimiser. The costs sum to the total cost of this segmentation. For k \ge 1 this generally differs from ⁠$getHistory()$cost[k + 1]⁠, which subtracts local gains computed on windows of 2 * radius points instead of re-evaluating the segments.

Temporary end-points are cleared by ⁠$fit()⁠, so ⁠$predict()⁠ must be run again after modifying the object via its active bindings.

Returns

A list with one element per segment (Start, End]. Each element is a list with:

Start

Start index of the segment (exclusive, 0-based), same convention as ⁠$eval()⁠.

End

End index of the segment (inclusive).

Cost

The segment cost, as returned by ⁠$eval(Start, End)⁠.

Params

A named list of the segment parameter estimates, e.g. list(mean = ...) for "L2". See costFactory for the fields returned by each cost function.

Method getHistory()

Retrieves the full cost history and sequentially added breakpoints.

Usage

Window$getHistory()

Returns

A data.frame with three columns:

k

The number of change-points.

cost

The total unpenalised cost of the segmentation.

added_bkp

The breakpoint added at this step to achieve the cost.

Method plotElbow()

Plots the elbow curve (Total Cost vs. Number of Change-Points).

Usage

Window$plotElbow(maxK = NULL)

Arguments

Returns

A ggplot object.

Method plot()

Plots change-point segmentation

Usage

Window$plot(
  d = 1L,
  endPts,
  dimNames,
  main,
  xlab,
  tsWidth = 0.25,
  tsCol = "#5B9BD5",
  bgCol = c("#A3C4F3", "#FBB1BD"),
  bgAlpha = 0.5,
  ncol = 1L
)

Arguments

Details

Plots change-point segmentation results. Based on ggplot2. Multiple plots can easily be horizontally and vertically stacked using patchwork's operators / and |, respectively.

Returns

An object of classes gg and ggplot.

Method clone()

The objects of this class are cloneable with this method.

Usage

Window$clone(deep = FALSE)

Arguments

Author(s)

Minh Long Nguyen edelweiss611428@gmail.com
Toby Dylan Hocking toby.hocking@r-project.org
Charles Truong ctruong@ens-paris-saclay.fr
Huy Nhat Minh Nguyen sleepysnorlax0115@gmail.com

References

Truong, C., Oudre, L., & Vayatis, N. (2020). Selective review of offline change point detection methods. Signal Processing, 167, 107299.

Examples

## L2 example
set.seed(1121)
signals = as.matrix(c(rnorm(100,0,1),
                     rnorm(100,5,1)))
# Default L2 cost function
WindowObj = Window$new(minSize = 1L, jump = 1L)
WindowObj$fit(signals)
WindowObj$predict(pen = 100)
WindowObj$plot()

## SIGMA example
set.seed(111)
signals = as.matrix(c(rnorm(100,-5,1),
                      rnorm(100,-5,10),
                      rnorm(100,-5,1)))
# L2 cost function
WindowObj = Window$new(minSize = 1L, jump = 1L)
WindowObj$fit(signals)
# We choose pen = 50.
WindowObj$predict(pen = 50)
WindowObj$plot()

# The standard L2 cost function is not suitable.
# Use the SIGMA cost function.
WindowObj$costFunc = costFunc$new(costFunc = "SIGMA")
WindowObj$predict(pen = 50)
WindowObj$plot()

Binary Segmentation (binSeg)

Description

An R6 class implementing binary segmentation for offline change-point detection.

Details

Binary segmentation is a classic algorithm for change-point detection that recursively splits the data at locations that minimise the cost function.

binSeg requires a R6 object of class costFunc, which can be created via costFunc$new(). Currently, the following cost functions are supported:

• "L1" and "L2" for (independent) piecewise Gaussian process with constant variance

• "SIGMA": for (independent) piecewise Gaussian process with varying variance

• "VAR": for piecewise Gaussian vector-regressive process with constant noise variance

• "LinearL2": for piecewise linear regression process with constant noise variance

• "LinearSIGMA": for piecewise linear regression process with varying noise covariance

• "LinearL1": for piecewise linear regression process under L1 (least absolute deviations) loss

See ⁠$eval()⁠ method for more details on computation of cost.

Some examples are provided below. See the package website for detailed usage!

Methods

$new()

Initialises a binSeg object.

$describe()

Describes the binSeg object.

$fit()

Constructs a binSeg module in ⁠C++⁠.

$eval()

Evaluates the cost of a segment.

$predict()

Performs binSeg given a linear penalty value.

$segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

$plot()

Plots change-point segmentation in ggplot style.

$clone()

Clones the R6 object.

Active bindings

Methods

Public methods

• binSeg$new()

• binSeg$describe()

• binSeg$fit()

• binSeg$eval()

• binSeg$predict()

• binSeg$segments()

• binSeg$getHistory()

• binSeg$plotElbow()

• binSeg$plot()

• binSeg$clone()

Method new()

Initialises a binSeg object.

Usage

binSeg$new(minSize, jump, costFunc)

Arguments

Returns

Invisibly returns NULL.

Method describe()

Describes a binSeg object.

Usage

binSeg$describe(printConfig = FALSE)

Arguments

Returns

Invisibly returns a list storing at least the following fields:

minSize

Minimum allowed segment length.

jump

Search grid step size.

costFunc

The costFunc object.

fitted

Whether or not ⁠$fit()⁠ has been run.

tsMat

Time series matrix.

covariates

Covariate matrix (if exists).

n

Number of observations.

p

Number of features.

Method fit()

Constructs a ⁠C++⁠ module for binary segmentation.

Usage

binSeg$fit(tsMat = NULL, covariates = NULL)

Arguments

Details

This method constructs a ⁠C++⁠ binSeg module and sets private$.fitted to TRUE, enabling the use of ⁠$predict()⁠ and ⁠$eval()⁠. Some precomputations are performed to allow ⁠$predict()⁠ to run in linear time with respect to the number of data points (see ⁠$predict()⁠ for more details).

Returns

Invisibly returns NULL.

Method eval()

Evaluate the cost of the segment (a,b]

Usage

binSeg$eval(a, b)

Arguments

Details

The segment cost is evaluated as follows:

• L1 cost function:

  c_{L_1}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \tilde{y}_{(a+1)...b} \|_1

  where \tilde{y}_{(a+1)...b} is the coordinate-wise median of the segment. If a \ge b - 1, return 0.

• L2 cost function:

  c_{L_2}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \bar{y}_{(a+1)...b} \|_2^2

  where \bar{y}_{(a+1)...b} is the empirical mean of the segment. If a \ge b - 1, return 0.

• SIGMA cost function:

  c_{\Sigma}(y_{(a+1)...b}) := (b - a)\log \det \hat{\Sigma}_{(a+1)...b}

  where \hat{\Sigma}_{(a+1)...b} is the empirical covariance matrix of the segment without Bessel's correction. Here, if addSmallDiag = TRUE, a small bias epsilon is added to the diagonal of estimated covariance matrices to improve numerical stability.
  
  By default, addSmallDiag = TRUE and epsilon = 1e-6. In case addSmallDiag = TRUE, if the covariance matrix is numerically singular (its log-determinant cannot be computed) or its log-determinant is smaller than the lower bound p*log(epsilon), return (b - a)*p*log(epsilon), otherwise, output an error message.

• VAR(r) cost function:

  c_{\mathrm{VAR}}(y_{(a+1)...b}) := \sum_{t = \max(a, r)+1}^{b} \left\| y_t - \hat c - \sum_{j=1}^r \hat A_j y_{t-j} \right\|_2^2

  where \hat c and \hat A_j are the OLS estimates of the intercept and VAR coefficients on the segment. The lagged values y_{t-j} may come from before a+1, so only the first r observations of the whole series lack a full set of lags. If the system is singular, an approximate (minimum-norm) least-squares solve is used. If b-a < p*r+1 (i.e., not enough observations), or a > n-r (where n is the time series length), return 0.

• "LinearL2" for piecewise linear regression process with constant noise variance

  c_{\text{LinearL2}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_2^2

  where \hat{\beta} are OLS estimates on segment (a+1):b. If segment is shorter than the minimum number of points needed for OLS, return 0.

• "LinearSIGMA" for piecewise linear regression process with varying noise covariance

  c_{\text{LinearSIGMA}}(y_{(a+1):b}) := (b-a)\log \det \hat\Sigma_{(a+1):b}

  where \hat\Sigma_{(a+1):b} is the empirical covariance matrix of OLS residuals y - X\hat{\beta} on segment (a+1):b, divided by b-a with no degrees-of-freedom correction for the fitted coefficients, and otherwise estimated the same way as in the SIGMA cost function.

• "LinearL1" for piecewise linear regression process under L1 (least absolute deviations) loss

  c_{\text{LinearL1}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_1

  where \hat{\beta} is fit column-by-column via IRLS on segment (a+1):b, iterated until convergence (tol) or maxIter. Unlike the other regression costs, this has no O(1)-per-segment closed form.

Returns

The segment cost.

Method predict()

Performs binSeg given a linear penalty value, or a target number of change-points.

Usage

binSeg$predict(pen = 0, nBkps = NULL)

Arguments

Details

The algorithm recursively partitions a time series to detect multiple change-points. At each step, the algorithm identifies the segment that, if split, would result in the greatest reduction in total cost. This process continues until no further splits are possible (e.g., each segment is of minimal length or each breakpoint corresponds to a single data point).

Then, the algorithm selects the "optimal" set of break-points given the linear penalty threshold. Let [c_1, \dots, c_k, c_{k+1}] denote the set of segment end-points with 0 = c_0 < c_1 < c_2 < \dots < c_k < c_{k+1} = n, where k is the number of detected change-points and n is the total number of data points. and k is the number of change-points. Let c_{(c_{i-1}, c_i]} be the cost of segment (c_{i-1}, c_i]. The total penalised cost is then

\text{TotalCost} = \sum_{i=1}^{k+1} c_{(c_{i-1}, c_i]} + \lambda \cdot k,

where \lambda is a linear penalty applied per change-point. We then optimise over k to minimise the penalised cost function.

This approach allows detecting multiple change-points in a time series while controlling model complexity through the linear penalty threshold.

In our implementation, the recursive step is carried out during ⁠$fit()⁠. Therefore, ⁠$predict()⁠ runs in linear time with respect to the number of data points.

Temporary segment end-points are saved to private$.tmpEndPoints after ⁠$predict()⁠, enabling users to call ⁠$plot()⁠ without specifying endpoints manually.

Returns

An integer vector of regime end-points. By design, the last element is the number of observations.

Method segments()

Returns the cost and parameter estimates of each segment from the latest ⁠$predict()⁠.

Usage

binSeg$segments()

Details

Let 0 = c_0 < c_1 < \dots < c_{k+1} = n be the end-points from the latest ⁠$predict()⁠, called with either pen or nBkps. Segment i is (c_{i-1}, c_i], Cost is c_{(c_{i-1}, c_i]} and Params is its minimiser. Both modes return the first k change-points of the greedy splitting path, so the costs sum to ⁠$getHistory()$cost[k + 1]⁠. This is the cost of the greedy segmentation, not necessarily the minimal cost for k change-points (see Dynp).

Temporary end-points are cleared by ⁠$fit()⁠, so ⁠$predict()⁠ must be run again after modifying the object via its active bindings.

Returns

A list with one element per segment (Start, End]. Each element is a list with:

Start

Start index of the segment (exclusive, 0-based), same convention as ⁠$eval()⁠.

End

End index of the segment (inclusive).

Cost

The segment cost, as returned by ⁠$eval(Start, End)⁠.

Params

A named list of the segment parameter estimates, e.g. list(mean = ...) for "L2". See costFactory for the fields returned by each cost function.

Method getHistory()

Retrieves the full cost history and sequentially added breakpoints.

Usage

binSeg$getHistory()

Returns

A data.frame with three columns:

k

The number of change-points.

cost

The total unpenalised cost of the segmentation.

added_bkp

The breakpoint added at this step to achieve the cost.

Method plotElbow()

Plots the elbow curve (Total Cost vs. Number of Change-Points).

Usage

binSeg$plotElbow(maxK = NULL)

Arguments

Returns

A ggplot object.

Method plot()

Plots change-point segmentation

Usage

binSeg$plot(
  d = 1L,
  endPts,
  dimNames,
  main,
  xlab,
  tsWidth = 0.25,
  tsCol = "#5B9BD5",
  bgCol = c("#A3C4F3", "#FBB1BD"),
  bgAlpha = 0.5,
  ncol = 1L
)

Arguments

Details

Plots change-point segmentation results. Based on ggplot2. Multiple plots can easily be horizontally and vertically stacked using patchwork's operators / and |, respectively.

Returns

An object of classes gg and ggplot.

Method clone()

The objects of this class are cloneable with this method.

Usage

binSeg$clone(deep = FALSE)

Arguments

Author(s)

Minh Long Nguyen edelweiss611428@gmail.com
Toby Dylan Hocking toby.hocking@r-project.org
Charles Truong ctruong@ens-paris-saclay.fr
Huy Nhat Minh Nguyen sleepysnorlax0115@gmail.com

References

Truong, C., Oudre, L., & Vayatis, N. (2020). Selective review of offline change point detection methods. Signal Processing, 167, 107299.

Hocking, T. D. (2024). Finite Sample Complexity Analysis of Binary Segmentation. arXiv preprint arXiv:2410.08654.

Examples

## L2 example
set.seed(1121)
signals = as.matrix(c(rnorm(100,0,1),
                     rnorm(100,5,1)))
# Default L2 cost function
binSegObj = binSeg$new(minSize = 1L, jump = 1L)
binSegObj$fit(signals)
binSegObj$predict(pen = 100)
binSegObj$plot()

## SIGMA example
set.seed(111)
signals = as.matrix(c(rnorm(100,-5,1),
                      rnorm(100,-5,10),
                      rnorm(100,-5,1)))
# L2 cost function
binSegObj = binSeg$new(minSize = 1L, jump = 1L)
binSegObj$fit(signals)
# We choose pen = 50.
binSegObj$predict(pen = 50)
binSegObj$plot()

# The standard L2 cost function is not suitable.
# Use the SIGMA cost function.
binSegObj$costFunc = costFunc$new(costFunc = "SIGMA")
binSegObj$predict(pen = 50)
binSegObj$plot()

costFactory class

Description

An R6 class for fast segment-cost evaluation and parameter estimation, without a detection algorithm.

Details

costFactory builds the ⁠C++⁠ cost module selected by ⁠$costFunc⁠ at ⁠$fit()⁠, and keeps it, so every query reuses its precomputations, as PELT, binSeg and Window do. ⁠$eval()⁠ and ⁠$get_params()⁠ call the module directly: segments are ⁠(a, b]⁠ with 0-based a, and all checks are done in ⁠C++⁠.

⁠$new()⁠ only stores the costFunc object; ⁠$fit()⁠ validates and attaches the data. ⁠$costFunc⁠ is an active binding, so it can be inspected or replaced after construction – if data has already been supplied, replacing it automatically triggers ⁠$fit()⁠ again.

⁠$get_params()⁠ returns:

• "L1": median.

• "L2": mean.

• "SIGMA": mean and cov (plus epsilon on the diagonal if addSmallDiag = TRUE).

• "VAR", "LinearL2" and "LinearL1": coef, intercept first.

• "LinearSIGMA": coef and cov (plus epsilon on the diagonal if addSmallDiag = TRUE).

• "Custom": params, the output of paramFun; an empty list if paramFun is NULL.

Both covs are biased maximum-likelihood estimates: divided by the segment length b - a, with no Bessel (n - 1) or degrees-of-freedom correction.

Methods

$new()

Initialises a costFactory object.

$fit()

Constructs the ⁠C++⁠ cost module.

$eval()

Evaluates the cost of a segment.

$get_params()

Returns the parameter estimates of a segment.

$segments()

Returns the cost and parameter estimates of each segment of a given segmentation.

$clone()

Clones the R6 object.

Active bindings

Methods

Public methods

• costFactory$new()

• costFactory$fit()

• costFactory$eval()

• costFactory$get_params()

• costFactory$segments()

• costFactory$clone()

Method new()

Initialises a costFactory object. Does not build the ⁠C++⁠ cost module; call ⁠$fit()⁠ for that.

Usage

costFactory$new(costFunc)

Arguments

Returns

Invisibly returns NULL.

Method fit()

Validates the supplied data and constructs the ⁠C++⁠ cost module selected by ⁠$costFunc⁠.

Usage

costFactory$fit(tsMat = NULL, covariates = NULL)

Arguments

Details

This method constructs the ⁠C++⁠ cost module and sets private$.fitted to TRUE, enabling the use of ⁠$eval()⁠ and ⁠$get_params()⁠.

Returns

Invisibly returns NULL.

Method eval()

Evaluates the cost of the segment (a, b] with the module's eval().

Usage

costFactory$eval(a, b)

Arguments

Returns

The segment cost.

Method get_params()

Returns the parameter estimates of the segment (a, b] with the module's get_params().

Usage

costFactory$get_params(a, b)

Arguments

Returns

A named list; see Details.

Method segments()

Returns the cost and parameter estimates of each segment of a given segmentation.

Usage

costFactory$segments(endPts)

Arguments

Returns

A list with one element per segment (Start, End], in the same format as the ⁠$segments()⁠ of the segmentation classes. Each element is a list with Start (exclusive, 0-based), End (inclusive), Cost (as returned by ⁠$eval(Start, End)⁠) and Params (as returned by ⁠$get_params(Start, End)⁠).

Method clone()

The objects of this class are cloneable with this method.

Usage

costFactory$clone(deep = FALSE)

Arguments

Author(s)

Minh Long Nguyen edelweiss611428@gmail.com
Huy Nhat Minh Nguyen sleepysnorlax0115@gmail.com

Examples

set.seed(1)
tsMat = cbind(c(rnorm(100, 0), rnorm(100, 5, 5)))
cf = costFactory$new(costFunc$new("L2"))
cf$fit(tsMat)
cf$eval(0, 100)
cf$get_params(0, 100)
cf$segments(c(100, 200))

# `costFunc` is an active binding: swapping it re-fits automatically.
cf$costFunc = costFunc$new("SIGMA")
cf$eval(0, 100)

costFunc class

Description

An R6 class specifying a cost function

Details

Creates an instance of costFunc R6 class, used in initialisation of change-point detection modules. Currently supports the following cost functions:

• L1 cost function:

  c_{L_1}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \tilde{y}_{(a+1)...b} \|_1

  where \tilde{y}_{(a+1)...b} is the coordinate-wise median of the segment. If a \ge b - 1, return 0.

• L2 cost function:

  c_{L_2}(y_{(a+1)...b}) := \sum_{t = a+1}^{b} \| y_t - \bar{y}_{(a+1)...b} \|_2^2

  where \bar{y}_{(a+1)...b} is the empirical mean of the segment. If a \ge b - 1, return 0.

• SIGMA cost function:

  c_{\Sigma}(y_{(a+1)...b}) := (b - a)\log \det \hat{\Sigma}_{(a+1)...b}

  where \hat{\Sigma}_{(a+1)...b} is the empirical covariance matrix of the segment without Bessel's correction. Here, if addSmallDiag = TRUE, a small bias epsilon is added to the diagonal of estimated covariance matrices to improve numerical stability.
  
  By default, addSmallDiag = TRUE and epsilon = 1e-6. In case addSmallDiag = TRUE, if the covariance matrix is numerically singular (its log-determinant cannot be computed) or its log-determinant is smaller than the lower bound p*log(epsilon), return (b - a)*p*log(epsilon), otherwise, output an error message.

• VAR(r) cost function:

  c_{\mathrm{VAR}}(y_{(a+1)...b}) := \sum_{t = \max(a, r)+1}^{b} \left\| y_t - \hat c - \sum_{j=1}^r \hat A_j y_{t-j} \right\|_2^2

  where \hat c and \hat A_j are the OLS estimates of the intercept and VAR coefficients on the segment. The lagged values y_{t-j} may come from before a+1, so only the first r observations of the whole series lack a full set of lags. If the system is singular, an approximate (minimum-norm) least-squares solve is used. If b-a < p*r+1 (i.e., not enough observations), or a > n-r (where n is the time series length), return 0.

• "LinearL2" for piecewise linear regression process with constant noise variance

  c_{\text{LinearL2}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_2^2

  where \hat{\beta} are OLS estimates on segment (a+1):b. If segment is shorter than the minimum number of points needed for OLS, return 0.

• "LinearSIGMA" for piecewise linear regression process with varying noise covariance

  c_{\text{LinearSIGMA}}(y_{(a+1):b}) := (b-a)\log \det \hat\Sigma_{(a+1):b}

  where \hat\Sigma_{(a+1):b} is the empirical covariance matrix of OLS residuals y - X\hat{\beta} on segment (a+1):b, divided by b-a with no degrees-of-freedom correction for the fitted coefficients, and otherwise estimated the same way as in the SIGMA cost function (including the addSmallDiag/epsilon stabilisation and lower-bound fallback).

• "LinearL1" for piecewise linear regression process under L1 (least absolute deviations) loss

  c_{\text{LinearL1}}(y_{(a+1):b}) := \sum_{t=a+1}^b \| y_t - X_t \hat{\beta} \|_1

  where \hat{\beta} is fit column-by-column via Iteratively Reweighted Least Squares (IRLS), iterated until the change in the fit's cost is within tol or maxIter iterations are reached. Unlike the other regression cost functions, this has no O(1)-per-segment closed form, since IRLS must be re-run on each queried segment.

• "Custom" for a user-defined cost function supplied from R

  c_{\text{Custom}}(y_{(a+1):b}) := \text{evalFun}(y_{(a+1):b}, a, b)

  where evalFun is a user-supplied function called on the raw segment matrix, plus the segment's own ⁠(a,b]⁠ bounds – the latter let evalFun align the segment against any externally-captured, position-indexed data (e.g. a weight vector or exogenous series evalFun closes over) without the package needing to know that data exists. Because each call crosses back into R, this is substantially slower per call than the built-in costs above; see ⁠$evalFun⁠ and ⁠$paramFun⁠.

If active binding ⁠$costFunc⁠ is modified (via assignment operator), the default parameters will be used.

Methods

$new()

Initialises a costFunc object.

$pass()

Describes the costFunc object.

$clone()

Clones the costFunc object.

Active bindings

Methods

Public methods

• costFunc$new()

• costFunc$pass()

• costFunc$clone()

Method new()

Initialises a costFunc object.

Usage

costFunc$new(costFunc, ...)

Arguments

Method pass()

Returns a list of configuration parameters to initialise detection modules.

Usage

costFunc$pass()

Method clone()

The objects of this class are cloneable with this method.

Usage

costFunc$clone(deep = FALSE)

Arguments

Author(s)

Minh Long Nguyen edelweiss611428@gmail.com

Examples

## L2 costFunc (default)
costFuncObj = costFunc$new()
costFuncObj$pass()
## SIGMA costFunc
costFuncObj = costFunc$new(costFunc = "SIGMA")
costFuncObj$pass()
# Modify active bindings
costFuncObj$epsilon = 10^-5
costFuncObj$pass()
costFuncObj$costFunc = "VAR"
costFuncObj$pass()