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Multivariate Multiple Independent Change-Point (MICH) Model

Source: R/mich_matrix.R
mich_matrix.Rd

Fits the multivariate version of the MICH model for mean change-points. Number of change-points can either be fixed or mich_matrix() will search for the number of changes that maximizes the ELBO when L_auto == TRUE.

Usage

mich_matrix(
  y,
  fit_intercept,
  fit_scale,
  standardize,
  L,
  L_auto,
  L_max,
  pi_l_weighted,
  tol,
  verbose,
  max_iter,
  reverse,
  detect,
  merge_level,
  merge_prob,
  restart,
  n_search,
  increment,
  omega_l,
  log_pi_l
)

Arguments

y

A numeric matrix. T x d matrix of observations.

fit_intercept

A logical. If fit_intercept == TRUE, then an intercept is estimated, otherwise mu_0 = rep(0,d).

fit_scale

A logical. If fit_scale == TRUE, then the precision matrix is estimated using the inverse of var(diff(y)), otherwise it is assumed that the precision matrix is equal to diag(d).

standardize

A logical. If standardize == TRUE, then y is centered and rescaled before fitting.

L

An integer. Number of mean-scp components included in model. If L_auto == TRUE then L lower bounds the number of change-points in the model.

L_auto

A logical. If L_auto == TRUE, then mich_matrix() returns the number of changes between L and L_max that maximizes the ELBO (see Appendix C.4 of Berlind, Cappello, Madrid Padilla (2025)).

L_max

L An integer. If L_auto == TRUE then L_max upper bounds the number of change-points included in the model.

pi_l_weighted

A logical. If pi_l_weighted == TRUE, then the weighted priors specified in Appendix C.2 of Berlind, Cappello, Madrid Padilla (2025) are used.

tol

A scalar. Convergence tolerance for relative increase in ELBO.

verbose

A logical. If verbose == TRUE and L_auto == FALSE, then the value of the ELBO is printed every 5000th iteration. If verbose == TRUE and L_auto == TRUE, the the value of the ELBO is printed for each L as mich_matrix() searches over [L, L_max].

max_iter

An integer. Maximum number of iterations. If ELBO does not converge before max_iter is reached, then converged == FALSE in the returned fit object.

reverse

A logical. If reverse == TRUE then MICH is fit to y[T:1,] and the model parameters are reversed in post-processing.

detect

A scalar. The detection criteria. Each component of the model detects a change-point only if the posterior credible set for that component contains fewer than detect indices.

merge_level

A scalar. A value between (0,1) for the significance level to construct credible sets at when merging. A model component is only considered to be a candidate for merging if its merge_level-level credible set contains fewer than detect indices.

merge_prob

A scalar. A value between (0,1) indicating the merge criterion. If the posterior probability that two components identify the same change is greater than merge_level, then those components are merged (see Appendix C.3 of Berlind, Cappello, Madrid Padilla (2025)).

restart

A logical. If restart == TRUE and L_auto == TRUE then after n_search increments of L, if the ELBO has not increased, mich_matrix() will restart by setting the L components to the null model initialization (except for the components with maximum posterior probabilities > 0.9) then refit and begin the search again.

An integer. Grid search parameter. Number of times to increment L before terminating automatic procedure when L_auto == TRUE.

increment

An integer. Number of components to increment L by when L_auto == TRUE.

omega_l

A scalar. Prior precision parameter for mean-scp components of model.

log_pi_l

A numeric matrix. T x L matrix of prior log change-point location probabilities for each of the L mean change-points.

Value

A list. Parameters of the variational approximation the MICH posterior distribution, including:

  • y: A numeric matrix. Original data.

  • Sigma: A numeric matrix. Estimate of the precision if fit_scale == TRUE.

  • L: An integer. Number of components included in model.

  • pi_bar: A numeric matrix. A T x L matrix of posterior change-point location probabilites.

  • residual: A numeric matrix. Residual y - mu.

  • mu: A numeric matrix. Posterior estimate of mean signal.

  • mu_0: A numeric vector. Estimate of the intercept.

  • post_params: A list. List of posterior parameters for each mean-scp component.

  • elbo: A numeric vector. Value of the ELBO after each iteration.

  • converged: A logical. Indicates whether relative increase in the ELBO is less than tol.