inscoreopt: In-Sample Score Optimisation by Stochastic Gradient Descent

In ProbReco: Score Optimal Probabilistic Forecast Reconciliation

In-Sample Score Optimisation by Stochastic Gradient Descent

Description

Function to find a reconciliation matrix that optimises total score using training data. Stochastic gradient descent is used for optimisation with gradients found using automatic differentiation. This function differs from scoreopt in two main ways. First, formulation of base probabilistic forecasts is carried out from one of four options depending on whether dependence and/or Gaussianity is assumed. Second, the optimistation is based on in-sample predictions rather than a rolling window of out-of sample forecasts. For more flexibility use scoreopt.

Usage

inscoreopt(
  y,
  yhat,
  S,
  Ginit = c(rep(0, ncol(S)), as.vector(solve(t(S) %*% S, t(S)))),
  control = list(),
  basedep = "joint",
  basedist = "gaussian",
  Q = 500,
  score = list(score = "energy", alpha = 1),
  trace = FALSE
)

Arguments

y	Matrix of data, each column responds to an observation, each row corresponds to a variable.
yhat	Matrix of predicted values, each column responds to an observation, each row corresponds to a variable.
S	Matrix encoding linear constraints.
Ginit	Initial values of reconciliation parameters d and G where \tilde{y}=S(d+G\hat{y}). The first m elements correspond to translation vector d, while the remaining elements correspond to the matrix G where the elements are filled in column-major order. Default is least squares.
control	Tuning parameters for SGD. See scoreopt.control for more details
basedep	Should base distributions be assumed to be dependent (joint) or independent? Default is "joint", set to "independent" for independence.
basedist	Should base distributions be assumed to be Gaussian or bootstrapped? Default is "gaussian" set to "bootstrap" for bootstrapping.
Q	Number of Monte Carlo iterations used to estimate score
score	Score to be used. This must be a list with two elements: score for the scoring rule (currently only energy supported) and alpha, an additional parameter used in the score (e.g. power in energy score, default is 1).
trace	Flag to keep details of SGD. Default is FALSE

Value

Optimised reconciliation parameters.

d	Translation vector for reconciliation.
G	Reconciliation matrix (G).
val	The estimated optimal total score.
Gvec_store	A matrix of Gvec (d and G vectorised) where each column corresponds to an iterate of SGD (only produced when trace=TRUE).
val_store	A vector where each element gives the value of the objective function for each iterate of SGD (only produced when trace=TRUE).

See Also

Other ProbReco functions: scoreopt.control(), scoreopt(), total_score()

Examples

#Define S matrix
S<-matrix(c(1,1,1,0,0,1),3,2, byrow = TRUE)
#Set data (only 10 training observations used for speed)
y<-S%*%(matrix(rnorm(20),2,10)+1)
#Set point forecasts (chosen randomly from (0,1))
yhat<-matrix(runif(nrow(y)*ncol(y)),nrow(y),ncol(y))
#Find weights by SGD (Q set to 20 so that example runs quickly)
out<-inscoreopt(y,yhat,S,Q=20)

ProbReco documentation built on April 5, 2023, 5:10 p.m.