Skip to content

Reducing the number of times the gradients and fit are computed to im… #98

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
jhorzek merged 1 commit into from
Jul 19, 2026
Merged

Reducing the number of times the gradients and fit are computed to im… #98

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
104 changes: 66 additions & 38 deletions include/lesstimate/glmnet_class.h
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -238,7 +238,15 @@ namespace lessSEM
const double sigma,
const double gamma,
const int maxIterLine,
const int verbose)
const int verbose,
// The line search needs to compute the fit and the gradients. Because
// the next optimization step also needs those, we can save them here and
// make them available to the caller by reference.
// The additional flag acceptedOut tells the caller if the line search
// created a non-acceptable step.
double &fitAcceptedOut,
arma::rowvec &modelGradientsAcceptedOut,
bool &acceptedOut)
{

static_cast<void>(verbose); // currently not used; for later use
Expand All @@ -253,6 +261,10 @@ namespace lessSEM
double p_k; // new penalty value
double f_k; // new combined fit

// signal to the caller that no accepted step is available yet
acceptedOut = false;
fitAcceptedOut = arma::datum::nan;

// get penalized M2LL for step size 0:

double pen_0 = penalty_.getValue(parameters_kMinus1,
Expand Down Expand Up @@ -348,6 +360,10 @@ namespace lessSEM
// go to next iteration and test smaller step size
continue;
}
// Update the fit / gradient and acceptOut flag for the caller
fitAcceptedOut = fit_k;
modelGradientsAcceptedOut = gradients_k;
acceptedOut = true;
// else
break;
}
Expand Down Expand Up @@ -403,17 +419,15 @@ namespace lessSEM
arma::rowvec direction(startingValues.n_elem);

// prepare fit elements
// fit of the smooth part of the fit function
double fit_k = model_.fit(parameters_k,
parameterLabels) +
smoothPenalty_.getValue(parameters_k,
parameterLabels,
tuningParameters);
double fit_kMinus1 = model_.fit(parameters_kMinus1,
parameterLabels) +
smoothPenalty_.getValue(parameters_kMinus1,
parameterLabels,
tuningParameters);
// fit of the smooth part of the fit function. At this part
// fit_k and fit_kMinus1 are identical.
double fit_starting = model_.fit(startingValues,
parameterLabels) +
smoothPenalty_.getValue(startingValues,
parameterLabels,
tuningParameters);
double fit_k = fit_starting;
double fit_kMinus1 = fit_starting;
// add non-differentiable part
double penalizedFit_k = fit_k +
penalty_.getValue(parameters_k,
Expand All @@ -432,17 +446,15 @@ namespace lessSEM

// prepare gradient elements
// NOTE: We combine the gradients of the smooth functions (the log-Likelihood)
// of the model and the smooth penalty function (e.g., ridge)
// of the model and the smooth penalty function (e.g., ridge). As above,
// parameters_k and parameters_kMinus1 are both equal to startingValues, so the
// model gradient and smooth penalty gradient only have to be evaluated once.
arma::rowvec gradients_k = model_.gradients(parameters_k,
parameterLabels) +
smoothPenalty_.getGradients(parameters_k,
parameterLabels,
tuningParameters); // ridge part
arma::rowvec gradients_kMinus1 = model_.gradients(parameters_kMinus1,
parameterLabels) +
smoothPenalty_.getGradients(parameters_kMinus1,
parameterLabels,
tuningParameters); // ridge part
arma::rowvec gradients_kMinus1 = gradients_k;

// prepare Hessian elements
arma::mat Hessian_k(startingValues.n_elem, startingValues.n_elem, arma::fill::zeros),
Expand Down Expand Up @@ -472,12 +484,6 @@ namespace lessSEM
Rcpp::checkUserInterrupt();
#endif

// the gradients will be used by the inner iteration to compute the new
// parameters
gradients_kMinus1 = model_.gradients(parameters_kMinus1, parameterLabels) +
smoothPenalty_.getGradients(parameters_kMinus1, parameterLabels, tuningParameters); // ridge part

// find step direction
direction = glmnetInner(parameters_kMinus1,
gradients_kMinus1,
Hessian_kMinus1,
Expand All @@ -487,7 +493,13 @@ namespace lessSEM
control_.breakInner,
control_.verbose);

// find length of step in direction
// find length of step in direction. The line search already evaluates the
// smooth fit and the (model-only) gradients at the accepted step; we reuse
// them below instead of re-evaluating.
double fit_ls;
arma::rowvec modelGradients_ls(gradients_kMinus1.n_elem);
modelGradients_ls.fill(arma::datum::nan);
bool ls_accepted = false;
parameters_k = glmnetLineSearch(model_,
penalty_,
smoothPenalty_,
Expand All @@ -504,20 +516,36 @@ namespace lessSEM
control_.sigma,
control_.gamma,
control_.maxIterLine,
control_.verbose);
control_.verbose,
fit_ls,
modelGradients_ls,
ls_accepted);

// get gradients of differentiable part
gradients_k = model_.gradients(parameters_k,
parameterLabels) +
smoothPenalty_.getGradients(parameters_k,
parameterLabels,
tuningParameters);
// fit of the smooth part of the fit function
fit_k = model_.fit(parameters_k,
parameterLabels) +
smoothPenalty_.getValue(parameters_k,
parameterLabels,
tuningParameters);
if (ls_accepted)
{
// reuse the fit and the model-only gradients from the accepted line
// search step (the smooth penalty parts are added here)
gradients_k = modelGradients_ls +
smoothPenalty_.getGradients(parameters_k,
parameterLabels,
tuningParameters);
fit_k = fit_ls;
}
else
{
// line search did not accept a step: fall back to a fresh evaluation at
// the returned parameters_k
gradients_k = model_.gradients(parameters_k,
parameterLabels) +
smoothPenalty_.getGradients(parameters_k,
parameterLabels,
tuningParameters);
fit_k = model_.fit(parameters_k,
parameterLabels) +
smoothPenalty_.getValue(parameters_k,
parameterLabels,
tuningParameters);
}
// add non-differentiable part
penalizedFit_k = fit_k +
penalty_.getValue(parameters_k,
Expand Down
32 changes: 17 additions & 15 deletions include/lesstimate/ista_class.h
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -213,12 +213,11 @@ namespace lessSEM
arma::mat quadr, parchTimeGrad;
numericVector randomNumber; // for stochastic Barzilai Borwein

// prepare fit elements
// prepare fit elements
double fit_k = (1.0 / control_.sampleSize) * model_.fit(startingValues, parameterLabels) +
smoothPenalty_.getValue(parameters_k, parameterLabels, smoothTuningParameters), // ridge penalty part
fit_kMinus1 = (1.0 / control_.sampleSize) * model_.fit(startingValues, parameterLabels) +
smoothPenalty_.getValue(parameters_kMinus1, parameterLabels, smoothTuningParameters), // ridge penalty part,
penalty_k = 0.0;
smoothPenalty_.getValue(parameters_k, parameterLabels, smoothTuningParameters),
fit_kMinus1 = fit_k,
penalty_k = 0.0;
double penalizedFit_k, penalizedFit_kMinus1;
arma::rowvec gradients_k, gradients_kMinus1, gradient_y_k;

Expand All @@ -235,14 +234,12 @@ namespace lessSEM

// prepare gradient elements
// NOTE: We combine the gradients of the smooth functions (the log-Likelihood)
// of the model and the smooth penalty function (e.g., ridge)
// of the model and the smooth penalty function (e.g., ridge).
gradients_k = (1.0 / control_.sampleSize) * model_.gradients(parameters_k, parameterLabels) +
smoothPenalty_.getGradients(parameters_k, parameterLabels, smoothTuningParameters); // ridge part
gradients_kMinus1 = (1.0 / control_.sampleSize) * model_.gradients(parameters_kMinus1, parameterLabels) +
smoothPenalty_.getGradients(parameters_kMinus1, parameterLabels, smoothTuningParameters); // ridge part
gradients_kMinus1 = gradients_k;
// for acceleration:
gradient_y_k = (1.0 / control_.sampleSize) * model_.gradients(parameters_kMinus1, parameterLabels) +
smoothPenalty_.getGradients(parameters_kMinus1, parameterLabels, smoothTuningParameters); // ridge part
gradient_y_k = gradients_k;

// breaking flags
bool breakInner = false, // if true, the inner iteration is exited
Expand Down Expand Up @@ -389,11 +386,16 @@ namespace lessSEM
continue;
}

gradients_k = (1.0 / control_.sampleSize) * model_.gradients(parameters_k,
parameterLabels) +
smoothPenalty_.getGradients(parameters_k,
parameterLabels,
smoothTuningParameters); // ridge part
// gradients_k is already computed at parameters_k when the inner
// loop converged. We recompute only if the inner loop did not converge.
if (!breakInner)
{
gradients_k = (1.0 / control_.sampleSize) * model_.gradients(parameters_k,
parameterLabels) +
smoothPenalty_.getGradients(parameters_k,
parameterLabels,
smoothTuningParameters); // ridge part
}

fits(outer_iteration + 1) = penalizedFit_k;

Expand Down
26 changes: 15 additions & 11 deletions include/lesstimate/model.h
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -24,8 +24,8 @@ namespace lessSEM
* @param parameterLabels stringVector with parameterLabels
* @return double
*/
virtual double fit(arma::rowvec parameterValues,
stringVector parameterLabels) = 0;
virtual double fit(const arma::rowvec& parameterValues,
const stringVector& parameterLabels) = 0;

/**
* @brief gradients method with arguments parameterValues(arma::rowvec) and parameterLabels(stringVector; see common_headers.h) * specifying the parameter values and the labels of the paramters. The function should return the gradients(arma::rowvec).
Expand All @@ -35,28 +35,32 @@ namespace lessSEM
* @param parameterLabels stringVector with parameterLabels
* @return arma::rowvec gradients
*/
virtual arma::rowvec gradients(arma::rowvec parameterValues,
stringVector parameterLabels)
virtual arma::rowvec gradients(const arma::rowvec& parameterValues,
const stringVector& parameterLabels)
{
arma::rowvec gradients(parameterValues.n_elem);
// The default central-difference implementation mutates the parameter
// vector to apply +/- stepSize. With a const reference interface, take a
// local copy here; the caller's value is left untouched.
arma::rowvec perturbedParameters = parameterValues;
arma::rowvec gradients(perturbedParameters.n_elem);
gradients.fill(arma::fill::zeros);
// define stepSize used in numerically approximated gradients:
double stepSize = 1e-5;

for (unsigned int i = 0; i < parameterValues.n_elem; i++)
for (unsigned int i = 0; i < perturbedParameters.n_elem; i++)
{

// step forward
parameterValues(i) += stepSize;
gradients(i) = fit(parameterValues,
perturbedParameters(i) += stepSize;
gradients(i) = fit(perturbedParameters,
parameterLabels);

// step backward
parameterValues(i) -= 2.0 * stepSize;
gradients(i) -= fit(parameterValues,
perturbedParameters(i) -= 2.0 * stepSize;
gradients(i) -= fit(perturbedParameters,
parameterLabels);
// reset
parameterValues(i) += stepSize;
perturbedParameters(i) += stepSize;

// compute gradient
gradients(i) /= 2.0 * stepSize;
Expand Down
Loading