specialized_models: Specialized High-Level Estimators Using Proximal HMC

In pHMC: Proximal Hamiltonian Monte Carlo for Non-Smooth Bayesian Inference

Specialized High-Level Estimators Using Proximal HMC

Description

Fits sparse logistic regression, nuclear-norm low-rank matrix recovery, and Bayesian Lasso linear regression models using the p-HMC algorithm, matching the case studies in Section VI of Shukla, Vats, and Chi (2025).

Usage

phmc_logistic(
  X,
  y,
  alpha = 1,
  lambda_g = 0.01,
  n_draws = 2000,
  epsilon = 0.002,
  L = 10,
  ...
)

phmc_matrix(
  X,
  alpha = 1,
  sigma_sq = 1,
  lambda_g = 1e-04,
  n_draws = 1000,
  epsilon = 0.001,
  L = 10,
  ...
)

phmc_lasso(
  X,
  y,
  alpha = 1,
  sigma_sq = 1,
  lambda_g = 0.01,
  n_draws = 2000,
  epsilon = 0.005,
  L = 10,
  ...
)

Arguments

X	Numeric design matrix (for regression models) or observed noisy matrix (for matrix recovery).
y	Numeric binary response vector for logistic regression or continuous response vector for Lasso.
alpha	Numeric scalar > 0. Regularization penalty parameter (default 1.0).
lambda_g	Numeric scalar > 0. Moreau-Yosida envelope regularization parameter.
n_draws	Integer > 0. Total number of MCMC iterations.
epsilon	Numeric scalar > 0. Step size parameter.
L	Integer >= 1. Number of leapfrog steps.
...	Additional arguments passed to phmc.
sigma_sq	Numeric scalar > 0. Error variance parameter (default 1.0).

Value

An object of class "phmc", which is a list containing posterior MCMC draws, parameter summary estimates matrix, log-likelihood, information criteria (AIC, BIC, DIC), acceptance rate, and execution metadata. See phmc for detailed descriptions of the list elements and output meaning.

References

Shukla A, Vats D, Chi EC (2025). “Proximal Hamiltonian Monte Carlo.” arXiv preprint, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.2510.22252")}.

pHMC documentation built on Aug. 21, 2026, 5:18 p.m.