Package {pHMC}

Type:	Package
Title:	Proximal Hamiltonian Monte Carlo for Non-Smooth Bayesian Inference
Version:	0.1.0
Description:	Implements the Proximal Hamiltonian Monte Carlo (p-HMC) algorithm for Bayesian sampling and estimation from non-differentiable target densities. The method decomposes a target potential into a smooth component f(x) and a non-smooth convex component g(x), approximating only g(x) via its Moreau-Yosida envelope while retaining exact gradient information for f(x). This approach, based on the methodology described in Shukla, Vats, and Chi (2025) <doi:10.48550/arXiv.2510.22252>, yields improved Hamiltonian conservation over full-potential smoothing approaches. The package provides generalized routines accepting user-defined probability density functions, log-likelihoods, priors, and proximal operators, together with automated hyperparameter tuning for the Moreau-Yosida regularization parameter, Markov chain Monte Carlo convergence diagnostics, effective sample size computation, and model evaluation metrics including the Akaike information criterion and Bayesian information criterion.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
RoxygenNote:	7.3.3
Imports:	stats, graphics, grDevices, utils, Matrix
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-08-05 11:36:31 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-21 12:40:09 UTC

Generalized Proximal Hamiltonian Monte Carlo Sampler and Estimator

Description

Fits Bayesian models and estimates parameters using the Proximal Hamiltonian Monte Carlo (p-HMC) algorithm for non-differentiable target densities as proposed by Shukla, Vats, and Chi (2025).

Usage

phmc(
  fn,
  grad_f = NULL,
  g = NULL,
  prox_fn = "l1",
  start,
  data = NULL,
  n_draws = 2000,
  burnin = floor(n_draws/2),
  thin = 1,
  epsilon = 0.01,
  L = 10,
  lambda_g = 0.01,
  M = NULL,
  tune_lambda = FALSE,
  verbose = FALSE,
  ...
)

Arguments

Value

An object of class "phmc", which is a list containing:

References

Shukla A, Vats D, Chi EC (2025). “Proximal Hamiltonian Monte Carlo.” arXiv preprint, doi:10.48550/arXiv.2510.22252.

Examples

set.seed(42)
y_data <- rnorm(100, mean = 1, sd = 0.5)
f_smooth <- function(x, y) 0.5 * sum((y - x)^2)
grad_f_smooth <- function(x, y) -sum(y - x)
fit <- phmc(fn = f_smooth, grad_f = grad_f_smooth,
            prox_fn = "l1", start = 0.5,
            data = y_data, lambda_g = 0.01,
            n_draws = 500)
summary(fit)

S3 Methods for Proximal Hamiltonian Monte Carlo Objects

Description

Provides summary, printing, extraction, and diagnostic plotting methods for objects returned by phmc.

Usage

## S3 method for class 'phmc'
print(x, ...)

## S3 method for class 'phmc'
summary(object, ...)

## S3 method for class 'summary.phmc'
print(x, ...)

## S3 method for class 'phmc'
coef(object, ...)

## S3 method for class 'phmc'
vcov(object, ...)

## S3 method for class 'phmc'
logLik(object, ...)

## S3 method for class 'phmc'
plot(x, type = c("all", "trace", "acf", "density"), par_indices = NULL, ...)

Arguments

Value

Depending on the S3 method invoked, returns the following:

print.phmc

Invisibly returns the input object x of class "phmc" (called for its side effect of printing summary metrics to the console).

summary.phmc

Returns an object of class "summary.phmc", which is a list containing model parameter estimates, acceptance rate, log-likelihood, information criteria (AIC, BIC, DIC), elapsed time, and regularization parameter lambda_g.

print.summary.phmc

Invisibly returns the input object x of class "summary.phmc" (called for its side effect of printing detailed summary results to the console).

coef.phmc

Returns a named numeric vector of class "numeric" containing posterior mean parameter estimates.

vcov.phmc

Returns a numeric matrix of class "matrix" containing the empirical posterior variance-covariance matrix of the MCMC parameter draws.

logLik.phmc

Returns an object of class "logLik" representing the log-likelihood value evaluated at the MAP estimate, with attributes "df" (number of estimated parameters) and "nobs" (number of retained MCMC draws).

plot.phmc

Invisibly returns the input object x of class "phmc" (called for its side effect of generating diagnostic MCMC trace plots, autocorrelation functions, and posterior density curves).

Hyperparameter Tuning for Moreau-Yosida Regularization Parameter

Description

Evaluates the relative Hamiltonian error metric across a grid of candidate lambda_g values to select the optimal regularization parameter balancing potential smoothness and Hamiltonian conservation, as detailed in Section V of Shukla, Vats, and Chi (2025).

Usage

phmc_tune(
  fn,
  grad_f = NULL,
  g = NULL,
  prox_fn = "l1",
  start,
  lambda_grid = 10^seq(-5, 0, length.out = 15),
  epsilon = 0.001,
  L = 10,
  M = NULL,
  target_rel_err = 1e-04,
  data = NULL,
  seed = NULL,
  ...
)

Arguments

Details

The relative Hamiltonian error metric is defined as

R_{\lambda_g} = \left| \frac{H(x_0, p_0) - H(\tilde{T}_{\epsilon, L}^{\lambda_g}(x_0, p_0))}{H(x_0, p_0)} \right|.

Value

An object of class "phmc_tune", which is a list containing:

References

Shukla A, Vats D, Chi EC (2025). “Proximal Hamiltonian Monte Carlo.” arXiv preprint, doi:10.48550/arXiv.2510.22252.

Proximal Mapping Operators and Moreau-Yosida Envelope Gradients

Description

Evaluates proximal operators for common non-smooth penalties (L1 norm, nuclear norm, L2 norm, elastic net) and computes the gradient of the Moreau-Yosida envelope as described in Shukla, Vats, and Chi (2025).

Usage

prox_l1(x, tau)

prox_l2(x, tau)

prox_elastic_net(x, tau, alpha = 0.5)

prox_nuclear(x, tau)

grad_my_envelope(x, prox_fn = "l1", lambda_g = 0.01, ...)

Arguments

Details

The Moreau-Yosida envelope of a proper, lower-semicontinuous, convex function g with scaling parameter \lambda_g > 0 is defined as

g_{\lambda_g}(x) = \inf_y \{g(y) + \frac{1}{2\lambda_g} \|y - x\|^2\}.

Its gradient is given by

\nabla g_{\lambda_g}(x) = \frac{1}{\lambda_g}(x - \mathrm{prox}_{\lambda_g}^{g}(x)).

Value

For prox_l1, prox_l2, prox_elastic_net, and prox_nuclear, returns a numeric vector or matrix of class "numeric" or "matrix" (matching the shape and dimensions of input x) representing the evaluated proximal point operator. For grad_my_envelope, returns a numeric vector or matrix of class "numeric" or "matrix" containing the computed gradient of the Moreau-Yosida envelope at x.

References

Shukla A, Vats D, Chi EC (2025). “Proximal Hamiltonian Monte Carlo.” arXiv preprint, doi:10.48550/arXiv.2510.22252.

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

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, doi:10.48550/arXiv.2510.22252.