set_smc_options {BayesMallows} | R Documentation |
Set SMC compute options
Description
Sets the SMC compute options to be used in
update_mallows.BayesMallows()
.
Usage
set_smc_options(
n_particles = 1000,
mcmc_steps = 5,
resampler = c("stratified", "systematic", "residual", "multinomial"),
latent_sampling_lag = NA_integer_,
max_topological_sorts = 1
)
Arguments
n_particles |
Integer specifying the number of particles. |
mcmc_steps |
Number of MCMC steps to be applied in the resample-move step. |
resampler |
Character string defining the resampling method to use. One of "stratified", "systematic", "residual", and "multinomial". Defaults to "stratified". While multinomial resampling was used in Stein (2023), stratified, systematic, or residual resampling typically give lower Monte Carlo error (Douc and Cappe 2005; Hol et al. 2006; Naesseth et al. 2019). |
latent_sampling_lag |
Parameter specifying the number of timesteps to go
back when resampling the latent ranks in the move step. See Section 6.2.3
of (Kantas et al. 2015) for details. The |
max_topological_sorts |
User when pairwise preference data are provided,
and specifies the maximum number of topological sorts of the graph
corresponding to the transitive closure for each user will be used as
initial ranks. Defaults to 1, which means that all particles get the same
initial augmented ranking. If larger than 1, the initial augmented ranking
for each particle will be sampled from a set of maximum size
|
Value
An object of class "SMCOptions".
Lag parameter in move step
The parameter latent_sampling_lag
corresponds to L
in
(Kantas et al. 2015). Its use in this package is can be
explained in terms of Algorithm 12 in
(Stein 2023). The
relevant line of the algorithm is:
for j = 1 : M_{t}
do
M-H step: update \tilde{\mathbf{R}}_{j}^{(i)}
with proposal
\tilde{\mathbf{R}}_{j}' \sim q(\tilde{\mathbf{R}}_{j}^{(i)} |
\mathbf{R}_{j}, \boldsymbol{\rho}_{t}^{(i)}, \alpha_{t}^{(i)})
.
end
Let L
denote the value of latent_sampling_lag
. With this parameter,
we modify for algorithm so it becomes
for j = M_{t-L+1} : M_{t}
do
M-H step: update \tilde{\mathbf{R}}_{j}^{(i)}
with proposal
\tilde{\mathbf{R}}_{j}' \sim q(\tilde{\mathbf{R}}_{j}^{(i)} |
\mathbf{R}_{j}, \boldsymbol{\rho}_{t}^{(i)}, \alpha_{t}^{(i)})
.
end
This means that with L=0
no move step is performed on any latent
ranks, whereas L=1
means that the move step is only applied to the
parameters entering at the given timestep. The default,
latent_sampling_lag = NA
means that L=t
at each timestep, and hence
all latent ranks are part of the move step at each timestep.
References
Douc R, Cappe O (2005).
“Comparison of resampling schemes for particle filtering.”
In ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005..
doi:10.1109/ispa.2005.195385, http://dx.doi.org/10.1109/ISPA.2005.195385.
Hol JD, Schon TB, Gustafsson F (2006).
“On Resampling Algorithms for Particle Filters.”
In 2006 IEEE Nonlinear Statistical Signal Processing Workshop.
doi:10.1109/nsspw.2006.4378824, http://dx.doi.org/10.1109/NSSPW.2006.4378824.
Kantas N, Doucet A, Singh SS, Maciejowski J, Chopin N (2015).
“On Particle Methods for Parameter Estimation in State-Space Models.”
Statistical Science, 30(3).
ISSN 0883-4237, doi:10.1214/14-sts511, http://dx.doi.org/10.1214/14-STS511.
Naesseth CA, Lindsten F, Schön TB (2019).
“Elements of Sequential Monte Carlo.”
Foundations and Trends® in Machine Learning, 12(3), 187–306.
ISSN 1935-8245, doi:10.1561/2200000074, http://dx.doi.org/10.1561/2200000074.
Stein A (2023).
Sequential Inference with the Mallows Model.
Ph.D. thesis, Lancaster University.
See Also
Other preprocessing:
get_transitive_closure()
,
set_compute_options()
,
set_initial_values()
,
set_model_options()
,
set_priors()
,
set_progress_report()
,
setup_rank_data()