Update a Bayesian Mallows model with new users
Update a Bayesian Mallows model estimated using the Metropolis-Hastings algorithm in compute_mallows() using the sequential Monte Carlo algorithm described in \insertCite steinSequentialInferenceMallows2023;textualBayesMallows.
update_mallows(model, new_data, ...) ## S3 method for class 'BayesMallowsPriorSamples' update_mallows( model, new_data, model_options = set_model_options(), smc_options = set_smc_options(), compute_options = set_compute_options(), priors = model$priors, pfun_estimate = NULL, ... ) ## S3 method for class 'BayesMallows' update_mallows( model, new_data, model_options = set_model_options(), smc_options = set_smc_options(), compute_options = set_compute_options(), priors = model$priors, ... ) ## S3 method for class 'SMCMallows' update_mallows(model, new_data, ...)
model: A model object of class "BayesMallows" returned from compute_mallows(), an object of class "SMCMallows" returned from this function, or an object of class "BayesMallowsPriorSamples" returned from sample_prior().new_data: An object of class "BayesMallowsData" returned from setup_rank_data(). The object should contain the new data being provided....: Optional arguments. Currently not used.model_options: An object of class "BayesMallowsModelOptions" returned from set_model_options().smc_options: An object of class "SMCOptions" returned from set_smc_options().compute_options: An object of class "BayesMallowsComputeOptions" returned from set_compute_options().priors: An object of class "BayesMallowsPriors" returned from set_priors(). Defaults to the priors used in model.pfun_estimate: Object returned from estimate_partition_function(). Defaults to NULL, and will only be used for footrule, Spearman, or Ulam distances when the cardinalities are not available, cf. get_cardinalities(). Only used by the specialization for objects of type "BayesMallowsPriorSamples".An updated model, of class "SMCMallows".
## Not run: set.seed(1) # UPDATING A MALLOWS MODEL WITH NEW COMPLETE RANKINGS # Assume we first only observe the first four rankings in the potato_visual # dataset data_first_batch <- potato_visual[1:4, ] # We start by fitting a model using Metropolis-Hastings mod_init <- compute_mallows( data = setup_rank_data(data_first_batch), compute_options = set_compute_options(nmc = 10000)) # Convergence seems good after no more than 2000 iterations assess_convergence(mod_init) burnin(mod_init) <- 2000 # Next, assume we receive four more observations data_second_batch <- potato_visual[5:8, ] # We can now update the model using sequential Monte Carlo mod_second <- update_mallows( model = mod_init, new_data = setup_rank_data(rankings = data_second_batch), smc_options = set_smc_options(resampler = "systematic") ) # This model now has a collection of particles approximating the posterior # distribution after the first and second batch # We can use all the posterior summary functions as we do for the model # based on compute_mallows(): plot(mod_second) plot(mod_second, parameter = "rho", items = 1:4) compute_posterior_intervals(mod_second) # Next, assume we receive the third and final batch of data. We can update # the model again data_third_batch <- potato_visual[9:12, ] mod_final <- update_mallows( model = mod_second, new_data = setup_rank_data(rankings = data_third_batch)) # We can plot the same things as before plot(mod_final) compute_consensus(mod_final) # UPDATING A MALLOWS MODEL WITH NEW OR UPDATED PARTIAL RANKINGS # The sequential Monte Carlo algorithm works for data with missing ranks as # well. This both includes the case where new users arrive with partial ranks, # and when previously seen users arrive with more complete data than they had # previously. # We illustrate for top-k rankings of the first 10 users in potato_visual potato_top_10 <- ifelse(potato_visual[1:10, ] > 10, NA_real_, potato_visual[1:10, ]) potato_top_12 <- ifelse(potato_visual[1:10, ] > 12, NA_real_, potato_visual[1:10, ]) potato_top_14 <- ifelse(potato_visual[1:10, ] > 14, NA_real_, potato_visual[1:10, ]) # We need the rownames as user IDs (user_ids <- 1:10) # First, users provide top-10 rankings mod_init <- compute_mallows( data = setup_rank_data(rankings = potato_top_10, user_ids = user_ids), compute_options = set_compute_options(nmc = 10000)) # Convergence seems fine. We set the burnin to 2000. assess_convergence(mod_init) burnin(mod_init) <- 2000 # Next assume the users update their rankings, so we have top-12 instead. mod1 <- update_mallows( model = mod_init, new_data = setup_rank_data(rankings = potato_top_12, user_ids = user_ids), smc_options = set_smc_options(resampler = "stratified") ) plot(mod1) # Then, assume we get even more data, this time top-14 rankings: mod2 <- update_mallows( model = mod1, new_data = setup_rank_data(rankings = potato_top_14, user_ids = user_ids) ) plot(mod2) # Finally, assume a set of new users arrive, who have complete rankings. potato_new <- potato_visual[11:12, ] # We need to update the user IDs, to show that these users are different (user_ids <- 11:12) mod_final <- update_mallows( model = mod2, new_data = setup_rank_data(rankings = potato_new, user_ids = user_ids) ) plot(mod_final) # We can also update models with pairwise preferences # We here start by running MCMC on the first 20 assessors of the beach data # A realistic application should run a larger number of iterations than we # do in this example. set.seed(3) dat <- subset(beach_preferences, assessor <= 20) mod <- compute_mallows( data = setup_rank_data( preferences = beach_preferences), compute_options = set_compute_options(nmc = 3000, burnin = 1000) ) # Next we provide assessors 21 to 24 one at a time. Note that we sample the # initial augmented rankings in each particle for each assessor from 200 # different topological sorts consistent with their transitive closure. for(i in 21:24){ mod <- update_mallows( model = mod, new_data = setup_rank_data( preferences = subset(beach_preferences, assessor == i), user_ids = i), smc_options = set_smc_options(latent_sampling_lag = 0, max_topological_sorts = 200) ) } # Compared to running full MCMC, there is a downward bias in the scale # parameter. This can be alleviated by increasing the number of particles, # MCMC steps, and the latent sampling lag. plot(mod) compute_consensus(mod) ## End(Not run)
Other modeling: burnin(), burnin<-(), compute_mallows(), compute_mallows_mixtures(), compute_mallows_sequentially(), sample_prior()
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