org.replikativ.foerster.smc2 — org.replikativ/foerster 0.1.61

Static parameters of state-space programs: particle marginal Metropolis-Hastings (PMMH; Andrieu, Doucet & Holenstein 2010) and SMC² (Chopin, Jacob & Papaspiliopoulos 2013).

A program's parameters are named sample sites (:params, a set of addresses). Run with those sites constrained to θ (foerster.trace/policy :constraints), SMC's evidence estimate is p(θ)·p̂(y | θ) — a constrained site adds its prior density to the weight — so the posterior ratio of two parameter values is the difference of two SMC log-evidences.

• pmmh is a Markov chain over θ whose every proposal runs an SMC over the program's other sites: exact for any number of particles.
• smc2 is online: θ-particles each carry an inner streaming SMC (foerster.smc/stream); a pushed observation reweights each by its inner evidence increment; when the θ-particles' ESS falls they are resampled — a duplicate forks its inner population's worlds, so copies evolve independently — and moved by a PMMH step that runs a fresh inner filter on the data so far.

Priors for θ come from the program itself: a θ-particle starts from a simulation of the program (foerster.gfi/simulate). Correlated PMMH, which needs SMC driven by explicit noise, is not provided.

pmmh clj/s

(pmmh model
      n
      iterations
      {:keys [params propose scale burn] :or {scale 0.1 burn 0} :as opts})

Particle marginal Metropolis-Hastings over the parameter sites of model (a spin): iterations proposals, each scored by an SMC of n particles over the program's other sites. Options:

:params the parameter addresses (required) :propose (fn [θ]) -> {:theta θ' :log-ratio log q(θ|θ') − log q(θ'|θ)}, drawing from the current generator (default: a Gaussian random walk of :scale, default 0.1, on every parameter) :burn iterations left out of the result (default 0) and SMC options (:resample-threshold, :resampling, :executor …)

Resolves an EmpiricalMeasure, equally weighted, of one particle per kept iteration drawn from that iteration's SMC: its value the program's, its trace with θ and a state trajectory. :acceptance is the acceptance rate, :thetas the chain.

smc2 clj/s

(smc2 model
      {:keys [params n-theta n-x ess-target moves scale]
       :or {n-theta 50 n-x 100 ess-target 0.5 moves 1 scale 2.38}
       :as opts})

SMC² over the parameter sites of model (a spin whose data arrive at stream sites, as for foerster.smc/stream). Options:

:params the parameter addresses (required) :n-theta θ-particles (default 50) :n-x particles of each inner filter (default 100) :ess-target resample and move the θ-particles when their ESS falls below this fraction (default 0.5) :moves PMMH moves per θ-particle after a resampling (default 1) :scale random-walk scale in population standard deviations (default 2.38, divided by √d) and inner SMC options (:resample-threshold, :resampling, :executor)

Resolves a step {:measure :push :done? :close} as smc/stream does: the measure is over the θ-particles (each a Sample whose value is θ, its trace empty), weighted, with the evidence of the data so far as m/log-marginal; :moves and :accepted count the PMMH steps.