Asymptotic optimality of adaptive importance sampling
Authors: François Portier, Bernard Delyon
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our numerical experiments shows that (i) w AIS accelerates significantly the convergence of AIS and (ii) small allocation policies (nt) (implying more frequent updates) give better results than large (nt). |
| Researcher Affiliation | Academia | Bernard Delyon IRMAR University of Rennes 1 bernard.delyon@univ-rennes1.fr François Portier Télécom Paris Tech University of Paris-Saclay francois.portier@gmail.com |
| Pseudocode | Yes | Algorithm 1 (AIS). Inputs: The number of stages T N , the allocation policy (nt)t=1,...T N , the sampler update procedure, the initial density q0. Set S0 = 0, N0 = 0. For t in 1, . . . T : (i) (Explore) Generate (xt,1, . . . xt,nt) from qt 1 (ii) (Exploit) (a) Update the estimate: St = St 1 + Pnt i=1 ϕ(xt,i) qt 1(xt,i) Nt = Nt 1 + nt It = N 1 t St (b) Update the sampler qt |
| Open Source Code | Yes | The code is made available at https://github.com/portierf/AIS. |
| Open Datasets | No | The paper uses a 'toy Gaussian example' as a synthetic dataset for numerical experiments, not a publicly available dataset with a formal citation or access link. 'The aim is to compute µ = R xφµ ,σ (x)dx where φµ,σ : Rd R is the probability density of N(µ, σ2Id), µ = (5, . . . 5)T Rd, σ = 1.' |
| Dataset Splits | No | The paper does not explicitly mention train/validation/test splits. It describes conducting numerical experiments and calculating MSE over '100 replicates', but not data splitting for model training and evaluation. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., GPU models, CPU types, memory) used for running the experiments. |
| Software Dependencies | No | The paper mentions that 'The code is made available at https://github.com/portierf/AIS', but it does not specify any software dependencies or their versions within the paper text. |
| Experiment Setup | Yes | We set NT = 1e5 and we consider d = 2, 4, 8, 16. The sampling policy is taken in the collection of multivariate Student distributions of degree ν = 3 denoted by {qµ,Σ0 : µ Rd} with Σ0 = σ0Id(ν 2)/ν and σ0 = 5. The initial sampling policy is set as µ0 = (0, . . . 0) Rd. The mean µt is updated at each stage t = 1, . . . T following the GMM approach as described in section 3. We compare the evolution of all the mentioned algorithms with respect to stages t = 1, . . . T = 50 with constant allocation policy nt = 2e3 (for AIS and w AIS). |