Robust and Scalable Bayes via a Median of Subset Posterior Measures
Authors: Stanislav Minsker, Sanvesh Srivastava, Lizhen Lin, David B. Dunson
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present both theoretical and numerical evidence illustrating the improvements achieved by our method. Section 4 presents details of algorithms, implementation, and numerical performance of the median posterior for several models. The simulation study and analysis of data examples convincingly show the robustness properties of the median posterior. In particular, we have used M-Posterior for scalable nonparametric Bayesian modeling of joint dependence in the multivariate categorical responses collected by the General Social Survey (gss.norc.org). Section 4.1 Numerical Analysis: Simulated Data. Section 4.2 Real Data Analysis: General Social Survey. |
| Researcher Affiliation | Academia | Stanislav Minsker EMAIL Department of Mathematics University of Southern California Los Angeles, CA 90089, USA. Sanvesh Srivastava EMAIL Department of Statistics and Actuarial Science University of Iowa Iowa City, IA 52242, USA. Lizhen Lin EMAIL Department of Applied and Computational Mathematics and Statistics The University of Notre Dame Notre Dame, IN 46556, USA. David B. Dunson EMAIL Departments of Statistical Science, Mathematics, and ECE Duke University Durham, NC 27708, USA. |
| Pseudocode | Yes | Algorithm 1: Evaluating the geometric median of probability distributions via Weiszfeld’s algorithm. Algorithm 2: Approximating the M-Posterior distribution. |
| Open Source Code | No | The paper does not provide a direct link to a source code repository or an explicit statement about releasing their implementation code. It mentions using 'Stan language (Carpenter et al., 2016)' for implementation, which is a third-party tool. |
| Open Datasets | Yes | Section 4.2 Real Data Analysis: General Social Survey. The General Social Survey (GSS; gss.norc.org) has collected responses to questions about evolution of American society since 1972. |
| Dataset Splits | Yes | The GSS data were randomly split into 10 test and training data sets. Samples from the overall posteriors of πci,cjs were obtained using the Gibbs sampling algorithm of Dunson and Xing (2009). We chose m as 10 and 20 and estimated M-Posteriors for πci,cjs in four steps: training data were randomly split into m subsets... |
| Hardware Specification | No | The paper mentions 'massive data require computer clusters for storage and processing' and discusses 'minimizing communication among cluster machines' but does not specify any particular hardware models, CPUs, GPUs, or other specific components used for their experiments. |
| Software Dependencies | No | The algorithms for sampling from the subset and overall posterior distributions of µ were implemented using Stan language (Carpenter et al., 2016). While 'Stan language' is mentioned, no specific version number is provided for Stan or any other software dependencies. |
| Experiment Setup | Yes | We simulated 25 data sets containing 200 observations each. Each data set xi = (xi,1, . . . , xi,200) contained 199 independent observations from the standard Gaussian distribution (xi,j ∼ N(0, 1) for i = 1, . . . , 25 and j = 1, . . . , 199). The last entry in each data set, xi,200, was an outlier, and its value increased linearly for i = 1, . . . , 25: xi,200 = i max(|xi,1|, . . . , |xi,199|). The true variance of observations was fixed at 1 and was assumed to be known. The algorithms for sampling from the subset and overall posterior distributions of µ were implemented using Stan language (Carpenter et al., 2016) based on Stan’s default Gaussian prior on µ. We used two likelihoods for the data, one was the standard Gaussian likelihood and the other was a (more robust) Student’s t-distribution likelihood with 3 degrees of freedom (t3). We generated 1000 samples from each posterior distribution Π200(·| xi) for i = 1, . . . , 25. Setting m = 10 in Algorithm 1, we generated 1000 samples from every subset posterior Π200,10(·|Gj,i), j = 1, . . . , 10 to form the empirical measures Qj,i; here, S10 j=1Gj,i = xi. Using these Qj,is, Algorithm 2 generated 10000 samples from the M-Posterior ˆΠst 2000,g(·| xi) for each i = 1, . . . , 25. This process was replicated 50 times. |