Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1]
Inference via Low-Dimensional Couplings
Authors: Alessio Spantini, Daniele Bigoni, Youssef Marzouk
JMLR 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Section 8 illustrates aspects of the theory with numerical examples. [...] Figures 10 and 11 show the resulting smoothing and filtering marginals of the states over time, respectively. Figures 12 and 13 collect the corresponding posterior marginals of the static parameters over time. Figure 14 illustrates marginals of the posterior predictive distribution of the data, together with the observed data (yk), showing excellent coverage overall. Our results rely on a numerical approximation of the desired transport maps. Each component of Mk is parameterized via the monotone representation (5), with (ak) and (bk) chosen to be Hermite polynomials and functions, respectively, of total degree seven.The expectation in (6) is approximated using tensorized Gauss quadrature rules. The resulting minimization problems are solved sequentially using the Newton CG method (Wright and Nocedal, 1999). |
| Researcher Affiliation | Academia | Alessio Spantini EMAIL Daniele Bigoni EMAIL Youssef Marzouk EMAIL Massachusetts Institute of Technology Cambridge, MA 02139 USA |
| Pseudocode | Yes | Appendix C. Algorithms for Inference on State-Space Models Here we digest the smoothing and joint state-parameter inference methodologies discussed in Section 7 into a handful of algorithms, described with pseudocode. Algorithms 1 and 2 below are building blocks: they describe, respectively, how to approximate a transport map given an (unnormalized) target density, and how to project a given transport map onto a set of monotone transformations. Algorithm 3 shows how to build a recursive approximation of πΘ,Z0:k+1|y0:k+1 i.e., the full Bayesian solution to the problem of sequential inference in state-space models with static parameters using a decomposable transport map. [...] Algorithm 1 (Computation of a monotone map) [...] Algorithm 2 (Regression of a monotone map) [...] Algorithm 3 (Joint parameter and state inference) [...] Algorithm 4 (Sample the smoothing distribution) [...] Algorithm 5 (Sample the filtering distribution) |
| Open Source Code | Yes | Code and all numerical examples are available online.1 1. http://transportmaps.mit.edu |
| Open Datasets | Yes | As a data set (yk)N k=0, we use the N + 1 daily differences of the pound/dollar exchange rate starting on 1 October 1981, with N = 944 (Rue et al., 2009; Durbin and Koopman, 2000). |
| Dataset Splits | No | The paper uses a dataset of daily differences of the pound/dollar exchange rate. However, it does not specify any training, testing, or validation splits for this dataset in the context of typical experimental reproduction (e.g., specific percentages, counts, or stratified methodologies). The data is used for sequential inference. |
| Hardware Specification | No | The paper discusses computational times and costs, and refers to "a dedicated software package", but it does not specify any particular hardware (e.g., GPU models, CPU types, or memory amounts) used for running the experiments. |
| Software Dependencies | No | The paper mentions "dedicated software package publicly available at http://transportmaps.mit.edu" and refers to using "Newton CG method (Wright and Nocedal, 1999)". However, it does not provide specific version numbers for any programming languages, libraries, or frameworks used in the implementation or experiments. |
| Experiment Setup | Yes | Each component of Mk is parameterized via the monotone representation (5), with (ak) and (bk) chosen to be Hermite polynomials and functions, respectively, of total degree seven.The expectation in (6) is approximated using tensorized Gauss quadrature rules. The resulting minimization problems are solved sequentially using the Newton CG method (Wright and Nocedal, 1999). This test case was run using the dedicated software package publicly available at http://transportmaps.mit.edu. The website contains details about additional possible parameterizations of the maps. |