Minimax Adaptive Estimation of Nonparametric Hidden Markov Models
Authors: Yohann De Castro, Élisabeth Gassiat, Claire Lacour
JMLR 2016 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Simulations are given that show the improvement obtained when applying the least-squares minimization consecutively to the spectral estimation. In this section we present the numerical performances of our method. We have considered K = 2 hidden states whose emission variables are distributed with respect to beta laws of parameters (2, 5) and (4, 2). This numerical experiment consolidates the idea that the least squares method significantly improves upon the spectral method. |
| Researcher Affiliation | Academia | Laboratoire de Mathématiques d Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France. |
| Pseudocode | Yes | Algorithm 1: Nonparametric spectral estimation of HMMs |
| Open Source Code | Yes | All the codes of the numerical experiments are available at https://mycore.core-cloud.net/public.php?service=files&t=44459ccb178a3240cfb8712f27a28d75. |
| Open Datasets | No | The paper uses simulated data based on statistical distributions (beta laws of parameters (2, 5) and (4, 2), and (1.5, 5), (6, 6) and (7, 2)) rather than referencing or providing access to a pre-existing public dataset. |
| Dataset Splits | No | The paper mentions generating "single chain observation of length N = 50,000" and performing "40 iterations on chains of length N = 5e4". This describes the amount of simulated data used for experiments but does not specify any training/test/validation dataset splits. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU, CPU models, memory) used to run the numerical experiments or simulations. |
| Software Dependencies | No | The paper mentions using "CMAES for Covariance Matrix Adaptation Evolution Strategy, see Hansen (2006)" and "CAPUSHE, the Matlab graphical user interface presented in Baudry et al. (2012)". However, it does not provide specific version numbers for these tools or for Matlab itself. |
| Experiment Setup | No | The paper describes the general experimental procedure, such as using CMAES for minimization, starting with spectral estimates, and tuning the penalty term using a slope heuristic. The penalty term is defined as pen(N, M) = ρ M log N, but concrete numerical values for ρ or other common hyperparameters (e.g., learning rates, batch sizes) that were actually used in the presented results are not provided in the main text. |