Learning HMMs with Nonparametric Emissions via Spectral Decompositions of Continuous Matrices
Authors: Kirthevasan Kandasamy, Maruan Al-Shedivat, Eric P. Xing
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our method is competitive with other baselines on synthetic and real problems and is also very computationally efficient. We implement our algorithm by approximating the density estimates via Chebyshev polynomials which enables efficient computation of many of the continuous matrix operations. Our method outperforms natural competitors in this setting on synthetic and real data and is computationally more efficient than most of them. The entire Section 6 is dedicated to 'Experiments' which includes comparison with other baselines on synthetic and real datasets, reporting L1 error, prediction error, and training time. |
| Researcher Affiliation | Academia | Kirthevasan Kandasamy Carnegie Mellon University Pittsburgh, PA 15213 kandasamy@cs.cmu.edu Maruan Al-Shedivat Carnegie Mellon University Pittsburgh, PA 15213 alshedivat@cs.cmu.edu Eric P. Xing Carnegie Mellon University Pittsburgh, PA 15213 epxing@cs.cmu.edu |
| Pseudocode | Yes | Algorithm 1 NP-HMM-SPEC Input: Data {X(j) = (X(j) 1 , X(j) 2 , X(j) 3 )}N j=1, number of states m. Obtain estimates b P1, b P21, b P321 for P1, P21, P321 via kernel density estimation (3). Compute the cmatrix SVD of b P21. Let b U 2 R[0,1] m be the first m left singular vectors of b P21. Compute the parameters observable representation. Note that b B is a Rm m valued function. bb1 = b U > b P1, bb1 = (P > 21 b U) b P1, b B(x) = (b U > b P3x1)(b U > b P21) −1 (b U > b P21) |
| Open Source Code | Yes | Our Matlab code is available at github.com/alshedivat/nphmm. |
| Open Datasets | Yes | We compare all the above methods (except NP-HMM-EM which was too slow) on prediction error on 3 real datasets: internet traffic [28], laser generation [29] and sleep data [30]. |
| Dataset Splits | No | The paper mentions that bandwidths for KDE estimates are chosen via cross-validation, but it does not specify explicit training/validation/test splits for the datasets used in the overall HMM experiments. |
| Hardware Specification | No | The paper does not provide specific details regarding the hardware used for running the experiments. |
| Software Dependencies | No | The paper mentions that the implementation uses 'Matlab code' and the 'Chebfun library [7]', but it does not provide specific version numbers for these software dependencies. |
| Experiment Setup | No | The paper mentions that bandwidths for KDE estimates are chosen via cross-validation and discusses some settings for baseline models (e.g., number of mixtures, binning intervals), but it does not provide specific numerical values for hyperparameters or detailed system-level training configurations for the proposed NP-HMM-SPEC method within the main text. |