Scalable Levy Process Priors for Spectral Kernel Learning
Authors: Phillip A. Jang, Andrew Loeb, Matthew Davidow, Andrew G. Wilson
NeurIPS 2017 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct four experiments in total. In order to motivate our model for kernel learning in later experiments, we first demonstrate the ability of a L evy process to recover through direct regression an observed noise-contaminated spectrum that is characteristic of sharply peaked naturally occurring spectra. In the second experiment we demonstrate the robustness of our RJMCMC sampler by automatically recovering the generative frequencies of a known kernel, even in presence of significant noise contamination and poor initializations. In the third experiment we demonstrate the ability of our method to infer the spectrum of airline passenger data, to perform long-range extrapolations on real data, and to demonstrate the utility of accounting for uncertainty in the kernel. In the final experiment we demonstrate the scalability of our method through training the model on a 100,000 data point sound waveform. |
| Researcher Affiliation | Academia | Phillip A. Jang Andrew E. Loeb Matthew B. Davidow Andrew Gordon Wilson Cornell University |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | Code is available at https: //github.com/pjang23/levy-spectral-kernel-learning. |
| Open Datasets | Yes | Figure 5 shows a time series of monthly airline passenger data from 1949 to 1961 (Hyndman, 2005). ... We consider a 100,000 data point waveform, taken from the field of natural sound modelling (Turner, 2010). |
| Dataset Splits | No | The paper describes training and testing splits but does not explicitly mention a separate validation split or how it was handled. |
| Hardware Specification | Yes | Training involved initialization from the signal empirical covariance and 500 RJ-MCMC samples, and took less than one hour using an Intel i7 3.4 GHz CPU and 8 GB of memory. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., specific libraries, frameworks, or programming language versions). |
| Experiment Setup | Yes | Based on these observed training data (depicted as black dots in Figure 4, right), we estimate the kernel of the Gaussian process by inferring its spectral density (Figure 4, left) using 1000 RJ-MCMC iterations. ... With an initialization from the empirical spectrum and 2500 RJ-MCMC steps, the model is able to automatically learn the necessary frequencies and the shape of the spectral density... A L evy kernel process is trained on a sound texture sample of howling wind with the middle 10% removed. Training involved initialization from the signal empirical covariance and 500 RJ-MCMC samples, and took less than one hour using an Intel i7 3.4 GHz CPU and 8 GB of memory. Four distinct mixture components in the model were automatically identified through the RJ-MCMC procedure. The learned kernel is then used for GP infilling with 900 training points, taken by down-sampling the training data, which is then applied to the original 44,100 Hz natural sound file for infilling. |