| --- |
| license: cc-by-4.0 |
| pretty_name: KernelSynth (annotated) |
| task_categories: |
| - time-series-forecasting |
| size_categories: |
| - 1M<n<10M |
| tags: |
| - synthetic |
| - gaussian-process |
| - kernel-synth |
| - interpretability |
| dataset_info: |
| features: |
| - name: start |
| dtype: timestamp[s] |
| - name: target |
| sequence: float64 |
| - name: selected_kernel_reprs |
| sequence: string |
| - name: kernel_formula |
| dtype: string |
| splits: |
| - name: train |
| num_bytes: 8478398125 |
| num_examples: 1000000 |
| download_size: 8493914077 |
| dataset_size: 8478398125 |
| configs: |
| - config_name: default |
| data_files: |
| - split: train |
| path: data/train-* |
| --- |
| |
| # KernelSynth (annotated) |
|
|
| One million synthetic univariate time series, each 1024 points long, drawn from a Gaussian |
| process prior whose kernel is a random composition of up to five base kernels. This is the |
| KernelSynth procedure from [Chronos](https://arxiv.org/abs/2403.07815) with one addition: |
| **the generating kernel is kept alongside each series**. The ground-truth structure behind |
| every series is therefore known, which makes the corpus usable for interpretability work |
| rather than only for pretraining. |
|
|
| ## Fields |
|
|
| - `start` — constant `2000-01-01T00:00:00`. The time index is arbitrary and carries no meaning. |
| - `target` — the series itself: 1024 `float64` values sampled from the GP prior. |
| - `selected_kernel_reprs` — the base kernels drawn from the kernel bank, as scikit-learn reprs. |
| - `kernel_formula` — the composed kernel with explicit precedence, e.g. |
| `RBF(length_scale=1) * (DotProduct(sigma_0=1) + WhiteKernel(noise_level=1))`. |
| scikit-learn's own repr omits parentheses, so `(a + b) * c` and `a + b * c` are |
| indistinguishable there; this field disambiguates them. |
|
|
| ## Generation |
|
|
| Produced by a script adapted from Chronos' |
| [`kernel-synth.py`](https://github.com/amazon-science/chronos-forecasting/blob/main/scripts/kernel-synth.py), |
| with these settings: 1,000,000 series, length 1024, at most 5 base kernels each, seed 1. |
| Kernels are drawn with replacement from the 33-entry Chronos kernel bank and combined |
| pairwise with random `+` / `*` operators. Each series draws from its own independent random |
| stream derived from the seed, so the corpus is reproducible and independent of worker count. |
|
|
| One deviation from upstream: a jitter of `1e-8 * mean(diag(cov))` is added to the covariance |
| diagonal to keep it numerically positive semi-definite, since composed kernels are often |
| ill-conditioned. |
|
|
| ## License and attribution |
|
|
| The data is released under [CC-BY-4.0](https://creativecommons.org/licenses/by/4.0/). |
|
|
| It was produced by a script adapted from Chronos' `kernel-synth.py` (Copyright Amazon.com, |
| Inc., Apache-2.0). That license covers the generator code, not the series it emits, and no |
| Chronos data is contained here — every series is sampled fresh from a GP prior. The method, |
| however, is theirs; please cite [the Chronos (1) paper](https://arxiv.org/abs/2403.07815). |
