---
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).