prteek/sparse-panel-demo

Sparse panel demo (Beijing air quality)

Precomputed scenarios behind the sparse-panel-demo Space (code: GitHub), which accompanies the blog post Smooth Levels from Sparse, Gappy Panels.

Daily PM2.5 and PM10 at 12 Beijing monitoring stations (March 2013 – February 2017) are thinned to a few hourly readings a day, with gaps, and three estimators try to recover the slow underlying level:

• joint: a small network modelling both pollutants together (area embedding + station offset, Gaussian time bumps, curvature penalty);
• single-target: the same network fitted to one pollutant at a time;
• ±15-day mean: hour-weighted mean of the readings within 15 days, falling back to the station's area where it has none.

The benchmark ("truth") is the centred 31-day moving average of the full daily means, on the log scale.

Scenarios

One global setting, lam: the Poisson mean number of hourly readings kept per station-day and pollutant (0.5, 1.2, 3.0). Each station also has a fixed label that degrades it relative to lam:

label	stations	treatment
regular	4	Poisson(lam) hours, two 20–60 day gaps per pollutant
sparse	2	Poisson(0.4 × lam) hours, same gaps
very sparse	2	as regular, then 15% of observed days kept
long gap	2	as regular, but the gaps are 90–120 days
dropped series	2	one pollutant removed entirely (dropped column)

Random draws are fixed per cell across scenarios, so a higher lam keeps a superset of a lower one's hours and gaps sit in the same place.

Files

file	rows	columns
labels.parquet	12	station, label, area, dropped
truth.parquet	35,064	station, pollutant, date, value (31-day MA, µg/m³)
readings.parquet	46,927	station, date, pollutant, value (daily mean of kept hours), n (hours kept), lam
gaps.parquet	2,454	station, pollutant, date (days inside a gap block; same for every lam)
predictions.parquet	315,576	station, date, pollutant, pred, lam, estimator
metrics.parquet	315	lam, label, pollutant, estimator, day_type, days, error, bias

error is the mean absolute log error against the 31-day MA (0.15 ≈ 15%), bias the mean log error. day_type is all, observed (a reading that day), unobserved (no reading, outside the gaps) or gap. For the dropped series label, pollutant is dropped and only the dropped series is scored. meta.json records the network settings (from look-ahead CV in the blog post: curvature penalty 1e5, 30-day bump spacing, 100 steps).

Reproduce with uv run python precompute.py in the GitHub repo (~30 s on a laptop CPU).

Source and license

Derived from the Beijing Multi-Site Air Quality dataset (Song Chen, 2017), UCI Machine Learning Repository, doi:10.24432/C5RK5G, licensed CC BY 4.0. This derived dataset is released under the same license. Changes: daily aggregation, thinning to sparse readings, gap removal, and model predictions as described above.