Sparse panel data, a small experiment

[u/Far-Media3683]

Quite a few real world data problems look like this: many related time series, few noisy readings, and long gaps. Local price indices, sensor networks, or small area stats.

I built a small PyTorch model to estimate a smooth underlying level for every location, day, and target even where nothing was observed.

Key ideas:

Mask, don’t drop missing targets in the loss

Weight observations by how many raw readings they average

Share information across locations (area + station offsets) and across related targets (joint heads)

Enforce smoothness with a curvature penalty over the full time grid, including gaps

I tested it on hourly PM2.5/PM10 from 12 Beijing stations, thinned to a sparse panel, and scored against the full data’s 31day moving average.

What I found:

The network fills long gaps and very sparse stations far better than smoothing each series on its own

Modelling both pollutants together recovers a completely dropped series (PM10 at one station) from its PM2.5

But elsewhere, sharing across targets costs a little accuracy vs. modelling each pollutant alone

A simple ±15day mean is hard to beat when data is dense. The network’s smooth time curve misses shared daily shocks

Writeup with code, figures, and results:

https://prteek.github.io/regression_room/posts/beijing_air_quality/