better support of spatiotemporal models

[martinfleis]

At the moment, if you define a Graph encoding spatiotemporal neighbourhoods, you can use it to fit the estimator and get a spatiotemporal regression. However, this breaks a bit when trying to do prediction (and score by extension), as we can identify local models to be used only by spatial dimension, as we only pass geometry.

We shall think about more explicit support of temporal dimension alongside the spatial one as the scaffolding is there. It would be a shame not to make use of it.

What I am less sure is how the API should look like. Temporal dimension should be treated in the same way as spatial one but that would mean adding args to init, fit and everything else.

We also need to figure out how to build the spatiotemporal graph with proper weights if we want to go this direction.

This will likely need some research and a few iterations to get it right. Some stuff related to the spatiotemporal graphs might even go to libpysal.

Here's an example how to build a simple spatiotemporal regression right now, with the caveat that the weights are binary and prediction is broken.

import geopandas as gpd
import pandas as pd
from libpysal import graph
from sklearn.metrics import pairwise_distances

from gwlearn.linear_model import GWLinearRegression

accidents = gpd.read_file(
    "https://martinfleischmann.net/sds/point_patterns/data/brno_pedestrian_accidents.gpkg"
)

timestamp = pd.to_datetime(
    accidents[["rok", "mesic", "den"]].rename(
        columns={"rok": "year", "mesic": "month", "den": "day"}
    )
)
accidents["days_since_first"] = (timestamp - timestamp.min()).dt.days

spatial_neighbors = graph.Graph.build_knn(accidents, k=200, coplanar="jitter")

temporal_distances = pairwise_distances(accidents["days_since_first"].values.reshape(-1, 1))
temporal_neighbors = graph.Graph.build_kernel(temporal_distances, metric="precomputed", bandwidth=365)

space_time_neighbors = temporal_neighbors.intersection(spatial_neighbors)

gwr = GWLinearRegression(graph=space_time_neighbors)
gwr.fit(
    X=accidents[["usmrceno_os", "tezce_zran_os", "lehce_zran_os"]],
    y=accidents['hmotna_skoda'])

[FirePheonix]

hey @martinfleis
I've been looking into this spatiotemporal prediction thing, I also went through serge's conference on spatiotemporal neighborhoods to understand the 'time' as a variable paint point we're having rn.... I was wondering, maybe rather than adding explicit time arguments to init() and fit(), we can lean on the existing Graph scaffolding.
So, basically, we can upgrade the predict() method, to accept an optional graph argument, (maybe name it prediction_graph). The user can calculate their own list of 'valid neighbors' (based on both time and space) and pass that list directly to the model... maybe i'm wrong on this, please correct if i am..

[martinfleis]

Such a graph would not be too straightforward to generate for a user. I still think that adding a variable capturing temporal dimension in the same way we have a variable capturing spatial dimension is the cleanest API.

[FirePheonix]

yeah, that'd definitely be better. it might be messy to put graph building things inside of gwlearn itself.

and as you said before, maybe we can add "build-spacetime" type utility inside of libpysal first?
gwlearn isn't a graph library after all... and we can simply expose the time parameter to the user, in a way that it can call the build graph under the hood.

model.fit (
    # rest variables/parameters can come here..
    time=accidents["days_since_first"],
    temporal_bandwidth= 10,
)

correct me if i'm wrong.
may i work on making the spatio-temporal graph in libpysal? (might need a few iterations) it looks like a first natural move to me since if even any other PySAL package like esda, ever wants to do spatio temporal work, they can reuse this utility instead of re-implementing it..

[martinfleis]

Yeah, that is the right direction though it may need some theoretical scoping first. It is unclear to me how we would derive the decay weight.

[FirePheonix]

can we try product of kernels approach? (i researched on google a bit here on other standard approaches to this, not all are suitable for libpysal)

we can do: spatial weight * temporal weight = final decay weight -> influence depends upon this number.

[martinfleis]

I'd need to read some literature on this first which I don't have time right now to give an answer. Product might be sensible but the kernel would be steep which may not be optimal.

[FirePheonix]

alright.. no rush here..