What would be a good way to structure this Heterogenous Graph Forecasting problem?

[snknitin]

Hello PyG Community ,

I'm working with a heterogenous graph with 2 node types , say A and B. Ideally for a forecasting task, but instead of temporal snapshots or sequential graphs, this is one large static graph. Every (a_1, b_1) pair is associated with a weekly-average(across 52 weeks) value of the forecasted variable, x . We want to predict this value for new combinations of A and B, that we haven't seen before. Basically we want to leverage the inductive nature and make an inference.

By this I mean, {b_1,b_2,b_3,....b_1000} with {a_1,a_2,a_3.....a_50} , have observed data x for some combinations , but if we introduce

• new nodes of type B, {b_1232 , b_2245 , b_9999} that didn't exist previously , OR
• new connections between existing B and A, that don't have an edge or data observed.

So given these possibilities,

1. Any ideas on what would be a good way to model this problem to build a dataset?
2. Is this a link prediction problem? or some sort of probability ranking/recommendation for nodes A with every combination of B?

Ideally we want to be able to predict or forecast these values for the upcoming year, based on the static graph

Please let me know if you've tried something like this before. Looking for some ideas on how to structure the labeled dataset for this "forecasting" problem for the next year , given the current year average values. Is there a better way to approach this, that comes to mind? I would love some help

[rusty1s]

Sorry for my late reply, this slipped under my radar. I think this is an edge regression problem: Given an unseen pair node (a_1, b_1), forecast a series of regression values (52?). To help with that, the model can integrate forecasting results from neighbors from both a_1 and b_1 during the forward pass via a GNN.

[snknitin]

Thanks for your response. I'm going down a similar line. I'm confused between keeping dynamic weekly snapshots and doing 52 graphs with a single dimension edge label or one static graph with a 52 dimension edge label. The idea is to learn from 2-3 years of data and predict on the next year, for 52 weeks. So if I do a static graph with a 52 dimension edge regression, how do I split the train , val , test, given that I want to predict the next year 52 week forecast ?

a1,b1 nodes and edge_label would be 52 dimensions , for say 2021. Then I need to predict for 2022 for both a_new , b_new but also a1,b1 which should now have a different forecast for next year.

OR

Do a weekly graph for 2 years and sequentially split the data into train, val, test. But then for inference I have to create 52 weekly graphs with random edges and predict based on that.

Wasn't sure which approach made more sense. Trying both

[rusty1s]

I think one static graph with a 52 dimension edge regression is easier to handle TBH. Best splitting depends on how much data you have. I would probably just use a random split on the last year of data, and use any information from earlier years for message passing inside the GNN.

[snknitin]

Oh, interesting. let's say we have 3000 nodes of one type and 50000 nodes of the other. I do a random Link split to make batches? Also when you say use info from earlier year for message passing, you mean convert those to node features? that's how they get passed right?

Would you suggest, I do a 52 dimension of current year as edge_feature and map it to next year's 52 dimension edge_label for predictions. Then I can pull in random combinations for both nodes to form edges, but the main issue is I wouldn't have any specific features to pull for edges of past year that didn't exist, but i want to predict them based on other existing edges . The objective is basically to learn from similar nodes of A and similar nodes of B and predict how b_x would perform in a_y, to do some sort of forecast and convert it to a ranking or recommendation problem. Given the sparsity and seasonality, i do expect some of the 52 dimensions would be 0

[rusty1s]

Let me try to clarify. From my understanding, you have a edge_index and a corresponding 52-dim feature vector edge_attr. Each edge belongs to a given year (e.g., edge_time vector). During training/evaluation, you make predictions for the last year t. As such, you can divide the set of edges into training/evaluation edges and message passing edges

# The edges to train/evaluate against:
mask = edge_time == t
edge_label_index = edge_index[:, mask]
edge_label = edge_attr[mask]

# Use previous information within GNN:
edge_index = edge_index[:, ~mask]
edge_attr = edge_attr[~mask]

You can then simple split edge_label_index randomly into training, validation and test sets.

[snknitin]

oh, it's a bit different. I thought you meant use the 52 dimensions as edge_label for the regression. I like this concept of edge_time vectors. But what would be the label for the edge_label_index for predictions of last year during training.

Let me rephrase my problem.

• Given 2 nodes types, let's say A (3000,250) and B (50000,430), I have some metric being tracked for 52 weeks for some (a,b) combinations.
• I have that for last year t0 ( 52 attr?) and this year t1( 52label?).
• I want to be able to predict the 52 week forecast for t2, next year.
• Not all the nodes in A and B are fully connected. Let's say we have maybe 1,250,000 edges (less than 50000 x 3000).
• Now we want to try, say expanding the number of edges to some new possibilities and maybe introduce even new nodes to make it 4000 and 70000 and try other combinations along with the existing 1.25 million edges for getting the 52 weeks of t2

The inductive nature and weekly sparsity in some combinations, makes Graphs a very good alternative to xgboost/lstm forecast or predict for future and unseen combinations. I've had pretty good success with heterogenous GNNs . In this case, i'm wondering what would be a proper way to frame the Graph dataset and Dataloader.

Dynamic but weekly snapshots

Obviously, if I had a weekly graph dataset to make (2*52) graphs, i could do a temporal split for train, val, test and i would make it a single dimension regression problem, but that would have scalability issues or a lot of reconstruction and generation of 52 new graphs for inference with all possible combinations that may predict a lot of 0's for some of the combinations and for parts of the 52 weeks.

Static Large graph

If I build a large static graph with 1.25 million edges, that already encapsulate the 52 weeks of history and 52 weeks of ground truth in the attr and label, a time based split won't work but i can create all edge sampling combinations or add some new nodes and create just one more graph and run inference on it. Batching would be easy but similarity(which is important for inductive) for message passing might be hard to take into account, if i take a random node split or link split. I'll miss out on leveraging the whole graph for weekly forecasts

So i'm trying to figure out how to let the model learn and predict out for 52 weeks. which will then be averaged out into a metric that helps rank better combinations of (a,b) including new unseen ones for recommendation. I'm leaning towards the static route while I keep doing some feature engineering for the nodes and edges right now.

[rusty1s]

Yes, I think that's how I understood the problem. My assumption is that you always use the previous year worth of data to make a prediction for the next year. So:

• Training/Evaluation: You train on t0 data and use data from t1 for supervision/evaluation/metrics
• Inference: You use the pre-trained model and apply it on data from t1 to make a prediction for t2

[snknitin]

yes. I'll frame it this way and test it out. I'm also thinking of doing a sliding window approach to look at 52 weeks on either side of the timeline when building edges for each week's graph, to set that temporal aspect in the model. That might make it a bit complicated though

[qoffee]

This is interesting discussion. I have a similar task where I have about 5 variables with data for the previous 20 years (I want to predict the number of articles and the popularity of objects in these articles) and taking into account the current version of PyG library interfaces it is not very clear how to properly make splitters with a sliding window.
How did you ultimately solve your problem?