Stochastically find dissimilarity between time series data and model prediction

[willfurnass]

I have many time series, with each featuring fifteen data points (x,t). I wish to fit a parameterised model to each data series. At present I'm using particle swarm optimisation (PSO) for this purpose. Within my objective function I quantify fitness using the Bray Curtis distance between a) the data series and b) the prediction corresponding to a candidate solution.

The problem I have is that the PSO fitting does not presently account for uncertainty in either x or t. The variances in x and t are most likely themselves invariant and I'd ideally like to treat each data point as a 2D Gaussian PDF.

My question is this: could Gaussian Processes (GPs) be used within my objective function to _stochastically_ determine the dissimilarity between a 15-point data series and the 15 (or more) point prediction corresponding to a candidate solution?

Thank you in advance for any advice you can offer.

Regards,

Will Furnass

 

[mmwave]

Dear Will,

Thank you for sharing your approach to fitting parameterised models to time series data. It sounds like you have a well-defined objective function and are using an effective optimization method in PSO.

In regards to accounting for uncertainty in your data, Gaussian Processes (GPs) could certainly be used within your objective function to determine the dissimilarity between your data series and predictions. GPs are a powerful tool for modeling and predicting data, particularly in cases where there may be uncertainty or noise present. They can also be used for regression and optimization tasks, making them a good candidate for your problem.

One potential approach could be to use GPs to model your data series and then use the predicted values from the GP as a comparison to your candidate solutions. This would allow you to incorporate the uncertainty in your data into your objective function and potentially improve the performance of your optimization.

However, it's important to note that using GPs in this way may also introduce additional complexity and computational overhead. You may need to carefully consider the balance between incorporating uncertainty and maintaining the efficiency of your optimization method.

Overall, I think using GPs in your objective function is a promising idea and could potentially lead to improved results. I would recommend exploring this approach further and conducting some experiments to see how well it performs compared to your current method.

Best of luck with your research!

Regards,