Direct method cuts prediction delays for accurate state estimates
Direct Inference on Admissible Sets (Diona)
Machine Learning
Summary
Making predictions about complex systems often takes a long time to train. The authors introduce a method called Diona that quickly estimates values and their changes at new points without extensive training. It can produce reliable uncertainty ranges and is especially fast when only a few predictions are needed after new data arrives. Compared to other methods like Gaussian processes and neural networks, Diona offers faster predictions while maintaining good accuracy and uncertainty estimates.
What this means in practice
- •For control system engineers: Estimate system states and their rates of change efficiently for real-time monitoring with quick updates from new sensor data.
- •For financial modelers: Generate uncertainty-aware predictions of market variables quickly when new data becomes available, supporting faster decision processes.
Authors
Lorenzo Sabug, Eric Kerrigan
Abstract
We propose a new regression method named Direct Inference on Admissible Sets (Diona) that directly uses samples to estimate the state and its derivatives at a query point, along with their admissible bounds, without long global training. By casting the values and derivatives at the query and neighbouring samples as latent variables in a constrained optimisation problem, the burden of long training loops becomes one of on-demand local solves. We establish Diona's theoretical properties including finite-sample coverage and, in the noiseless case, convergence to the true state and derivatives under dense sampling. In a nonlinear regression benchmark on six functions of three to eight dimensions, Diona was more accurate than a Gaussian process (GP) on noiseless data especially with denser data sets. Furthermore, as with GP, it produced uncertainty bounds that contained the true value at more than 95% of query points in four functions. Diona's time to a first prediction after a data set update was three to four orders of magnitude shorter than that of the GP, and two to three orders shorter than that of a neural network, which was more accurate but offers no uncertainty quantification. This low latency is paid for by on-demand predictions, so this latency advantage applies when relatively few predictions are needed between data updates.