Welcome

This page documents the FunctionObservers package for MATLAB, which can be found at the git repository here. Modern machine learning has focused largely on developing increasingly powerful tools for characterizing the geometric and statistical properties of static data. In reality, however, most learning problems in the world involve data that evolves with time. The main fields of study focusing on time-series data are statistics (including geostatistics), which focuses on modeling and inference for stochastic processes, and control/systems theory, which focuses on the control of and prediction for dynamical systems, which may or may not be random. The function observer paradigm borrows ideas liberally from these two fields, and fuses them with the elegant machine learning paradigm of kernel methods.

The primary goal of these methods is the modeling and control of spatiotemporally varying processes (i.e. stochastic phenomena that vary over space AND time). Practical applications of these types of methods include ocean temperature modeling and monitoring, control of diffusive processes in power plants, optimal decision-making in contested areas with a patrolling enemy, disease propagation in urban population centers, and so on. In all of these scenarios, there are some commonalities:

  1. Modeling: building a predictive model of the process in play. The following image shows an example of inferring mean ocean surface temperature from AVVHR satellite data, at a given day: the full algorithm would build a model of how these temperatures will change over time.
_images/inference_example.png
  1. Monitoring: estimating the latent state of the process from a set of measurements, gathered from sensors. The image below demonstrates the tracking of an abstract process using a series of measurements from fixed sensor locations.
_images/monitoring_example.png
  1. Control/Exploitation: either affecting the future state of the process directly, or using the current state of the process to make a decision. The image below shows an example of driving a system with an initial temperature distribution diffusing according to the heat equation to a final, fixed temperature distribution.
_images/controlled_pde_heat.jpg

The geostatistics community has done a great deal of work in the modeling aspects of this area. Our contributions lie in utilizing ideas from reproducing kernel Hilbert space theory to make modeling easier and more efficient, and utilizing ideas from systems theory to minimize the number of sensors, and the control effort required for actuation. This toolbox will allow researchers to utilize and explore these ideas in their own work.

Indices and tables