Nonlinear Filters. Simon Haykin

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      1 (i) Is it possible to identify the governing dynamics from data?

      2 (ii) Is it possible to perform inference from observables to the latent state variables?

      1 (i) Prediction: ,

      2 (ii) Filtering: ,

      3 (iii) Smoothing: .

      1 (i) The underlying assumptions for building a state‐space model must allow for reliable system identification and plausible long‐term prediction of the system behavior.

      2 (ii) The inference mechanism must be able to capture rich dependencies.

      3 (iii) The algorithm must be able to inherit the merit of learning machines to be trainable on raw data such as sensory inputs in a control system.

      4 (iv) The algorithm must be scalable to big data regarding the optimization of model parameters based on the stochastic gradient descent method.

      1 (i) Empirical criterion: Doing justice to practice by keeping the analysis grounded in real‐world examples.

      2 (ii) Conceptual criterion: Being understandable in terms of what it says, where it comes from, and what it costs.

      3 (iii) Cognitive criterion: Providing an intelligible foundation for the computational theory of mind that underlies both artificial intelligence and cognitive science.

      1 Formal symbol manipulation is rooted in formal logic and metamathematics. The idea is to build machines that are capable of manipulating symbolic or meaningful expressions regardless of their interpretation or semantic content.

      2 Effective computability deals with the question of what can be done, and how hard it is to do it mechanically.

      3 Execution of an algorithm or rule following focuses on what is involved in following a set of rules or instructions, and what behavior would be produced.

      4 Calculation of a function considers the behavior of producing the value of a mathematical function as output, when a set of arguments is given as input.

      5 Digital state machine is based on the idea of a finite‐state automaton.

      6 Information processing focuses on what is involved in storing, manipulating, displaying, and trafficking of information.

      7 Physical symbol systems is based on the idea that the way computers interact with symbols depends on their mutual physical embodiment. In this regard, computers may be assumed to be made of symbols.

      8 Dynamics must be taken into account in terms of the roles that nonlinear elements, attractors, criticality, and emergence play in computing.

      9 Interactive agents are capable of interacting and communicating with other agents and even people.

      10 Self‐organizing or complex adaptive systems are capable of adjusting their organization or structure in response to changes in their environment in order to survive and improve their performance.

      11 Physical implementation emphasizes on the occurrence of computational practice in real‐world systems.

       Data modeling culture is based on the idea that a given stochastic model generates the data.

       Algorithmic modeling culture uses algorithmic models to deal with an unknown data mechanism.