Advanced topics in machine learning (CK0255)
Linear systems (TIP7244)

We overview some basic facts in the study of deterministic and random Markovian functions.
  1. Refreshers: Probability and random variable theory, vector calculus, signals and systems;
  2. Deterministic Markov processes: State-space analysis, Lagrange formula, similarity transformations;
  3. Stochastic Markov processes: General features, characterising functions, time-evolution equations;
  4. Discrete Markov processes: Classification of states, irreducibility, important matrixes and distributions.
Stuff from the past: Previous edition for 2017.2 (internal links may need adjustment.)

Instructor : Francesco Corona (FC), francesco döt corona ät ufc döt br

Physical location : Wednesdays, 14:00-18:00, Bloco 726, Sala 13.
Internet location : Here! Or, here (CK0255/TIP7244) for mambojumbo related to administration.

Evaluation : Approximately half a dozen theoretical and practical problem sets will be assigned as homework: Home assignments are for training but are not mandatory, they can be handed-in but they will not be evaluated. The actual evaluation will be based on three partial evaluations (APs) in class (weight 70%) and a final project (weight 30%). If needed a final evaluation (AF) will be arranged.

Go to:   Lectures and schedule | Problem sets | Supplementary material | As it pops out |


>>>>> Assignment (PART A) <<<<< Deadline: Sunday December 02, 2018 (23:59 Fortaleza time >> SIGAA)

Lectures and schedule

  1. About this course

    A Preliminaries (FC)

  2. Refreshers

    A Dynamical systems (FC)
    • Input-output and state-space representations, characteristics
    • (Elements of ordinary differential equations, theory of distributions)
    B Probability theory (FC)
    • Laws of probability, random variables, useful theorems, random numbers
    C Vector calculus (FC)
    • Vector and matrix stuff

  3. Deterministic Markov processes

    A Input-output and state-space representation (FC)
    • Representation and analysis
    • Homogeneus equation and modes

    • Analysis and state transition matrix
    • Sylvester expansion
    B Time evolution (FC)
    • Force-free evolution and types of modes
    • Impulse response and forced evolution
    • Durhamel's integral

    • Lagrange formula, force-free and forced evolution
    • Similarity transformations and diagonalisation
    • Jordan's form, generalised eigenvectors
    • Generalised modal matrix and state transition matrix
    • State transition matrix and modes

  4. Stochastic Markov processes

    A Discrete-time discrete-space (FC)
    • Definitions, dependence and embeddeability
    • Chapman-Kolmogorov equations
    • Probability distributions
    • Classification of states
    B Continuous-time discrete-space (FC)
    • Propagator and time-evolution equations
    • Stable processes and weak noise approximation
    C General processes (FC)
    • State density function, Chapman-Kolmogorov equations
    • Propagators and time-evolution equations

Problem sets

As we use problem set questions covered by books, papers and webpages, we expect you not to copy, refer to, or look at the solutions in preparing your answers. We expect you to want to learn and not google for answers: If you do happen to use other material, it must be acknowledged clearly with a citation on the submitted solution.

The purpose of problem sets is to help you think about the material, not just give us the right answers.

Homeworks must be done individually: Each of you must hand in his/her own answers. In addition, each of you must write his/her own code when requested. It is acceptable, however, for you to collaborate in figuring out answers. We are assuming that you take the responsibility to make sure you personally understand the solution to any work arising from collaboration (though, you must indicate on each homework with whom you collaborated).

To typeset assignments, students are encouraged to use this LaTeX template: Source (PDF).

Assignments must be returned via SIGAA.



Course slides will suffice. Slides are mostly based on the following textbook: The material can be complemented using material from the following textbooks (list not exhaustive):
  1. Linear system theory, by Lofti Zadeh and Charles Desoer.
  2. Markov chains, by James Norris.
Copies of these books are floating around.

>>>>>> Course material is prone to a typo or two - Please inbox FC to report <<<<<<


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