Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Modelare Interdisciplinară - în limba maghiară
Limba de predare: Engleză

SYLLABUS

I. Általános adatok
Kód	Tantárgy neve	
MIG1001	Modelarea stocastică a datelor	

Félév	Órák: C+S+L	Kategória	Típus	
3	2+1+0	specialitate	obligatorie	

II. Foállásban az Egyetem oktatói
Név	Tudományos	Oktatói	Tanszék	Tevékenység	
	fokozat	státus		E	Sz	L	
CSATO Lehel	Dr. 	Conf.	Limbaje şi Metode de Programare	*			

Társult oktatók
Név	Tudományos	Intézmény	Állás	Tevékenység 	
	fokozat		típusa	E	Sz	L	

III. A tantárgy célkitűzései
Stochastic data modelling is the application to various types of data of algorithms that exploit the rules of probability and allow direct representation of the stochastic nature of the real world. Different data types require different algorithms, therefore we need some a-priori knowledge that has to be included in the algorithm. Depending on this a-priori information one can extract more useful information from a set of data. The lectures present different algorithms and help evaluate them empirically for different sets of data.	

IV. A tantárgy tartalma
Stochastic data modelling is the application to various types of data of algorithms that exploit the rules of probability and allow direct representation of the stochastic nature of the real world. In order to extract information, usually one has to include prior knowledge into the algorithm. The inclusion of the prior knowledge is possible via the rules of probability. Prior knowledge is the model we want to use. If there are huge data-sets available, then one must use statistical methods, for a few data a lot more emphasis is to be put on the model. The algorithms depend also on the type of the problem we want to solve. The course is aimed as a practical introduction to various models from machine learning and to familiarise the students with the use of randomness and stochastic models.	

V. Könyvészet
[1]. Russell S, Norvig P. (2003) Artificial Intelligence: A Modern Approach (Second Edition), Prentice Hall.
[2]. Mitchell T (1997) Machine Learning, McGraw Hill.
[3]. Bernardo J.M, Smith A.F.M (2000) Bayesian Theory, John Wiley & Sons.
[4]. MacKay D.J.C (2003) Information Theory, Inference and Learning Algorithms, Cambridge University Press, HTTP: http://wol.ra.phy.cam.ac.uk/mackay/itila/book.html.
[5]. Rasmussen C.E, Williams C.K.I (2006) Gaussian Processes for Machine Learning, The MIT Press.
[6]. Rabiner L.R, Juang, B.H (1986) An introduction to Hidden Markov models, IEEE ASSP Magazine, pp: 4-15.
[7]. Durbin R, Eddy S.R, Krogh A, Mitchison G (1999) Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press.
[8]. Hyvärinen A, Karhunen J, Oja E (2001) Independent Component Analysis, Wiley-Interscience.
[9]. Barto A. (2002): Statistical Pattern Recognition, John Wiley & Sons.	

VI. Az oktatói tevékenység heti tematikája
Thematic overview of the lectures:

• Component analysis (weeks 1-4) ref. [2,4,8,9]:
  • Basics of statistical modelling – matrices and eigenvalues [9],
  • Principal components used in signal de-noising [2,4].
  • Independent components used in blind source separation of signals [8].

• Bayesian modelling (weeks 5-7) ref. [1,2,3,4,5]:
  • Introduction to various estimation methods [1, 2, 3],
  • Hierarchical model specification and parameter estimation [1,2,4],
  • Bayesian modelling: obtaining the posterior distribution [4, 5].

• Hidden Markov models (HMMs) weeks (8-11) ref. [7,8]:
  • HMM definitions [7],
  • Estimating the latent states [7],
  • Applications of HMMs (1) speech recognition [7,8],
  • Applications of HMMs (2) gene segmentation [7,8].

• Gaussian Process models (weeks 12-14) ref. [5,6]:
  • Joint Gaussians, kernel functions, Functional Bayesian models [4,5,6],
  • Approximations: using the KL-projection, sparse approximations,
  • Applications of Gaussian process inference.	

VII. Alkalmazott didaktikai módszerek
The students are presented applications written in Matlab and are required to write their own add-ons. The code-writing is followed by an analysis step where the students examine the results of an algorithm and compare with baselines.	

VIII. Értékelés
The exam consists of (40%) a presentation of a topic chosen in the first 6 weeks of the semester, (20%) the solution of the laboratory examples, (40%) oral examination based on the topics of the lectures and the seminars presented by the students.	

IX. Kiegészíto könyvészet
[1]. Bishop C.M (2006) Pattern Recognition and Machine Learning, Springer Verlag
[2]. Nabney I.T (2002) NETLAB - Algorithms for Pattern Recognition, Springer.
[3] Smola A.J, Schölkopf B (2002) Learning with Kernels, The MIT Press.	

	Dékán,						Tanszékvezető,

Dátum,								Előadás felelőse,

2009. okt. 4								Lect. Dr. CSATÓ Lehel