Kernel based Machine Learning and Multivariate Modeling
Teachers
Person in charge
Luis Antonio Belanche Muñoz (
)
Pedro Delicado Useros (
)
Weekly hours
Theory
3
Problems
0
Laboratory
0
Guided learning
0.2
Autonomous learning
6
Competences
Generic Technical Competences
Generic
CG3 - Capacity for mathematical modeling, calculation and experimental designing in technology and companies engineering centers, particularly in research and innovation in all areas of Computer Science.
Transversal Competences
Information literacy
CTR4 - Capability to manage the acquisition, structuring, analysis and visualization of data and information in the area of informatics engineering, and critically assess the results of this effort.
Reasoning
CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.
Technical Competences of each Specialization
Specific
CEC1 - Ability to apply scientific methodologies in the study and analysis of phenomena and systems in any field of Information Technology as well as in the conception, design and implementation of innovative and original computing solutions.
CEC3 - Ability to apply innovative solutions and make progress in the knowledge that exploit the new paradigms of Informatics, particularly in distributed environments.
Objectives
Understand the foundations of Kernel-Based Learning Methods
Related competences:
CG3,
CEC1,
CEC3,
CTR6,
Get acquainted with specific kernel-based methods, such as the Support Vector Machine
Related competences:
CG3,
CTR4,
Know methods for kernelizing existing statistical or machine learning algorithms
Related competences:
CTR6,
Know the theoretical foundations of kernel functions and kernel methods
Related competences:
CG3,
Know the structure of the main unsupervised learning problems.
Related competences:
CG3,
CEC1,
CTR4,
CTR6,
Learn different methods for dimensionality reduction when the standard assumptions in classical Multivariate Analysis are not fulfilled
Related competences:
CG3,
CEC1,
CEC3,
CTR4,
CTR6,
Learn how to combine dimensionality reduction techniques with prediction algorithms
Related competences:
CG3,
CEC1,
CEC3,
CTR4,
CTR6,
Contents
Introduction to Kernel-Based Learning
This topic introduces the student the foundations of Kernel-Based Learning focusing on Kernel Linear Regression
The Support Vector Machine (SVM)
This topic develops Support Vector Machine (SVM) for classification, regression and novelty detection
Kernels: properties & design
This topic defines kernel functions, their properties and construction. Introduces specific kernels for different data types, such as real vectors, categorical information, feature subsets, strings, probability distributions and graphs.
Kernelizing ML algorithms
This topic reviews different techniques for kernelizing existent algorithms
Theoretical underpinnings
This topic reviews the basic theoretical underpinnings of kernel-based methods, focusing on statistical learning theory
Introduction to unsupervised learning
Unsupervised versus supervised learning. Main problems in unsupervised learning (density estimation, dimensionality reduction, latent variables, clustering).
Nonlinear dimensionality reduction
a. Principal curves.
b. Local Multidimensional Scaling.
c. ISOMAP.
d. t-Stochastic Neighbor Embedding.
e. Applications: (i) Visualization of high- or infinite-dimensional data. (ii) Exploratory analysis of functional data in Demography.
Dimensionality reduction with sparsity
a. Matrix decompositions, approximations, and completion.
b. Sparse Principal Components and Canonical Correlation.
c. Applications: (i) Recommender systems. (ii) Estimating causal effects.
Prediction after dimensionality reduction.
a. Reduced rank regression and canonical correlation.
b. Principal Component regression.
c. Distance based regression.
Objectives:1234567 Week:
15 (Outside class hours) Type:
final exam
Theory
0h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
12h
Teaching methodology
Learning is done through a combination of theoretical explanations and their application to practising exercises and real cases. The lectures will develop the necessary scientific knowledge, including its application to problem solving. These problems constitute the practical work of the students on the subject, which will be developed as autonomous learning. The software used will be primarily R.
Evaluation methodology
The course evaluation will be based on the marks obtained in the practical works delivered during the semester plus the mark obtained in the written test for global evaluation.
Each practical work will lead to the drafting of the corresponding written report which will be evaluated by the teachers resulting in a mark denoted P.
The exam will take place at the end of the semester and will evaluate the assimilation of the basic concepts on the whole subject, resulting in a mark denoted T.