87198 - Statistics and Architectures for Big Data Processing M

Learning outcomes

The course provides students with a basic knowledge of problems and corresponding techniques of solutions implied by the ever increasing amount and complexity of the data available for analyses and decisions, i.e., the so called Big-Data (BD). The corresponding issues are tackled by multiple points of view: from the abstract characterization of the mathematical properties of BD, to the hardware architectures needed to process them.

Course contents

The two dimensions of "Big" in Big Data.

Data dimensionality

• geometrical effect of high dimensionality and consequences
  

Dimensionality reduction

• multidimensional Gaussian vectors and their properties
• dimensionality reduction by Johnson-Lindenstrauss
• dimensionality reduction by SVD/PCA (relationship with Gaussian clustering) 
• dimensionality reduction by sparse signal recovery/compressed sensing
• other uses of SVD/eigenstructures: the hub-authority ranking, the pagerank core idea, document collection summaries)

Interpolation

• grid-data multilinear interpolation
• grid-data piecewise-linear interpolation
• scattered-data interpolation by radial-basis functions

Streaming algorithms

• the streaming computation model
• streaming random picks and multiplication of huge matrices
• streaming estimation of features of occurences histogram
• hashing for flattening of distributions
• random computation: estimations instead of exact results

 

Teaching methods

Class teaching

Assessment methods

Oral examination

Office hours

See the website of Riccardo Rovatti

See the website of Francesco Conti