Tutorial
Peter Grünwald Center Wiskunde & Informatica Amsterdam;
Matematisch Instituut – Universiteit Leiden
Universal Prediction
UNIVERSAL DATA COMPRESSION
Minimum description length
Prediction, learning and games
Related to Bayesian Inference
“Objectiv subjectivity”
Kolmogorov complexity
Vovk-Shafer approach to probability
Example: weather forecast
Prediction strategy
Combine predictions so that we do better than individual
Universe is a set of candidate strategies
Gambling interpretation of probability
Gambling game with reinvestments
You cannot be better of any of candidate strategies
Paul the Octopus perfect predictor
Follow the leader is the bad strategy
If of predictor is FIFA official for good reson unlike huge numbers of random
predictors – OVERFITTING
Bayes theorem
ON-LINE PROBABILISTIC PREDICTION
Prediction strategy = DISTRIBUTION
Conditional probabilities
Log loss & likelihood
Prediction strategy P (probability distribution)
How fast you learn (here learning is central)
For uncountable sets you prior belief
LEARNING IN RELATIVE SENSE WITHOUT ANY ASSUMPTIONS (about data)
HIGH PERFORMANCE COMPUTING IN BIOINFORMATICS
Baysean algorithm works better than follow the leader
Generalization of Bayesian
Universal Prediction with 0/1 loss
Learning weight
“The older you get, the less attention you pay to everything that happens in your
life”
The HEDGE algorithm used for calculating electricity consumptions in great
Paris great Region
Multi-armed Bandit & other limited feedback
Learning the learning rate
MDL MINIMUM DESCRIPTION LENGTH
Data compression
Log-loss prediction
Predictors – statistical models
Nested Models
Meta-priors
Minimax optimum predictions
Ockham + Luckiness
Objective component
Subjective component
Lars Wienbrandt
The FPGA-based High-Performance Computer RIVYERA for Applications in Bioinformatics
Lars Wienbrandt
FPGA-based high-performance computer RIVYERA
Puzzle of DNA pieces “I think I found a corner piece” … cartoon Interpretation
Databases searches
VHDL language
Parallel computing
128 FPGA
Memory
Protein alignment is different from DNA alignment
Modelling genotypes
Pairwise information
Contingency table – pairs of genotypes
Q: length of query sequence
A: p to 500
Q: Why no improvement
Q Can you go beyond pairwise to multiple alignments
Programming FPGA is difficult, most computationally intense
Q: Maybe a possible language could apply
Programming assembler vs. C optimizing compiler
Q: programming for RIVYERA
VHTL compilation takes hours
Claudio Zandron
Using Membrane Features to Compute
P systems (introduced by Paun) discrete nondeterministic
Rules applied in maximally parallel way
Delta means membrane is destroyed
Only one outer skin-membrane
Active membranes
Polarization (positive, neutral, negative)
Division of membranes
P systems web page
Q: how this compares to process calculi?
M. T. Godziszewski and D. Kalociński
Computational Hardness of Mathematical Concepts and Algorithmic Learnability
Learnability or cognitive accessibility
Mind-changing procedure
Cognitive accessability of Provability
Determinig consistency of axiomatic system with recursive set of axioms
Mind changes and stabilize on the right
N. Dershowitz and E. Falkovich
Generic Parallel Algorithms
Levels of abstractions
Physicist
Molecules
Organism
Biology
Ecology
Algorithms
All sorts of algorithms apart from Turing
Basic operations
1 dim
TM is not generic
It works on strings
An algorithm is a finite way of describing state transitions
Knuth algorithms before Turing
Gdc algorithms euclides
Geometry compass Ruler
Eve’s Algorithm of dividing aples
Finite describes transitions
STATE ENCAPSULATES ALL RELEVANT DATA AND OPERATIONS NECESSARY
FOR TH ENEXT STATE
Not only trings but any data structures.
ABSTRACT STATE
GENERICH PARALLEL ALGORITHMS
ANALOGUE ALGORITHMS
CONTINUous time Oliver Bournez
The finite description & finite transition = effectiveness
Tractable algorithms
GENERIC COMPLEXITY
Q: Gurewich and Blas