Artificial intelligence for flavour physics and economyfeindt/Flavianet.pdf · Prediction of the complete probability distribution – event by event unfolding - Expectation value

Ziele f(t|x) Beispiele Prinzip Funktion Konkurrenz Forschung SpielIdee NeuroBayes A BHintergrund Anwendung Beispiel Projekt l Projekt llHistorie AblaufStart Idee Summary A

Michael Feindt Artificial Intelligence for Flavour Physics and Economy FlaviaNet School 2009

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Prof. Dr. Michael FeindtInstitut für Experimentelle KernphysikUniversität Karlsruhe

Wissenschaftlicher Beirat der Phi-T Physics Information Technologies GmbH

Prof. Dr. Michael Feindt

EKP, KCETA Universität Karlsruhe, KIT

Wissenschaftlicher Beirat Phi-T Physics Information Technologies GmbH

Artificial intelligence for flavour physicsand economy

Summer School 2009



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Prof. Dr. Michael Feindt

EKP, KCETAUniversität Karlsruhe, KIT

Wissenschaftlicher Beirat Phi-T Physics Information Technologies GmbH

Artificial intelligence for flavour physicsand economy

Summer School 2009



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Predictable

The result of simple classical physics processes is exactly predictable(one cause leads to one definite unique result, determinism)

Examples:

pendulum, planets,billard, electromagnetism…



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Unpredictable

Purely random processes are not predictable at all (even if the initial conditions are completely known!)

Examples:

Lottery(Too many tiny influences and branchings, deterministic chaos)

radioactive decay(quantum mechanics)

electronic noise



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Probability

Many systems in nature and life: Mixture of predictable and unpredictable (quasi-) random or chaotic components.

Probability statements, statistics.



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Extraction of a predictable component from empirical data (or Monte Carlo simulations)

Statistically relevant predictions for future events

Individualisisation of probability statements:

conditional probabilities: f(t|x),dependent on individual event with properties xinstead of general (a priori) probability f(t)

mean event

individual event

Our core technology:



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Particle physics experimentsMany 1.000.000.000 identical experiments for many years: Collisions of e.g. electrons and positrons (at LEP)



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OPA

L ex

perim

ent

at L

EP

Quantum Mechanics: In every collision something elsehappens!

Experiments:Observe meanvalues, distributions,correlations,determine parameters(mean lifetime, spin,parity etc) from that.



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Neural networks

Neural networks:Self learning procedures, copied from nature

Parietal CortexFrontal Lobe

Motor Cortex

Temporal Lobe

Brain Stem

Occipital Lobe

Cerebellum



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Neural networks

The information (the knowledge, the expertise)is coded in the connectionsbetween the neurons

Each neuron performs fuzzy decisions

A neural network can learn fromexamples

Human brain: about 100 billion ( 1011 ) neurons about 100 trillion ( 1014 ) connections



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Neural Network

basic functions



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Neural network transfer functions



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Neural network training



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Neural network trainingDifficulty: find global minimum of highly non-linear functionin high (~ >100) dimensional space.Imagine task to find deepest valley in the Alps (just 2 dimensions)

Easy to find the next local minimum...

but globally......impossible!



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Naïve neural networks and criticizmWe‘ve tried that but it didn‘t give good results - Stuck in local minimum - Learning not robustWe‘ve tried that but it was worse than our 100 person-years analytical high tech algorithm - Selected too naive input variables - Use your fancy algorithm as INPUT ! We‘ve tried that but the predictions were wrong - Overtraining: the net learned statistical fluctuationsYeah but how can you estimate systematic errors? - How can you with cuts when variables are correlated? - Tests on data, data/MC agreement possible and done.



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Address all these topics and build a professional robust and flexible neural network package for physics, insurance, bank and industry applications:NeuroBayes®



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NeuroBayes® principle

NeuroBayes® Teacher:Learning of complex relationships from existingdata bases (e.g. Monte Carlo)

NeuroBayes® Expert:Prognosis for unknown data

Output

Input

Sign

ific

ance

con

trol

Postprocessing

Preprocessing



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Probability that hypothesis is correct (classification)

or probability densityfor variable t

How it works: training and application

Historic or simulated data

Data seta = ...b = ...c = .......t = …!

NeuroBayes®Teacher

NeuroBayes®Expert

Actual (new real) data

Data seta = ...b = ...c = .......t = ?

Expertise

Expert system



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Classification: Binary targets: Each single outcome will be “yes“ or “no“ NeuroBayes output is the Bayesian posterior probability that answer is “yes“ (given that inclusive rates are the same in trainingand test sample, otherwise simple transformation necessary).

Examples:> This elementary particle is a K meson. > This event is a Higgs candidate.> Germany will become soccer world champion in 2010. > Customer Meier will have liquidity problems next year.> This equity price will rise.

NeuroBayes® task 1:Classifications



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NeuroBayes® task 2:Conditional probability densities

Probability density for real valued targets: For each possible (real) value a probability (density) is given. From that all statistical quantities like mean value, median, mode, standard deviation, percentiles etc can be deduced. Examples:> Energy of an elementary particle (e.g a semileptonically decaying B meson with missing neutrino) > Q value of a decay> Lifetime of a decay > Price change of an equity or option > Company turnaround or earnings



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Prediction of the complete probability distribution – event by event unfolding -

ModeExpectation value

Standard deviationvolatility

Deviations from normal distribution,e.g. crash probability



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Conditional probability densities in particle physics

What is the probability density of the true B momentum in this semileptonic B candidate event taken with the CDF II detector

with these n tracks with those momenta and rapidities in the hemisphere, which are forming this secondary vertex with this decay length and probability, this invariant mass and transverse momentum, this lepton information, this missing transverse momentum, this difference in Phi and Theta between momentum sum and vertex topology, etc pp



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Press (Die Welt, April 21, 2006)‏



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After having looked outside the ivory tower, realized:

These methods are not only applicable in physics

<phi-t>: Foundation of private company out of University of Karlsruhe, initially sponsored by exist-seed- programme of the federal ministery for Education and Research BMBF



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2000-2002 NeuroBayes®-specialisation for economy at the University of Karlsruhe

Oct. 2002: GmbH founded, first industrial projects

June 2003: Removal into new office 199 sqm IT-Portal Karlsruhe

May 2008: Expansion to 700 sqm office Foundation of sub-company Phi-T products&services

May 2009: Opening of second office inHamburg

Exclusive rights for NeuroBayes® Staff almost all physicists (mainly from HEP)Continuous further development of NeuroBayes®

History



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(among others): BGV and VKB car insurances AXA and Central health insurances Lupus Alpha Asset Management dm drogerie markt (drugstore chain) Otto Versand (mail order business) Libri (book wholesale) Thyssen Krupp (steel industry)

customers (excerpt)



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Main message:NeuroBayes is a very powerful algorithm • robust – (unless fooled) does not overtrain, always finds good solution - and fast • can automatically select significant variables • output interpretable as Bayesian a posteriori probability• can train with weights and background subtraction• has potential to improve many analyses significantly • in density mode it can be used to improve resolutions (e.g. lifetime in semileptonic B decays)NeuroBayes is easy to use • Examples and documentation available• Good default values for all options fast start! • Direct interface to TMVA available• Introduction into root planned



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<phi-t> NeuroBayes®

> is based on neural 2nd generation algorithms, Bayesian regularisation, optimised preprocessing with transformations and decorrelation of input variables and linear correlation to output. > learns extremely fast due to 2nd order methods and 0-iteration mode> is extremly robust against outliers > is immune against learning by heart statistical noise > tells you if there is nothing relevant to be learned> delivers sensible prognoses already with small statistics> has advanced boost and cross validation features> is steadily further developed



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Ramler-plot (extended correlation matrix)



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Ramler-II-plot (visualize correlation to target)



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Visualisation of single input-variables



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Visualisation of correlation matrix

Variable 1: Training target



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Visualisation of network performance

Purity vs. efficiency

Signal-effiziency vs. total efficiency(Lift chart)



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More than 50 diploma and Ph.D. theses…

from experiments DELPHI, CDF II, AMS, CMS and Belle used NeuroBayes® or predecessors very successfully.

Many of these can be found at www.phi-t.de Wissenschaft NeuroBayes

Talks about NeuroBayes® and applications:www-ekp.physik.uni-karlsruhe.de/~feindt Forschung



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NeuroBayes soft electron identification for CDF II(Ulrich Kerzel, Michael Milnik, M.F.)

Thesis U. Kerzel: on basis of Soft Electron Collection(much more efficient than cut selectionor JetNet with same inputs)- after clever preprocessing by hand and careful learning parameter choice this could also be as good as NeuroBayes®

Just a few examples…



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Just a few examples…

NeuroBayes® selection



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Just a few examples… First observation of B_s1 and most precise of B_s2*

Selection using NeuroBayes®



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Nice new methods…

Training with weighted events (e.g for JPC-determination)

Data-only training with sideband subtraction (i.e. negative weights)And ssPlot

Construction of weights for MC phase space events such thatthey are distributed like real data

Interpretation of NeuroBayes output as Bayesian a posteriori probability allows to avoid cuts on output variable but instead-- inclusion into likelihood-fits (B-mixing, CP-violation)-- usage with sPlot to produce “background free“ plots

Research on finding signals in data without having good backgroundmodel



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Example for data-only training (on1.resonance)(scan through cuts on network output)



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NeuroBayes Bs to J/ψ Φ selection without MC (Michal Kreps)

soft preselection, input to first NeuroBayes training

soft cut on net 1, input to second NeuroBayes training

cut on net 2

all data



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NeuroBayes Bs to J/ψ Φ selection without MC (Michal Kreps)

Significance S/B

# Signal #Background

N_signal = 757.4+-28.7, mass 5366.6 +- 0.4 MeV lifetime 432.3 +- 17.6 mu

no lifetime bias by input variables or NeuroBayes

NNout

NNout



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Successfulin competitionwith otherdata-mining-methods



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and in 2009…

new rules: only two teams per Universitytask: to predict turnaround of 8 book titles in about 2500 book stores (Libri)Winning team: Uni Karlsruhe II (my students, with help of NeuroBayes)

team represented byMichael PrimFabian KellerJohannes Munk

Foto

: Pru

dsys



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Phi-T: Applications of NeuroBayes® in Economy

> Medicine and Pharma research e.g. effects and undesirable effects of drugs early tumor recognition> Banks e.g. credit-scoring (Basel II), finance time series prediction, valuation of derivates, risk minimised trading strategies, client valuation> Insurances e.g. risk and cost prediction for individual clients, probability of contract cancellation, fraud recognition, justice in tariffs > Trading chain stores: turnover prognosis for individual articles/stores Necessary prerequisite: Historic or simulated data must be available!



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Individual risk prognosesfor car insurances:

Accident probabilityCost probability distributionLarge damage prognosisContract cancellation prob.

very successful at



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Turnover prognosis for mail order business



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Presse

Physicists modernise sales management …



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Prognosis of individual health costs

Kunde N. 00000

Mann, 44

Tarif XYZ123 seit ca. 17 Jahre

Pilot project for a large private health insurance

Prognosis of costs in following year for each person insured with confidence intervals

4 years of training, test on following year

Results:

Probability density for each customer/tarif combination

Very good test results!

Has potential for a real and objective cost reduction in health management



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Prognosis of sports events from historical data

Results: Probabilities for home - tie - guest



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Test

VDI-Nachrichten, 9.3.2007

Prognosis of financial marketsNeuroBayes® based risk averse market neutral fonds for institutional investors

Lupus Alpha NeuroBayes® Short Term Trading Fonds (up to now 20 Mio ¤€, aim: 250 Mio ¤€ end of 2008)

Test

Börsenzeitung, 6.2.2008



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Test

Test

35 (2009)



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CAPM capital asset pricing model

Higher risk σ– higher reward µ

Equity movements are correlated: correlation coefficient β

Diversification: a broad portfolio of many equities (index) has less risk than single equities

Good fund manager tries to beat the market, but portfolio valuewill go up and down with market

Markowitz (nobel price): best risk-return when on capital market line

αphysicists: design strategies to be above line: generate intercept α



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Test

Test

NB® fund

market

NB® 2009 (projected)NB® since startup 2007EuroStoxx 50 since 1986 (friendly –rising- choice)risk free (Libor)

CAPM and capital market lineNB® generates a !

single equities



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Expected 1-Month-Return Comparison (2009)

La NB® Fonds vs. equity index(Euro-Stoxx 50)

Mean: x 4Volatility: / 4Loss probability: /40Risks of higher moments: ≈noneβ: 0

NB® fund

market



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Fund for institutional investors (pension funds).

Alpha trading leads to efficient markets: justice in prices,price changes unpredictabe, i.e.you may buy or sell equites atany time without getting ripped.

Competition between many high frequency traders and market makers leads to small bid-ask-spread and fees, thus small transaction costs.

In old days banks made this money, without risk, like a used car dealer.

Good algorithmic trading machines tend to stabilize the markets:They are more rational than human traders: don‘t know greed and don‘t know panic, if well debugged, don‘t do fat finger errors.



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The <phi-t> mouse game:or: even your ``free will´´ is predictable

//www.phi-t.de/mousegame



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NeuroBayes® for high energy physics research

If you have a complicated prediction task and you have real and/or Monte Carlo simulation data…

Probably NeuroBayes® can help you!

Always when you have lots of individual datasets with many input variables and a difficult prediction task to be solved for each individually.



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Bindings and Licenses NeuroBayes® is commercial software. Special rates for public research.Essentially free for high energy physics research.License files needed. Separately for expert and teacher.Please contact Phi-T.

NeuroBayes core code written in Fortran. Libraries for many platforms (Linux, Windows, …) available. Bindings exist for C++, Fortran, java, lisp, etc. Code generator for easy usage exists for Fortran and C++.New: Interface to root-TMVA available (classification only) Integration into root planned



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Documentation

Basics:M. Feindt, A Neural Bayesian Estimator for Conditional Probability Densities, E-preprint-archive physics 0402093

M. Feindt, U. Kerzel, The NeuroBayes Neural Network Package,NIM A 559(2006) 190

Web Sites:www.phi-t.de (Company web site, German & English)www.neurobayes.de (English site on physics results with NeuroBayes & all diploma and PhD theses using NeuroBayes)www-ekp.physik.uni-karlsruhe.de/~feindt (some NeuroBayes talks can be found here under -> Forschung)



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Phi-T and Phi-T p&s as employers:

Have large impact in industry, economy and businesswith strictly scientific methods and world-leading technologies.Bring scientific and economic worlds together. Move something!

Phi-T one of the coolest places to work. Very successful and influential projects. Enthusiastic team of high-level scientists.

We always look for highly intelligent young people • with excellent scientific education, • excellent analytic mind, • excellent mathematical and programming skills,• the right amount of pragmatism,• the will to take responsability, • the ability to work in a team.



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Employees at Phi-T and Phi-T p&s…

Recently introduced tabletop soccerfor recreation.Lots of fun, getting better with experience.

Players started to take notes aboutteams and scores and fill them intoa database. To be able to train a NeuroBayes program to predict the outcomes of future games….

Documents

Artificial intelligence for flavour physics and economyfeindt/Flavianet.pdf · Prediction of the complete probability distribution – event by event unfolding - Expectation value