Physics, Big Data Analysis and Philosophy (and all the rest) - - PowerPoint PPT Presentation

Physics, Big Data Analysis and Philosophy (and all the rest)

Wolfgang Rhode

... eritis sicut Deus ...

Plato‘s Cave Analogy

Are true conclusions possible?

´ Within the world of logic? Yes ´ Within the world of mathematics? Yes ´ Within the world of observations? No

´ Accuracy of observations ´ Conclusion from the observed effect to it’s cause

´ Within the world of teleology ? No

´ To reach a goal ? The program running on us -? > Big Data Analysis

Consequence

´ Ancient and middle age philosophy:

´ Rationally invented systems based on logic and mathematics ´ However: these systems are inappropriate to describe the nature.

´ Galileo Galilei:

´ Introduction of the experiment as mean to understand the nature ´ Book of nature is written in the language of mathematics

How to justify conclusions from experiments to the world of theories?

´ Success of classical physics (Newton … Einstein)

´ Btw:. Classical physics: deterministic, no probability elements

´ Aggravating: Success of Thermodynamics and Quantum Mechanics (etc.)

´ In very different ways probability based.

´ Epistemology: Different tries to answer the question, but no success … until ...

Karl Popper: Logic of scientific discovery (1934)

´ Theories are (somehow) more or less rationally invented ´ Scientific theories allow an experimental test

´ Disagreement: rejection & search for a better theory ´ Agreement: acceptance for the moment & search for a more decisive experiment

´ Critical Rationalism

´ Logic based theory

´ Is it necessary to reject a theory, just because of one non-fitting experiment?

Plato‘s Cave Revisited

Plato‘s Cave Revisited

Plato‘s Cave Revisited

Plato‘s Cave Revisited

The physical Problem: “Cave equation”

g = measured numbers b = background A = Kernel = transfer function = detector properties f = wanted function

Computer Science View

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Scientific Question

Experiment Sensors, Data Acquisition Data Reduction, Data Pre- Processing Analysis Evaluation Regulation, Improvements Data

Trigger Streams Signal Identification Concept Shift Storage Inverse Problems Evaluation Complex Programming Models Monte Carlo Simulation

Monte Carlo: Virtual Reality

´ Physics … all that we know ...

´ Energy Spectra ´ Directional Distributions ´ Sky Maps

´ Data: … all we can measure ...

´ Charges, ´ Times, ´ Locations

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Data Analysis: Monte Carlo Description

(Goal: Measurement of the neutrino energy spectrum) ´ Monte Carlo Simulation of

´ Signal: Neutrinos

´ close to correct spatial and energy distribution ´ Neutrino interactions leading to charged particles (i.e. muons) ´ Muon interactions (path, range, deposited energy...) ´ Cherenkov-Light (Production by charged particles, propagation in ice) ´ Light detection and measurement (photomultiplier, read out electronics)

´ Physical Background: Cosmic Ray interaction in the Atmosphere

´ à (....) recorded light in the detector, correct simulation

´ Technical Background: correct simulation

´ Radioactivity of the ice or the detector itself à light ´ Photomultiplier noise (“signal without external reason“) ´ Artefacts of the readout electronics à fake signal

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Atmospheric Muons (Corsika)

• 1 Year Run Time of the Detector
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Computer Science View

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Scientific Question

Experiment Sensors, Data Acquisition Data Reduction, Data Pre- Processing Analysis Evaluation Regulation, Improvements Data

Trigger Streams Signal Identification Concept Shift Storage Inverse Problems Evaluation Complex Programming Models Monte Carlo Simulation

TRIGGER: Which Data might we want?

´ Keep as much from the signal as possible . ´ Discard as much of the background as possible. ´ Decide within ~1 ms ´ à Write data to disk, if ´ N Detectors within a ´ Volume V and a ´ Time Interval T have seen a signal. ´ Hardware (FPGA) and Software realization possible.

First Analysis Steps: Which Events might we want?

´ Still: Keep as much from the signal as possible . ´ Still: Discard as much of the background as possible. ´ Decide within ~ minutes - hours (Computing Farm) ´ Can the event be reconstructed at all? ´ Is the result physical?

(IceCube: Movement with velocity of light?, Upward?)

´ Do different algorithms lead to compatible results?

The Problem:

g = measured numbers b = background A = Kernel = transfer function = detector properties f = wanted function

Signal – Background Separation

How to obtain a clean signal data set?

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Stability of the MRMR Selection:

MRMR: Minimum Redundancy Maximum Relevance

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Attributes at knot Attributes for the complete RF Signal/Background -Relation at training

Signal Selection

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Data

A new way of doing data science

´ Classical: ´ Simple Signature ´ à Physical Interpretation: Information loss ´ à Continue as Human (Physicist;) ´ à Compare to a predictive Theory ´ New: ´ Multidimensional Signature ´ à Probability Cloud ´ à Find & Calculate & Add Relevant Attributes ´ à Remove: Irrelevant Attributes / Information Noise ´ à Unfolding / inverse Problem:

´ à Collapse of the Probability Cloud into a Physical Distribution

´ à Compare to a structural Theory

´ à limit Ranges of Physical Relevant Parameters

35

http://cerncourier.com/cws/article/cern/27925

Phase 2: Unfolding

Unfolding …

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The problem, to be filled with life:

g = measured numbers b = background, small A = Kernel = transfer function = detector properties f = wanted physical distribution

Change of paradigm !

´ Separation:

´ Monte Carlo describes the data as perfect as possible.

´ Unfolding:

´ Monte Carlo description of the detector is “perfect” ´ However, the searched for physical input is unknown!

´ Completely unknown?

´ … good guessing allowed ( a good start value saves CPU time) ´ ... prove, that the unfolding algorithm works Monte Carlo independent

Are there variables correlated to the searched-for energy ?

´ Number of hit detectors... ´ ... and many others: Number of hit detectors...

´ Number of hit detectors... ´ ... and many others: Number of hit detectors... ... and many others

Are there variables correlated to the searched-for energy ?

Inverse Problems: ill-posed, bad condition number

Translate to the matrix equation:

g = Af + b

f = A-1(g- b)

Damp elements of A, leading to oscillating results:

Regularization ßà Addition of Assumptions

Example: Unfolding of the Muon Neutrino Energy Spectrum

g(y) = Z A(E, y)f(E)dx + b(y)

Background well understood Reconstructed Track length Energy Estimator Number of direct Photons

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• 1. Problem solution in the Monte Carlo world:

´ Many parameter combinations to be evaluated:

´ Number of elements in the input & output vectors, ´ regularization strength ...

• 2. Optimize the Regularization

à Growing fluctuations ´ à Growing correlations

• 3. Test the Stability of the Result

(Pull-Mode)

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• but what about the reweighted control variables?

• 5. Acceptance correction :

Event Numbers Detector Area = geom. Area x Reconstruction prob. Flux = Events / ( Area x Time)

• 6. Physical Signal (Muon Neutrino Flux)

Preliminary

Computer Science View

50

Scientific Question

Experiment Sensors, Data Acquisition Data Reduction, Data Pre- Processing Analysis Evaluation Regulation, Improvements Data

Trigger Streams Signal Identification Concept Shift Storage Inverse Problems Evaluation Complex Programming Models

Monte Carlo Simulation

Monte Carlo: Virtual Reality

´ Structures of Theories:

´ Monte Carlo Parameter Selection

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´ Experimental Physics:

´ Energy Spectra ´ Directional Distributions

´ Data: Charges, Times, Locations ´ Translation: Monte Carlo Simulation

´ Extreme resource requesting ´ à Code/System Optimization (GPU) ´ à Abort needles Branches ´ à Active Learning

Signal Selection

´ Real Time Analysis in Data Streams

´ Fast Trigger (FPGA) ´ Feature Generation ´ Feature Extraction ´ Data Mining: Random Forests & Co.

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Data Mining: Random Forests & Co.

Inverse Problems – ill-posed Problems

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g(y) = Z A(E, y)f(E)dx + b(y)

g = Af + b f = A-1(g- b)

Preliminary

A new way of doing data science

´ Classical: ´ Simple Signature ´ à Physical Interpretation ´ à Continue as Human (Physicist;) ´ à Compare to a predictive Theory ´ New: ´ Multidimensional Signature ´ à Probability Cloud ´ à Find & Calculate & Add Relevant Attributes ´ à Remove: Irrelevant Attributes / Information Noise ´ à Unfolding / inverse Problem:

´ à Collapse of the Probability Cloud into a Physical Distribution

´ à Compare to a structural Theory

´ à limit Ranges of Physical Relevant Parameters

54

http://cerncourier.com/cws/article/cern/27925

Automated discovery of hypotheses and their validations?

´ Physics Data à Multi-dimensional Probability Clouds ´ Physics Theories à Multi-parameter Ranges of Possibilities ´ Data Analysis à Limit the Parameter Range ´ Theorists à Simplify your Theory ´ Computer Science

´ à Resource Aware (fast, cheap) Hypotheses Testing ´ à Towards Automated Testing of the Hypothesis Space

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Why we need new methods for machine learning:

´ Typical finance needs for present Experiments: ´ Hardware ~ Computing ~ 100 Mio. $ | € ´ Next generation: ´ Sensitivity 10 x higher à 100 x more data ´ Increasing theory parameter space to test ´ Constant or decreasing financial resources ´ Consequence: ´ Replace learning Physicists by learning machines ´ Distributed computing ´ Minimize data transfer, storage, memory, CPU

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Challenge of distributed computational power and data

´ Distributed Data: ´ Big Data Volume: ´Intelligent Access, ´Intelligent Transfer, ´Information Conserving Data Reduction ´ Distributed Computing: ´ Platform independent code ´ Accepted and well tested Methods ´ Optimized in every respect

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„Probabilistic Rationalism“

´ g(y), f(x) 2dim ? à World of language & logic ´ g(y), f(x) analytic functions ? à World of classical physics ´ g(y), f(x) probability distributions? à World of big data analysis

Conclusion

Big Data Analysis leads to new Perspectives: Physics: A New way of understanding Data Analysis Computer Science: A New Integral View on Problem Solution Philosophy: A New Perspective in Epistemology

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