Machine Learning and Multivariate Techniques in HEP data Analyses
Prof. dr hab. Elżbieta Richter-Wąs
Extracted from slides by:
G. Cowan’s lectures at RH London Univ., H. Voss at SOS 2016, K. Reygers lectures at Heilderbeg Univ.
What is: Machine Learning (ML) & Multivariate Analysis/Technique (MVA)
Basics (classification, regression)
ROC-curve
generative vs predictive models
MVA/ML algorithms
Naïve Basian, KNN,
Linear discriminators, SVM
model fitting – gradient decent and loss function
General comments about MVAs
HEP Experiments: Simulated Higgs event in CMS
2
HEP Experiments: Simulated Higgs event in CMS
3
HEP Experiments: Event Signatures in the Detector
4
NOnA long baseline oscillation exp.
(nm)/ne (dis-)/appearance
O(100k) background, O(100) nm , O(10) ne per year 5
Machine Learning ‚elsewhere’
6
HEP: Everything started Multivariate
7
Outline
8
What is: Machine Learning (ML) & Multivariate Analysis/Technique (MVA)
Basics (classification, regression)
ROC-curve
generative vs predictive models
MVA/ML algorithms
Naïve Basian, KNN,
Linear discriminators, SVM
model fitting – gradient decent and loss function
General comments about MVAs
What is Machine Learning
9
What are Multivariate Techniques
10
Background
Signal
Machine Learning - Multivariate Techniques
11
Regression
12
Regression -> model functional behaviour
13
Multi-Variate Classification
14
Classification: Different Approaches
15
Signal Probability Instead of Hard Decisions
16
Event Classification
17
Event Classification
18
efficiency and purity
Classification <-> Regression
19
Event Classification
20
Receiver Operation Characteristic (ROC) curve
21
Receiver Operation Characteristic (ROC) curve
22
Receiver Operation Characteristic (ROC) curve
23
Event Classification -> finding the mapping function y(x)
24
Machine Learning Categories
25
Kernel Density Estimator
26
Kernel Density Estimator
27
K- Nearest Neighbour
28
Kernel Density Estimator
29
„Curse of Dimensionality”
30
Naive Bayesian Classifier
(Projective Likelihood Classifier)
31
De-Correlation
32
De-Correlation via PCA
(Principal Component Analysis)
33
Decorrelation at Work
34
Correlation Coefficients
35
Discriminative Classifiers
36
Linear Discriminant
37
Fisher’s Linear Discriminant
38
Linear Discriminant and non linear correlations
39
Classifier Training and Loss Function
40
Classifier Training and Loss Function
41 -
Logistic Regression
42
Logistic Regression
43
Logistic Regression
44
(Stochastic) Gradient Decent SDG
45
Overtraining
46
Regulatisation
47
Cross Validation
48
General Advice for (MVA) Analyses
49
MVA Categories
50
About Systematic Errors
51
MVA and Systematic Uncertainties
52
Classifiers and Their Properties
53
Summary
54
