Appendix A — Results when optimizing a neural network observable and binning simultaneously
Data Analysis in High-Energy Physics as a Differentiable Program
Preface
Citing this thesis
This is the Most Important Chapter
Fundamentals
1
Physics background
2
Probability and Statistics, in theory
3
Probability and Statistics, in practice
4
Gradient descent
5
Automatic differentiation
6
Machine learning
Applications
7
Data Analysis in High-Energy Physics as a Differentiable Program
8
Signal Model Interpolation using Normalizing Flows
9
Search for a heavy scalar particle
\(X\)
decaying to a scalar
\(S\)
and a Higgs boson, with final state
\(b\bar{b}\gamma\gamma\)
in the ATLAS detector
References
Appendices
A
Results when optimizing a neural network observable and binning simultaneously
On this page:
A.1
5-bin observable
Metrics
Histograms
Neural network contours in data space
A.2
20-bin observable
Metrics
Histograms
Neural network contours in data space
Appendix A — Results when optimizing a neural network observable and binning simultaneously
A.1
5-bin observable
Metrics
Plots of the different metrics calculated on the test set for different training strategies using a 5-bin neural network observable. The results are averaged across 9 random seeds for the weight initializations. The scatter points on some of the curves represent the model that we would select in practice if using that training strategy (provided we decide to use the loss as the selection metric).
Histograms
Histograms from optimizing with respect to the discovery
\(p\)
-value
\(p_0\)
.
Histograms from optimizing with respect to the
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to a combination of discovery
\(p\)
-value and
\(\mathrm{CL}_s\)
.
Neural network contours in data space
Histograms from optimizing with respect to the discovery
\(p\)
-value
\(p_0\)
.
Histograms from optimizing with respect to the
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to a combination of discovery
\(p\)
-value and
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to the Fisher information estimate of
\(\sigma_{\hat{\mu}}\)
.
A.2
20-bin observable
Metrics
Plots of the different metrics calculated on the test set for different training strategies using a 20-bin neural network observable. The results are averaged across 9 random seeds for the weight initializations. The scatter points on some of the curves represent the model that we would select in practice if using that training strategy (provided we decide to use the loss as the selection metric).
Histograms
Histograms from optimizing with respect to the discovery
\(p\)
-value
\(p_0\)
.
Histograms from optimizing with respect to the
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to a combination of discovery
\(p\)
-value and
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to the Fisher information estimate of
\(\sigma_{\hat{\mu}}\)
.
Neural network contours in data space
Histograms from optimizing with respect to the discovery
\(p\)
-value
\(p_0\)
.
Histograms from optimizing with respect to the
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to a combination of discovery
\(p\)
-value and
\(\mathrm{CL}_s\)
.
Histograms from optimizing with respect to the Fisher information estimate of
\(\sigma_{\hat{\mu}}\)
.
References