Probability, Decision and Information Theory Applied to Physics Data

From sets of physics data (e.g., particle physics, astronomical observations, nuclear physics, etc.), determine statistical quantities such as probability density, expected values and covariance, Bayesian probability etc. In the context of using machine learning methods, define the concepts of misclassification, expected loss, inference and decision making. Followed by an overview of the use of quantities such as relative entropy and mutual information in physics examples.

Probability Distributions in Physics Examples

Treatment and classification of binary, multinomial and other discrete probability distributions and classifications in physics data. Continuous distributions such as Gaussian and exponential distributions in physics models and measurements. Use of machine learning in the context of determining the parameters of probability distributions.

Basics of Monte-Carlo methods and their implementation in machine learning methods with physics examples.

Examples:

-Introduction of multinomial distributions in particle physics measurements, determination of their statistical and systematic measurement errors. Approach to the optimal selection of the number of compartments (bin) and interval evaluated by different methods, taking into account the limitations of the intrinsic resolution of the measured parameters.

-Simple simulation of the decay chain of unstable particles by considering the decay widths and measurement resolution.

Modeling in physics by using machine learning methods

By using examples from different branches of physics (from condensed and soft matter, particle physics, medical physics to meteorology and astronomy, etc.) one introduces the application of the following concepts:

Linear Regression: Cost Function, Gradient Descent, Bayesian regression

Logistic Regression: Binary and Multiclass Classification, Regularization, Probabilistic generative and discriminative models.

Neural Networks: Curse of dimensionality, Universal approximation theorem, Backpropagation, Stochastic Gradient Descent. Special cases: Convolutional networks (CNN), RNNs, GANs, Variational Autoencoders (VAE).

Kernels and Support Vector Machines, Gaussian processes

Clustering: Mixture models, K-Means, Mixed membership and LDA, Principal Component Analysis, Anomaly Detection

Approximate inference: variational inference, expectation maximization

A special emphasis is given on the methods of optimal model selection in physics, e.g. in problems involving biases and minimal variance.

Examples:

- Anomaly detection in nuclear physics and evaluation/classification of these by weight coefficients with respect to physics impact.

-Use of GAN and VAE to simulate detector response to the passage of particles through matter, emphasis on adding physics criteria to the loss function (e.g. maintaining the moving amount etc.).

-Use machine learning methods to identify tumors and appropriate iradiation configuration in medical physics. Emphasis on measurement resolution and consideration of the types of physical processes arising from irradiation.