Stochastic Processes and Simulations – A Machine Learning Perspective

✍ Scribed by Vincent Granville

• Publisher: Machine Learning Techniques
• Year: 2022
• Tongue: English
• Leaves: 96
• Edition: 2
• Category: Library

✦ Synopsis

Written for machine learning practitioners, software engineers and other analytic professionals interested in expanding their toolset and mastering the art. Discover state-of-the-art techniques explained in simple English, applicable to many modern problems, especially related to spatial processes and pattern recognition. This textbook includes numerous visualization techniques (for instance, data animations using video libraries in R), a true test of independence, simple illustration of dual confidence regions (more intuitive than the classic version), minimum contrast estimation (a simple generic estimation technique encompassing maximum likelihood), model fitting techniques, and much more. The scope of the material extends far beyond stochastic processes.

✦ Table of Contents

About this Textbook
Target Audience
About the Author
Poisson-binomial or Perturbed Lattice Process
Definitions
Point Count and Interarrival Times
Limiting Distributions, Speed of Convergence
Properties of Stochastic Point Processes
Stationarity
Ergodicity
Independent Increments
Homogeneity
Transforming and Combining Multiple Point Processes
Marked Point Process
Rotation, Stretching, Translation and Standardization
Superimposition and Mixing
Hexagonal Lattice, Nearest Neighbors
Applications
Modeling Cluster Systems in Two Dimensions
Generalized Logistic Distribution
Illustrations
Infinite Random Permutations with Local Perturbations
Probabilistic Number Theory and Experimental Maths
Poisson Limit of the Poisson-binomial Distribution, with Applications
Perturbed Version of the Riemann Hypothesis
Videos: Fractal Supervised Classification and Riemann Hypothesis
Dirichlet Eta Function
Fractal Supervised Classification
Statistical Inference, Machine Learning, and Simulations
Model-free Tests and Confidence Regions
Methodology and Example
Periodicity and Amplitude of Point Counts
A New Test of Independence
Estimation of Core Parameters
Intensity and Scaling Factor
Model Selection to Identify F
Theoretical Values Obtained by Simulations
Hard-to-Detect Patterns and Model Identifiability
Spatial Statistics, Nearest Neighbors, Clustering
Stochastic Residues
Inference for Two-dimensional Processes
Clustering Using GPU-based Image Filtering
Black-box Elbow Rule to Detect Outliers and Number of Clusters
Boundary Effect
Quantifying some Biases
Extreme Values
Poor Random Numbers and Other Glitches
A New Type of Pseudo-random Number Generator
Theorems
Notations
Link between Interarrival Times and Point Count
Point Count Arithmetic
Link between Intensity and Scaling Factor
Expectation and Limit Distribution of Interarrival Times
Convergence to the Poisson Process
The Inverse or Hidden Model
Special Cases with Exact Formula
Fundamental Theorem of Statistics
Exercises, with Solutions
Full List
Probability Distributions, Limits and Convergence
Features of Poisson-binomial Processes
Lattice Networks, Covering Problems, and Nearest Neighbors
Miscellaneous
Source Code, Data, Videos, and Excel Spreadsheets
Interactive Spreadsheets and Videos
Source Code: Point Count, Interarrival Times
Compute E[N(B)], Var[N(B)] and P[N(B)=0]
Compute E[T], Var[T] and E[Tr]
Produce random deviates for various F's
Compute F(x) for Various F
Source Code: Radial Cluster Simulation
Source Code: Nearest Neighbor Distances
Source Code: Detection of Connected Components
Source Code: Visualizations, Density Maps
Visualizing the Nearest Neighbor Graph
Clustering and Density Estimation via Image Filtering
Source Code: Production of the Videos
Dirichlet Eta Function
Fractal Supervised Clustering
Glossary
List of Figures
References
Index