Informatics and Machine Learning: From Martingales to Metaheuristics

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Title Page
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Contents
Chapter 1 Introduction
	1.1 Data Science: Statistics, Probability, Calculus  Python (or Perl) and Linux
	1.2 Informatics and Data Analytics
	1.3 FSA-Based Signal Acquisition and Bioinformatics
	1.4 Feature Extraction and Language Analytics
	1.5 Feature Extraction and Gene Structure Identification
		1.5.1 HMMs for Analysis of Information Encoding Molecules
		1.5.2 HMMs for Cheminformatics and Generic Signal Analysis
	1.6 Theoretical Foundations for Learning
	1.7 Classification and Clustering
	1.8 Search
	1.9 Stochastic Sequential Analysis (SSA) Protocol (Deep Learning Without NNs)
		1.9.1 Stochastic Carrier Wave (SCW) Analysis–Nanoscope Signal Analysis
		1.9.2 Nanoscope Cheminformatics–A Case Study for Device ``Smartening´´
	1.10 Deep Learning using Neural Nets
	1.11 Mathematical Specifics and Computational Implementations
Chapter 2 Probabilistic Reasoning and Bioinformatics
	2.1 Python Shell Scripting
		2.1.1 Sample Size Complications
	2.2 Counting, the Enumeration Problem, and Statistics
	2.3 From Counts to Frequencies to Probabilities
	2.4 Identifying Emergent/Convergent Statistics and Anomalous Statistics
	2.5 Statistics, Conditional Probability, and Bayes' Rule
		2.5.1 The Calculus of Conditional Probabilities: The Cox Derivation
		2.5.2 Bayes' Rule
		2.5.3 Estimation Based on Maximal Conditional Probabilities
	2.6 Emergent Distributions and Series
		2.6.1 The Law of Large Numbers (LLN)
		2.6.2 Distributions
		2.6.3 Series
	2.7 Exercises
Chapter 3 Information Entropy and Statistical Measures
	3.1 Shannon Entropy, Relative Entropy, Maxent, Mutual Information
		3.1.1 The Khinchin Derivation
		3.1.2 Maximum Entropy Principle
		3.1.3 Relative Entropy and Its Uniqueness
		3.1.4 Mutual Information
		3.1.5 Information Measures Recap
	3.2 Codon Discovery from Mutual Information Anomaly
	3.3 ORF Discovery from Long-Tail Distribution Anomaly
		3.3.1 Ab initio Learning with smORF´s, Holistic Modeling, and Bootstrap Learning
	3.4 Sequential Processes and Markov Models
		3.4.1 Markov Chains
	3.5 Exercises
Chapter 4 Ad Hoc, Ab Initio, and Bootstrap Signal Acquisition Methods
	4.1 Signal Acquisition, or Scanning, at Linear Order Time-Complexity
	4.2 Genome Analytics: The Gene-Finder
	4.3 Objective Performance Evaluation: Sensitivity and Specificity
	4.4 Signal Analytics: The Time-Domain Finite State Automaton (tFSA)
		4.4.1 tFSA Spike Detector
		4.4.2 tFSA-Based Channel Signal Acquisition Methods with Stable Baseline
		4.4.3 tFSA-Based Channel Signal Acquisition Methods Without Stable Baseline
	4.5 Signal Statistics (Fast): Mean, Variance, and Boxcar Filter
		4.5.1 Efficient Implementations for Statistical Tools (O(L))
	4.6 Signal Spectrum: Nyquist Criterion, Gabor Limit, Power Spectrum
		4.6.1 Nyquist Sampling Theorem
		4.6.2 Fourier Transforms, and Other Classic Transforms
		4.6.3 Power Spectral Density
		4.6.4 Power-Spectrum-Based Feature Extraction
		4.6.5 Cross-Power Spectral Density
		4.6.6 AM/FM/PM Communications Protocol
	4.7 Exercises
Chapter 5 Text Analytics
	5.1 Words
		5.1.1 Text Acquisition: Text Scraping and Associative Memory
		5.1.2 Word Frequency Analysis: Machiavelli´s Polysemy on Fortuna and Virtu
		5.1.3 Word Frequency Analysis: Coleridge´s Hidden Polysemy on Logos
		5.1.4 Sentiment Analysis
	5.2 Phrases–Short (Three Words)
		5.2.1 Shakespearean Insult Generation–Phrase Generation
	5.3 Phrases–Long (A Line or Sentence)
		5.3.1 Iambic Phrase Analysis: Shakespeare
		5.3.2 Natural Language Processing
		5.3.3 Sentence and Story Generation: Tarot
	5.4 Exercises
Chapter 6 Analysis of Sequential Data Using HMMs
	6.1 Hidden Markov Models (HMMs)
		6.1.1 Background and Role in Stochastic Sequential Analysis (SSA)
		6.1.2 When to Use a Hidden Markov Model (HMM)?
		6.1.3 Hidden Markov Models (HMMs)–Standard Formulation and Terms
	6.2 Graphical Models for Markov Models and Hidden Markov Models
		6.2.1 Hidden Markov Models
		6.2.2 Viterbi Path
		6.2.3 Forward and Backward Probabilities
		6.2.4 HMM: Maximum Likelihood discrimination
		6.2.5 Expectation/Maximization (Baum–Welch)
	6.3 Standard HMM Weaknesses and their GHMM Fixes
	6.4 Generalized HMMs (GHMMs – "Gems"): Minor Viterbi Variants
		6.4.1 The Generic HMM
		6.4.2 pMM/SVM
		6.4.3 EM and Feature Extraction via EVA Projection
		6.4.4 Feature Extraction via Data Absorption (a.k.a. Emission Inversion)
		6.4.5 Modified AdaBoost for Feature Selection and Data Fusion
	6.5 HMM Implementation for Viterbi (in C and Perl)
	6.6 Exercises
Chapter 7 Generalized HMMs (GHMMs): Major Viterbi Variants
	7.1 GHMMs: Maximal Clique for Viterbi and Baum–Welch
	7.2 GHMMs: Full Duration Model
		7.2.1 HMM with Duration (HMMD)
		7.2.2 Hidden Semi-Markov Models (HSMM) with sid-information
		7.2.3 HMM with Binned Duration (HMMBD)
	7.3 GHMMs: Linear Memory Baum–Welch Algorithm
	7.4 GHMMs: Distributable Viterbi and Baum–Welch Algorithms
		7.4.1 Distributed HMM processing via "Viterbi-overlap-chunking" with GPU speedup
		7.4.2 Relative Entropy and Viterbi Scoring
	7.5 Martingales and the Feasibility of Statistical Learning (further details in Appendix)
	7.6 Exercises
Chapter 8 Neuromanifolds and the Uniqueness of Relative Entropy
	8.1 Overview
	8.2 Review of Differential Geometry
		8.2.1 Differential Topology – Natural Manifold
		8.2.2 Differential Geometry – Natural Geometric Structures
	8.3 Amari´s Dually Flat Formulation
		8.3.1 Generalization of Pythagorean Theorem
		8.3.2 Projection Theorem and Relation Between Divergence and Link Formalism
	8.4 Neuromanifolds
	8.5 Exercises
Chapter 9 Neural Net Learning and Loss Bounds Analysis
	9.1 Brief Introduction to Neural Nets (NNs)
		9.1.1 Single Neuron Discriminator
		9.1.2 Neural Net with Back-Propagation
	9.2 Variational Learning Formalism and Use in Loss Bounds Analysis
		9.2.1 Variational Basis for Update Rule
		9.2.2 Review and Generalization of GD Loss Bounds Analysis
		9.2.3 Review of the EG Loss Bounds Analysis
	9.3 The The “sinh−1(ω)” link algorithm (SA)
		9.3.1 Motivation for “sinh−1(ω)” link algorithm (SA)
		9.3.2 Relation of sinh Link Algorithm to the Binary Exponentiated Gradient Algorithm
	9.4 The Loss Bounds Analysis for sinh−1(ω)
		9.4.1 Loss Bounds Analysis Using the Taylor Series Approach
		9.4.2 Loss Bounds Analysis Using Taylor Series for the sinh Link (SA) Algorithm
	9.5 Exercises
Chapter 10 Classification and Clustering
	10.1 The SVM Classifier–An Overview
	10.2 Introduction to Classification and Clustering
		10.2.1 Sum of Squared Error (SSE) Scoring
		10.2.2 K-Means Clustering (Unsupervised Learning)
		10.2.3 k-Nearest Neighbors Classification (Supervised Learning)
		10.2.4 The Perceptron Recap (See Chapter for Details)
	10.3 Lagrangian Optimization and Structural Risk Minimization (SRM)
		10.3.1 Decision Boundary and SRM Construction Using Lagrangian
		10.3.2 The Theory of Classification
		10.3.3 The Mathematics of the Feasibility of Learning
		10.3.4 Lagrangian Optimization
		10.3.5 The Support Vector Machine (SVM)–Lagrangian with SRM
		10.3.6 Kernel Construction Using Polarization
		10.3.7 SVM Binary Classifier Derivation
	10.4 SVM Binary Classifier Implementation
		10.4.1 Sequential Minimal Optimization (SMO)
		10.4.2 Alpha-Selection Variants
		10.4.3 Chunking on Large Datasets: O(N2) ➔ n O(N2/n2) = O(N2)/n
		10.4.4 Support Vector Reduction (SVR)
		10.4.5 Code Examples (in OO Perl)
	10.5 Kernel Selection and Tuning Metaheuristics
		10.5.1 The ``Stability´´ Kernels
		10.5.2 Derivation of ``Stability´´ Kernels
		10.5.3 Entropic and Gaussian Kernels Relate to Unique, Minimally Structured, Information Divergence and Geometric Distance ...
		10.5.4 Automated Kernel Selection and Tuning
	10.6 SVM Multiclass from Decision Tree with SVM Binary Classifiers
	10.7 SVM Multiclass Classifier Derivation (Multiple Decision Surface)
		10.7.1 Decomposition Method to Solve the Dual
		10.7.2 SVM Speedup via Differentiating BSVs and SVs
	10.8 SVM Clustering
		10.8.1 SVM-External Clustering
		10.8.2 Single-Convergence SVM-Clustering: Comparative Analysis
		10.8.3 Stabilized, Single-Convergence Initialized, SVM-External Clustering
		10.8.4 Stabilized, Multiple-Convergence, SVM-External Clustering
		10.8.5 SVM-External Clustering–Algorithmic Variants
	10.9 Exercises
Chapter 11 Search Metaheuristics
	11.1 Trajectory-Based Search Metaheuristics
		11.1.1 Optimal-Fitness Configuration Trajectories – Fitness Function Known and Sufficiently Regular
		11.1.2 Optimal-Fitness Configuration Trajectories – Fitness Function not Known
		11.1.3 Fitness Configuration Trajectories with Nonoptimal Updates
	11.2 Population-Based Search Metaheuristics
		11.2.1 Population with Evolution
		11.2.2 Population with Group Interaction – Swarm Intelligence
		11.2.3 Population with Indirect Interaction via Artifact
	11.3 Exercises
Chapter 12 Stochastic Sequential Analysis (SSA)
	12.1 HMM and FSA-Based Methods for Signal Acquisition and Feature Extraction
	12.2 The Stochastic Sequential Analysis (SSA) Protocol
		12.2.1 (Stage 1) Primitive Feature Identification
		12.2.2 (Stage 2) Feature Identification and Feature Selection
		12.2.3 (Stage 3) Classification
		12.2.4 (Stage 4) Clustering
		12.2.5 (All Stages) Database/Data-Warehouse System Specification
		12.2.6 (All Stages) Server-Based Data Analysis System Specification
	12.3 Channel Current Cheminformatics (CCC) Implementation of the Stochastic Sequential Analysis (SSA) Protocol
	12.4 SCW for Detector Sensitivity Boosting
		12.4.1 NTD with Multiple Channels (or High Noise)
		12.4.2 Stochastic Carrier Wave
	12.5 SSA for Deep Learning
	12.6 Exercises
Chapter 13 Deep Learning Tools–TensorFlow
	13.1 Neural Nets Review
		13.1.1 Summary of Single Neuron Discriminator
		13.1.2 Summary of Neural Net Discriminator and Back-Propagation
	13.2 TensorFlow from Google
		13.2.1 Installation/Setup
		13.2.2 Example: Character Recognition
		13.2.3 Example: Language Translation
		13.2.4 TensorBoard and the TensorFlow Profiler
		13.2.5 Tensor Cores
	13.3 Exercises
Chapter 14 Nanopore Detection–A Case Study
	14.1 Standard Apparatus
		14.1.1 Standard Operational and Physiological Buffer Conditions
		14.1.2 α-Hemolysin Channel Stability–Introduction of Chaotropes
	14.2 Controlling Nanopore Noise Sources and Choice of Aperture
	14.3 Length Resolution of Individual DNA Hairpins
	14.4 Detection of Single Nucleotide Differences (Large Changes in Structure)
	14.5 Blockade Mechanism for 9bphp
	14.6 Conformational Kinetics on Model Biomolecules
	14.7 Channel Current Cheminformatics
		14.7.1 Power Spectra and Standard EE Signal Analysis
		14.7.2 Channel Current Cheminformatics for Single-Biomolecule/Mixture Identifications
		14.7.3 Channel Current Cheminformatics: Feature Extraction by HMM
		14.7.4 Bandwidth Limitations
	14.8 Channel-Based Detection Mechanisms
		14.8.1 Partitioning and Translocation-Based ND Biosensing Methods
		14.8.2 Transduction Versus Translation
		14.8.3 Single-Molecule Versus Ensemble
		14.8.4 Biosensing with High Sensitivity in Presence of Interference
		14.8.5 Nanopore Transduction Detection Methods
	14.9 The NTD Nanoscope
		14.9.1 Nanopore Transduction Detection (NTD)
		14.9.2 NTD: A Versatile Platform for Biosensing
		14.9.3 NTD Platform
		14.9.4 NTD Operation
		14.9.5 Driven Modulations
		14.9.6 Driven Modulations with Multichannel Augmentation
	14.10 NTD Biosensing Methods
		14.10.1 Model Biosensor Based on Streptavidin and Biotin
		14.10.2 Model System Based on DNA Annealing
		14.10.3 Y-Aptamer with Use of Chaotropes to Improve Signal Resolution
		14.10.4 Pathogen Detection, miRNA Detection, and miRNA Haplotyping
		14.10.5 SNP Detection
		14.10.6 Aptamer-Based Detection
		14.10.7 Antibody-Based Detection
	14.11 Exercises
Appendix A Python and Perl System Programming in Linux
	A.1 Getting Linux and Python in a Flash (Drive)
	A.2 Linux and the Command Shell
	A.3 Perl Review: I/O, Primitives, String Handling, Regex
Appendix B B Physics
	B.1 The Calculus of Variations
Appendix C Math
	C.1 Martingales
		Martingale Definition
		Induced Martingales with Markov Chains
		In HMM Learning Have Sequences of Likelihood Ratios, Which Is a Martingale, Proof
		Supermartingales and Submartingales
		Martingale Convergence Theorems
		``Maximal´´ Inequalities for Martingales
		Mean-Square Convergence Theorem for Martingales
		Martingales w.r.t s-Field Formalism
		Backwards Martingale Definition (w.r.t Sigma Sub-fields)
		Backwards Martingale Convergence Theorem
		Strong Law of Large Numbers Proof
		Stationary Processes
		Strong Ergodic Theorem
		Asymptotic Equipartition Property (AEP)
		De Finetti´s Theorem
	C.2 Hoeffding Inequality
		Hoeffding Lemma Proof
		Hoeffding Inequality Proof (for Further Details, See [104])
		Chernoff Bounding Technique:
References
Index
EULA