Informatics and Machine Learning

Stephen Winters-Hilt, PhD, is Sole Proprietor at Meta Logos Systems, Albuquerque, NM, USA, which specializes in Machine Learning, Signal Analysis, Financial Analytics, and Bioinformatics. He received his doctorate in Theoretical Physics from the University of Wisconsin, as well as a PhD in Computer Science and Bioinformatics from the University of California, Santa Cruz.

1 Introduction 1

1.1 Data Science: Statistics, Probability, Calculus ... Python (or Perl) and Linux 2

1.2 Informatics and Data Analytics 3

1.3 FSA-Based Signal Acquisition and Bioinformatics 4

1.4 Feature Extraction and Language Analytics 7

1.5 Feature Extraction and Gene Structure Identification 8

1.6 Theoretical Foundations for Learning 13

1.7 Classification and Clustering 13

1.8 Search 14

1.9 Stochastic Sequential Analysis (SSA) Protocol (Deep Learning Without NNs) 15

1.10 Deep Learning using Neural Nets 20

1.11 Mathematical Specifics and Computational Implementations 21

2 Probabilistic Reasoning and Bioinformatics 23

2.1 Python Shell Scripting 23

2.2 Counting, the Enumeration Problem, and Statistics 34

2.3 From Counts to Frequencies to Probabilities 35

2.4 Identifying Emergent/Convergent Statistics and Anomalous Statistics 35

2.5 Statistics, Conditional Probability, and Bayes' Rule 37

2.6 Emergent Distributions and Series 39

2.7 Exercises 42

3 Information Entropy and Statistical Measures 47

3.1 Shannon Entropy, Relative Entropy, Maxent, Mutual Information 48

3.2 Codon Discovery from Mutual Information Anomaly 58

3.3 ORF Discovery from Long-Tail Distribution Anomaly 66

3.4 Sequential Processes and Markov Models 72

3.5 Exercises 75

4 Ad Hoc, Ab Initio, and Bootstrap Signal Acquisition Methods 77

4.1 Signal Acquisition, or Scanning, at Linear Order Time-Complexity 77

4.2 Genome Analytics: The Gene-Finder 80

4.3 Objective Performance Evaluation: Sensitivity and Specificity 93

4.4 Signal Analytics: The Time-Domain Finite State Automaton (tFSA) 93

4.5 Signal Statistics (Fast): Mean, Variance, and Boxcar Filter 107

4.6 Signal Spectrum: Nyquist Criterion, Gabor Limit, Power Spectrum 110

4.7 Exercises 112

5 Text Analytics 125

5.1 Words 125

5.2 Phrases - Short (Three Words) 145

5.3 Phrases - Long (A Line or Sentence) 150

5.4 Exercises 153

6 Analysis of Sequential Data Using HMMs 155

6.1 Hidden Markov Models (HMMs) 155

6.2 Graphical Models for Markov Models and Hidden Markov Models 162

6.3 Standard HMM Weaknesses and their GHMM Fixes 168

6.4 Generalized HMMs (GHMMs - "Gems"): Minor Viterbi Variants 171

6.5 HMM Implementation for Viterbi (in C and Perl) 179

6.6 Exercises 206

7 Generalized HMMs (GHMMs): Major Viterbi Variants 207

7.1 GHMMs: Maximal Clique for Viterbi and Baum-Welch 207

7.2 GHMMs: Full Duration Model 216

7.3 GHMMs: Linear Memory Baum-Welch Algorithm 228

7.4 GHMMs: Distributable Viterbi and Baum-Welch Algorithms 230

7.5 Martingales and the Feasibility of Statistical Learning (further details in Appendix) 232

7.6 Exercises 234

8 Neuromanifolds and the Uniqueness of Relative Entropy 235

8.1 Overview 235

8.2 Review of Differential Geometry 236

8.3 Amari's Dually Flat Formulation 243

8.4 Neuromanifolds 247

8.5 Exercises 250

9 Neural Net Learning and Loss Bounds Analysis 253

9.1 Brief Introduction to Neural Nets (NNs) 254

9.2 Variational Learning Formalism and Use in Loss Bou ds Analysis 261

9.3 The "sinh 1( )" link algorithm (SA) 266

9.4 The Loss Bounds Analysis for sinh 1( ) 269

9.5 Exercises 277

10 Classification and Clustering 279

10.1 The SVM Classifier - An Overview 281

10.2 Introduction to Classification and Clustering 282

10.3 Lagrangian Optimization and Structural Risk Minimization (SRM) 296

10.4 SVM Binary Classifier Implementation 318

10.5 Kernel Selection and Tuning Metaheuristics 346

10.6 SVM Multiclass from Decision Tree with SVM Binary Classifiers 356

10.7 SVM Multiclass Classifier Derivation (Multiple Decision Surface) 359

10.8 SVM Clustering 364

10.9 Exercises 385

11 Search Metaheuristics 389

11.1 Trajectory-Based Search Metaheuristics 389

11.2 Population-Based Search Metaheuristics 399

11.3 Exercises 404

12 Stochastic Sequential Analysis (SSA) 407

12.1 HMM and FSA-Based Methods for Signal Acquisition and Feature Extraction 408

12.2 The Stochastic Sequential Analysis (SSA) Protocol 410

12.3 Channel Current Cheminformatics (CCC) Implementation of the Stochastic Sequential Analysis (SSA) Protocol 420

12.4 SCW for Detector Sensitivity Boosting 423

12.5 SSA for Deep Learning 430

12.6 Exercises 431

13 Deep Learning Tools - TensorFlow 433

13.1 Neural Nets Review 433

13.2 TensorFlow from Google 435

13.3 Exercises 444

14 Nanopore Detection - A Case Study 445

14.1 Standard Apparatus 447

14.2 Controlling Nanopore Noise Sources and Choice of Aperture 449

14.3 Length Resolution of Individual DNA Hairpins 451

14.4 Detection of Single Nucleotide Differences (Large Changes in Structure) 454

14.5 Blockade Mechanism for 9bphp 455

14.6 Conformational Kinetics on Model Biomolecules 459

14.7 Channel Current Cheminformatics 460

14.8 Channel-Based Detection Mechanisms 467

14.9 The NTD Nanoscope 474

14.10 NTD Biosensing Methods 495

14.10.1 Model Biosensor Based on Streptavidin and Biotin 495

14.10.2 Model System Based on DNA Annealing 501

14.10.3 Y-Aptamer with Use of Chaotropes to Improve Signal Resolution 506

14.10.4 Pathogen Detection, miRNA Detection, and miRNA Haplotyping 508

14.10.5 SNP Detection 510

14.10.6 Aptamer-Based Detection 512

14.10.7 Antibody-Based Detection 512

14.11 Exercises 516

Appendix A: Python and Perl System Programming in Linux 519

A.1 Getting Linux and Python in a Flash (Drive) 519

A.2 Linux and the Command Shell 520

A.3 Perl Review: I/O, Primitives, String Handling, Regex 521

Appendix B: Physics 529

B.1 The Calculus of Variations 529

Appendix C: Math 531

C.1 Martingales 531

C.2 Hoeffding Inequality 537

References 000