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Calculus of Thought

Book Description

Calculus of Thought: Neuromorphic Logistic Regression in Cognitive Machines is a must-read for all scientists about a very simple computation method designed to simulate big-data neural processing. This book is inspired by the Calculus Ratiocinator idea of Gottfried Leibniz, which is that machine computation should be developed to simulate human cognitive processes, thus avoiding problematic subjective bias in analytic solutions to practical and scientific problems.

The reduced error logistic regression (RELR) method is proposed as such a "Calculus of Thought." This book reviews how RELR's completely automated processing may parallel important aspects of explicit and implicit learning in neural processes. It emphasizes the fact that RELR is really just a simple adjustment to already widely used logistic regression, along with RELR's new applications that go well beyond standard logistic regression in prediction and explanation. Readers will learn how RELR solves some of the most basic problems in today’s big and small data related to high dimensionality, multi-colinearity, and cognitive bias in capricious outcomes commonly involving human behavior.

  • Provides a high-level introduction and detailed reviews of the neural, statistical and machine learning knowledge base as a foundation for a new era of smarter machines
  • Argues that smarter machine learning to handle both explanation and prediction without cognitive bias must have a foundation in cognitive neuroscience and must embody similar explicit and implicit learning principles that occur in the brain
  • Offers a new neuromorphic foundation for machine learning based upon the reduced error logistic regression (RELR) method and provides simple examples of RELR computations in toy problems that can be accessed in spreadsheet workbooks through a companion website

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Preface
    1. A Personal Perspective
  6. Chapter 1. Calculus Ratiocinator
    1. Abstract
    2. 1 A Fundamental Problem with the Widely Used Methods
    3. 2 Ensemble Models and Cognitive Processing in Playing Jeopardy
    4. 3 The Brain's Explicit and Implicit Learning
    5. 4 Two Distinct Modeling Cultures and Machine Intelligence
    6. 5 Logistic Regression and the Calculus Ratiocinator Problem
  7. Chapter 2. Most Likely Inference
    1. Abstract
    2. 1 The Jaynes Maximum Entropy Principle
    3. 2 Maximum Entropy and Standard Maximum Likelihood Logistic Regression
    4. 3 Discrete Choice, Logit Error, and Correlated Observations
    5. 4 RELR and the Logit Error
    6. 5 RELR and the Jaynes Principle
  8. Chapter 3. Probability Learning and Memory
    1. Abstract
    2. 1 Bayesian Online Learning and Memory
    3. 2 Most Probable Features
    4. 3 Implicit RELR
    5. 4 Explicit RELR
  9. Chapter 4. Causal Reasoning
    1. Abstract
    2. 1 Propensity Score Matching
    3. 2 RELR's Outcome Score Matching
    4. 3 An Example of RELR's Causal Reasoning
    5. 4 Comparison to Other Bayesian and Causal Methods
  10. Chapter 5. Neural Calculus
    1. Abstract
    2. 1 RELR as a Neural Computational Model
    3. 2 RELR and Neural Dynamics
    4. 3 Small Samples in Neural Learning
    5. 4 What about Artificial Neural Networks?
  11. Chapter 6. Oscillating Neural Synchrony
    1. Abstract
    2. 1 The EEG and Neural Synchrony
    3. 2 Neural Synchrony, Parsimony, and Grandmother Cells
    4. 3 Gestalt Pragnanz and Oscillating Neural Synchrony
    5. 4 RELR and Spike-Timing-Dependent Plasticity
    6. 5 Attention and Neural Synchrony
    7. 6 Metrical Rhythm in Oscillating Neural Synchrony
    8. 7 Higher Frequency Gamma Oscillations
  12. Chapter 7. Alzheimer's and Mind–Brain Problems
    1. Abstract
    2. 1 Neuroplasticity Selection in Development and Aging
    3. 2 Brain and Cognitive Changes in Very Early Alzheimer's Disease
    4. 3 A RELR Model of Recent Episodic and Semantic Memory
    5. 4 What Causes the Medial Temporal Lobe Disturbance in Early Alzheimer's?
    6. 5 The Mind–Brain Problem
  13. Chapter 8. Let Us Calculate
    1. Abstract
    2. 1 Human Decision Bias and the Calculus Ratiocinator
    3. 2 When the Experts are Wrong
    4. 3 When Predictive Models Crash
    5. 4 The Promise of Cognitive Machines
  14. Appendix
    1. A1 RELR Maximum Entropy Formulation
    2. A2 Derivation of RELR Logit from Errors-in-Variables Considerations
    3. A3 Methodology for Pew 2004 Election Weekend Model Study
    4. A4 Derivation of Posterior Probabilities in RELR's Sequential Online Learning
    5. A5 Chain Rule Derivation of Explicit RELR Feature Importance
    6. A6 Further Details on the Explicit RELR Low Birth Weight Model in Chapter 3
    7. A7 Zero Intercepts in Perfectly Balanced Stratified Samples
    8. A8 Detailed Steps in RELR's Causal Machine Learning Method
  15. Notes and References
  16. Index