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.

Key Features

  • 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


Data Mining, Applied Math and Statistics, Modeling, and Cognitive Neuroscience

Table of Contents


A Personal Perspective

Chapter 1. Calculus Ratiocinator


1 A Fundamental Problem with the Widely Used Methods

2 Ensemble Models and Cognitive Processing in Playing Jeopardy

3 The Brain's Explicit and Implicit Learning

4 Two Distinct Modeling Cultures and Machine Intelligence

5 Logistic Regression and the Calculus Ratiocinator Problem

Chapter 2. Most Likely Inference


1 The Jaynes Maximum Entropy Principle

2 Maximum Entropy and Standard Maximum Likelihood Logistic Regression

3 Discrete Choice, Logit Error, and Correlated Observations

4 RELR and the Logit Error

5 RELR and the Jaynes Principle

Chapter 3. Probability Learning and Memory


1 Bayesian Online Learning and Memory

2 Most Probable Features

3 Implicit RELR

4 Explicit RELR

Chapter 4. Causal Reasoning


1 Propensity Score Matching

2 RELR's Outcome Score Matching

3 An Example of RELR's Causal Reasoning

4 Comparison to Other Bayesian and Causal Methods

Chapter 5. Neural Calculus


1 RELR as a Neural Computational Model

2 RELR and Neural Dynamics

3 Small Samples in Neural Learning

4 What about Artificial Neural Networks?

Chapter 6. Oscillating Neural Synchrony


1 The EEG and Neural Synchrony

2 Neural Synchrony, Parsimony, and Grandmother Cells

3 Gestalt Pragnanz and Oscillating Neural Synchrony

4 RELR and Spike-Timing-Dependent Plasticity

5 Attention and Neural Synchrony

6 Metrical Rhythm in Oscillating Neural Synchrony

7 Higher Frequency Gamma Oscillations

Chapter 7. Alzheimer's and Mind–Brain Problems


1 Neuroplasticity Selection in Development and Aging

2 Brain and


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© 2014
Academic Press
Print ISBN:
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About the author

Daniel Rice

Daniel M. Rice is Principal and Senior Scientist of Rice Analytics. He founded the business in early 1996 as a sole proprietorship, but it was incorporated into its current structure in 2006. Prior to 1996, he was an assistant professor at the University of California-Irvine and the University of Southern California. Dan has almost 25 years of research project and advanced statistical modeling experience for major organizations that include the National Institute on Aging, Eli Lilly, Anheuser-Busch, Sears Portrait Studios, Hewlett-Packard, UBS, and Bank of America. He has a Ph.D. from the University of New Hampshire in Cognitive Neuroscience and Postdoctoral training in Applied Statistics from the University of California-Irvine. Dan is a previous recipient of an Individual National Research Service Award from the National Institutes of Health and is author of more than 20 publications, many of which are in conference proceedings and peer-reviewed journals in cognitive neuroscience and statistics.

Affiliations and Expertise

Principal and Senior Scientist and founder of Rice Analytics, St Louis, MO, USA


"…Rice argues that cognitive machines will need to be neuromorphic, that is, based upon neuroscience, in order to simulate aspects of human cognition. He sets out the most fundamental and important concepts in modern cognitive neuroscience, including neural dynamics, implicit and explicit learning, neural synchrony, Hebbian spike-timing dependent plasticity, and neural Darwinism.", February 2014