Data-Driven Computational Neuroscience: Machine Learning and Statistical Models

Description

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with point processes (complete spatial randomness and cluster, regular and Gibbs processes). Cellular, structural, functional, medical and behavioral neuroscience levels are considered. Copyright Contents Preface List of Acronyms Part I Introduction 1 Computational Neuroscience 1.1 The Multilevel Organization of the Brain 1.2 The Human Brain 1.3 Brain Research Initiatives 1.4 Neurotechnologies 1.5 Data-Driven Computational Neuroscience 1.6 Real Examples Discussed in This Book Part II Statistics 2 Exploratory Data Analysis 2.1 Data Types 2.2 Univariate Data 2.3 Bivariate Data 2.4 Multivariate Data 2.5 Imputation of Missing Data 2.6 Variable Transformation 2.7 Bibliographic Notes 3 Probability Theory and Random Variables 3.1 Probability Theory 3.2 Univariate Discrete Distributions 3.3 Univariate Continuous Distributions 3.4 Multivariate Probability Distributions 3.5 Simulating Random Variates 3.6 Information Theory 3.7 Bibliographic Notes 4 Probabilistic Inference 4.1 Parameter Estimation 4.2 Hypothesis Tests 4.3 Bibliographic Notes Part III Supervised Classification 5 Performance Evaluation 5.1 The Learning Problem 5.2 Performance Measures 5.3 Performance Estimation 5.4 Statistical Significance Testing 5.5 Imbalanced Data Sets and Anomaly Detection 5.6 Bibliographic Notes 6 Feature Subset Selection 6.1 Overview of Feature Subset Selection 6.2 Filter Approaches 6.3 Wrapper Methods 6.4 Embedded Methods 6.5 Hybrid Feature Selection 6.6 Feature Selection Stability 6.7 Example: GABAergic Interneuron Nomenclature 6.8 Bibliographic Notes 7 Non-probabilistic Classifiers 7.1 Nearest Neighbors 7.2 Classification Trees 7.3 Rule Induction 7.4 Artificial Neural Networks 7.5 Support Vector Machines 7.6 Bibliographic Notes 8 Probabilistic Classifiers 8.1 Bayes Decision Rule 8.2 Discriminant Analysis 8.3 Logistic Regression 8.4 Bayesian Network Classifiers 8.5 Bibliographic Notes 9 Metaclassifiers 9.1 Main Ideas on Metaclassifiers 9.2 Combining the Outputs of Different Classifiers 9.3 Popular Metaclassifiers 9.4 Example: Interneurons versus Pyramidal Neurons 9.5 Example: Interneurons versus Pyramidal Neurons; Comparison of All Classifiers 9.6 Bibliographic Notes 10 Multidimensional Classifiers 10.1 Multi-label and Multidimensional Classification 10.2 Equivalent Notations for Multi-label Classification 10.3 Performance Evaluation Measures 10.4 Learning Methods 10.5 Example: Quality of Life in Parkinson’s Disease 10.6 Bibliographic Notes Part IV Unsupervised Classification 11 Non-probabilistic Clustering 11.1 Similarity/Dissimilarity between Objects 11.2 Hierarchical Clustering 11.3 Partitional Clustering 11.4 Choice of the Number of Clusters 11.5 Subspace Clustering 11.6 Cluster Ensembles 11.7 Evaluation Criteria 11.8 Example: Dendritic Spines 11.9 Bibliographic Notes 12 Probabilistic Clustering 12.1 The Expectation-Maximization Algorithm 12.2 Finite-Mixture Models for Clustering 12.3 Clustering with Bayesian Networks 12.4 Example: Dendritic Spines 12.5 Bibliographic Notes Part V Probabilistic Graphical Models 13 Bayesian Networks 13.1 Basics of Bayesian Networks 13.2 Inference in Bayesian Networks 13.3 Learning Bayesian Networks from Data 13.4 Dynamic Bayesian Networks 13.5 Example: Basal Dendritic Trees 13.6 Bibliographic Notes 14 Markov Networks 14.1 Definition and Basic Properties 14.2 Factorization of the Joint Probability Distribution 14.3 Inference in Markov Networks 14.4 Learning Continuous Markov Networks 14.5 Learning Discrete Markov Networks 14.6 Conditional Random Fields 14.7 Example: Functional Brain Connectivity of Alzheimer’s Disease 14.8 Bibliographic Notes Part VI Spatial Statistics 15 Spatial Statistics 15.1 Basic Concepts of Spatial Point Processes 15.2 Complete Spatial Randomness 15.3 Goodness-of-Fit Tests via Simulation 15.4 Data Collection Issues 15.5 Common Models of Spatial Point Processes 15.6 Example: Spatial Location of Synapses in the Neocortex 15.7 Bibliographic Notes Bibliography Subject Index