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Bishop Chapter 1

Author: maxalex

Introduction

Pattern Recognition

Machine Learning

Training Set

Target Vector

Training/Learning Phase

Test Set

Generalization

Preprocessing / Feature Extraction

Supervised Learning

Classification

Regression

Unsupervised Learning

Clustering

Density Estimation

Visualization

Reinforcement Learning

Credit Assignment Problem

Exploration

Exploitation

Probability Theory

Decision Theory

Information Theory

Polynomial Curve Fitting

Polynomial Function

Linear Models

Error Function

Sum-of-Squares Error Function

Model Comparison / Model Selection

Over-Fitting

Maximum Likelihood

Bayesian Approach

Effective Number of Parameters

Regularization

Ridge Regression

Weight Decay

Validation Set / Hold-Out Set

Probability Theory

Sum Rule

Marginal Probability

Product Rule

Joint Probability

Conditional Probability

Random Variable

Symmetry Property

Bayes' Theorem

Prior Probability

Posterior Probability

Independence

Probability Densities

Probability Density over x

Integrals

Cumulative Distribution Function

Probability Mass Function

Densities and Continuous Variables

Expectations & Covariances

Expectation

Conditional Expectation

Variance

Variance of the variable x

Covariance

Bayesian Probablities

Classical / Frequentist interpretation of probablity

Bayesian View

Bayes' Theorem

Likelihood Function

Maximum Likelihood

Error Function

Bootstrap

Noninformative Prior

The Guassian Distribution

Guassian / Normal Distribution

Mean, Variance, Standard Deviation, Precision

Moment

Second Order Moment

Variance

Independent & Identically distributed

Log Likelihood

Sample Mean

Sample Variance

Bias

Curve fitting re-visited

Gaussian Noise Distribution

Sum of Squares Error Function

Predictive Distribution

Hyperparameters

Maximum Posterior

Guassian Prior

Bayesian Curve Fitting

Bayesian Treatment

Point Estimate

Full Bayesian

Model Selection

Validation Set

Test Set

Cross-Validation

Akaike Information Criterion

Bayesian Information Criterion

The Curse of Dimensionality

Curse of Dimensionality

Cartesian vs. Polar Coordinates

Directional Variables

Reasons for effective techniques in high dimensional data

Manifold

Decision Theory

Inference

Subject of Decision Theory

Decison Step

Extract any quantities in Bayes Theorem

Minimizing the missclassification rate

Decision Regions

Decision Boundaries or Surfaces

Mistake Probability

Correct Probability

Decision Rule

Minimizing the expected loss

Loss, Cost and Utility Function

Loss Matrix

Expected Loss

Decision Rule

The reject option

Reject Option

Rejection Criterion

Inference and decision

Inference Stage

Decision Stage

Generative Models

Discriminative Models

Discriminant Function

Simple way for Prior Calculation

Outlier Detection

Advantages of Posterior Probability Estimation (4)

Conditional Independence

Naive Bayes Model

Loss functions for regression

Loss function in regression

Regression Function

Irreducible Minimum Value of Loss Function

Three distinct Approaches

Poor Results of Squared Loss

Minkowski Loss

Information Theory

Idea of Information Theory

Monotonic Function

Definition of Information

Entropy

Noiseless Coding Theorem

nats

Multiplicity

Microstate, Macrostate, weight of Macrostate

H[p]

Lagrange Multiplier

Maximum Entropy Configuration

Jensen's inequality

Mean Value Theorem

Differential Entropy

Maximum of Differential Entropy

Calculus of Variation

Negativity of Differential Entropy

Conditional Entropy

Relation between differential & conditional entropy

Relative entropy & mutual information

Rlative Entropy / KL divergence

Properties of KL divergence

Convex Function

Chord

Strictly Convex

Concave

Jensen's Inequality

Relationship to Data Compression

Minimizing KL Divergence

Mutual Information

Relation of MI to Conditional Entropy

Bayesian Perspective