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Oreilly - The Essential Machine Learning Foundations Math, Probability, Statistics, and Computer Science 2022-3

0 students Last updated Apr 2025

About the course

Course content

Sections: 45

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Activities: 0

•

Resources: 273

1 Introduction

2 Topics
3 11 Defining Linear Algebra
4 12 Solving a System of Equations Algebraically
5 13 Linear Algebra in Machine Learning and Deep Learning
6 14 Historical and Contemporary Applications
7 15 Exercise

8 Topics
9 21 Tensors
10 22 Scalars
11 23 Vectors and Vector Transposition
12 24 Norms and Unit Vectors
13 25 Basis Orthogonal and Orthonormal Vectors
14 26 Matrices
15 27 Generic Tensor Notation
16 28 Exercises

17 Topics
18 31 Tensor Transposition
19 32 Basic Tensor Arithmetic
20 33 Reduction
21 34 The Dot Product
22 35 Exercises

23 Topics
24 41 The Substitution Strategy
25 42 Substitution Exercises
26 43 The Elimination Strategy
27 44 Elimination Exercises

28 Topics
29 51 Matrix by Vector Multiplication
30 52 Matrix by Matrix Multiplication
31 53 Symmetric and Identity Matrices
32 54 Exercises
33 55 Machine Learning and Deep Learning Applications

34 Topics
35 61 The Frobenius Norm
36 62 Matrix Inversion
37 63 Diagonal Matrices
38 64 Orthogonal Matrices
39 65 The Trace Operator

40 Topics
41 71 The Eigenconcept
42 72 Exercises
43 73 Eigenvectors in Python
44 74 High Dimensional Eigenvectors

45 Topics
46 81 The Determinant of a 2 x 2 Matrix
47 82 The Determinants of Larger Matrices
48 83 Exercises
49 84 Determinants and Eigenvalues
50 85 Eigendecomposition

51 Topics
52 91 Singular Value Decomposition
53 92 Media File Compression
54 93 The Moore Penrose Pseudoinverse
55 94 Regression via Pseudoinversion
56 95 Principal Component Analysis
57 96 Resources for Further Study of Linear Algebra

58 Linear Algebra for Machine Learning Machine Learning Foundations Summary

59 Introduction

60 Topics
61 11 Differential versus Integral Calculus
62 12 A Brief History
63 13 Calculus of the Infinitesimals
64 14 Modern Applications

65 Topics
66 21 Continuous versus Discontinuous Functions
67 22 Solving via Factoring
68 23 Solving via Approaching
69 24 Approaching Infinity
70 25 Exercises

71 Topics
72 31 Delta Method
73 32 The Most Common Representation
74 33 Derivative Notation
75 34 Constants
76 35 Power Rule
77 36 Constant Product Rule
78 37 Sum Rule
79 38 Exercises

80 Topics
81 41 Product Rule
82 42 Quotient Rule
83 43 Chain Rule
84 44 Exercises
85 45 Power Rule on a Function Chain

86 Topics
87 51 Introduction
88 52 Autodiff withPyTorch
89 53 Autodiff with TensorFlow
90 54 Directed Acyclic Graph of a Line Equation
91 55 Fitting a Line with Machine Learning

92 Topics
93 61 Derivatives of Multivariate Functions
94 62 Partial Derivative Exercises
95 63 Geometrical Examples
96 64 Geometrical Exercises
97 65 Notation
98 66 Chain Rule
99 67 Chain Rule Exercises

100 Topics
101 71 Single Point Regression
102 72 Partial Derivatives of Quadratic Cost
103 73 Descending the Gradient of Cost
104 74 Gradient of Mean Squared Error
105 75 Backpropagation
106 76 Higher Order Partial Derivatives
107 77 Exercise

108 Topics
109 81 Binary Classification
110 82 The Confusion Matrix and ROC Curve
111 83 Indefinite Integrals
112 84 Definite Integrals
113 85 Numeric Integration with Python
114 86 Exercises
115 87 Finding the Area Under the ROC Curve
116 88 Resources for Further Study of Calculus

117 Calculus for Machine Learning Summary

118 Introduction

119 Topics
120 11 Orientation to the Machine Learning Foundations Series
121 12 What Probability Theory Is
122 13 Events and Sample Spaces
123 14 Multiple Observations
124 15 Factorials and Combinatorics
125 16 Exercises
126 17 The Law of Large Numbers and the Gamblers Fallacy
127 18 Probability Distributions in Statistics
128 19 Bayesian versus Frequentist Statistics
129 110 Applications of Probability to Machine Learning

130 Topics
131 21 Discrete and Continuous Variables
132 22 Probability Mass Functions
133 23 Probability Density Functions
134 24 Exercises on Probability Functions
135 25 Expected Value
136 26 Exercises on Expected Value

137 Topics
138 31 The Mean a Measure of Central Tendency
139 32 Medians
140 33 Modes
141 34 Quantiles Percentiles Quartiles and Deciles
142 35 Box and Whisker Plots
143 36 Variance a Measure of Dispersion
144 37 Standard Deviation
145 38 Standard Error
146 39 Covariance a Measure of Relatedness
147 310 Correlation

148 Topics
149 41 Joint Probability Distribution
150 42 Marginal Probability
151 43 Conditional Probability
152 44 Exercises
153 45 Chain Rule of Probabilities
154 46 Independent Random Variables
155 47 Conditional Independence

156 Topics
157 51 Uniform
158 52 Gaussian Normal and Standard Normal
159 53 The Central Limit Theorem
160 54 Log Normal
161 55 Exponential and Laplace
162 56 Binomial and Multinomial
163 57 Poisson
164 58 Mixture Distributions
165 59 Preprocessing Data for Model Input
166 510 Exercises

167 Topics
168 61 What Information Theory Is
169 62 Self Information Nats and Bits
170 63 Shannon and Differential Entropy
171 64 Kullback Leibler Divergence and Cross Entropy

172 Topics
173 71 Applications of Statistics to Machine Learning
174 72 Review of Essential Probability Theory
175 73 z scores and Outliers
176 74 Exercises on z scores
177 75 p values
178 76 Exercises on p values

185 86 Confidence Intervals
186 87 ANOVA Analysis of Variance
179 Topics
180 81 Single Sample t tests and Degrees of Freedom
181 82 Independent t tests
182 83 Paired t tests
183 84 Applications to Machine Learning
184 85 Exercises

187 Topics
188 91 The Pearson Correlation Coefficient
189 92 R squared Coefficient of Determination
190 93 Correlation versus Causation
191 94 Correcting for Multiple Comparisons

192 Topics
193 101 Independent versus Dependent Variables
194 102 Linear Regression to Predict Continuous Values
195 103 Fitting a Line to Points on a Cartesian Plane
196 104 Linear Least Squares Exercise
197 105 Ordinary Least Squares
198 106 Categorical Dummy Features
199 107 Logistic Regression to Predict Categories
200 108 Open Ended Exercises

201 Topics
202 111 Machine Learning versus Frequentist Statistics
203 112 When to Use Bayesian Statistics
204 113 Prior Probabilities
205 114 Bayes Theorem
206 115 Resources for Further Study of Probability and Statistics

207 Probability and Statistics for Machine Learning Summary

208 Introduction

209 Topics
210 11 Orientation to the Machine Learning Foundations Series
211 12 A Brief History of Data
212 13 A Brief History of Algorithms
213 14 Applications to Machine Learning

214 Topics
215 21 Introduction
216 22 Constant Time
217 23 Linear Time
218 24 Polynomial Time
219 25 Common Runtimes
220 26 Best versus Worst Case

221 Topics
222 31 Lists
223 32 Arrays
224 33 Linked Lists
225 34 Doubly Linked Lists
226 35 Stacks
227 36 Queues
228 37 Deques

229 Topics
230 41 Binary Search
231 42 Bubble Sort
232 43 Merge Sort
233 44 Quick Sort

234 Topics
235 51 Maps and Dictionaries
236 52 Sets
237 53 Hash Functions
238 54 Collisions
239 55 Load Factor
240 56 Hash Maps
241 57 String Keys
242 58 Hashing in ML

243 Topics
244 61 Introduction
245 62 Decision Trees
246 63 Random Forests
247 64 XGBoost Gradient Boosted Trees
248 65 Additional Concepts

249 Topics
250 71 Introduction
251 72 Directed versus Undirected Graphs
252 73 DAGs Directed Acyclic Graphs
253 74 Additional Concepts
254 75 Bonus Pandas DataFrames
255 76 Resources for Further Study of DSA

256 Topics
257 81 Statistics versus Machine Learning
258 82 Objective Functions
259 83 Mean Absolute Error
260 84 Mean Squared Error
261 85 Minimizing Cost with Gradient Descent
262 86 Gradient Descent from Scratch with PyTorch
263 87 Critical Points
264 88 Stochastic Gradient Descent
265 89 Learning Rate Scheduling
266 810 Maximizing Reward with Gradient Ascent

267 Topics
268 91 Jacobian Matrices
269 92 Second Order Optimization and Hessians
270 93 Momentum
271 94 Adaptive Optimizers
272 95 Congratulations and Next Steps

273 Data Structures Algorithms and Machine Learning Optimization Summary

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Oreilly - The Essential Machine Learning Foundations Math, Probability, Statistics, and Computer Science 2022-3

Oreilly - The Essential Machine Learning Foundations Math, Probability, Statistics, and Computer Science 2022-3

Course modified date: 7 Apr 2025

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