This lecture overviews Probability Theory that has many applications in a multitude of scientific and engineering disciplines, notably in Pattern Recognition and Machine Learning. It covers the following topics in detail: Probability Space, Bayes theorem. One random variable, cumulative probability functions, probability density functions, expectation operators, mean, variance, functions of random variables, normal, uniform, Laplacian… Continue reading Probability Theory
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Introduction to Statistics
This lecture provides an Introduction to Statistics that has many applications in Data Analytics, Machine Learning and Signal Analysis. It covers the following topics in detail: Random Variables. Data Types. Data Sampling. Descriptive statistics: Graphs (pie charts, bar charts, histograms), Location and Dispersion Measures.
Set Theory
This lecture overviews Set Theory that has many applications in Probability/Statistics, Machine Learning and Computer Vision. It covers the following topics in detail: Sets (operations, properties), Fields, Fuzzy sets (operations, properties), Applications (Mathematical Morphology, Image Segmentation, Data Clustering, Object detection/tracking performance metics).
Linear Algebra
This lecture overviews Linear Algebra that has many applications in Machine Learning, Computer Vision and Scientific Computing. It covers the following topics in detail: Vectors, matrices, System of linear equations, Eigenanalysis, Singular value Decomposition, Other matrix decompositions, Tensors Fundamentals, Tensor decompositions, BLAS.
Geometric Spaces
This lecture overviews Geometric Spaces that has many applications in Machine Learning and Digital Signal Processing and Analysis. It covers the following topics in detail: Vector Spaces, Affine Spaces, Metric Spaces.
Geometry
This lecture overviews Geometry that has many applications in Computer Vision and Machine Learning. It covers the following topics in detail: Vector calculus (inner/cross vector products, coplanarity), 3D geometric transformations (rotation, translation,quarternions), Projective geometry: homogenous coordinates, Perspective (or central) projections, Vanishing points, Cross-ratio, Conic sections.