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Statistics and linear algebra for machine learning

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By Team EasyExamNotes

Statistics:

1. Descriptive Statistics:

  • Mean, Median, Mode: Measures of central tendency help summarize and understand the distribution of data.
  • Standard Deviation, Variance: Measures of dispersion provide insights into the spread of data points.

2. Inferential Statistics:

  • Probability Distributions: Understanding probability distributions is essential for modeling uncertainties in data.
  • Hypothesis Testing: Used to make inferences about population parameters based on sample data.

3. Statistical Learning:

  • Regression Analysis: Modeling the relationship between variables.
  • Classification: Assigning labels or categories to data points based on statistical models.

4. Sampling Techniques:

  • Random Sampling: Ensures representative subsets for training and testing data.
  • Bootstrapping: Resampling technique used for estimating the distribution of a statistic.

Linear Algebra:

1. Vectors and Matrices:

  • Vectors: Representing data points and features.
  • Matrices: Used for transformations, such as feature scaling and data manipulation.

2. Matrix Operations:

  • Addition, Subtraction, Multiplication: Fundamental operations for manipulating data and parameters.
  • Transpose: Flipping rows and columns, often used in calculations.

3. Eigenvalues and Eigenvectors:

  • Principal Component Analysis (PCA): Dimensionality reduction technique.
  • Spectral Clustering: Clustering algorithm based on eigenvectors.

4. Matrix Decompositions:

  • Singular Value Decomposition (SVD): Used in latent semantic analysis and collaborative filtering.
  • LU Decomposition: Solving linear equations efficiently.

5. Linear Transformations:

6. Linear Independence and Rank:

  • Determining Rank: Assessing the number of linearly independent columns or rows in a matrix.
  • Rank-Nullity Theorem: Essential in understanding the dimensionality of the solution space.
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