Data-Science

Covering topics across theoretical mathematical underpinings of ML and practical applications through PySpark, Pandas, Scikit , Matplotlib and Tensorflow.

Deep dive across four main sections:

• 1. Python for data Science
• 2. Statistics and Probability
• 3. Machine Learning Fundamentals
• 4. Big Data and Spark

1 Python for data Science

Covers foundational Python concepts utilised for data analysis, covering:

• Jupyter Notebooks
• NumPy
• Pandas (Series & DataFrames)
• Matplotlib
• Scikit
• NLTK
• Plus some Unix for data analysis

2 Statistics and Probability

Reviewing statistical concepts with probability, foundational for machine learning, covering:

• Set Theory

• Combinatronics

• Probability (Axiomatic Formulations)

• Conditional Probability

• Random variables, Cumulative Dist, Expectation, Variance and Covariance

• Discrete Distribution Families

  • Bernoulli
  • Binomial
  • Poisson
  • Geometric

• Continuous Distribution Families

  • Uniform
  • Exponential
  • Gaussian

• Inequalities (Markov, Chebyshev, MGF & Law of large numbers) and Limits (Chernoff Bound and Central Limit Theorem)

• Parameter Estimation and Confidence Interval

• Regression (Linear and Polynomial) and Principal Component Analysis (PCA)

• Hypothesis Testing (P Values, Z and T tests)

3 Machine Learning Fundamentals

Reviewing foundational ML concepts from mathematical perspective following up with practical applications in Python, Covering:

• K Nearest Neighbour (K-NN) and Distance Functions
• Generative Modelling; Probability Spaces and Bivariate Guassians
• Further Generative Modelling; Multivariate Gaussians
• Regression; Linear/Logistic and Regularisation
• Optimisation: Unconstrained, Convexity, Positive Semidefinite Matrices
• Linear Classification; Support Vector Machines (SVM) and Multiclass Linear Prediction
• Further Classifiers; Kernels, Kernel SVM, Decision Trees, Boosting and Random Forests
• Representational Learning; Clustering with; K-Means, Gaussians and Hierarchical Clustering
• Further Representational Learning; Linear Projections, Principal Component Analysis (PCA) , Eigenvalues/Eigenvectors and Spectral Decomposition
• Deep Learning; Autoencoders, Distributed Representation, Feedforward Neural Networks and Training

4 Big Data and Spark

Reviewing Machine Learning concepts and their practical application through Spark using PySpark, RDD's Spark SQL, DataFrames and TensorFlow.

• Spark, PySpark infrastructure setup
• MapReduce concepts and RDD's
• Spark SQL and DataFrames
• Covariance and principal Component Analysis (PCA) with Python
• PCA Coefficients and PCA Residuals with Python
• K-Means Clustering and Intrinsic Dimensions
• Decision Trees,Ensembles and Boosting
• Neural Networks (NN) review and TensorFlow (Base and Estimator API)