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Data Science

We are convinced that a data analyst both today and in the coming decades will need a deep understanding of the mathematics used in Data Science. The differentiator for being a competitive analyst contains among its qualities the fluency with which mathematical language is spoken. We know that just as knowing mathematics is not enough to succeed in Data Science - other factors such as data engineering, programmer skills etc ... are essential to an analyst's preparation - the complex nature of problems it requires analysis that is sustained by firm scientific steps, many of them written in the form of theorems. In addition to the above, the capacity for improvement for an analyst with a strong mathematical background provides value with the flavor of an informed investment.

Objectives

  1. Provide the student with the correct intuition behind data science problems and some of the algorithms to solve them, including:

    • The geometric interpretation

    • Both theoretical and practical limitations

    • Comparison with other algorithms

  2. Provide the student with the necessary language to translate fluently:

    • The problems of Catho science to the mathematical language used in machine learning.

    • The algorithms exposed in the literature -either in scientific articles or textbooks- to the specific problems.

Syllabus

 

Block one is focused on two main objectives:

 

  • Using three algorithms (perceptron, linear regressions and logistic regressions) invite the student to the methods and language of Data Science.

  • Make an accurate diagnosis of the student in order to offer a better planned program for the rest of the blocks.

 

1. Perceptron (Classification)

  • Statement of a binary classification problem.

  • Stages of a learning problem.

  • Geometric interpretation of linear classification

  • Algebraic formulation of linear classification

 

2. Linear regressions (Forecasting)

  • Statement of a regression problem

  • Linear regressions

  • Correlation

  • Exact solution and matrix algebra

  • Approach using the gradient method

  • Stochastic noise

  • Polynomial regressions

 

3. Logistic regression (Bayesian inference)

  • Binary classification using logistic regression

  • Bayes' theorem

  • Sigmoid function and interpretation

  • Likelihood Maximization

  • Approach algorithms

 

 

Block two

 

 

The main objective is to continue the two algorithms we studied in block one, as well as to introduce the first non-parametric and unsupervised algorithms.

 

On the one hand, the decision trees generalize the perceptron by allowing non-linear classification, and with them we will begin the study of non-parametric algorithms.

 

The PCA method will be the first example of an unsupervised algorithm that we will study, in addition to reinforcing the idea of ​​correlation studied in the previous block.

 

Finally, we will begin the study of proximity algorithms, which in addition to being the second unsupervised and non-paramedical example will allow us to introduce the idea of ​​clusterization.

 

 

Syllabus

 

  1. Decision trees

  • What is not your decision tree?
  • Geometric interpretation

  • ID3

  • Entropy and Gini function

2. Principal component analysis (PCA)

  • Interpretation in terms of variance

  • Interpretation in terms of distance

  • Relationship to linear algebra

    • Enigenvalues

    • Singular value decomposition

    • QR-decomposition

  • Usual algorithms

 

 

3. Closeness and clusterization algorithms

  • Euclidean distances and other metrics

  • K-nearest neighbors

    • 1-NN

    • General algorithm

    • The curse of dimension

  • K-means

  • Clustering

 

Block three

 

 

There are three objectives of block three:

  • Firstly, we seek to introduce the concept of regularization in machine learning, which is essential to compare algorithms through their generalization capacity.

  • The second objective is to expand the palette of algorithms that the student understands by means of two fundamental techniques for classification and forecasting: neural networks and time series.

  • Finally we begin the presentation and analysis of another family of useful and common algorithms in machine learning, the so-called stochastic algorithms, we will focus on their relationship with neural networks, linear regressions and decision trees. We will complement this block with an invitation to boosting.

 

 

Syllabus

 

1. Regularization in Machine Learning

 

  • Fitting vs overfitting
  • In linear regressions

    • Ridge

    • Lasso

    • Elastic

    • In decision trees: pruning

    • Perceptron: support vector machines

    •  

2. Invitation to Deep learning

 

  • Activation functions
  • Back-propagation algorithm

  • Neural network architectures

  • Convolution and its interpretation: CNN

 

3. Stochastic algorithms

  • Stochastic gradient descent (regressions and neural networks)
  • Random forests (decision trees)

  • Boosting

 

4. Invitation to time series

  • Components of a time series

  • White stochastic noise

  • Moving-average

  • ARIMA