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How Does Math Matter in Data Science
- 1. How Does Math Matter in Data Science? Prepared by Mutia Ulfi
- 2. Outline Part I Required Math in Data Science Part II Algorithm Used in Data Science
- 3. What Actually Data Science Is? HACKING SKILLS DATA SCIENCE Math & Stats SUBSTANSIVE EXPERTISE DANGER ZONE! TRADITIONAL RESEARCH
- 4. What Are Needed in Data Science?
- 5. Part I Required Mathematics in Data Science
- 6. 25% 15% 35% 15% 10% Required Mathematics in Data Science
- 9. Why Probability & Statistics? • To understand whether data is meaningful, including: • optimization, • inference, • testing, • and other methods. • Therefore, we are able to analyze patterns in data and using them to predict, understand, and improve results. Prob: to predict likelihood of future Stats: to analyze frequency of past events
- 10. Calculus
- 11. Why Calculus? Calculus: to find values that maximize or minimize outcomes Optimizing cost for online dating
- 12. Optimization
- 13. Why Optimization? Opt: to find values that maximize or minimize outcomes
- 14. Linear Algebra
- 15. Why Linear Algebra? Linear Algebra: to simplify codes by understandi ng matrix algebra and eigenvalues
- 16. Part II Algorithms Used in Data Science
- 17. Regression Supervised Learning Task Given Probs & Stats Linear Algebra • Linear Regression • Logistic Regression • Neural Network Optimization
- 18. Linear Regression • Purpose to estimate real values based on continuous variables (e.g. forecasting) • Mathematically speaking 𝑦 = dependent variable 𝑎 = slope 𝑥 = independent variable 𝑏 = intercept 𝑦 = 𝑎𝑥 + 𝑏
- 19. Linear Regression • The Code
- 20. Logistic Regression • Purpose to estimate the probability of a binary response based on ≥ 1 predictor variables (features) • Mathematically speaking 𝑦 = dependent variable 𝑎 = slope 𝑥 = independent variable 𝑏 = intercept Ɛ = error 𝑦 = {0 𝑒𝑙𝑠𝑒 1 𝑎𝑥+𝑏+Ɛ
- 21. Logistic Regression • The Code
- 22. Neural Network • Purpose to find out the output of complex input by modeling the relationship • To find patterns in data (pattern recognition) • To predict sampled functions given no form of the functions (function estimation) • Mathematically speaking Let input and weight, then activation, a = = 𝑥1, 𝑥2, 𝑥3, … , 𝑥 𝑛 𝑤1, 𝑤2, 𝑤3, … , 𝑤 𝑛 𝑖=1 𝑛 𝑥𝑖 𝑤𝑖𝑥1 𝑤1 + 𝑥2 𝑤2 + 𝑥3 𝑤3 + ⋯ + 𝑤 𝑛
- 23. Classification • Decision Tree • Random Forest • Naïve Bayes • Support Vector Machine • k-Nearest Neighbor • Neural Network Supervised Learning Task Given Probs & Stats Linear Algebra Calculus
- 25. Decision Tree • Purpose to model the relationships among the features and the possible outcomes in tree structures • Mathematically speaking • Gini impurity • Information gain • Variance reduction
- 26. Decision Tree • The Code
- 27. Random Forest • Purpose to model the relationships among the features and the possible outcomes in tree structures (but bigger features than decision tree, weights are also varied: BOOSTING) • Mathematically speaking • Predictions, With , if 𝑥𝑖 is one of the 𝑘’ points in the same leaf as 𝑥’ , and 0 otherwise.
- 28. Random Forest
- 29. Naïve Bayes • Purpose to describe the probability of events and how probabilities should be revised in the light of additional information. • Mathematically speaking
- 30. Naïve Bayes
- 31. Support Vector Machine • Purpose to create flat boundary called a hyperplane, which divides the space to create fairly homogeneous partition on either side. • Mathematically Speaking Kernel 𝐾 𝑥𝑖, 𝑥𝑗 = 𝑥𝑖, 𝑥𝑗 2
- 33. k-Nearest Neighbor • Purpose to classify one of data into a class based on its similarity to its nearest neighbor • Mathematically speaking 𝑦 = argmax 𝑦 𝑝 𝑦|𝑥, 𝐷 𝑦 = majority vote (predictor) D = a set of points in the circle 𝑝 𝑦|𝑥, 𝐷 = portion of points in k-nearest points We intend to find a class for question-tagged object. HOW? x y 1. Make a circle to get k-nearest neighbors of object (it’s a majority vote of k-nearest points, refer to the figure). 2. Repeat the process 3. Calculate the distance between object and its nearest neighbors 4. Find the probability of object by portion of points in k-nearest points (refer to figure: portion of A and B in the circles) , or we can write it mathematically as above.
- 35. Clustering Supervised Learning Task Given Probs & Stats Linear Algebra • k-Means Clustering • Association Rules
- 36. k-Means Clustering • Purpose to minimize the differences within each cluster and maximize the differences between the clusters. • Mathematically speaking • Data assignment 𝑐𝑖 = collection of centroids 𝐶𝑖 = set of 𝑐𝑖 𝑥 = data point • Centroid update step 𝑐𝑖 = collection of centroids 𝑆𝑖 = set of data point assignments for each 𝑖 𝑡ℎ cluster centroid 𝑥𝑖 = data point
- 38. • Purpose to give suggestion of possible outcome by predicting historical input (e.g. recommendation of a product to buy) • Mathematically speaking Association Rules
- 39. Reinforcement Learning Supervised Learning Task Given Probs & Stats Linear Algebra Calculus Optimization
- 41. It’s not about equation BUT Mathematical intuitions • Choose the right algorithms for problem • Make good choices on parameter settings, validation strategies • Recognize underfitting or overfitting • Troubleshoot poor or ambiguous results • Put appropriate bounds of confidence or uncertainty on results • Do a better job of coding algorithms or incorporating them into more complex analysis pipelines
- 42. And the most important thing is… Understand the concept NOT The packages
- 43. Want to deep dive in particula algorithm? Simply request! :D
- 44. References • https://courses.washington.edu/css490/2012.Winter/lecture_slides/0 2_math_essentials.pdf • https://www.quora.com/How-do-I-learn-mathematics-for-machine- learning • https://www.analyticsvidhya.com • https://en.wikipedia.org/wiki/Decision_tree_learning • http://csyue.nccu.edu.tw/ch/Cartoon%20Statistics.pdf • https://www.datascience.com/blog/k-means-clustering