Downloads & Free Reading Options - Results

This six-week online course was held from October 08 through November 27, 2019. It comprised 3-4 hours of learning effort per week, 6 weekly assignments, and 1 final exam. The course covered the following topics: Introduction to Statistics Descriptive Statistics Correlation and Linear Regression Introduction to Probability Probability Distributions Connecting to Your SAP Solutions Maximum score possible for this course: 360 points.

MIT 6.0002 Introduction to Computational Thinking and Data Science, Fall 2016 View the complete course: http://ocw.mit.edu/6-0002F16 Instructor: John Guttag This course provides students with an understanding of the role computation can play in solving problems. Student will learn to write small programs using the Python 3.5 programming language. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

Trimester 2 2016/2017

Trimester 1 2017/2018

Trimester 1 2017/2018

A first section of 365 Data Science Course.

Smoothing Spline ANOVA (SS-ANOVA) models in reproducing kernel Hilbert spaces (RKHS) provide a very general framework for data analysis, modeling and learning in a variety of fields. Discrete, noisy scattered, direct and indirect observations can be accommodated with multiple inputs and multiple possibly correlated outputs and a variety of meaningful structures. The purpose of this paper is to give a brief overview of the approach and describe and contrast a series of applications, while noting some recent results.

Smoothing Spline ANOVA (SS-ANOVA) models in reproducing kernel Hilbert spaces (RKHS) provide a very general framework for data analysis, modeling and learning in a variety of fields. Discrete, noisy scattered, direct and indirect observations can be accommodated with multiple inputs and multiple possibly correlated outputs and a variety of meaningful structures. The purpose of this paper is to give a brief overview of the approach and describe and contrast a series of applications, while noting some recent results.

This book introduces the field of data science in a practical and accessible manner, using a hands-on approach that assumes no prior knowledge of the subject. The foundational ideas and techniques of data science are provided independently from technology, allowing students to easily develop a firm understanding of the subject without a strong technical background, as well as being presented with material that will have continual relevance even after tools and technologies change. Using popular data science tools such as Python and R, the book offers many examples of real-life applications, with practice ranging from small to big data. A suite of online material for both instructors and students provides a strong supplement to the book, including datasets, chapter slides, solutions, sample exams, and curriculum suggestions. This entry-level textbook is ideally suited to readers from a range of disciplines wishing to build a practical, working knowledge of data science.

Tri 2 – 2018/2019

Trimester 2 2019/2020

Trimester 2 2019/2020

After Work Data Science Introduction To Machine Learning Project

After Work Data Science Introduction To Machine Learning Project

Bibliography: p. 404-411

Trimester 1 2018/2019

Applied Data Science Part 1

Applied Data Science Part 1

Trimester 2 2017/2018

Trimester 1 2019/2020

Introduction to Data Science, by Jeffrey Stanton, provides non-technical readers with a gentle introduction to essential concepts and activities of data science. For more technical readers, the book provides explanations and code for a range of interesting applications using the open source R language for statistical computing and graphics. The book is suitable for an introductory course in data science where students have a varied background or as a supplement to an advanced analytics course where students would benefit from an introduction to R. This book is distributed under a Creative Commons license that permits adaptation and redistribution for non-commercial purposes. What's New in Version 3.0 Version 3.0 of this book contains a new chapter on data mining with support vector machines. Instructions for using Twitter's OAuth functions have been enhanced with additional information for Windows users.

Introduction to Data Science, by Jeffrey Stanton, provides non-technical readers with a gentle introduction to essential concepts and activities of data science. For more technical readers, the book provides explanations and code for a range of interesting applications using the open source R language for statistical computing and graphics. The book is suitable for an introductory course in data science where students have a varied background or as a supplement to an advanced analytics course where students would benefit from an introduction to R. This book is distributed under a Creative Commons license that permits adaptation and redistribution for non-commercial purposes. What's New in Version 3.0 Version 3.0 of this book contains a new chapter on data mining with support vector machines. Instructions for using Twitter's OAuth functions have been enhanced with additional information for Windows users.

Introduction to Data Science, by Jeffrey Stanton, provides non-technical readers with a gentle introduction to essential concepts and activities of data science. For more technical readers, the book provides explanations and code for a range of interesting applications using the open source R language for statistical computing and graphics. The book is suitable for an introductory course in data science where students have a varied background or as a supplement to an advanced analytics course where students would benefit from an introduction to R. This book is distributed under a Creative Commons license that permits adaptation and redistribution for non-commercial purposes. What's New in Version 3.0 Version 3.0 of this book contains a new chapter on data mining with support vector machines. Instructions for using Twitter's OAuth functions have been enhanced with additional information for Windows users.

Free download at https://services.publishing.umich.edu/publications/ee/ [with additional bookmarking & cropping] CONTENTS  Cover page   ...1 About the author   ...2 Copyright page   ...5 Preface   ...8 Contents    ...10 1 Mathematical Background    ...18 1.1 Infinite Series   ...19 1.1.1 Geometric Series   ...20 1.1.2 Binomial Series   ...23 1.2 Approximation   ...27 1.2.1 Taylor approximation   ...27 1.2.2 Exponential series   ...29 1.2.3 Logarithmic approximation   ...30 1.3 Integration   ...32 1.3.1 Odd & even functions   ...32 1.3.2 Fundamental Theorem of Calculus   ...34 1.4 Linear Algebra   ...37 1.4.1 Why do we need linear algebra in data science?   ...37 1.4.2 Everything you need to know about linear algebra   ...38 1.4.3 Inner products & norms   ...41 1.4.4 Matrix calculus   ...45 1.5 Basic Combinatorics   ...48 1.5.1 Birthday paradox   ...48 1.5.2 Permutation   ...50 1.5.3 Combination   ...52 1.6 Summary   ...54 1.7 Reference   ...55 1.8 Problems   ...56 2 Probability   ...60 2.1 Set Theory   ...61 2.1.1 Why study set theory?   ...61 2.1.2 Basic concepts of a set   ...62 2.1.3 Subsets   ...64 2.1.4 Empty set & universal set   ...65 2.1.5 Union   ...65 2.1.6 Intersection   ...67 2.1.7 Complement & difference   ...69 2.1.8 Disjoint & partition   ...71 2.1.9 Set operations   ...73 2.1.10 Closing remarks about set theory   ...74 2.2 Probability Space   ...75 2.2.1 Sample space fi   ...76 2.2.2 Event space F   ...78 2.2.3 Probability law P   ...83 2.2.4 Measure zero sets   ...88 2.2.5 Summary of the probability space   ...91 2.3 Axioms of Probability   ...91 2.3.1 Why these three probability axioms?   ...92 2.3.2 Axioms through the lens of measure   ...93 2.3.3 Corollaries derived from the axioms   ...94 2.4 Conditional Probability   ...97 2.4.1 Definition of conditional probability   ...98 2.4.2 Independence   ...102 2.4.3 Bayes’ theorem & the law of total probability   ...106 2.4.4 The Three Prisoners problem   ...109 2.5 Summary   ...112 2.6 References   ...113 2.7 Problems   ...114 3 Discrete Random Variables   ...120 3.1 Random Variables   ...122 3.1.1 A motivating example   ...122 3.1.2 Definition of a random variable   ...122 3.1.3 Probability measure on random variables   ...124 3.2 Probability Mass Function   ...127 3.2.1 Definition of probability mass function   ...127 3.2.2 PMF & probability measure   ...127 3.2.3 Normalization property   ...129 3.2.4 PMF versus histogram   ...130 3.2.5 Estimating histograms from real data   ...134 3.3 Cumulative Distribution Functions (Discrete)   ...138 3.3.1 Definition of the cumulative distribution function   ...138 3.3.2 Properties of the CDF   ...140 3.3.3 Converting between PMF & CDF   ...141 3.4 Expectation   ...142 3.4.1 Definition of expectation   ...142 3.4.2 Existence of expectation   ...147 3.4.3 Properties of expectation   ...147 3.4.4 Moments & variance   ...150 3.5 Common Discrete Random Variables   ...153 3.5.1 Bernoulli random variable   ...154 3.5.2 Binomial random variable   ...160 3.5.3 Geometric random variable   ...166 3.5.4 Poisson random variable   ...169 3.6 Summary   ...182 3.7 References   ...183 3.8 Problems   ...184 4 Continuous Random Variables    ...188 4.1 Probability Density Function   ...189 4.1.1 Some intuitions about probability density functions   ...189 4.1.2 More in-depth discussion about PDFs   ...191 4.1.3 Connecting with the PMF   ...195 4.2 Expectation, Moment, & Variance   ...197 4.2.1 Definition & properties   ...197 4.2.2 Existence of expectation   ...200 4.2.3 Moment & variance   ...201 4.3 Cumulative Distribution Function   ...202 4.3.1 CDF for continuous random variables   ...203 4.3.2 Properties of CDF   ...205 4.3.3 Retrieving PDF from CDF   ...210 4.3.4 CDF: Unifying discrete & continuous random variables   ...211 4.4 Median, Mode, & Mean   ...213 4.4.1 Median   ...213 4.4.2 Mode   ...215 4.4.3 Mean   ...216 4.5 Uniform & Exponential Random Variables   ...218 4.5.1 Uniform random variables   ...219 4.5.2 Exponential random variables   ...222 4.5.3 Origin of exponential random variables   ...224 4.5.4 Applications of exponential random variables   ...226 4.6 Gaussian Random Variables   ...228 4.6.1 Definition of a Gaussian random variable   ...228 4.6.2 Standard Gaussian   ...230 4.6.3 Skewness & kurtosis   ...233 4.6.4 Origin of Gaussian random variables   ...237 4.7 Functions of Random Variables   ...240 4.7.1 General principle   ...240 4.7.2 Examples   ...242 4.8 Generating Random Numbers   ...245 4.8.1 General principle   ...246 4.8.2 Examples   ...247 4.9 Summary   ...251 4.10 Reference   ...252 4.11 Problems   ...253 5 Joint Distributions   ...258 5.1 Joint PMF & Joint PDF   ...261 5.1.1 Probability measure in 2D   ...261 5.1.2 Discrete random variables   ...262 5.1.3 Continuous random variables   ...264 5.1.4 Normalization   ...266 5.1.5 Marginal PMF & marginal PDF   ...267 5.1.6 Independent random variables   ...269 5.1.7 Joint CDF   ...272 5.2 Joint Expectation   ...274 5.2.1 Definition & interpretation   ...274 5.2.2 Covariance & correlation coefficient   ...279 5.2.3 Independence & correlation   ...281 5.2.4 Computing correlation from data   ...282 5.3 Conditional PMF & PDF   ...284 5.3.1 Conditional PMF   ...284 5.3.2 Conditional PDF   ...289 5.4 Conditional Expectation   ...292 5.4.1 Definition   ...292 5.4.2 The law of total expectation   ...293 5.5 Sum of Two Random Variables   ...297 5.5.1 Intuition through convolution   ...297 5.5.2 Main result   ...298 5.5.3 Sum of common distributions   ...299 5.6 Random Vectors & Covariance Matrices   ...303 5.6.1 PDF of random vectors   ...303 5.6.2 Expectation of random vectors   ...305 5.6.3 Covariance matrix   ...306 5.6.4 Multidimensional Gaussian   ...307 5.7 Transformation of Multidimensional Gaussians   ...310 5.7.1 Linear transformation of mean & covariance   ...310 5.7.2 Eigenvalues & eigenvectors   ...312 5.7.3 Covariance matrices are always positive semi-definite   ...314 5.7.4 Gaussian whitening   ...316 5.8 Principal-Component Analysis   ...320 5.8.1 The main idea: Eigendecomposition   ...320 5.8.2 The eigenface problem   ...326 5.8.3 What cannot be analyzed by PCA?   ...328 5.9 Summary   ...329 5.10 References   ...330 5.11 Problems   ...332 6 Sample Statistics    ...336 6.1 Moment-Generating & Characteristic Functions   ...341 6.1.1 Moment-generating function   ...341 6.1.2 Sum of independent variables via MGF   ...344 6.1.3 Characteristic functions   ...346 6.2 Probability Inequalities   ...350 6.2.1 Union bound   ...350 6.2.2 The Cauchy-Schwarz inequality   ...352 6.2.3 Jensen’s inequality   ...353 6.2.4 Markov’s inequality   ...356 6.2.5 Chebyshev’s inequality   ...358 6.2.6 Chernoff’s bound   ...360 6.2.7 Comparing Chernoff & Chebyshev   ...361 6.2.8 Hoeffding’s inequality   ...365 6.3 Law of Large Numbers   ...368 6.3.1 Sample average   ...368 6.3.2 Weak law of large numbers (WLLN)   ...371 6.3.3 Convergence in probability   ...373 6.3.4 Can we prove WLLN using Chernoff’s bound?   ...376 6.3.5 Does the weak law of large numbers always hold?   ...377 6.3.6 Strong law of large numbers   ...378 6.3.7 Almost sure convergence   ...379 6.3.8 Proof of the strong law of large numbers   ...381 6.4 Central Limit Theorem   ...384 6.4.1 Convergence in distribution   ...385 6.4.2 Central Limit Theorem   ...389 6.4.3 Examples   ...394 6.4.4 Limitation of the Central Limit Theorem   ...396 6.5 Summary   ...398 6.6 References   ...399 6.7 Problems   ...401 7 Regression   ...406 7.1 Principles of Regression   ...411 7.1.1 Intuition: How to fit a straight line?   ...412 7.1.2 Solving the linear regression problem   ...414 7.1.3 Extension: Beyond a straight line   ...418 7.1.4 Overdetermined & underdetermined systems   ...426 7.1.5 Robust linear regression   ...429 7.2 Overfitting   ...435 7.2.1 Overview of overfitting   ...436 7.2.2 Analysis of the linear case   ...437 7.2.3 Interpreting the linear analysis results   ...442 7.3 Bias & Variance Trade-Off   ...446 7.3.1 Decomposing the testing error   ...447 7.3.2 Analysis of the bias   ...450 7.3.3 Variance   ...453 7.3.4 Bias & variance on the learning curve   ...455 7.4 Regularization   ...457 7.4.1 Ridge regularization   ...457 7.4.2 LASSO regularization   ...466 7.5 Summary   ...474 7.6 References   ...475 7.7 Problems   ...476 8 Estimation    ...482 8.1 Maximum-Likelihood Estimation   ...485 8.1.1 Likelihood function   ...485 8.1.2 Maximum-likelihood estimate   ...489 8.1.3 Application 1: Social network analysis   ...495 8.1.4 Application 2: Reconstructing images   ...498 8.1.5 More examples of ML estimation   ...501 8.1.6 Regression versus ML estimation   ...505 8.2 Properties of ML Estimates   ...508 8.2.1 Estimators   ...508 8.2.2 Unbiased estimators   ...509 8.2.3 Consistent estimators   ...511 8.2.4 Invariance principle   ...517 8.3 Maximum A Posteriori Estimation   ...520 8.3.1 The trio of likelihood, prior, & posterior   ...520 8.3.2 Understanding the priors   ...521 8.3.3 MAP formulation & solution   ...523 8.3.4 Analyzing the MAP solution   ...525 8.3.5 Analysis of the posterior distribution   ...529 8.3.6 Conjugate prior   ...530 8.3.7 Linking MAP with regression   ...534 8.4 Minimum Mean-Square Estimation   ...538 8.4.1 Positioning the minimum mean-square estimation   ...538 8.4.2 Mean squared error   ...539 8.4.3 MMSE estimate = conditional expectation   ...541 8.4.4 MMSE estimator for multidimensional Gaussian   ...547 8.4.5 Linking MMSE & neural networks   ...550 8.5 Summary   ...551 8.6 References   ...552 8.7 Problems   ...553 9 Confidence & Hypothesis    ...560 9.1 Confidence Interval   ...562 9.1.1 The randomness of an estimator   ...562 9.1.2 Understanding confidence intervals   ...564 9.1.3 Constructing a confidence interval   ...567 9.1.4 Properties of the confidence interval   ...570 9.1.5 Student’s t-distribution   ...573 9.1.6 Comparing Student’s t-distribution & Gaussian   ...577 9.2 Bootstrapping   ...578 9.2.1 A brute force approach   ...579 9.2.2 Bootstrapping   ...581 9.3 Hypothesis Testing   ...585 9.3.1 What is a hypothesis?   ...585 9.3.2 Critical-value test   ...586 9.3.3 p-value test   ...590 9.3.4 Z -test & T -test   ...593 9.4 Neyman-Pearson Test   ...596 9.4.1 Null & alternative distributions   ...596 9.4.2 Type 1 & type 2 errors   ...598 9.4.3 Neyman-Pearson decision   ...601 9.5 ROC & Precision-Recall Curve   ...608 9.5.1 Receiver Operating Characteristic (ROC)   ...608 9.5.2 Comparing ROC curves   ...611 9.5.3 The ROC curve in practice   ...617 9.5.4 The Precision-Recall (PR) curve   ...620 9.6 Summary   ...624 9.7 Reference   ...625 9.8 Problems   ...626 10 Random Processes   ...630 10.1 Basic Concepts   ...631 10.1.1 Everything you need to know about a random process   ...631 10.1.2 Statistical & temporal perspectives   ...633 10.2 Mean & Correlation Functions   ...637 10.2.1 Mean function   ...637 10.2.2 Autocorrelation function   ...641 10.2.3 Independent processes   ...648 10.3 Wide-Sense Stationary Processes   ...649 10.3.1 Definition of a WSS process   ...650 10.3.2 Properties of RX (t)   ...651 10.3.3 Physical interpretation of RX(t)   ...652 10.4 Power Spectral Density   ...656 10.4.1 Basic concepts   ...656 10.4.2 Origin of the power spectral density   ...660 10.5 WSS Process through LTI Systems   ...663 10.5.1 Review of linear time-invariant systems   ...663 10.5.2 Mean & autocorrelation through LTI Systems   ...664 10.5.3 Power spectral density through LTI systems   ...666 10.5.4 Cross-correlation through LTI Systems   ...669 10.6 Optimal Linear Filter   ...673 10.6.1 Discrete-time random processes   ...673 10.6.2 Problem formulation   ...674 10.6.3 Yule-Walker equation   ...676 10.6.4 Linear prediction   ...678 10.6.5 Wiener filter   ...682 10.7 Summary   ...689 10.8 Appendix   ...690 10.8.1 The Mean-Square Ergodic Theorem   ...694 10.9 References   ...695 10.10 Problems   ...696 Appendix    ...700 Useful Identities   ...700 Common Distributions   ...700 Sum of Two Random Variables   ...701 Fourier Transform Table   ...701 Basic Trigonometric Identities   ...702 Index    ...703 e n d   ...710

After Work Data Science Introduction To Machine Learning Project

This introductory talk, will cover the basics of datascience. From the incluence of artificial intelligence, and the quest to replicate a human mind, to a practical demo on how to build a hello world machine learning in Python. The talk will try to answer questions such as: What do we understand by data science? What do we know about the human mind, that can be an inspiration for our programs? Which problems can we solve with data science? What tools are available to do data science in Python? Please see our speaker release agreement for details: https://ep2017.europython.eu/en/speaker-release-agreement/