Basic principles of Probabilities. Basic theorems in Probability e.g. law of large numbers, the Central Limit theorem etc. Common probability distributions. Principles of statistics. Data summarization. Statistical inference and causality, Experimental design and sampling methods, Estimation and hypothesis testing. Bootstrap and variants.

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The course gives students a set of practical skills for handling data that comes in a variety of formats and sizes, such as texts, spatial and time series data. These skills cover the data analysis lifecycle from initial access and acquisition, modeling, transformation, integration, querying, application of statistical learning and data mining methods, and presentation of results. (The course is hands-on, using python, in iPython interactive computing framework.)

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Methods and techniques for database design and management, operational data management and transaction processing, data warehouse creation, and information retrieval. New approaches for storage and querying (column stores, NewSQL) will be discussed and experimented upon. Management of large scale structured and unstructured data in different information systems environments.

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Introduction to the basic ideas of statistical learning models (supervised and unsupervised learning). Model selection, feature selection and cross-validation. Linear regression and logistic regression. Generalized linear models. K-nearest neighbor classification, Bayes and naive Bayes classifiers. Kernel Discriminant Analysis and Support Vector Machines. Unsupervised learning methods. Clustering using k-means and mixtures models. The EM algorithm. Dimensionality reduction using PCA, probabilistic PCA, factor analysis and independent component analysis.

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Floating point arithmetic; Stability of numerical algorithms; Norms; Fundamentals of matrix theory; Solution of systems of linear equations: direct methods, error analysis, structured matrices; Iterative methods for linear equations and least squares; Eigenanalysis; important matrix factorizations and their algorithms. Application to case studies.

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Communicating clearly and effectively about the patterns we find in data is a key skill for a successful data scientist. Visualizations are graphical depictions that can improve comprehension. Collaborative filtering Visualizations will be paired with verbal analyses and reporting. Different tools will be used to transform data and create visualizations, including Python, Google Charts, Tableau, and Spotfire. Assignments will give students experience with reporting on complex patterns and results with graphics and prose.

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Discusses issues of privacy, surveillance, security, classification, discrimination and decisional autonomy from a legal, ethical, and policy perspective (whether business or public policy). Areas of relevance include health, marketing, employment, law enforcement, and education.

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Language models, text normalization. Applying feature extraction, classification, sequence labeling algorithms (e.g., PCA, naive Bayes, logistic regression, SVMs, HMMs, CRFs) to texts (for document classification, entity recognition etc.). Parsing (CKY, Earley, probabilistic CFGs). Semantics (logic-based, distributional, word embeddings, sense disambiguation) and discourse analysis (co-reference, rhetorical relations). Machine translation. Information extraction (incl., relation extraction) and sentiment analysis. Question answering. Text summarization. Concept-to-text generation. Speech recognition fundamentals.

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