Data analysis in applied sciences - free course from the School of Data Analysis, training 4 semesters, Date: December 5, 2023.

The main feature of the Data Analysis in Applied Sciences major is that students spend most of the second year of study working on applied research projects. The final grade for studying at the ShAD will largely be determined by the quality of this project.

For students who, in parallel with the ShAD, will be preparing theses (bachelor's or master's), the ShAD projects can be used as the basis for their university work.

Mandatory
Reconstruction of functional patterns from empirical data

01 General formulation of the problem of dependency recovery
02 Maximum likelihood method
03 Examples of specific dependency recovery problems: regression, pattern identification, pattern recognition and their applications
04 Construction of nonparametric estimates of distributions using the maximum likelihood method
05 Least squares method for regression estimation. Maximum likelihood method for model selection
06 Likelihood ratio test
07 Search for a decision rule that minimizes the number of errors or the average value of the penalty function on training data in pattern recognition problems
08 Multivariate linear estimation
09 Perceptron. Potential functions. Neural networks
10 Taking into account a priori information in linear estimation
11 Generalized portrait method in classification problem
12 Bayesian estimation
13 Support Vector Machine (SVM)
14 Some classification methods
15 Criticism of the empirical risk minimization method
16 Optimal hyperplane
17 Criteria for uniform convergence of frequencies to probabilities. Growth function. VC dimension
18 The dual problem of constructing an optimal hyperplane
19 Criteria for uniform convergence of frequencies to probabilities. Relation to the tasks of learning pattern recognition
20 Construction of nonparametric spline regression
21 Criteria for uniform convergence of averages to mathematical expectations
22 Construction of nonparametric kernel regression
23 The problem of choosing the optimal model complexity
24 Different types of regression dependencies

Basics of stochastics. Stochastic models

01 Classic definition of probability
02 Conditional probabilities. Independence. Conditional mathematical expectation.
03 Discrete random variables and their characteristics
04 Limit theorems
05 Random walk
06 Martingales
07 Discrete Markov chains. Ergodic theorem.
08 Probabilistic model of an experiment with an infinite number of events. Kolmogorov's axiomatics. Different types of convergence of random variables.
09 Weak convergence of probability measures. The method of characteristic functions in the proof of limit theorems.
10 Random processes

Algorithms and data structures, part 1

01 Complexity and computational models. Analysis of accounting values ​​(beginning)
02 Analysis of accounting values ​​(end)
03 Merge-Sort and Quick-Sort algorithms
04 Ordinal statistics. Heaps (beginning)
05 Heaps (end)
06 Hashing
07 Search Trees (beginning)
08 Search Trees (continued)
09 Search trees (end). System of disjoint sets
10 Objectives of RMQ and LCA
11 Data structures for geometric search
12 Problem of dynamic connectivity in an undirected graph

01 Basic concepts and examples of applied problems
02 Metric classification methods
03 Logical classification methods and decision trees
04 Gradient linear classification methods
05 Support Vector Machine
06 Multivariate Linear Regression
07 Nonlinear and nonparametric regression, non-standard loss functions
08 Time series forecasting
09 Bayesian classification methods
10 Logistic regression
11 Search for association rules

Fundamentals of Statistics in Machine Learning

01 Introduction
02 Basic tasks and methods of the theory of statistical inference
03 Distribution estimation and statistical functionals
04 Monte Carlo simulation, bootstrap
05 Parametric estimation
06 Testing hypotheses
07 Reducing the dimensionality of multidimensional data
08 Model sensitivity assessment
09 Linear and logistic regression
10 Design of Experiments
11 Different types of regularization in linear regression
12 Nonlinear methods for constructing regression dependencies
13 Nonparametric estimation
14 Bayesian approach to estimation
15 Bayesian approach to regression
16 Bayesian approach to regression and optimization
17 Using the random Gaussian field model in data analysis problems
18 Use of statistical models and methods in surrogate modeling and optimization problems

01 Convex functions and sets
02 Optimality conditions and duality
03 Introduction to optimization methods
04 Complexity for classes of convex smooth and convex nonsmooth problems
05 Smoothing technique
06 Penalty functions. Barrier method. Modified Lagrange function method
07 ADMM
08 Introduction to Mirror Imposition Techniques
09 Newton method and quasi-Newton methods. BFGS
10 Introduction to Robust Optimization
11 Introduction to stochastic optimization
12 Randomized optimization algorithms
13 Introduction to Online Optimization

Machine learning, part 2

01 Neural network methods of classification and regression
02 Compositional classification and regression methods
03 Criteria for selecting models and methods for selecting features
04 Ranking
05 Reinforcement learning
06 Learning without a teacher
07 Problems with partial training
08 Collaborative filtering
09 Topic Modeling

Project work