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Interesting picture summarizing several types of techniques used in machine learning, contrasting unsupervised learning with unsupervised learning and reinforcement learning.The difference between supervised and unsupervised learning is described here. See also this article about how this relates to reinforcement learning. The above picture was posted here. The author mentions the following techniques:supervised learningNaive BayesKNNDecision TreesSupport Vector MachineLinear RegressionLogistic RegressionDeep Learning modelsUnsupervised LearningK-meansDBSCANOPTICS algorithmMixture modelsSee More

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Course material for Richard Weber's course on Probability for first year mathematicians at Cambridge. You can also check Richard's blog (a former colleague of my dad) here. It also includes exams question. This is the base material that needs to be mastered before being accepted in the prestigious Tripo III curriculum at Cambridge. The book (PDF) can be downloaded here. Below is the table other contents. Other similar books can be found here. Source: see section 24.3 in the book1 Classical probability1.1 Diverse notions of `probability' 1.2 Classical probability 1.3 Sample space and events 1.4 Equalizations in random walk2 Combinatorial analysis2.1 Counting 2.2 Sampling with or without replacement 2.2.0.1 Remarks. 2.3 Sampling with or without regard to ordering 2.4 Four cases of enumerative combinatorics3 Stirling's formula3.1 Multinomial coefficient 3.2 Stirling's formula 3.3 Improved Stirling's formula4 Axiomatic approach4.1 Axioms of probability 4.2 Boole's inequality 4.3 Inclusion-exclusion formula5 Independence5.1 Bonferroni's inequalities 5.2 Independence of two events 5.2.0.1 Independent experiments. 5.3 Independence of multiple events 5.4 Important distributions 5.5 Poisson approximation to the binomial6 Conditional probability6.1 Conditional probability 6.2 Properties of conditional probability 6.3 Law of total probability 6.4 Bayes' formula 6.5 Simpson's paradox 6.5.0.1 Remark.7 Discrete random variables7.1 Continuity of $P$ 7.2 Discrete random variables 7.3 Expectation 7.4 Function of a random variable 7.5 Properties of expectation8 Further functions of random variables8.1 Expectation of sum is sum of expectations 8.2 Variance 8.2.0.1 Binomial. 8.2.0.2 Poisson. 8.2.0.3 Geometric. 8.3 Indicator random variables 8.4 Reproof of inclusion-exclusion formula 8.5 Zipf's law9 Independent random variables9.1 Independent random variables 9.2 Variance of a sum 9.3 Efron's dice 9.4 Cycle lengths in a random permutation 9.4.0.1 Names in boxes problem.10 Inequalities10.1 Jensen's inequality 10.2 AM--GM inequality 10.3 Cauchy-Schwarz inequality 10.4 Covariance and correlation 10.5 Information entropy11 Weak law of large numbers11.1 Markov inequality 11.2 Chebyshev inequality 11.3 Weak law of large numbers 11.3.0.1 Remark. 11.3.0.2 Strong law of large numbers 11.4 Probabilistic proof of Weierstrass approximation theorem 11.5 Probabilistic proof of Weierstrass approximation theorem 11.6 Benford's law12 Probability generating functions12.1 Probability generating function 12.2 Combinatorial applications 12.2.0.1 Dyck words.13 Conditional expectation13.1 Conditional distribution and expectation 13.2 Properties of conditional expectation 13.3 Sums with a random number of terms 13.4 Aggregate loss distribution and VaR 13.5 Conditional entropy14 Branching processes14.1 Branching processes 14.2 Generating function of a branching process 14.3 Probability of extinction15 Random walk and gambler's ruin15.1 Random walks 15.2 Gambler's ruin 15.3 Duration of the game 15.4 Use of generating functions in random walk16 Continuous random variables16.1 Continuous random variables 16.1.0.1 Remark. 16.2 Uniform distribution 16.3 Exponential distribution 16.4 Hazard rate 16.5 Relationships among probability distributions17 Functions of a continuous random variable17.1 Distribution of a function of a random variable 17.1.0.1 Remarks. 17.2 Expectation 17.3 Stochastic ordering of random variables 17.4 Variance 17.5 Inspection paradox18 Jointly distributed random variables18.1 Jointly distributed random variables 18.2 Independence of continuous random variables 18.3 Geometric probability 18.4 Bertrand's paradox 18.5 Last arrivals problem19 Normal distribution19.1 Normal distribution 19.2 Calculations with the normal distribution 19.3 Mode, median and sample mean 19.4 Distribution of order statistics 19.5 Stochastic bin packing20 Transformations of random variables20.1 Convolution 20.2 Cauchy distribution21 Moment generating functions21.1 What happens if the mapping is not 1--1? 21.2 Minimum of exponentials is exponential 21.3 Moment generating functions 21.4 Gamma distribution 21.5 Beta distribution22 Multivariate normal distribution22.1 Moment generating function of normal distribution 22.2 Functions of normal random variables 22.3 Multivariate normal distribution 22.4 Bivariate normal 22.5 Multivariate moment generating function 22.6 Buffon's needle23 Central limit theorem23.1 Central limit theorem 23.1.0.1 Remarks. 23.2 Normal approximation to the binomial 23.3 Estimating $\pi$ with Buffon's needle24 Continuing studies in probability 24.1 Large deviations 24.2 Chernoff bound 24.3 Random matrices 24.4 Concluding remarksAppendicesA Problem solving strategies B Fast Fourier transform and p.g.fs C The Jacobian D Beta distribution E Kelly criterion F Ballot theorem G Allais paradox H IB courses in applicable mathematicsSee More

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