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Concentration inequalities

Engineering Academy

Engineering Academy

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Rating 4 (6)
Course typeWatch to learn anytime
Duration 1209 Min
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Language English
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Concentration inequalities

Why enroll

People join this course to build a strong theoretical foundation in probability that is essential for advanced studies and research in data science, machine learning, artificial intelligence, and applied mathematics. It is particularly valuable for students preparing for research-oriented careers, higher education, or competitive exams, as concentration inequalities are frequently used in analyzing algorithms and large-scale data behavior. Learners also benefit from understanding how uncertainty and randomness are controlled in real-world systems

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Course content

The course is readily available, allowing learners to start and complete it at their own pace.

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Concentration Inequality

26 Lectures

1209 min

  • mod01lec01 Why study concentration inequalities?

    Preview icon

    Preview

    53 min

  • mod01lec02 Chernoff bound

    29 min

  • mod01lec03 Examples of Chernoff bound for common distributions

    40 min

  • mod02lec04 Hoeffding and Bernstein inequalities

    41 min

  • mod03lec06 Bounding variance using the Efron-Stein inequality

    58 min

  • mod03lec07 The Gaussian-Poincare inequality

    33 min

  • mod03lec08 Tail bounds using the Efron-Stein inequality

    47 min

  • mod04lec09 Herbst's argument and the entropy method

    46 min

  • mod04lec10 Log-Sobolev inequalities

    52 min

  • mod04lec11 Binary and Gaussian Log-Sobolev inequalities and concentration

    52 min

  • mod05lec12 Variational formulae forKullback-Leibler and Bregman Divergence

    42 min

  • mod02lec05 Azuma and McDiarmid inequalities

    52 min

  • mod05lec13 A modified log-Sobolev inequality and concentration

    28 min

  • mod05lec14 Introduction to the transportation method for showing concentration bounds

    65 min

  • mod05lec15 Transportationlemma and a proof of McDiarmid's inequality using the transportation method

    42 min

  • mod06lec16 Concentration bounds for functions beyond bounded difference using transportation method

    32 min

  • mod06lec17 Marton's conditional transportation cost inequality

    44 min

  • mod06lec18 Isoperimetry and concentration of measure

    35 min

  • mod06lec19 Isoperimetry and bounded difference

    23 min

  • mod07lec20 Equivalence of Stam's inequality and log Sobolev inequality

    48 min

  • mod07lec21 An information theoretic proof of log Sobolev inequality

    40 min

  • mod07lec22 Hypercontractivity and strong data processing inequality for Rényi divergence

    67 min

  • mod07lec23 An information theoretic characterization of hypercontractivity

    47 min

  • mod07lec24 Equivalence of Gaussian hypercontractivity and Gaussian log Sobolev inequality

    72 min

  • mod08lec25 Uniform deviation bounds for random walks and the law of the iterated logarithm

    67 min

  • mod08lec26 Self normalized concentration inequalities and application to online regression

    54 min

Course details

The NPTEL course on Concentration Inequalities introduces powerful mathematical tools used to analyze how random variables deviate from their expected values. The course focuses on probabilistic bounds that quantify the likelihood of large deviations in random processes. These inequalities form the backbone of modern probability theory and are widely used in statistics, machine learning, randomized algorithms, and data science to provide theoretical performance guarantees.

SOURCE - NPTEL [YOUTUBE]

Course suitable for

  • Telecommunication
  • Electronics & Telecommunication
  • Instrumentation

Key topics covered

  1. Review of probability theory and random variables

  2. Markov and Chebyshev inequalities

  3. Hoeffding’s inequality

  4. Chernoff and Bernstein bounds

  5. Azuma–Hoeffding inequality and martingales

  6. McDiarmid’s inequality

  7. Sub-Gaussian and sub-exponential random variables

  8. Applications in machine learning and randomized algorithms

  9. High-dimensional probability concepts

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