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Lower Bounds Using Information Theory Tools

Learn about the principles of utilizing information theory tools for deriving lower bounds with this free online course.

Publisher: NPTEL
Upper bounds are primarily used to advertise the popularity of an algorithm. However, what if one wants to argue that no other algorithm can be better, or perhaps that some problem is so hard that one can't possibly hope to find a good solution to it? This implies the need for a lower bound. Learn about the procedure for establishing lower bounds for estimation problems through concise information-theoretic arguments by taking this course now.
Lower Bounds Using Information Theory Tools
  • Duration

    1.5-3 Hours
  • Students

    5
  • Accreditation

    CPD

Description

Modules

Outcome

Certification

View course modules

Description

The implication of contemporary research is about finding answers to real-life problems. Nevertheless, the primary focus of these researches is aimed at comprehending the impossible. The portrayals of principal limits, spot unreasonable targets, give optimality assurances to helpful systems and perceive bottlenecks in issue details that may call for development are the core outcomes of impossibility. The process of ascertaining the best possible solution to a problem is a common task in various fields of information theory. For instance, what is the minimum time required for an algorithm in computing the distributed function? How many repetitions are required for determining the optimal solution in optimization? How much memory is required for learning the data or portability distribution? What is the procedure for ascertaining the best encoding and decoding methods in a communication channel? This calls for the need for deriving using the original applications of some well-known information-theoretic inequalities for determining the shortest route to a given problem.

The prime focus of this course relies on two important topics: “Information Theory” and “Lower Bounds”. It begins by describing the importance of lower bounds for data compression and generating randomness. You will study the process of a precise depiction of information by excluding redundancy using Shannon's source coding theorem. Following this, the implication of the strong converse theorem for discrete memoryless channels is explained. You will explore the procedure of establishing a threshold between perfectly reliable and completely unreliable communication. In addition to this, the process of determining the reliability functions for the source coding with a fidelity criterion at lower rates by establishing a strong converse is discussed. The applications of round elimination lemma including the proof of information theory and other direct sum theorems and conjecture towards lower bounds are highlighted. The course explores various data structure lower bounds based on communication complexity for classifying the various tasks of estimation and optimization problems.

Finally, the course illustrates the lower bounds for the minmax risk in general decision-theoretic problems. You will discover the role of minimax redundancy in acting as a lower bound for the majority of the sources. This will comprise of the techniques used for bounding the minmax risk of a statistical problem, including the Markov and Fano methods. Following this, you will study the methods for deriving lower bounds based on the integration of various contrasting notions from diverse fields and problems. This will include the procedure for determining the appropriate method for a specified problem. Lastly, the course describes the efficiency of applying these lower bounds to a wide range of statistical estimation problems. Lower bounds are the solution, to the problems that are very difficult to solve or one is too dumb to come up with a better solution. ‘Lower Bounds Using Information Theory Tools’ is an informative course that portrays the current landscape in constructing lower bounds using the frameworks of information theory. Enrol in this course now and learn the techniques and principles of lower bounds in finding the shortest solution to a given task.

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