Lower Bounds Using Information Theory Tools

The implication of contemporary research is about finding answers to real-life problems. Nevertheless, the primary focus of this research aims to comprehend the impossible. The core outcomes of impossibility are the portrayals of principal limits, spot unreasonable targets, giving optimality assurances to helpful systems and perceiving bottlenecks in issue details that may call for development. 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 to determine the optimal solution in optimisation and how much memory is required to learn 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 to derive 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’. First, it describes 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, we explain the implication of the strong converse theorem for discrete memoryless channels. Then, you will explore the procedure of establishing a threshold between perfectly reliable and completely unreliable communication. Next, investigate the process of determining the reliability functions for the source coding with a fidelity criterion at lower rates by establishing a strong converse. The applications of round elimination lemma, including the proof of information theory and other direct sum theorems and conjectures towards lower bounds, are highlighted. The course explores various data structure lower bounds based on communication complexity for classifying the various estimation and optimisation problems tasks.

Finally, the course illustrates the lower bounds for the minimax 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 the techniques used to bind the minimax risk of a statistical problem, including the Markov and Fano methods. Following this, you will study the methods for deriving lower bounds based on integrating 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 complicated problems. ‘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 and learn the techniques and principles of lower bounds in finding the shortest solution to a given task.