Measurements of information are widely used in artificial intelligence and machine learning, such as in the construction of decision trees and the optimization of classifier models.
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RSS, Privacy | Calculate the Entropy for a Random Variable, H(X) = -sum(each k in K p(k) * log(p(k))).
Brains are the ultimate compression and communication systems. Recall that entropy is the number of bits required to represent a randomly drawn even from the distribution, e.g. Calculate the Entropy for a Random Variable
The less frequent tails are the greater the price you’re willing to pay to mark the tail event – because the longer that marker is, the cheaper it is to describe run length (easier to avoid the magic multi-bit code that marked the tail event). Secondly, for your argument: I admit I skimmed the later chapters dealing with noise, and skipped the chapters on language and music entirely. I think the weighted coin example is kind of confusing because the coin still only has two states. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. Another pioneer was Nyquist’s colleague R.V.L. the scope of values it could have when transmitted on a communication channel.
— Page v, Information Theory, Inference, and Learning Algorithms, 2003. I was wondering if you could elaborate more on the usage of entropy value with real time examples. Intriguing, so I bought the book, and really liked it. A key question that had to be answered in the early days of telecommunication was how best to maximize the physical plant—in particular, how to transmit the maximum number of telephone conversations over existing cables.
Is there any advantages/reason to calculate entropy using the base-2 logarithm VS natural logarithm? Information theory, a mathematical representation of the conditions and parameters affecting the transmission and processing of information. I had a course in Digital Communications and Signal Processing at the University of Michigan, where Shannon did his undergraduate work, and was looking for a clear and coherent refresher on what I learned there.
Reviewed in the United States on January 27, 2016. no latex).
Welcome! It is related to the idea of entropy from physics by analogy, in that both are concerned with uncertainty.
Each outcome has the same probability of 1/6, therefore it is a uniform probability distribution. Let’s make this concrete with some examples. INTRODUCTION Information Theory is one of the few scientific fields fortunate enough to have an identifiable beginning - Claude Shannon's 1948 paper.
Do you have any questions? Calculating information and entropy is a useful tool in machine learning and is used as the basis for techniques such as feature selection, building decision trees, and, more generally, fitting classification models. The author made a halfhearted attempt to update it in the early days of the digital revolution, but these touch-ups were superficial, and devoid of imagination. The formal study of information theory did not begin until 1924, when Harry Nyquist, a researcher at Bell Laboratories, published a paper entitled “Certain Factors Affecting Telegraph Speed.” Nyquist realized that communication channels had maximum data transmission rates, and he derived a formula for calculating these rates in finite bandwidth noiseless channels. I think I’m suffering from the same conceptual barrier that Evgenii is and, even with your reply, I’m still stuck. I have been working my way slowly through this book, as it reads like a typical non-fiction STEM text. Information is an idea of how well we can compress events from a distribution.
Articles from Britannica Encyclopedias for elementary and high school students. Consider a flip of a single fair coin. the information in rolling a 6.
Base-2 lets you use the units of “bits”, the most common usage. The intuition behind quantifying information is the idea of measuring how much surprise there is in an event. A cornerstone of information theory is the idea of quantifying how much information there is in a message. Reviewed in the United States on April 27, 2013. The author explains things well, and uses examples from other areas of physics to explain difficult topics like entropy.
Running the example creates the 6 probability distributions with [0,1] probability through to [0.5,0.5] probabilities. Contact |
Much of their work was done using Fourier analysis, a technique described later in this article, but in all of these cases the analysis was dedicated to solving the practical engineering problems of communication systems. Quantifying information is the foundation of the field of information theory. I got this on a whim (Dover books are cheap) as I was starting an Information Theory Course. If there is more or less surprise, we need more information to encode the variable – e.g. Ltd. All Rights Reserved.
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