Inductive probabilityInductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem.
Binary entropy functionIn information theory, the binary entropy function, denoted or , is defined as the entropy of a Bernoulli process with probability of one of two values. It is a special case of , the entropy function. Mathematically, the Bernoulli trial is modelled as a random variable that can take on only two values: 0 and 1, which are mutually exclusive and exhaustive. If , then and the entropy of (in shannons) is given by where is taken to be 0. The logarithms in this formula are usually taken (as shown in the graph) to the base 2.
Information engineering (field)_Information engineering Information engineering is the engineering discipline that deals with the generation, distribution, analysis, and use of information, data, and knowledge in systems. The field first became identifiable in the early 21st century. The components of information engineering include more theoretical fields such as machine learning, artificial intelligence, control theory, signal processing, and information theory, and more applied fields such as computer vision, natural language processing, bioinformatics, , cheminformatics, autonomous robotics, mobile robotics, and telecommunications.
Maxwell's demonMaxwell's demon is a thought experiment that would hypothetically violate the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867. In his first letter, Maxwell referred to the entity as a "finite being" or a "being who can play a game of skill with the molecules". Lord Kelvin would later call it a "demon". In the thought experiment, a demon controls a small massless door between two chambers of gas.
Hartley (unit)The hartley (symbol Hart), also called a ban, or a dit (short for decimal digit), is a logarithmic unit that measures information or entropy, based on base 10 logarithms and powers of 10. One hartley is the information content of an event if the probability of that event occurring is . It is therefore equal to the information contained in one decimal digit (or dit), assuming a priori equiprobability of each possible value. It is named after Ralph Hartley.
Rényi entropyIn information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is important in ecology and statistics as index of diversity.
Cross-entropyIn information theory, the cross-entropy between two probability distributions and over the same underlying set of events measures the average number of bits needed to identify an event drawn from the set if a coding scheme used for the set is optimized for an estimated probability distribution , rather than the true distribution . The cross-entropy of the distribution relative to a distribution over a given set is defined as follows: where is the expected value operator with respect to the distribution .
Error exponentIn information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiting ratio of the negative logarithm of the error probability to the block length of the code for large block lengths. For example, if the probability of error of a decoder drops as , where is the block length, the error exponent is . In this example, approaches for large .
A Mathematical Theory of Communication"A Mathematical Theory of Communication" is an article by mathematician Claude E. Shannon published in Bell System Technical Journal in 1948. It was renamed The Mathematical Theory of Communication in the 1949 book of the same name, a small but significant title change after realizing the generality of this work. It has tens of thousands of citations which is rare for a scientific article and gave rise to the field of information theory. The article was the founding work of the field of information theory.
