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Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
The information gain in decision trees (,), which is equal to the difference between the entropy of and the conditional entropy of given , quantifies the expected information, or the reduction in entropy, from additionally knowing the value of an attribute . The information gain is used to identify which attributes of the dataset provide the ...
An information diagram is a type of Venn diagram used in information theory to illustrate relationships among Shannon's basic measures of information: entropy, joint entropy, conditional entropy and mutual information. [1] [2] Information
The Gaussian or normal probability distribution plays an important role in the relationship between variance and entropy: it is a problem of the calculus of variations to show that this distribution maximizes entropy for a given variance, and at the same time minimizes the variance for a given entropy.
The expected value of the information gain is the mutual information (;) of and – i.e. the reduction in the entropy of achieved by learning the state of the random variable . In machine learning, this concept can be used to define a preferred sequence of attributes to investigate to most rapidly narrow down the state of X .
A great many important inequalities in information theory are actually lower bounds for the Kullback–Leibler divergence.Even the Shannon-type inequalities can be considered part of this category, since the interaction information can be expressed as the Kullback–Leibler divergence of the joint distribution with respect to the product of the marginals, and thus these inequalities can be ...
To do this, one must acknowledge the difference between the measured entropy of a system—which depends only on its macrostate (its volume, temperature etc.)—and its information entropy, [6] which is the amount of information (number of computer bits) needed to describe the exact microstate of the system.
The health informatics section in the Hospital Authority [100] has a close relationship with the information technology department and clinicians to develop health care systems for the organization to support the service to all public hospitals and clinics in the region.