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Topic: Conditional entropy

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	ONLamp.com -- Calculating Entropy for Data Miners
		The specific conditional entropy formula computes the amount of uncertainty remaining after performing conditioning on one value of the signal distribution, whereas the conditional entropy is the amount of uncertainty remaining after summing the products of specific signal probabilities and specific conditional entropies.
		The specific conditional entropy column can be useful to examine in some detail, because low values are telling you that there is an uncertainty-reducing relationship between levels of your variables.
		The specific entropy value in the fifth column is then multiplied by the corresponding probability in the second column to obtain the values in the sixth column.
	www.onlamp.com /pub/a/php/2005/03/24/joint_entropy.html?page=3 (843 words)

	IngentaConnect Conditional entropy as an indicator of pleomorphism in astrocytic... (Site not responding. Last check: )
		IngentaConnect Conditional entropy as an indicator of pleomorphism in astrocytic...
		Conditional entropy as an indicator of pleomorphism in astrocytic tumors
		Thus, conditional entropy of nuclear arrangement is useful for grading of astrocytic tumors and it is proposed as an indicator of pleomorphism.
	www.ingentaconnect.com /content/bsc/neu/2004/00000024/00000003/art00003 (330 words)

	Conditional Entropy
		Conditional entropy and hit rate are used as measures of correspondence of the test data with the reference dictionary.
		The performance of existing data compression algorithms is often used as a rough estimate of the entropy of a block of data.
		For strings of length 7, the maximum entropy of 29.76 is twice the observed entropy.
	mcs.une.edu.au /~cwatson7/I/ConditionalEntropy.html (1471 words)

	Voynich MS - Analysis Section - Introduction
		The entropy of the language of the Voynich MS was first studied by Bennett (1976), and when he found rather anomalous values for the Voynich MS text, compared with most European languages (old and new), this became one of the main topics for subsequent investigations.
		Entropy is a quantity that could be interpreted as amount of 'chaos' or unpredictability, in the sense that lower values of entropy are equivalent with higher amounts of order or predictability.
		It can be shown mathematically that the conditional single-character entropy (the entropy of the probability distribution of a single character, given that the preceding one is known) equals the difference between the character pair (=digraph) entropy and the single character entropy.
	www.voynich.nu /a_intro.html (1986 words)

	4. Entropy
		Entropy is an important concept in many fields, and one field where it is extensively used is QKG.
		Entropy is a measure of uncertainty regarding a discrete random variable.
		That is, the guessing entropy is simply the average number of guesses needed to guess the value of a random variable using the optimal strategy.
	www.lysator.liu.se /~jc/mthesis/4_Entropy.html (1458 words)

	PlanetMath: conditional entropy
		The results for discrete conditional entropy will be assumed to hold for the continuous case unless we indicate otherwise.
		Cross-references: interpretation, inequalities, equalities, function, joint entropy, continuous, conditional probability, discrete random variables, probability space
		This is version 6 of conditional entropy, born on 2002-02-21, modified 2006-10-30.
	planetmath.org /encyclopedia/ConditionalEntropy.html (89 words)

	Dr. Dobb's \| Security & PseudoRandom Number Generators \| February 2, 2004
		It's enough that attackers cannot, by brute force, deduce the original entropy (cryptographers tend to use the term "entropy" to mean the actual random data, as well as a measure of its randomness), by comparing output from the PRNG with candidate values of the entropy with the output as observed from the actual PRNG.
		The entropy a data source has given to any knowledge the adversary has (or might have) is known as "conditional entropy," and the entropy ignoring any such knowledge, I call (to avoid confusion) "unconditional entropy." For instance, the entropy of a data source X is written H(X).
		Therefore, I use "unconditional entropy" to mean the amount of entropy a data source has, ignoring any access attackers may have to it; and "conditional entropy" to mean the amount it has given an attacker's potential knowledge.
	www.ddj.com /184405584 (2118 words)

	Science Fair Projects - Conditional entropy
		The conditional entropy is an entropy measure used in information theory.
		The conditional entropy measures how much entropy a random variable Y has remaining if we have already learned completely the value of a second random variable X.
		In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Conditional_entropy (334 words)

	ONLamp.com -- Calculating Entropy for Data Miners
		The main difference is that the joint entropy formula has two summation signs instead of one, and the probability distribution being summed over is a joint probability distribution instead of a univariate probability distribution.
		The calculation of the joint entropy score is the same as the calculation of the univariate entropy score.
		The joint entropy score thus signifies the minimum number of questions you need to ask, on average, to identify a signal coming from this bivariate distribution of signals.
	www.onlamp.com /pub/a/php/2005/03/24/joint_entropy.html (601 words)

	PUBLICATIONS (Site not responding. Last check: )
		Bayesian rule is utilized to estimate the conditional probabilities of VQ indexes based on causal context in order to drive the arithmetic entropy coder, and the compression performance of this method can compare with the best VQ performance we have known.
		Based on such context, the conditional probabilities of VQ indexes can be estimated so good that the compression gains of this method are 10% higher than Address VQ(A-VQ), which first used lossless idea to code VQ index, with the same compression distortion and a tiny fraction of A-VQ's computational cost are needed.
		Based on the encouraging results from conditional entropy coding of VQ index, we tailor this idea to medical images by refining the context modeling for a given class of medical images.
	www-mddsp.enel.ucalgary.ca /People/jiang/publications.html (439 words)

	Conditional entropy
		The conditional entropy is an entropy measure used in information theory.
		The conditional entropy measures how much entropy a random variable Y has remaining if we have already learned completely the value of a second random variable X.
		In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy.
	www.askfactmaster.com /Conditional_entropy (178 words)

	ANSDIT - The letter "C" (Site not responding. Last check: )
		The mean value of the conditional information content of the events in a finite set of mutually exclusive and jointly exhaustive events, given the occurrence of the events in another set of mutually exclusive and jointly exhaustive events; in mathematical notation, this measure is
		A register in which bits are set according to specified conditions that occur during the execution of instructions.
		One of a number of subproblems or conditions of a conjunction, all of which are required to be satisfied in order for the conjunction as a whole to be satisfied.
	www.ncits.org /tc_home/k5htm/c4.htm (2104 words)

	[No title] (Site not responding. Last check: )
		Entropy is defined as the degree of uncertainty.
		The principle of maximum entropy encourages one to choose the model with the "maximum entropy" from among those that are consistent with the constraints.
		Maximizing the entropy of the model is a useful metric for ensuring that--selected distinctive features notwithstanding--the model is as unbiased as possible with regards to the observed data.
	www.cs.wisc.edu /~apirak/cs/cs838/reviews_score_7.html (6578 words)

	Detecting Anomalies in Network Traffic Using Maximum Entropy Estimation
		By computing a measure related to the relative entropy of the network traffic under observation with respect to the baseline distribution, we are able to distinguish anomalies that change the traffic either abruptly or slowly.
		The relative entropy of the packet classes in the observed traffic trace with respect to the baseline distribution is computed.
		Maximum Entropy estimation is a framework for obtaining a parametric probability distribution model from the training data and a set of constraints on the model.
	www.usenix.org /events/imc05/tech/full_papers/gu/gu_html/re.html (3410 words)

	Computer Laboratory - Information Theory and Coding
		Marginal entropy, joint entropy, conditional entropy, and the Chain Rule for entropy.
		Extensions of the discrete entropies and measures to the continuous case.
		Definition of the algorithmic complexity of a data sequence, and its relation to the entropy of the distribution from which the data was drawn.
	www.cl.cam.ac.uk /Teaching/current/InfoTheory (477 words)

	Direct method
		is the conditional entropy of the output given the inputs.
		From the conditional distribution, the conditional entropy in response to this particular input ensemble is computed as
		The average conditional entropy per spike is calculated by repeating this procedure for a large (ideally, infinite) number of input patterns
	www.cnl.salk.edu /~zador/MI-final/node10.html (744 words)

	Dr. Dobb's \| Classifying Text with ID3 and C4.5 \| July 22, 2001
		Entropy is used to construct a decision tree, which is then used for testing future cases.
		If you partition data in some meaningful way, the total entropy of the parts will be lower than the entropy of the set you started with.
		The conditional entropy is then defined in Figure 1(b).
	www.ddj.com /184410304 (2845 words)

	Entropy in Information and Coding Theory
		His ideas created a sensation and were rapidly developed along two main lines of development: information theory, which employs probability and ergodic theory to study the statistical characteristics of data and communication systems, and coding theory, which uses mainly algebraic and geometric tools to contrive efficient codes for various situations.
		Typical Sequences and All That: Entropy, Pattern Matching, and Data Compression, the 1994 Shannon Lecture by the late Aaron D. Wyner (formerly of the Mathematics of Communication Department, Bell Labs).
		Focuses on the contrast between the traditional interpretation of the entropy of a stationary ergodic source in terms of the number of typical sequences of a given length and the interpretation in terms of the recurrence of blocks of symbols ("patterns") in a single typical sequence.
	www.math.uni-hamburg.de /home/gunesch/Entropy/infcode.html (1024 words)

	Entropy.html
		Then the entropy of this probability distribution is defined to be the quantity
		Let the conditional entropy H(XY) be defined to be the weighted average (with respect to the probabilities p(y)) of the entropies H(Xy) over all possible values y.
		This means that, if you assume class conditional independence, you gain greater information by computing the information of the feature vector than by computing the information of the individual features.
	cgm.cs.mcgill.ca /~soss/cs644/projects/simon/Entropy.html (564 words)

	Information rate depends on firing rate
		Here as elsewhere, the exact sequence of action potentials arriving at each of the presynaptic terminals is the ``signal'', and any variability response to repeated trials on which precisely the same sequence is presented represents the ``noise''.
		If there were no quantal variability, the conditional entropy would be zero, and all the entropy would be information.
		The behavior of the total entropy per spike at low firing rates can be understood in terms of the results for the limiting case of a Poisson model outlined in Section 2.6.
	www.cnl.salk.edu /~zador/MI-final/node15.html (673 words)

	Entropy of FDI for Redundant Structures
		The mean conditional entropy of the error function H(e S) is defined as the uncertainty of the error for a given state averaged over all possible states of the structure.
		The entropy of the system state set H(S t) is formulated directly from Shannon's equation for discrete events (Equation 5) and exhibits a characteristic, "humped" curve (Figure 2).
		For the majority of the mission, the mean conditional entropy is found to increase with additional levels of redundancy because of the corrupting effect of any single controller failure to the estimation algorithm.
	www.ececs.uc.edu /~vhunt/journal2.htm (4142 words)

	Shannon's Entropy
		The conditional entropy of a variable Y knowing variable X is defined as the average of the entropies of Y for each value
		The conditional entropy expresses how uncertain we are of Y the average when we know X (which could be any of the values
		The lower the entropy (uncertainty) the more structure is already given in the relation.
	www-lehre.informatik.uni-osnabrueck.de /~ftprang/papers/tproject/node10.html (408 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		The measure of data, known as information entropy, is usually expressed by the average number of bits needed for storage or communication.
		The most important quantities of information are entropy, the information in a random variable, and mutual information, the amount of information in common between two random variables.
		Because entropy can be conditioned on a random variable or on that random variable being a certain value, care should be taken not to confuse these two definitions of conditional entropy, the former of which is in more common use.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=information_theory (3005 words)

	Information theory
		For the random variables x and y from the sets X and J respectively, the joint entropy is defined for the continuous case as:
		Joint entropy is a measure of overall uncertainty of a set of variables.
		Taking the entropy of a random vector as H(x) we mean the joint entropy between all of the vector elements.
	www.infomationtheory.org /condentropy.html (102 words)

	Relationships with other entropies
		The relationship between conditional entropy and the other types of entropy is as follows:
		Conditional entropy of Y given X is the joint entropy of X and Y minus the entropy of X; in other words, it is the difference between the information of X and Y, and the information brought by X. This is clearly the meaning of this type of entropy, a reduction of uncertainty.
		Conditioning on a variable or the other does not give the same result.
	tecfa.unige.ch /~lemay/thesis/THX-Doctorat/node156.html (148 words)

	CiteULike: Question on Conditional Entropy
		The problems of conditional entropy's definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented.
		Examples are given to prove the conclusion that conditional entropy never be increased is not absolute, thus the representation that information is to decrease uncertainty in the definition of information is not absolutely correct.
		@misc{citeulike:1587549, abstract = {The problems of conditional entropy's definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented.
	www.citeulike.org /user/ansobol/article/1587549 (122 words)

	Information Theory
		Entropy = the smallest possible number of bits needed to encode X's distribution.
		The uncertainty in X given knowledge of Y. Higher conditional entropy means more knowledge about the state of X given Y. Information Gain
		Maximizing mutual information is often equivalent to minimizing conditional entropy.
	www.stanford.edu /~maureenh/quals/html/ml/node22.html (110 words)

	Definition of Entropy and related functions
		The entropy is a measure of the information content or `uncertainty' of x.
		The question of why entropy is a fundamental measure of information content will be discussed in the forthcoming chapters.
		The joint entropy, conditional entropy and marginal entropy are related by:
	www.cs.toronto.edu /~mackay/itprnn/l1/node23.html (230 words)

	Assgn 1 / NLP (Site not responding. Last check: )
		An application has been prepared to make this a bit of fun, too: this application will calculate the entropy of the sequence of numbers S generated as you try and guess the next letter given a sequence of N letters that come immediately before it in a chosen text.
		Since there is some randomness to the outcome of the experiment, run the experiment 10 times, each time measuring the conditional entropy of the resulting text, and give the min, max, and average entropy from these experiments.
		Will the conditional entropy of this new text be greater than, equal to, or less than E? Explain.
	www.cs.jhu.edu /~hajic/courses/cs465/assign1.html (1317 words)

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