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Information theory
particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random
Conditional mutual information
Conditional_mutual_information
Measure of dependence between two variables
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two
Mutual_information
Measure of relative information in probability theory
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable Y {\displaystyle
Conditional_entropy
Scientific study of digital information
generalization of quantities of information to continuous distributions), and the conditional mutual information. Also, pragmatic information has been proposed as
Information_theory
Process in machine learning and statistics
)}{\bigr ]}\end{aligned}}} The score uses the conditional mutual information and the mutual information to estimate the redundancy between the already
Feature_selection
Non-parametric statistic on information transfer
entropy measures such as Rényi entropy. Transfer entropy is conditional mutual information, with the history of the influenced variable Y t − 1 : t − L
Transfer_entropy
Average uncertainty in variable's states
Redundancy (information theory). The characterization here imposes an additive property with respect to a partition of a set. Meanwhile, the conditional probability
Entropy_(information_theory)
Concept in information processing
Z {\displaystyle Z} are conditionally independent, given Y {\displaystyle Y} , which means the conditional mutual information, I ( X ; Z ∣ Y ) = 0 {\displaystyle
Data_processing_inequality
Generalization of mutual information for more than two variables
interpretation in algebraic topology. The conditional mutual information can be used to inductively define the interaction information for any finite number of variables
Interaction_information
Venn diagram to illustrate relationship
measures of information: entropy, joint entropy, conditional entropy and mutual information. Information diagrams are a useful pedagogical tool for teaching
Information_diagram
of the information content of random variables and a measure over sets. Namely the joint entropy, conditional entropy, and mutual information can be considered
Information theory and measure theory
Information_theory_and_measure_theory
Concept in information theory
expressed as special cases of a single inequality involving the conditional mutual information, namely I ( A ; B | C ) ≥ 0 , {\displaystyle I(A;B|C)\geq 0
Inequalities in information theory
Inequalities_in_information_theory
Information-theoretic measure
method Logistic regression Conditional entropy Kullback–Leibler divergence Maximum-likelihood estimation Mutual information Perplexity Thomas M. Cover
Cross-entropy
Time density of the average information in a stochastic process
to infinity. The n {\displaystyle n} th entropy change is itself the conditional entropy H ( X n | X n − 1 , X n − 2 , . . . ) {\displaystyle H(X_{n}|X_{n-1}
Entropy_rate
i | Y i − 1 ) {\displaystyle I(X^{i};Y_{i}|Y^{i-1})} is the conditional mutual information I ( X 1 , X 2 , . . . , X i ; Y i | Y 1 , Y 2 , . . . , Y i
Directed_information
Probability of an event occurring, given that another event has already occurred
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption
Conditional_probability
The differential analogies of entropy, joint entropy, conditional entropy, and mutual information are defined as follows: h ( X ) = − ∫ X f ( x ) log
Quantities_of_information
Information-theoretical limit on transmission rate in a communication channel
of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the maximization
Channel_capacity
( A : B | Λ ) {\displaystyle S(A:B|\Lambda )} , the quantum Conditional Mutual Information (CMI), below. A more general version of Eq.(1) replaces the
Squashed_entanglement
Theorem that tells the maximum rate at which information can be transmitted
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified
Shannon–Hartley_theorem
Distributed source coding concept
In information theory and communication, the Slepian–Wolf coding, also known as the Slepian–Wolf bound, is a result in distributed source coding discovered
Slepian–Wolf_coding
Measure of information in probability and information theory
(X)+\mathrm {H} (Y|X)} . Joint entropy is also used in the definition of mutual information I ( X ; Y ) = H ( X ) + H ( Y ) − H ( X , Y ) {\displaystyle \operatorname
Joint_entropy
Gain from observing another random variable
the context of decision trees in information theory and machine learning, information gain refers to the conditional expected value of the Kullback–Leibler
Information gain (decision tree)
Information_gain_(decision_tree)
Establishes the limits to possible data compression
In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for
Shannon's source coding theorem
Shannon's_source_coding_theorem
Theory about lossy data compression
{\displaystyle X} , and I Q ( Y ; X ) {\displaystyle I_{Q}(Y;X)} is the mutual information between Y {\displaystyle Y} and X {\displaystyle X} defined as I (
Rate–distortion_theory
Notion in information theory
In information theory, the limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy. It was formulated
Limiting density of discrete points
Limiting_density_of_discrete_points
Mathematical statistics distance measure
0{\text{.}}} Another information-theoretic metric is variation of information, which is roughly a symmetrization of conditional entropy. It is a metric
Kullback–Leibler_divergence
Concept in information theory
significance as a measure of discrete information since it is actually the limit of the discrete mutual information of partitions of X {\displaystyle X}
Differential_entropy
package for computing all information distances and volumes, multivariate mutual information, conditional mutual information, joint entropies, total correlations
Information_distance
Topic in mathematics
{\displaystyle I_{P}:=-\ln \mu (P(x))} Similarly, the conditional information of partition P {\textstyle P} , conditional on partition Q {\textstyle Q} , about x {\textstyle
Asymptotic equipartition property
Asymptotic_equipartition_property
Relationship of various quantum subsystems
classical intuition, except that quantum conditional entropies can be negative, and quantum mutual informations can exceed the classical bound of the marginal
Strong subadditivity of quantum entropy
Strong_subadditivity_of_quantum_entropy
profiles of candidate RNAs and their common miRNA regulators using conditional mutual information. software (MATLAB) Linc2GO a human LincRNA function annotation
CeRNA_database
X_{2})\leq H(X_{1})+H(X_{2})} Other information-theoretic measures such as conditional information, mutual information, or total correlation can be expressed
Entropic_vector
State-dependent measures that converge to the mutual information
state-dependent measures that in expectation converge to the mutual information. State-dependent informations often appear in neuroscience applications. Let X {\displaystyle
State-dependent_information
When the occurrence of one event does not affect the likelihood of another
if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking
Independence (probability theory)
Independence_(probability_theory)
Complexity of sending information in a distributed algorithm
;Y|X)+I(\Pi ;X|Y),} where I denotes conditional mutual information. The first summand measures the amount of information that Alice learns about Bob's input
Communication_complexity
Measure of distance between two clusterings related to mutual information
closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the
Variation_of_information
Theorem in probability theory
expresses the variance of a random variable Y in terms of its conditional variances and conditional means given another random variable X. Informally, it states
Law_of_total_variance
Problem in information theory and communication
important problem in information theory and communication. DSC problems regard the compression of multiple correlated information sources that do not communicate
Distributed_source_coding
Number measuring the chance an event occurs
number of events. Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written
Probability
Probability theory concept
hypothesis. It is the opposite of conditional dependence. Conditional independence is usually formulated in terms of conditional probability, as a special case
Conditional_independence
Randomly determined process
actuarial science, image processing, signal processing, computer science, information theory, telecommunications, chemistry, ecology, neuroscience, physics
Stochastic
in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information. It is also known
Total_correlation
Concept in probability theory
are mutually dependent conditional on C . {\displaystyle C.} Conditional independence – Probability theory concept de Finetti's theorem – Conditional independence
Conditional_dependence
Measure of nonclassical correlations between two subsystems of a quantum system
mathematical terms, quantum discord is defined in terms of the quantum mutual information. More specifically, quantum discord is the difference between two
Quantum_discord
Notion in statistics
Fisher information represents the curvature of the relative entropy of a conditional distribution with respect to its parameters. The Fisher information was
Fisher_information
Table in statistics
statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities
Conditional_probability_table
Probability theory term
available information. This idea is formalized in probability theory by conditioning. Conditional probabilities, conditional expectations, and conditional probability
Conditioning_(probability)
Technique in information theory
condition to capture some fraction of the mutual information with the relevant variable Y. The information bottleneck can also be viewed as a rate distortion
Information_bottleneck_method
British mutual insurance company
Farmers Union Mutual Insurance Society Ltd (CL-2024-000309) came to court it was filed with an initial 37 claimants under a conditional fee arrangement
NFU_Mutual
Type of probability distribution
other variables, and the conditional probability distribution giving the probabilities for any subset of the variables conditional on particular values of
Joint probability distribution
Joint_probability_distribution
Mathematical concept
definition of probability spaces gives rise to the natural concept of conditional probability. Every set A with non-zero probability (that is, P(A) > 0)
Probability_space
Measure of dependence
information is one of several known non-negative generalizations of mutual information. While total correlation is bounded by the sum entropies of the n
Dual_total_correlation
probability Probability-generating function Vysochanskiï–Petunin inequality Mutual information Kullback–Leibler divergence Le Cam's theorem Large deviations theory
List_of_probability_topics
Measure of algorithmic complexity
be thought of as the minimal amount of information necessary to produce x {\displaystyle x} , the conditional Kolmogorov complexity K ( x | y ) {\displaystyle
Kolmogorov_complexity
Eastern European military alliance (1955–1991)
The Warsaw Pact (WP), formally the Treaty of Friendship, Cooperation and Mutual Assistance (TFCMA), was a collective defence treaty signed in Warsaw, Poland
Warsaw_Pact
Two propositions or events that cannot both be true
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example
Mutual_exclusivity
expression makes clear that the uncertainty coefficient is a normalised mutual information I(X;Y). In particular, the uncertainty coefficient ranges in [0, 1]
Uncertainty_coefficient
Mathematical rule for inverting probabilities
after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities, allowing the probability of a cause to be found given
Bayes'_theorem
Anarchist school of thought and socialist economic theory
Mutualism is an anarchist school of thought and economic theory that advocates for workers' control of the means of production, a free market made up
Mutualism_(economic_theory)
Concept in information theory
{\displaystyle \alpha =1} quantities allow the definition of conditional information and mutual information from communication theory. The Rényi entropies and divergences
Rényi_entropy
American indie pop band
Conditionally, was released on March 5, 2017, on the band's own label, Mutually Detrimental. Record club Vinyl Me, Please chose Yours Conditionally as
Tennis_(band)
Diagram to represent a probability space in probability theory
represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the
Tree diagram (probability theory)
Tree_diagram_(probability_theory)
Monte Carlo algorithm
mutual information, posterior differential entropy, and posterior conditional differential entropy, respectively. We can similarly define information
Gibbs_sampling
Measure of "category goodness"
to the information gain metric used in decision tree learning. In certain presentations, it is also formally equivalent to the mutual information, as discussed
Category_utility
where I ( X i ; X j ( i ) ) {\displaystyle I(X_{i};X_{j(i)})} is the mutual information between variable X i {\displaystyle X_{i}} and its parent X j ( i
Chow–Liu_tree
Set of all possible outcomes or results of a statistical trial or experiment
meet some conditions in order to be a sample space: The outcomes must be mutually exclusive, i.e. if s j {\displaystyle s_{j}} occurs, then no other s i
Sample_space
Graphical tool in probability
vine is a special case for which all constraints are two-dimensional or conditional two-dimensional. Regular vines generalize trees, and are themselves specializations
Vine_copula
Probability distribution modeling a coin toss which need not be fair
{\displaystyle p=1} , where one outcome is certain. Fisher information measures the amount of information that an observable random variable X {\displaystyle
Bernoulli_distribution
West Slavic language
Czech Republic. Czech is closely related to Slovak, to the point of high mutual intelligibility, as well as to Polish to a lesser degree. Czech is a fusional
Czech_language
Estimate of the importance of a word in a document
Latent semantic analysis Mutual information Noun phrase Okapi BM25 PageRank Vector space model Word count SMART Information Retrieval System Rajaraman
Tf–idf
Stochastic process with discrete movements
Complementary event Joint probability Marginal probability Conditional probability Independence Conditional independence Law of total probability Law of large
Jump_process
Concurrent programming algorithm for mutual exclusion
algorithm (or Peterson's solution) is a concurrent programming algorithm for mutual exclusion that allows two or more processes to share a single-use resource
Peterson's_algorithm
Philosophical concept
system cannot be predicted, the problem is due to lack of fine-grained information, so that a sufficiently detailed investigation would eventually result
Indeterminism
Compiler that processes each compilation unit only once
(B) THEN ! start conditional block IF (B) THEN = 3.1 ! conditional assignment to variable THEN IF (B) X = 10 ! single conditional statement IF (B) GOTO
One-pass_compiler
How one process influences another
future"), if the information that A occurred increases the likelihood of B's occurrence. Formally, P{B|A}≥ P{B} where P{B|A} is the conditional probability
Causality
Generalization of the one-dimensional normal distribution to higher dimensions
Retrieved 2020-08-12. Proof: Mutual information of the multivariate normal distribution MacKay, David J. C. (2003-10-06). Information Theory, Inference and Learning
Multivariate normal distribution
Multivariate_normal_distribution
Aspect of probability and statistics
reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values
Marginal_distribution
Person's assent to the reality of a situation
the initial conditions before the final acceptance is made, is called conditional acceptance, or qualified acceptance. For instance, in a contract involving
Acceptance
Probabilistic graphical representation of causal relationships
probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several
Bayesian_network
Event that contains only one outcome
Complementary event Joint probability Marginal probability Conditional probability Independence Conditional independence Law of total probability Law of large
Elementary_event
Assumed context surrounding an utterance
presupposes Hans exists. A presupposition is information that is linguistically presented as being mutually known or assumed by the speaker and addressee
Presupposition
Probabilistic classification algorithm
that the features are conditionally independent, given the target class. In other words, a naive Bayes model assumes the information about the class provided
Naive_Bayes_classifier
Borel–Kolmogorov paradox / iex (2:CM) Conditional expectation / (2:BDR) Conditional independence / (3F:BR) Conditional probability Conditional probability distribution /
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Machine learning algorithm
expected information gain is the mutual information, meaning that on average, the reduction in the entropy of T is the mutual information. Information gain
Decision_tree_learning
Lower bound for size of software program
logarithmic factor. The results implies that algorithmic mutual information, an analogue of mutual information for Kolmogorov complexity is symmetric: I ( x
Chain rule for Kolmogorov complexity
Chain_rule_for_Kolmogorov_complexity
Statistics concept
\wedge \pi \right)\end{aligned}}} Conditional independence hypotheses then allow further simplifications. A conditional independence hypothesis for variable
Bayesian_programming
Random process independent of past history
that could be made knowing the process's full history. In other words, conditional on the present state of the system, its future and past states are independent
Markov_chain
Policy on permits required to enter Morocco
of the following countries and regions cannot apply for a regular and conditional e-Visa: Transit through Morocco is divided into two categories: airside
Visa_policy_of_Morocco
Cue validity is the conditional probability that an object falls in a particular category given a particular feature or cue. The term was popularized
Cue_validity
Fictional character from The Blacklist
terrorists, many of whom are unknown to law enforcement. His cooperation is conditional on working exclusively with newly appointed FBI profiler Elizabeth Keen
Raymond_Reddington
Early programming language for lists
push/pop the symbol in S to the list attached to S; copy value to S; conditional branch. In these instructions, S is the target. S is either the value
Information Processing Language
Information_Processing_Language
of these trades twice. Hover over retained salary or conditional transactions for more information. Once an NHL player has played in a certain number of
2023–24_NHL_transactions
Ongoing armed conflict in West Asia
be included as part of a ceasefire deal, thereby making a ceasefire conditional on an end to the 2026 Lebanon war against Hezbollah. On 24 March, Israel
2026_Iran_war
Subfield of information theory and computer science
"Algorithmic Information Theory". Archived from the original on January 23, 2016. Retrieved May 3, 2010. or, for the mutual algorithmic information, informing
Algorithmic information theory
Algorithmic_information_theory
of these trades twice. Hover over retained salary or conditional transactions for more information. Once an NHL player has played in a certain number of
2021–22_NHL_transactions
Belgian physicist
Quantum Information and Communication at the Université libre de Bruxelles. Together with Christoph Adami, he defined the quantum version of conditional and
Nicolas_J._Cerf
Regulation of the European Union and Euratom
The Rule of Law Conditionality Regulation is a regulation of the European Union and Euratom, which allows the European Commission to adopt measures, including
Rule of Law Conditionality Regulation
Rule_of_Law_Conditionality_Regulation
of these trades twice. Hover over retained salary or conditional transactions for more information. Once an NHL player has played in a certain number of
2024–25_NHL_transactions
Method of data analysis
the PCA maximizes the mutual information I ( y ; s ) {\displaystyle I(\mathbf {y} ;\mathbf {s} )} between the desired information s {\displaystyle \mathbf
Principal_component_analysis
travel, tourism, insurance
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
CONDITIONAL MUTUAL-INFORMATION
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