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Markovian Discrimination
Within the probability theory Markov model, Markovian discrimination in spam filtering is a method used in CRM114 and other spam filters to model the statistical behaviors of spam and nonspam more accurately than in simple Bayesian methods. A simple Bayesian model of written text contains only the dictionary of legal words and their relative probabilities. A Markovian model adds the relative transition probabilities that given one word, predict what the next word will be. It is based on the theory of Markov chains by Andrey Markov, hence the name. In essence, a Bayesian filter works on single words alone, while a Markovian filter works on phrases or entire sentences. There are two types of Markov models; the visible Markov model, and the hidden Markov model or HMM. The difference is that with a visible Markov model, the current word is considered to contain the entire state of the language model, while a hidden Markov model hides the state and presumes only that the current word ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Model
In probability theory, a Markov model is a stochastic model used to Mathematical model, model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be Intractability (complexity), intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property. Introduction There are four common Markov models used in different situations, depending on whether every sequential state is observable or not, and whether the system is to be adjusted on the basis of observations made: Markov chain The simplest Markov model is the Markov chain. It models the state of a system with a random variable that changes through time. In this context, the Markov property suggests that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CRM114 (program)
CRM114 (full name: "The CRM114 Discriminator") is a program based upon a statistical approach for classifying data, and especially used for filtering email spam. Origin of the name The name comes from the CRM-114 Discriminator in the Stanley Kubrick movie Dr. Strangelove - a piece of radio equipment designed to filter out messages lacking a specific code-prefix. Operation While others have done statistical Bayesian spam filtering based upon the frequency of single word occurrences in email, CRM114 achieves a higher rate of spam recognition through creating hits based upon phrases up to five words in length. These phrases are used to form a Markov Random Field representing the incoming texts. With this additional contextual recognition, it is one of the more accurate spam filters available. Initial testing in 2002 by author Bill Yerazunis gave a 99.87% accuracy; Holden and TREC 2005 and 2006 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Spam Filtering
Naive Bayes classifiers are a popular statistical technique of e-mail filtering. They typically use bag-of-words features to identify email spam, an approach commonly used in text classification. Naive Bayes classifiers work by correlating the use of tokens (typically words, or sometimes other things), with spam and non-spam e-mails and then using Bayes' theorem to calculate a probability that an email is or is not spam. Naive Bayes spam filtering is a baseline technique for dealing with spam that can tailor itself to the email needs of individual users and give low false positive spam detection rates that are generally acceptable to users. It is one of the oldest ways of doing spam filtering, with roots in the 1990s. History Bayesian algorithms were used for email filtering as early as 1996. Although naive Bayesian filters did not become popular until later, multiple programs were released in 1998 to address the growing problem of unwanted email. The first scholarly publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Markov
Andrey Andreyevich Markov, first name also spelled "Andrei", in older works also spelled Markoff) (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. Markov and his younger brother Vladimir Andreevich Markov (1871–1897) proved the Markov brothers' inequality. His son, another Andrey Markov (Soviet mathematician), Andrey Andreyevich Markov (1903–1979), was also a notable mathematician, making contributions to constructive mathematics and Recursion#Functional recursion, recursive function theory. Biography Andrey Markov was born on 14 June 1856 in Russia. He attended the St. Petersburg Grammar School, where some teachers saw him as a rebellious student. In his academics he performed poorly in most subjects other than mathematics. Later in life he attended Saint Petersburg Imperial University (now Saint Petersburg State University). Among his t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Models
In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property. Introduction There are four common Markov models used in different situations, depending on whether every sequential state is observable or not, and whether the system is to be adjusted on the basis of observations made: Markov chain The simplest Markov model is the Markov chain. It models the state of a system with a random variable that changes through time. In this context, the Markov property suggests that the distribution for this variable depends only on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Markov Model
A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it X — with unobservable ("''hidden''") states. As part of the definition, HMM requires that there be an observable process Y whose outcomes are "influenced" by the outcomes of X in a known way. Since X cannot be observed directly, the goal is to learn about X by observing Y. HMM has an additional requirement that the outcome of Y at time t=t_0 must be "influenced" exclusively by the outcome of X at t=t_0 and that the outcomes of X and Y at t handwriting recognition, handwriting, gesture recognition, part-of-speech tagging, musical score following, partial discharges and bioinformatics. Definition Let X_n and Y_n be discrete-time stochastic processes and n\geq 1. The pair (X_n,Y_n) is a ''hidden Markov model'' if * X_n is a Markov process whose behavior is not directly observable ("hidden"); * \operatorname\bigl(Y_n \i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Random Field
In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties. The concept originates from the Sherrington–Kirkpatrick model. A Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies ); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies ). The underlying graph of a Markov random field may be finite or infinite. When the joint probability density of the random variables is strictly positive, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum-entropy Markov Model
In statistics, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs) and maximum entropy (MaxEnt) models. An MEMM is a discriminative model that extends a standard maximum entropy classifier by assuming that the unknown values to be learnt are connected in a Markov chain rather than being conditionally independent of each other. MEMMs find applications in natural language processing, specifically in part-of-speech tagging and information extraction. Model Suppose we have a sequence of observations O_1, \dots, O_n that we seek to tag with the labels S_1, \dots, S_nthat maximize the conditional probability P(S_1, \dots, S_n \mid O_1, \dots, O_n). In a MEMM, this probability is factored into Markov transition probabilities, where the probability of transitioning to a particular label depends only on the observation at that position and the previous position's label: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spam Filtering
Various anti-spam techniques are used to prevent email spam (unsolicited bulk email). No technique is a complete solution to the spam problem, and each has trade-offs between incorrectly rejecting legitimate email (false positives) as opposed to not rejecting all spam email (false negatives) – and the associated costs in time, effort, and cost of wrongfully obstructing good mail. Anti-spam techniques can be broken into four broad categories: those that require actions by individuals, those that can be automated by email administrators, those that can be automated by email senders and those employed by researchers and law enforcement officials. End-user techniques There are a number of techniques that individuals can use to restrict the availability of their email addresses, with the goal of reducing their chance of receiving spam. Discretion Sharing an email address only among a limited group of correspondents is one way to limit the chance that the address will be "harvest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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