1117:" in spam email, but will seldom see it in other email. The filter doesn't know these probabilities in advance, and must first be trained so it can build them up. To train the filter, the user must manually indicate whether a new email is spam or not. For all words in each training email, the filter will adjust the probabilities that each word will appear in spam or legitimate email in its database. For instance, Bayesian spam filters will typically have learned a very high spam probability for the words "Viagra" and "refinance", but a very low spam probability for words seen only in legitimate email, such as the names of friends and family members.
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which would contain the sensitive words like «Viagra». However, since many mail clients disable the display of linked pictures for security reasons, the spammer sending links to distant pictures might reach fewer targets. Also, a picture's size in bytes is bigger than the equivalent text's size, so the spammer needs more bandwidth to send messages directly including pictures. Some filters are more inclined to decide that a message is spam if it has mostly graphical contents. A solution used by
3127:. More generally, some bayesian filtering filters simply ignore all the words which have a spamicity next to 0.5, as they contribute little to a good decision. The words taken into consideration are those whose spamicity is next to 0.0 (distinctive signs of legitimate messages), or next to 1.0 (distinctive signs of spam). A method can be for example to keep only those ten words, in the examined message, which have the greatest
1888:. This condition is not generally satisfied (for example, in natural languages like English the probability of finding an adjective is affected by the probability of having a noun), but it is a useful idealization, especially since the statistical correlations between individual words are usually not known. On this basis, one can derive the following formula from Bayes' theorem:
3308:
1563:
36:
3145:(sequences of words) instead of isolated natural languages words. For example, with a "context window" of four words, they compute the spamicity of "Viagra is good for", instead of computing the spamicities of "Viagra", "is", "good", and "for". This method gives more sensitivity to context and eliminates the Bayesian noise better, at the expense of a bigger database.
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Words that normally appear in large quantities in spam may also be transformed by spammers. For example, «Viagra» would be replaced with «Viaagra» or «V!agra» in the spam message. The recipient of the message can still read the changed words, but each of these words is met more rarely by the
Bayesian
3393:
Another technique used to try to defeat
Bayesian spam filters is to replace text with pictures, either directly included or linked. The whole text of the message, or some part of it, is replaced with a picture where the same text is "drawn". The spam filter is usually unable to analyze this picture,
1871:
is approximated to the frequency of messages containing "replica" in the messages identified as ham during the learning phase. For these approximations to make sense, the set of learned messages needs to be big and representative enough. It is also advisable that the learned set of messages conforms
1053:
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 publication on Bayesian spam filtering was by Sahami
3385:
tactics include insertion of random innocuous words that are not normally associated with spam, thereby decreasing the email's spam score, making it more likely to slip past a
Bayesian spam filter. However, with (for example) Paul Graham's scheme only the most significant probabilities are used, so
3153:
There are other ways of combining individual probabilities for different words than using the "naive" approach. These methods differ from it on the assumptions they make on the statistical properties of the input data. These different hypotheses result in radically different formulas for combining
3611:
Sharpen your pencils, this is the mathematical background (such as it is).* The paper that started the ball rolling: Paul Graham's A Plan for Spam.* Gary
Robinson has an interesting essay suggesting some improvements to Graham's original approach.* Gary Robinson's Linux Journal article discussed
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The spam that a user receives is often related to the online user's activities. For example, a user may have been subscribed to an online newsletter that the user considers to be spam. This online newsletter is likely to contain words that are common to all newsletters, such as the name of the
1193:". Most people who are used to receiving e-mail know that this message is likely to be spam, more precisely a proposal to sell counterfeit copies of well-known brands of watches. The spam detection software, however, does not "know" such facts; all it can do is compute probabilities.
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Of course, determining whether a message is spam or ham based only on the presence of the word "replica" is error-prone, which is why bayesian spam software tries to consider several words and combine their spamicities to determine a message's overall probability of being spam.
3381:, a technique used by spammers in an attempt to degrade the effectiveness of spam filters that rely on Bayesian filtering. A spammer practicing Bayesian poisoning will send out emails with large amounts of legitimate text (gathered from legitimate news or literary sources).
2779:
More generally, the words that were encountered only a few times during the learning phase cause a problem, because it would be an error to trust blindly the information they provide. A simple solution is to simply avoid taking such unreliable words into account as well.
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In the case a word has never been met during the learning phase, both the numerator and the denominator are equal to zero, both in the general formula and in the spamicity formula. The software can decide to discard such words for which there is no information available.
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The legitimate e-mails a user receives will tend to be different. For example, in a corporate environment, the company name and the names of clients or customers will be mentioned often. The filter will assign a lower spam probability to emails containing those names.
1124:) are used to compute the probability that an email with a particular set of words in it belongs to either category. Each word in the email contributes to the email's spam probability, or only the most interesting words. This contribution is called the
2058:
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The word probabilities are unique to each user and can evolve over time with corrective training whenever the filter incorrectly classifies an email. As a result, Bayesian spam filtering accuracy after training is often superior to pre-defined rules.
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While
Bayesian filtering is used widely to identify spam email, the technique can classify (or "cluster") almost any sort of data. It has uses in science, medicine, and engineering. One example is a general purpose classification program called
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The initial training can usually be refined when wrong judgements from the software are identified (false positives or false negatives). That allows the software to dynamically adapt to the ever-evolving nature of spam.
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filter, which hinders its learning process. As a general rule, this spamming technique does not work very well, because the derived words end up recognized by the filter just like the normal ones.
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The filters that use this hypothesis are said to be "not biased", meaning that they have no prejudice regarding the incoming email. This assumption permits simplifying the general formula to:
916:
2765:
2711:
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954:
3925:
Zheng, J.; Tang, Yongchuan (2005). "One
Generalization of the Naive Bayes to Fuzzy Sets and the Design of the Fuzzy Naive Bayes Classifier". In Mira, Jose; Ălvarez, Jose R (eds.).
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1132:. Then, the email's spam probability is computed over all words in the email, and if the total exceeds a certain threshold (say 95%), the filter will mark the email as a spam.
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3871:. Lyon, France: Software and Knowledge Engineering Laboratory Institute of Informatics and Telecommunications National Centre for Scientific Research âDemokritosâ: 1â13.
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Most bayesian spam filtering algorithms are based on formulas that are strictly valid (from a probabilistic standpoint) only if the words present in the message are
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1154:(pre-defined rules about the contents, looking at the message's envelope, etc.), resulting in even higher filtering accuracy, sometimes at the cost of adaptiveness.
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used in this formula is approximated to the frequency of messages containing "replica" in the messages identified as spam during the learning phase. Similarly,
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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
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newsletter and its originating email address. A Bayesian spam filter will eventually assign a higher probability based on the user's specific patterns.
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Androutsopoulos, Ion; Paliouras, Georgios; Karkaletsis, Vangelis; Sakkis, Georgios; Spyropoulos, Constantine D.; Stamatopoulos, Panagiotis (2000).
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3123:"Neutral" words like "the", "a", "some", or "is" (in English), or their equivalents in other languages, can be ignored. These are also known as
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a second time, to compute the probability that the message is spam, taking into consideration all of its words (or a relevant subset of them);
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technique, email marked as spam can then be automatically moved to a "Junk" email folder, or even deleted outright. Some software implement
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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.
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Applying again Bayes' theorem, and assuming the classification between spam and ham of the emails containing a given word ("replica") is a
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1101:, oft cited as a Bayesian filter, is not intended to use a Bayes filter in production, but includes the âłunigramâł feature for reference.
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3867:; Rajman, M; Zaragoza, H (eds.). "Learning to Filter Spam E-Mail: A Comparison of a Naive Bayesian and a Memory-Based Approach".
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Some software products take into account the fact that a given word appears several times in the examined message, others don't.
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which was originally used to classify stars according to spectral characteristics that were otherwise too subtle to notice.
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This is functionally equivalent to asking, "what percentage of occurrences of the word 'replica' appear in spam messages?"
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is a baseline technique for dealing with spam that can tailor itself to the email needs of individual users and give low
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to the 50% hypothesis about repartition between spam and ham, i.e. that the datasets of spam and ham are of same size.
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of occurring in spam email and in legitimate email. For instance, most email users will frequently encounter the word "
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a first time, to compute the probability that the message is spam, knowing that a given word appears in this message;
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is lower than the threshold, the message is considered as likely ham, otherwise it is considered as likely spam.
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that padding the text out with non-spam-related words does not affect the detection probability significantly.
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2053:{\displaystyle p={\frac {p_{1}p_{2}\cdots p_{N}}{p_{1}p_{2}\cdots p_{N}+(1-p_{1})(1-p_{2})\cdots (1-p_{N})}}}
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This quantity is called "spamicity" (or "spaminess") of the word "replica", and can be computed. The number
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3929:. Lecture Notes in Computer Science. Vol. 3562. Berlin: Springer, Berlin, Heidelberg. p. 281.
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mechanisms that define a time frame during which the user is allowed to review the software's decision.
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is the corrected probability for the message to be spam, knowing that it contains a given word ;
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1093:, make use of Bayesian spam filtering techniques, and the functionality is sometimes embedded within
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44:
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3836:; Jin, Q; Jiang, X; Park, J (eds.). "A Modified Minimum Risk Bayes and It's Application in Spam".
3448:
2417:{\displaystyle {\frac {1}{p}}-1={\frac {(1-p_{1})(1-p_{2})\dots (1-p_{N})}{p_{1}p_{2}\dots p_{N}}}}
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Variants of the basic technique have been implemented in a number of research works and commercial
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4th
European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD-2000)
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Statistics show that the current probability of any message being spam is 80%, at the very least:
1351:{\displaystyle \Pr(S|W)={\frac {\Pr(W|S)\cdot \Pr(S)}{\Pr(W|S)\cdot \Pr(S)+\Pr(W|H)\cdot \Pr(H)}}}
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3775:"Bayesian Noise Reduction: Contextual Symmetry Logic Utilizing Pattern Consistency Analysis"
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is typically compared to a given threshold to decide whether the message is spam or not. If
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is equal to zero (and where the spamicity is not defined), and evaluates in this case to
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Artificial
Intelligence and Knowledge Engineering Applications: A Bioinspired Approach
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This corrected probability is used instead of the spamicity in the combining formula.
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is the probability that a message is a spam, knowing that the word "replica" is in it;
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that the second word (for example "watches") appears, given that the message is spam;
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that the first word (for example "replica") appears, given that the message is spam;
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can be computed in the log domain by rewriting the original equation as follows:
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Some spam filters combine the results of both
Bayesian spam filtering and other
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Depending on the implementation, Bayesian spam filtering may be susceptible to
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Spam filtering software based on this formula is sometimes referred to as a
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3808:"Gmail uses Google's innovative technology to keep spam out of your inbox"
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is the number of occurrences of this word during the learning phase ;
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is the overall probability that any given message is not spam (is "ham");
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Computing the probability that a message containing a given word is spam
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2896:{\displaystyle \Pr '(S|W)={\frac {s\cdot \Pr(S)+n\cdot \Pr(S|W)}{s+n}}}
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672:
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3583:
Gary Robinson's f(x) and combining algorithms, as used in SpamAssassin
2553:{\displaystyle \ln \left({\frac {1}{p}}-1\right)=\sum _{i=1}^{N}\left}
2259:
Other expression of the formula for combining individual probabilities
3395:
1114:
423:
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Individual probabilities can be combined with the techniques of the
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Hence the alternate formula for computing the combined probability:
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is the probability that the word "replica" appears in spam messages;
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The formula used by the software to determine that, is derived from
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is the probability that the word "replica" appears in ham messages.
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implement Bayesian spam filtering. Users can also install separate
4278:
4037:
3904:. London; Berlin: Springer- Verlag Heidelberg Berlin. p. 70.
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667:
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389:
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The NaĂŻve Bayes Model for Unsupervised Word Sense Disambiguation
3832:
Zhu, Z.; Jia, Z; Xiao, H; Zhang, G; Liang, H.; Wang, P. (2014).
3965:
1170:. Bayes' theorem is used several times in the context of spam:
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1784:{\displaystyle \Pr(S|W)={\frac {\Pr(W|S)}{\Pr(W|S)+\Pr(W|H)}}}
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29:
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on every mid to large size image, analyzing the text inside.
3264:{\displaystyle p=C^{-1}(-2\ln(p_{1}p_{2}\cdots p_{N}),2N)\,}
3157:
For example, assuming the individual probabilities follow a
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is the probability of any incoming message to be spam ;
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we give to background information about incoming spam ;
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to calculate a probability that an email is or is not spam.
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is the overall probability that any given message is spam;
3517:. AAAI'98 Workshop on Learning for Text Categorization.
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is not directly computed using the above formula due to
955:
List of datasets in computer vision and image processing
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M. Sahami; S. Dumais; D. Heckerman; E. Horvitz (1998).
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mail client with native implementation of Bayes filters
2791:, some programs decide to use a corrected probability:
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Let's suppose the suspected message contains the word "
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After training, the word probabilities (also known as
3328:. Please help to ensure that disputed statements are
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1583:. Please help to ensure that disputed statements are
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is the probability that the suspect message is spam;
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1180:sometimes a third time, to deal with rare words.
3165:degrees of freedom, one could use the formula:
3079:This formula can be extended to the case where
3665:"State of Spam, a Monthly Report - Report #33"
3512:"A Bayesian approach to filtering junk e-mail"
950:List of datasets for machine-learning research
3977:
2247:assumptions between the features. The result
983:
8:
3749:"SpamProbe - Bayesian Spam Filtering Tweaks"
3719:"A statistical approach to the spam problem"
3570:. Ubuntu manuals. 2010-09-18. Archived from
43:It has been suggested that this article be
4005:
3984:
3970:
3962:
3410:General applications of Bayesian filtering
2760:{\displaystyle p={\frac {1}{1+e^{\eta }}}}
2706:{\displaystyle {\frac {1}{p}}-1=e^{\eta }}
2657:{\displaystyle \eta =\sum _{i=1}^{N}\left}
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3348:Learn how and when to remove this message
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1603:Learn how and when to remove this message
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3663:Dylan Mors & Dermot Harnett (2009).
3324:Relevant discussion may be found on the
1579:Relevant discussion may be found on the
3838:Lecture Notes in Electrical Engineering
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76:
3648:: CS1 maint: archived copy as title (
3641:
3471:Spam: A Shadow History of the Internet
3602:from the original on 6 September 2010
1667:{\displaystyle \Pr(S)=0.8;\Pr(H)=0.2}
7:
3612:using the chi squared distribution.
3404:OCR (Optical Character Recognition)
3280:inverse of the chi-squared function
945:Glossary of artificial intelligence
27:Technique for filtering spam e-mail
4171:Distributed Checksum Clearinghouse
3844:. Dordrecht: Springer: 2155â2159.
3696:Introduction to Bayesian Filtering
2243:, as "naive" refers to the strong
1880:Combining individual probabilities
25:
4156:Challengeâresponse spam filtering
3993:Unsolicited digital communication
3598:. SpamBayes project. 2010-09-18.
1109:Particular words have particular
3306:
1561:
34:
3900:Hristea, Florentina T. (2013).
3814:from the original on 2015-09-13
3755:from the original on 2012-03-01
3729:from the original on 2010-10-22
3631:from the original on 2016-10-07
3549:from the original on 2012-10-23
3524:from the original on 2007-09-27
3492:from the original on 2019-03-23
1545:(For a full demonstration, see
1024:, an approach commonly used in
3773:Jonathan A. Zdziarski (2004).
3545:. MozillaZine. November 2009.
3402:email system is to perform an
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3154:the individual probabilities.
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3069:is the spamicity of this word.
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365:Relevance vector machine (RVM)
1:
3850:10.1007/978-94-007-7618-0_261
854:Computational learning theory
418:Expectationâmaximization (EM)
1547:Bayes' theorem#Extended form
811:Coefficient of determination
658:Convolutional neural network
370:Support vector machine (SVM)
3141:Some software products use
2427:Taking logs on both sides:
1061:products. Many modern mail
962:Outline of machine learning
859:Empirical risk minimization
60:Proposed since August 2024.
4373:
4191:Naive Bayes spam filtering
2944:{\displaystyle \Pr '(S|W)}
2225:{\displaystyle p(W_{2}|S)}
2152:{\displaystyle p(W_{1}|S)}
1039:Naive Bayes spam filtering
599:Feedforward neural network
350:Artificial neural networks
582:Artificial neural network
4166:Disposable email address
4028:Directory harvest attack
3444:Markovian discrimination
3287:Markovian discrimination
3159:chi-squared distribution
3062:{\displaystyle \Pr(S|W)}
2269:floating-point underflow
1864:{\displaystyle \Pr(W|H)}
1827:{\displaystyle \Pr(W|S)}
1553:The spamliness of a word
1534:{\displaystyle \Pr(W|H)}
1464:{\displaystyle \Pr(W|S)}
1394:{\displaystyle \Pr(S|W)}
1067:email filtering programs
891:Journals and conferences
838:Mathematical foundations
748:Temporal difference (TD)
604:Recurrent neural network
524:Conditional random field
447:Dimensionality reduction
195:Dimensionality reduction
157:Quantum machine learning
152:Neuromorphic engineering
112:Self-supervised learning
107:Semi-supervised learning
3131: |0.5 â
2771:Dealing with rare words
1158:Mathematical foundation
1073:email filters, such as
1003:Naive Bayes classifiers
300:Apprenticeship learning
18:Bayesian spam filtering
3468:Brunton, Finn (2013).
3265:
3109:
3063:
3024:
3002:
3001:{\displaystyle \Pr(S)}
2967:
2945:
2897:
2761:
2707:
2658:
2596:
2554:
2492:
2418:
2241:naive Bayes classifier
2226:
2182:
2153:
2109:
2080:
2054:
1865:
1828:
1785:
1668:
1535:
1496:
1495:{\displaystyle \Pr(H)}
1465:
1426:
1425:{\displaystyle \Pr(S)}
1395:
1352:
1128:and is computed using
849:Biasâvariance tradeoff
731:Reinforcement learning
707:Spiking neural network
117:Reinforcement learning
50:Naive Bayes classifier
3747:Brian Burton (2003).
3266:
3110:
3108:{\displaystyle Pr(S)}
3064:
3025:
3003:
2968:
2946:
2898:
2762:
2708:
2659:
2576:
2555:
2472:
2419:
2227:
2183:
2181:{\displaystyle p_{2}}
2154:
2110:
2108:{\displaystyle p_{1}}
2081:
2055:
1866:
1829:
1786:
1669:
1536:
1497:
1466:
1427:
1396:
1353:
1126:posterior probability
1020:features to identify
1016:. They typically use
685:Neural radiance field
507:Structured prediction
230:Structured prediction
102:Unsupervised learning
4176:Email authentication
3787:Paul Graham (2002),
3596:"Background Reading"
3574:on 29 September 2010
3543:"Junk Mail Controls"
3429:Anti-spam techniques
3317:factual accuracy is
3172:
3087:
3036:
3014:
2983:
2957:
2913:
2798:
2723:
2671:
2567:
2434:
2282:
2192:
2165:
2119:
2092:
2070:
1895:
1838:
1801:
1684:
1622:
1572:factual accuracy is
1508:
1477:
1438:
1407:
1368:
1206:
1122:likelihood functions
874:Statistical learning
772:Learning with humans
564:Local outlier factor
4357:Bayesian estimation
4023:Bulk email software
3935:10.1007/11499305_29
3887:2000cs........9009A
3449:Mozilla Thunderbird
2188:is the probability
2115:is the probability
1026:text classification
717:Electrochemical RAM
624:reservoir computing
355:Logistic regression
274:Supervised learning
260:Multimodal learning
235:Feature engineering
180:Generative modeling
142:Rule-based learning
137:Curriculum learning
97:Supervised learning
72:Part of a series on
3794:2004-04-04 at the
3701:2012-02-06 at the
3694:Process Software,
3434:Bayesian poisoning
3379:Bayesian poisoning
3261:
3105:
3059:
3020:
2998:
2963:
2941:
2893:
2757:
2703:
2654:
2550:
2414:
2222:
2178:
2149:
2105:
2076:
2050:
1886:independent events
1861:
1824:
1781:
1664:
1531:
1492:
1461:
1422:
1391:
1348:
285: •
200:Density estimation
4334:
4333:
4161:Context filtering
4137:
4136:
3944:978-3-540-26319-7
3911:978-3-642-33692-8
3358:
3357:
3350:
3073:(Demonstration:)
3023:{\displaystyle n}
2966:{\displaystyle s}
2891:
2789:beta distribution
2755:
2682:
2456:
2412:
2293:
2079:{\displaystyle p}
2048:
1779:
1613:
1612:
1605:
1346:
1097:software itself.
1000:
999:
805:Model diagnostics
788:Human-in-the-loop
631:Boltzmann machine
544:Anomaly detection
340:Linear regression
255:Ontology learning
250:Grammar induction
225:Semantic analysis
220:Association rules
205:Anomaly detection
147:Neuro-symbolic AI
67:
66:
62:
16:(Redirected from
4364:
4302:Advance-fee scam
4249:Keyword stuffing
4006:
3986:
3979:
3972:
3963:
3957:
3956:
3922:
3916:
3915:
3897:
3891:
3890:
3880:
3860:
3854:
3853:
3829:
3823:
3822:
3820:
3819:
3804:
3798:
3785:
3779:
3778:
3770:
3764:
3763:
3761:
3760:
3744:
3738:
3737:
3735:
3734:
3711:
3705:
3692:
3686:
3685:
3683:
3682:
3676:
3670:. Archived from
3669:
3660:
3654:
3653:
3647:
3639:
3637:
3636:
3621:
3615:
3614:
3608:
3607:
3592:
3586:
3585:
3580:
3579:
3564:
3558:
3557:
3555:
3554:
3539:
3533:
3532:
3530:
3529:
3523:
3516:
3507:
3501:
3500:
3498:
3497:
3465:
3353:
3346:
3342:
3339:
3333:
3330:reliably sourced
3310:
3309:
3302:
3270:
3268:
3267:
3262:
3244:
3243:
3231:
3230:
3221:
3220:
3193:
3192:
3119:Other heuristics
3114:
3112:
3111:
3106:
3068:
3066:
3065:
3060:
3052:
3029:
3027:
3026:
3021:
3007:
3005:
3004:
2999:
2972:
2970:
2969:
2964:
2950:
2948:
2947:
2942:
2934:
2923:
2902:
2900:
2899:
2894:
2892:
2890:
2879:
2872:
2830:
2819:
2808:
2766:
2764:
2763:
2758:
2756:
2754:
2753:
2752:
2733:
2712:
2710:
2709:
2704:
2702:
2701:
2683:
2675:
2663:
2661:
2660:
2655:
2653:
2649:
2648:
2647:
2626:
2625:
2595:
2590:
2559:
2557:
2556:
2551:
2549:
2545:
2544:
2543:
2522:
2521:
2491:
2486:
2468:
2464:
2457:
2449:
2423:
2421:
2420:
2415:
2413:
2411:
2410:
2409:
2397:
2396:
2387:
2386:
2376:
2372:
2371:
2347:
2346:
2325:
2324:
2305:
2294:
2286:
2231:
2229:
2228:
2223:
2215:
2210:
2209:
2187:
2185:
2184:
2179:
2177:
2176:
2158:
2156:
2155:
2150:
2142:
2137:
2136:
2114:
2112:
2111:
2106:
2104:
2103:
2085:
2083:
2082:
2077:
2059:
2057:
2056:
2051:
2049:
2047:
2043:
2042:
2018:
2017:
1996:
1995:
1974:
1973:
1961:
1960:
1951:
1950:
1940:
1939:
1938:
1926:
1925:
1916:
1915:
1905:
1870:
1868:
1867:
1862:
1854:
1833:
1831:
1830:
1825:
1817:
1790:
1788:
1787:
1782:
1780:
1778:
1771:
1748:
1733:
1726:
1711:
1700:
1673:
1671:
1670:
1665:
1608:
1601:
1597:
1594:
1588:
1585:reliably sourced
1565:
1564:
1557:
1540:
1538:
1537:
1532:
1524:
1501:
1499:
1498:
1493:
1470:
1468:
1467:
1462:
1454:
1431:
1429:
1428:
1423:
1400:
1398:
1397:
1392:
1384:
1357:
1355:
1354:
1349:
1347:
1345:
1323:
1285:
1270:
1248:
1233:
1222:
1135:As in any other
1054:et al. in 1998.
1014:e-mail filtering
992:
985:
978:
939:Related articles
816:Confusion matrix
569:Isolation forest
514:Graphical models
293:
292:
245:Learning to rank
240:Feature learning
78:Machine learning
69:
58:
38:
37:
30:
21:
4372:
4371:
4367:
4366:
4365:
4363:
4362:
4361:
4337:
4336:
4335:
4330:
4314:Make Money Fast
4288:
4284:URL redirection
4210:
4133:
4067:
4018:Address munging
3995:
3990:
3960:
3945:
3924:
3923:
3919:
3912:
3899:
3898:
3894:
3862:
3861:
3857:
3831:
3830:
3826:
3817:
3815:
3806:
3805:
3801:
3796:Wayback Machine
3789:A Plan for Spam
3786:
3782:
3772:
3771:
3767:
3758:
3756:
3746:
3745:
3741:
3732:
3730:
3713:
3712:
3708:
3703:Wayback Machine
3693:
3689:
3680:
3678:
3674:
3667:
3662:
3661:
3657:
3640:
3634:
3632:
3625:"Archived copy"
3623:
3622:
3618:
3605:
3603:
3594:
3593:
3589:
3577:
3575:
3566:
3565:
3561:
3552:
3550:
3541:
3540:
3536:
3527:
3525:
3521:
3514:
3509:
3508:
3504:
3495:
3493:
3486:
3478:. p. 136.
3467:
3466:
3462:
3458:
3439:Email filtering
3425:
3412:
3375:
3354:
3343:
3337:
3334:
3323:
3315:This section's
3311:
3307:
3300:
3295:
3235:
3222:
3212:
3181:
3170:
3169:
3151:
3121:
3085:
3084:
3034:
3033:
3012:
3011:
2981:
2980:
2955:
2954:
2916:
2911:
2910:
2880:
2831:
2801:
2796:
2795:
2785:random variable
2773:
2744:
2737:
2721:
2720:
2693:
2669:
2668:
2639:
2617:
2601:
2597:
2565:
2564:
2535:
2513:
2497:
2493:
2447:
2443:
2432:
2431:
2401:
2388:
2378:
2377:
2363:
2338:
2316:
2306:
2280:
2279:
2261:
2201:
2190:
2189:
2168:
2163:
2162:
2128:
2117:
2116:
2095:
2090:
2089:
2068:
2067:
2034:
2009:
1987:
1965:
1952:
1942:
1941:
1930:
1917:
1907:
1906:
1893:
1892:
1882:
1836:
1835:
1799:
1798:
1734:
1712:
1682:
1681:
1620:
1619:
1609:
1598:
1592:
1589:
1578:
1570:This section's
1566:
1562:
1555:
1506:
1505:
1475:
1474:
1436:
1435:
1405:
1404:
1366:
1365:
1271:
1234:
1204:
1203:
1187:
1160:
1107:
1051:
996:
967:
966:
940:
932:
931:
892:
884:
883:
844:Kernel machines
839:
831:
830:
806:
798:
797:
778:Active learning
773:
765:
764:
733:
723:
722:
648:Diffusion model
584:
574:
573:
546:
536:
535:
509:
499:
498:
454:Factor analysis
449:
439:
438:
422:
385:
375:
374:
295:
294:
278:
277:
276:
265:
264:
170:
162:
161:
127:Online learning
92:
80:
63:
39:
35:
28:
23:
22:
15:
12:
11:
5:
4370:
4368:
4360:
4359:
4354:
4349:
4339:
4338:
4332:
4331:
4329:
4328:
4327:
4326:
4316:
4311:
4310:
4309:
4298:
4296:
4294:Internet fraud
4290:
4289:
4287:
4286:
4281:
4276:
4271:
4266:
4261:
4256:
4251:
4246:
4244:Google bombing
4241:
4236:
4231:
4226:
4220:
4218:
4212:
4211:
4209:
4208:
4203:
4198:
4193:
4188:
4186:List poisoning
4183:
4178:
4173:
4168:
4163:
4158:
4153:
4147:
4145:
4139:
4138:
4135:
4134:
4132:
4131:
4126:
4121:
4116:
4111:
4106:
4101:
4096:
4091:
4086:
4081:
4075:
4073:
4069:
4068:
4066:
4065:
4060:
4055:
4050:
4045:
4043:Email spoofing
4040:
4035:
4030:
4025:
4020:
4014:
4012:
4003:
3997:
3996:
3991:
3989:
3988:
3981:
3974:
3966:
3959:
3958:
3943:
3917:
3910:
3892:
3855:
3824:
3799:
3780:
3765:
3739:
3706:
3687:
3655:
3616:
3587:
3568:"Installation"
3559:
3534:
3502:
3484:
3459:
3457:
3454:
3453:
3452:
3446:
3441:
3436:
3431:
3424:
3421:
3411:
3408:
3374:
3371:
3356:
3355:
3314:
3312:
3305:
3299:
3296:
3294:
3291:
3272:
3271:
3259:
3256:
3253:
3250:
3247:
3242:
3238:
3234:
3229:
3225:
3219:
3215:
3211:
3208:
3205:
3202:
3199:
3196:
3191:
3188:
3184:
3180:
3177:
3150:
3147:
3129:absolute value
3120:
3117:
3104:
3101:
3098:
3095:
3092:
3071:
3070:
3058:
3055:
3051:
3047:
3044:
3041:
3031:
3019:
3009:
2997:
2994:
2991:
2988:
2978:
2962:
2952:
2940:
2937:
2933:
2929:
2926:
2922:
2919:
2904:
2903:
2889:
2886:
2883:
2878:
2875:
2871:
2867:
2864:
2861:
2858:
2855:
2852:
2849:
2846:
2843:
2840:
2837:
2834:
2828:
2825:
2822:
2818:
2814:
2811:
2807:
2804:
2772:
2769:
2768:
2767:
2751:
2747:
2743:
2740:
2736:
2731:
2728:
2714:
2713:
2700:
2696:
2692:
2689:
2686:
2681:
2678:
2652:
2646:
2642:
2638:
2635:
2632:
2629:
2624:
2620:
2616:
2613:
2610:
2607:
2604:
2600:
2594:
2589:
2586:
2583:
2579:
2575:
2572:
2561:
2560:
2548:
2542:
2538:
2534:
2531:
2528:
2525:
2520:
2516:
2512:
2509:
2506:
2503:
2500:
2496:
2490:
2485:
2482:
2479:
2475:
2471:
2467:
2463:
2460:
2455:
2452:
2446:
2442:
2439:
2425:
2424:
2408:
2404:
2400:
2395:
2391:
2385:
2381:
2375:
2370:
2366:
2362:
2359:
2356:
2353:
2350:
2345:
2341:
2337:
2334:
2331:
2328:
2323:
2319:
2315:
2312:
2309:
2303:
2300:
2297:
2292:
2289:
2260:
2257:
2237:
2236:
2233:
2221:
2218:
2214:
2208:
2204:
2200:
2197:
2175:
2171:
2160:
2148:
2145:
2141:
2135:
2131:
2127:
2124:
2102:
2098:
2087:
2075:
2061:
2060:
2046:
2041:
2037:
2033:
2030:
2027:
2024:
2021:
2016:
2012:
2008:
2005:
2002:
1999:
1994:
1990:
1986:
1983:
1980:
1977:
1972:
1968:
1964:
1959:
1955:
1949:
1945:
1937:
1933:
1929:
1924:
1920:
1914:
1910:
1903:
1900:
1881:
1878:
1860:
1857:
1853:
1849:
1846:
1843:
1823:
1820:
1816:
1812:
1809:
1806:
1792:
1791:
1777:
1774:
1770:
1766:
1763:
1760:
1757:
1754:
1751:
1747:
1743:
1740:
1737:
1732:
1729:
1725:
1721:
1718:
1715:
1709:
1706:
1703:
1699:
1695:
1692:
1689:
1675:
1674:
1663:
1660:
1657:
1654:
1651:
1648:
1645:
1642:
1639:
1636:
1633:
1630:
1627:
1611:
1610:
1569:
1567:
1560:
1554:
1551:
1543:
1542:
1530:
1527:
1523:
1519:
1516:
1513:
1503:
1491:
1488:
1485:
1482:
1472:
1460:
1457:
1453:
1449:
1446:
1443:
1433:
1421:
1418:
1415:
1412:
1402:
1390:
1387:
1383:
1379:
1376:
1373:
1359:
1358:
1344:
1341:
1338:
1335:
1332:
1329:
1326:
1322:
1318:
1315:
1312:
1309:
1306:
1303:
1300:
1297:
1294:
1291:
1288:
1284:
1280:
1277:
1274:
1269:
1266:
1263:
1260:
1257:
1254:
1251:
1247:
1243:
1240:
1237:
1231:
1228:
1225:
1221:
1217:
1214:
1211:
1198:Bayes' theorem
1186:
1183:
1182:
1181:
1178:
1175:
1168:Bayes' theorem
1159:
1156:
1137:spam filtering
1130:Bayes' theorem
1106:
1103:
1050:
1047:
1043:false positive
1033:Bayes' theorem
1005:are a popular
998:
997:
995:
994:
987:
980:
972:
969:
968:
965:
964:
959:
958:
957:
947:
941:
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864:Occam learning
861:
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851:
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840:
837:
836:
833:
832:
829:
828:
823:
821:Learning curve
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305:Decision trees
302:
296:
282:classification
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175:Classification
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132:Batch learning
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64:
42:
40:
33:
26:
24:
14:
13:
10:
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6:
4:
3:
2:
4369:
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4320:
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4312:
4308:
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4300:
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4297:
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4291:
4285:
4282:
4280:
4277:
4275:
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4270:
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4265:
4262:
4260:
4259:Referrer spam
4257:
4255:
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4235:
4232:
4230:
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4124:Telemarketing
4122:
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4112:
4110:
4107:
4105:
4102:
4100:
4097:
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4090:
4087:
4085:
4082:
4080:
4077:
4076:
4074:
4070:
4064:
4061:
4059:
4058:Pink contract
4056:
4054:
4051:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4016:
4015:
4013:
4011:
4007:
4004:
4002:
3998:
3994:
3987:
3982:
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3975:
3973:
3968:
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3940:
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3913:
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3866:
3859:
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3809:
3803:
3800:
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3790:
3784:
3781:
3776:
3769:
3766:
3754:
3750:
3743:
3740:
3728:
3724:
3723:Linux Journal
3720:
3716:
3715:Gary Robinson
3710:
3707:
3704:
3700:
3697:
3691:
3688:
3677:on 2009-10-07
3673:
3666:
3659:
3656:
3651:
3645:
3630:
3626:
3620:
3617:
3613:
3601:
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3548:
3544:
3538:
3535:
3520:
3513:
3506:
3503:
3491:
3487:
3485:9780262018876
3481:
3477:
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3455:
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3447:
3445:
3442:
3440:
3437:
3435:
3432:
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3427:
3426:
3422:
3420:
3418:
3409:
3407:
3405:
3401:
3397:
3391:
3387:
3384:
3380:
3373:Disadvantages
3372:
3370:
3366:
3362:
3352:
3349:
3341:
3331:
3327:
3321:
3320:
3313:
3304:
3303:
3297:
3292:
3290:
3288:
3283:
3281:
3277:
3254:
3251:
3248:
3240:
3236:
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3227:
3223:
3217:
3213:
3206:
3203:
3200:
3197:
3189:
3186:
3182:
3178:
3175:
3168:
3167:
3166:
3164:
3160:
3155:
3149:Mixed methods
3148:
3146:
3144:
3139:
3136:
3134:
3130:
3126:
3118:
3116:
3099:
3093:
3090:
3082:
3077:
3074:
3053:
3045:
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3017:
3010:
2992:
2979:
2976:
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2927:
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2887:
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2718:
2717:
2698:
2694:
2690:
2687:
2684:
2679:
2676:
2667:
2666:
2665:
2664:. Therefore,
2650:
2644:
2640:
2636:
2633:
2630:
2622:
2618:
2614:
2611:
2605:
2602:
2598:
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2570:
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2510:
2507:
2501:
2498:
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2477:
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2453:
2450:
2444:
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2437:
2430:
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2428:
2406:
2402:
2398:
2393:
2389:
2383:
2379:
2368:
2364:
2360:
2357:
2351:
2343:
2339:
2335:
2332:
2321:
2317:
2313:
2310:
2301:
2298:
2295:
2290:
2287:
2278:
2277:
2276:
2274:
2270:
2266:
2258:
2256:
2254:
2250:
2246:
2242:
2234:
2216:
2206:
2202:
2195:
2173:
2169:
2161:
2143:
2133:
2129:
2122:
2100:
2096:
2088:
2073:
2066:
2065:
2064:
2039:
2035:
2031:
2028:
2022:
2014:
2010:
2006:
2003:
1992:
1988:
1984:
1981:
1975:
1970:
1966:
1962:
1957:
1953:
1947:
1943:
1935:
1931:
1927:
1922:
1918:
1912:
1908:
1901:
1898:
1891:
1890:
1889:
1887:
1879:
1877:
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1855:
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1810:
1795:
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1764:
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1749:
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1707:
1701:
1693:
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1640:
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1631:
1618:
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1616:
1607:
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1596:
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1568:
1559:
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1548:
1525:
1517:
1504:
1486:
1473:
1455:
1447:
1434:
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1403:
1385:
1377:
1364:
1363:
1362:
1339:
1330:
1324:
1316:
1307:
1301:
1292:
1286:
1278:
1264:
1255:
1249:
1241:
1229:
1223:
1215:
1202:
1201:
1200:
1199:
1194:
1192:
1184:
1179:
1176:
1173:
1172:
1171:
1169:
1165:
1164:email filters
1157:
1155:
1153:
1148:
1144:
1142:
1138:
1133:
1131:
1127:
1123:
1118:
1116:
1112:
1111:probabilities
1104:
1102:
1100:
1096:
1092:
1088:
1084:
1080:
1076:
1072:
1068:
1064:
1060:
1055:
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1040:
1036:
1034:
1029:
1027:
1023:
1019:
1015:
1011:
1008:
1004:
993:
988:
986:
981:
979:
974:
973:
971:
970:
963:
960:
956:
953:
952:
951:
948:
946:
943:
942:
936:
935:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
894:
888:
887:
880:
877:
875:
872:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
841:
835:
834:
827:
824:
822:
819:
817:
814:
812:
809:
808:
802:
801:
794:
791:
789:
786:
784:
783:Crowdsourcing
781:
779:
776:
775:
769:
768:
759:
756:
755:
754:
751:
749:
746:
744:
741:
739:
736:
735:
732:
727:
726:
718:
715:
713:
712:Memtransistor
710:
708:
705:
703:
700:
696:
693:
692:
691:
688:
686:
683:
679:
676:
674:
671:
669:
666:
664:
661:
660:
659:
656:
654:
651:
649:
646:
644:
641:
637:
634:
633:
632:
629:
625:
622:
620:
617:
615:
612:
610:
607:
606:
605:
602:
600:
597:
595:
594:Deep learning
592:
590:
587:
586:
583:
578:
577:
570:
567:
565:
562:
560:
558:
554:
552:
549:
548:
545:
540:
539:
530:
529:Hidden Markov
527:
525:
522:
520:
517:
516:
515:
512:
511:
508:
503:
502:
495:
492:
490:
487:
485:
482:
480:
477:
475:
472:
470:
467:
465:
462:
460:
457:
455:
452:
451:
448:
443:
442:
435:
432:
430:
427:
425:
421:
419:
416:
414:
411:
409:
407:
403:
401:
398:
396:
393:
391:
388:
387:
384:
379:
378:
371:
368:
366:
363:
361:
358:
356:
353:
351:
348:
346:
343:
341:
338:
336:
334:
330:
326:
325:Random forest
323:
321:
318:
316:
313:
312:
311:
308:
306:
303:
301:
298:
297:
290:
289:
284:
283:
275:
269:
268:
261:
258:
256:
253:
251:
248:
246:
243:
241:
238:
236:
233:
231:
228:
226:
223:
221:
218:
216:
213:
211:
210:Data cleaning
208:
206:
203:
201:
198:
196:
193:
191:
188:
186:
183:
181:
178:
176:
173:
172:
166:
165:
158:
155:
153:
150:
148:
145:
143:
140:
138:
135:
133:
130:
128:
125:
123:
122:Meta-learning
120:
118:
115:
113:
110:
108:
105:
103:
100:
98:
95:
94:
88:
87:
84:
79:
75:
71:
70:
61:
56:
52:
51:
46:
41:
32:
31:
19:
4307:Lottery scam
4264:Scraper site
4234:Doorway page
4190:
4104:Mobile phone
4084:Cold calling
3926:
3920:
3901:
3895:
3868:
3865:Gallinari, P
3858:
3841:
3837:
3827:
3816:. Retrieved
3802:
3783:
3768:
3757:. Retrieved
3742:
3731:. Retrieved
3722:
3709:
3690:
3679:. Retrieved
3672:the original
3658:
3633:. Retrieved
3619:
3610:
3604:. Retrieved
3590:
3582:
3576:. Retrieved
3572:the original
3562:
3551:. Retrieved
3537:
3526:. Retrieved
3505:
3494:. Retrieved
3470:
3463:
3413:
3392:
3388:
3376:
3367:
3363:
3359:
3344:
3335:
3316:
3284:
3275:
3273:
3162:
3156:
3152:
3142:
3140:
3137:
3132:
3122:
3080:
3078:
3075:
3072:
2974:
2905:
2782:
2778:
2774:
2715:
2562:
2426:
2272:
2264:
2262:
2252:
2248:
2245:independence
2238:
2062:
1883:
1874:
1796:
1793:
1676:
1614:
1599:
1590:
1571:
1544:
1360:
1195:
1188:
1161:
1149:
1145:
1134:
1119:
1108:
1079:SpamAssassin
1056:
1052:
1038:
1037:
1030:
1018:bag-of-words
1001:
869:PAC learning
556:
405:
400:Hierarchical
332:
286:
280:
59:
48:
4269:Social spam
4181:Greylisting
4151:Client-side
4079:Auto dialer
2271:. Instead,
1095:mail server
1071:Server-side
1007:statistical
753:Multi-agent
690:Transformer
589:Autoencoder
345:Naive Bayes
83:data mining
4341:Categories
4274:Spam blogs
4239:Forum spam
4216:Spamdexing
4089:Flyposting
4048:Image spam
4010:Email spam
3878:cs/0009009
3818:2015-09-05
3759:2009-01-19
3733:2007-07-19
3681:2009-12-30
3635:2016-07-09
3606:2010-09-18
3578:2010-09-18
3553:2010-01-16
3528:2007-08-15
3496:2017-09-13
3456:References
3298:Advantages
3293:Discussion
3125:Stop words
1152:heuristics
1141:quarantine
1087:Bogofilter
1022:email spam
738:Q-learning
636:Restricted
434:Mean shift
383:Clustering
360:Perceptron
288:regression
190:Clustering
185:Regression
4352:Anti-spam
4254:Link farm
4224:Blog spam
4143:Anti-spam
4109:Newsgroup
4099:Messaging
4001:Protocols
3953:0302-9743
3476:MIT Press
3417:AutoClass
3326:talk page
3233:⋯
3207:
3198:−
3187:−
2857:⋅
2836:⋅
2750:η
2699:η
2685:−
2637:
2631:−
2615:−
2606:
2578:∑
2571:η
2533:
2527:−
2511:−
2502:
2474:∑
2459:−
2441:
2399:…
2361:−
2352:…
2336:−
2314:−
2296:−
2032:−
2023:⋯
2007:−
1985:−
1963:⋯
1928:⋯
1581:talk page
1331:⋅
1293:⋅
1256:⋅
1162:Bayesian
1083:SpamBayes
1010:technique
897:ECML PKDD
879:VC theory
826:ROC curve
758:Self-play
678:DeepDream
519:Bayes net
310:Ensembles
91:Paradigms
4347:Spamming
4319:Phishing
4229:Cloaking
4206:Spamhaus
4114:Robocall
4094:Junk fax
3812:Archived
3792:Archived
3753:Archived
3727:Archived
3717:(2003).
3699:Archived
3644:cite web
3629:Archived
3600:Archived
3547:Archived
3519:Archived
3490:Archived
3423:See also
3338:May 2013
3319:disputed
3143:patterns
2975:strength
2921:′
2806:′
2263:Usually
1593:May 2024
1574:disputed
1166:utilize
1059:software
320:Boosting
169:Problems
4201:SpamCop
4119:Spambot
4063:Spambot
4053:Joe job
3883:Bibcode
3398:in its
3383:Spammer
3278:is the
2973:is the
2906:where:
2063:where:
1361:where:
1191:replica
1105:Process
1063:clients
1049:History
902:NeurIPS
719:(ECRAM)
673:AlexNet
315:Bagging
55:Discuss
3951:
3941:
3908:
3482:
3396:Google
3274:where
3161:with 2
2235:etc...
1115:Viagra
1099:CRM114
1089:, and
695:Vision
551:RANSAC
429:OPTICS
424:DBSCAN
408:-means
215:AutoML
45:merged
4324:Voice
4279:Sping
4196:SORBS
4072:Other
4038:DNSWL
4033:DNSBL
3873:arXiv
3834:Li, S
3675:(PDF)
3668:(PDF)
3522:(PDF)
3515:(PDF)
3400:Gmail
3289:too.
2787:with
1075:DSPAM
917:IJCAI
743:SARSA
702:Mamba
668:LeNet
663:U-Net
489:t-SNE
413:Fuzzy
390:BIRCH
47:into
4129:VoIP
3949:ISSN
3939:ISBN
3906:ISBN
3650:link
3480:ISBN
2563:Let
1091:ASSP
927:JMLR
912:ICLR
907:ICML
793:RLHF
609:LSTM
395:CURE
81:and
3931:doi
3846:doi
3842:269
3135:|.
1662:0.2
1641:0.8
1549:.)
1012:of
653:SOM
643:GAN
619:ESN
614:GRU
559:-NN
494:SDL
484:PGD
479:PCA
474:NMF
469:LDA
464:ICA
459:CCA
335:-NN
53:. (
4343::
3947:.
3937:.
3881:.
3840:.
3810:.
3751:.
3725:.
3721:.
3646:}}
3642:{{
3627:.
3609:.
3581:.
3488:.
3474:.
3282:.
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