Diagnostically acceptable irreversible compression (DAIC) is the amount of lossy compression which can be used on a medical image to produce a result that does not prevent the reader from using the image to make a medical diagnosis. The term was first introduced at a workshop on irreversible compression convened by the European Society of Radiology (ESR) in Palma de Mallorca October 13, 2010, the results of which were reported in a subsequent position paper. == Determination == The "amount of compression" in irreversible compression used to be determined by the compression ratio, where the acceptable minimum is determined by the algorithm (typically JPEG or J2K) and the data type (body part and imaging method). Such a definition is easy to follow, and has been used by medical bodies in 2010 around the world. However, its downside is obvious: the compression ratio tells nothing about the real quality of the image, as different compressors can produce vastly different qualities under the same file size. For example, the JPEG format of 1992 can perform as well as many modern formats given newer techniques exploited in mozjpeg and ISO libjpeg, yet they would be lumped together with the legacy encoders in such a scheme. The image compression community has long used objective quality metrics like SSIM to measure the effects of compression. In the absence of good data regarding SSIM, the ESR review of 2010 concluded that it is still difficult to establish a criterion for whether a particular irreversible compression scheme applied with particular parameters to a particular individual image, or category of images, avoids the introduction of some quantifiable risk of a diagnostic error for any particular diagnostic task. A 2017 study showed that a SSIM variant called 4-G-r (4-component, gradient, structural component of SSIM) best reflects changes in images that affect the decision of radiologists out of 16 SSIM variants. A 2020 study shows that visual information fidelity (VIF), feature similarity index (FSIM), and noise quality metric (NQM) best reflect radiologist preferences out of ten metrics. It also mentions that the original version of SSIM works as poorly as a basic root-mean-square distance (RMSD) for this purpose, a result echoed by the 2017 study. The 4-G-r modification is not tested in the study.
Computational intelligence
In computer science, computational intelligence (CI) refers to concepts, paradigms, algorithms and implementations of systems that are designed to show "intelligent" behavior in complex and changing environments. These systems are aimed at mastering complex tasks in a wide variety of technical or commercial areas and offer solutions that recognize and interpret patterns, control processes, support decision-making or autonomously manoeuvre vehicles or robots in unknown environments, among other things. These concepts and paradigms are characterized by the ability to learn or adapt to new situations, to generalize, to abstract, to discover and associate. Nature-analog or nature-inspired methods play a key role in this. CI approaches primarily address those complex real-world problems for which traditional or mathematical modeling is not appropriate for various reasons: the processes cannot be described exactly with complete knowledge, the processes are too complex for mathematical reasoning, they contain some uncertainties during the process, such as unforeseen changes in the environment or in the process itself, or the processes are simply stochastic in nature. Thus, CI techniques are properly aimed at processes that are ill-defined, complex, nonlinear, time-varying and/or stochastic. A recent definition of the IEEE Computational Intelligence Societey describes CI as the theory, design, application and development of biologically and linguistically motivated computational paradigms. Traditionally the three main pillars of CI have been Neural Networks, Fuzzy Systems and Evolutionary Computation. ... CI is an evolving field and at present in addition to the three main constituents, it encompasses computing paradigms like ambient intelligence, artificial life, cultural learning, artificial endocrine networks, social reasoning, and artificial hormone networks. ... Over the last few years there has been an explosion of research on Deep Learning, in particular deep convolutional neural networks. Nowadays, deep learning has become the core method for artificial intelligence. In fact, some of the most successful AI systems are based on CI. However, as CI is an emerging and developing field there is no final definition of CI, especially in terms of the list of concepts and paradigms that belong to it. The general requirements for the development of an “intelligent system” are ultimately always the same, namely the simulation of intelligent thinking and action in a specific area of application. To do this, the knowledge about this area must be represented in a model so that it can be processed. The quality of the resulting system depends largely on how well the model was chosen in the development process. Sometimes data-driven methods are suitable for finding a good model and sometimes logic-based knowledge representations deliver better results. Hybrid models are usually used in real applications. According to actual textbooks, the following methods and paradigms, which largely complement each other, can be regarded as parts of CI: Fuzzy systems Neural networks and, in particular, convolutional neural networks Evolutionary computation and, in particular, multi-objective evolutionary optimization Swarm intelligence Bayesian networks Artificial immune systems Learning theory Probabilistic methods == Relationship between hard and soft computing and artificial and computational intelligence == Artificial intelligence (AI) is used in the media, but also by some of the scientists involved, as a kind of umbrella term for the various techniques associated with it or with CI. Craenen and Eiben state that attempts to define or at least describe CI can usually be assigned to one or more of the following groups: "Relative definition” comparing CI to AI Conceptual treatment of key notions and their roles in CI Listing of the (established) areas that belong to it The relationship between CI and AI has been a frequently discussed topic during the development of CI. While the above list implies that they are synonyms, the vast majority of AI/CI researchers working on the subject consider them to be distinct fields, where either CI is an alternative to AI AI includes CI CI includes AI The view of the first of the above three points goes back to Zadeh, the founder of the fuzzy set theory, who differentiated machine intelligence into hard and soft computing techniques, which are used in artificial intelligence on the one hand and computational intelligence on the other. In hard computing (HC) and traditional AI (e.g. expert systems), inaccuracy and uncertainty are undesirable characteristics of a system, while soft computing (SC) and thus CI focus on dealing with these characteristics. The adjacent figure illustrates this view and lists the most important CI techniques. Another frequently mentioned distinguishing feature is the representation of information in symbolic form in AI and in sub-symbolic form in CI techniques. Hard computing is a conventional computing method based on the principles of certainty and accuracy and it is deterministic. It requires a precisely stated analytical model of the task to be processed and a prewritten program, i.e. a fixed set of instructions. The models used are based on Boolean logic (also called crisp logic), where e.g. an element can be either a member of a set or not and there is nothing in between. When applied to real-world tasks, systems based on HC result in specific control actions defined by a mathematical model or algorithm. If an unforeseen situation occurs that is not included in the model or algorithm used, the action will most likely fail. Soft computing, on the other hand, is based on the fact that the human mind is capable of storing information and processing it in a goal-oriented way, even if it is imprecise and lacks certainty. SC is based on the model of the human brain with probabilistic thinking, fuzzy logic and multi-valued logic. Soft computing can process a wealth of data and perform a large number of computations, which may not be exact, in parallel. For hard problems for which no satisfying exact solutions based on HC are available, SC methods can be applied successfully. SC methods are usually stochastic in nature i.e., they are a randomly defined processes that can be analyzed statistically but not with precision. Up to now, the results of some CI methods, such as deep learning, cannot be verified and it is also not clear what they are based on. This problem represents an important scientific issue for the future. AI and CI are catchy terms, but they are also so similar that they can be confused. The meaning of both terms has developed and changed over a long period of time, with AI being used first. Bezdek describes this impressively and concludes that such buzzwords are frequently used and hyped by the scientific community, science management and (science) journalism. Not least because AI and biological intelligence are emotionally charged terms and it is still difficult to find a generally accepted definition for the basic term intelligence. == History == In 1950, Alan Turing, one of the founding fathers of computer science, developed a test for computer intelligence known as the Turing test. In this test, a person can ask questions via a keyboard and a monitor without knowing whether his counterpart is a human or a computer. A computer is considered intelligent if the interrogator cannot distinguish the computer from a human. This illustrates the discussion about intelligent computers at the beginning of the computer age. The term Computational Intelligence was first used as the title of the journal of the same name in 1985 and later by the IEEE Neural Networks Council (NNC), which was founded 1989 by a group of researchers interested in the development of biological and artificial neural networks. On November 21, 2001, the NNC became the IEEE Neural Networks Society, to become the IEEE Computational Intelligence Society two years later by including new areas of interest such as fuzzy systems and evolutionary computation. The NNC helped organize the first IEEE World Congress on Computational Intelligence in Orlando, Florida in 1994. On this conference the first clear definition of Computational Intelligence was introduced by Bezdek: A system is computationally intelligent when it: deals with only numerical (low-level) data, has pattern-recognition components, does not use knowledge in the AI sense; and additionally when it (begins to) exhibit (1) computational adaptivity; (2) computational fault tolerance; (3) speed approaching human-like turnaround and (4) error rates that approximate human performance. Today, with machine learning and deep learning in particular utilizing a breadth of supervised, unsupervised, and reinforcement learning approaches, the CI landscape has been greatly enhanced, with novell intelligent approaches. == The main algorithmic approaches of CI and their applicati
Leslie P. Kaelbling
Leslie Pack Kaelbling is an American roboticist and the Panasonic Professor of Computer Science and Engineering at the Massachusetts Institute of Technology. She is widely recognized for adapting partially observable Markov decision processes from operations research for application in artificial intelligence and robotics. Kaelbling received the IJCAI Computers and Thought Award in 1997 for applying reinforcement learning to embedded control systems and developing programming tools for robot navigation. In 2000, she was elected as a Fellow of the Association for the Advancement of Artificial Intelligence. == Career == Kaelbling received an A. B. in Philosophy in 1983 and a Ph.D. in Computer Science in 1990, both from Stanford University. During this time she was also affiliated with the Center for the Study of Language and Information. She then worked at SRI International and the affiliated robotics spin-off Teleos Research before joining the faculty at Brown University. She left Brown in 1999 to join the faculty at MIT. Her research focuses on decision-making under uncertainty, machine learning, and sensing with applications to robotics. == Journal of Machine Learning Research == In the spring of 2000, she and two-thirds of the editorial board of the Kluwer-owned journal Machine Learning resigned in protest to its pay-to-access archives with simultaneously limited financial compensation for authors. Kaelbling co-founded and served as the first editor-in-chief of the Journal of Machine Learning Research, a peer-reviewed open access journal on the same topics which allows researchers to publish articles for free and retain copyright with its archives freely available online. In response to the mass resignation, Kluwer changed their publishing policy to allow authors to self-archive their papers online after peer-review. Kaelbling responded that this policy was reasonable and would have made the creation of an alternative journal unnecessary, but the editorial board members had made it clear they wanted such a policy and it was only after the threat of resignations and the actual founding of JMLR that the publishing policy finally changed. == Selected works == Reinforcement Learning: A Survey (LP Kaelbling, ML Littman, AW Moore). Journal of Artificial Intelligence Research (JAIR) 4 (1996) 237-285. A highly cited survey on the field of reinforcement learning. Planning and acting in partially observable stochastic domains (LP Kaelbling, ML Littman, AR Cassandra). Artificial Intelligence 101 (1), 99-134. Acting under uncertainty: Discrete Bayesian models for mobile-robot navigation (AR Cassandra, LP Kaelbling, JA Kurien). Intelligent Robots and Systems (2) 963-972. The synthesis of digital machines with provable epistemic properties (SJ Rosenschein, LP Kaelbling). Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge, 83-98. Practical reinforcement learning in continuous spaces (WD Smart, LP Kaelbling). 2000 International Conference on Machine Learning (ICML), 903-910. Hierarchical task and motion planning in the now (LP Kaelbling, T Lozano-Pérez). 2011 IEEE International Conference on Robotics and Automation (ICRA), 1470-1477.
Robert Wilensky
Robert Wilensky (26 March 1951 – 15 March 2013) was an American computer scientist and professor at the UC Berkeley School of Information, with his main focus of research in artificial intelligence. == Academic career == In 1971, Wilensky received his bachelor's degree in mathematics from Yale University, and in 1978, a Ph.D. in computer science from the same institution. After finishing his thesis, "Understanding Goal-Based Stories", Wilensky joined the faculty from the EECS Department of UC Berkeley. In 1986, he worked as the doctoral advisor of Peter Norvig, who then later published the standard textbook of the field: Artificial Intelligence: A Modern Approach. From 1993 to 1997, Wilensky was the Berkeley Computer Science Division Chair. During this time, he also served as director of the Berkeley Cognitive Science Program, director of the Berkeley Artificial Intelligence Research Project, and board member of the International Computer Science Institute. In 1997, he became a fellow of the Association for Computing Machinery "for research contributions to the areas of natural language processing and digital libraries as well as outstanding leadership in Computer Science." Furthermore, he also was a Fellow of the Association for the Advancement of Artificial Intelligence. He retired from faculty in 2007 and died on Friday, March 15, 2013, of a bacterial infection at the Alta Bates Summit Medical Center. Wilensky was married to Ann Danforth and he is survived by her and their two children, Avi and Eli Wilensky == Research == Throughout his career, Wilensky authored and co-authored over 60 scholarly articles and technical reports on AI, natural language processing, and information dissemination. In addition to his numerous technical publications, Wilensky also published two books on the programming language LISP, LISPcraft and Common LISPcraft, and had almost completed another book manuscript when he suffered a cardiac arrest and stopped writing. Among his publications are: R. Wilensky, (1986-09-17). Common LISPcraft. W. W. Norton & Company. ISBN 9780393955446. T. A. Phelps and R. Wilensky, "Toward active, extensible, networked documents: Multivalent architecture and applications," in Proc. 1st ACM Intl. Conf. on Digital Libraries, E. A. Fox and G. Marchionini, Eds., New York, NY: ACM Press, 1996, pp. 100–108. J. Traupman and R. Wilensky, "Experiments in Improving Unsupervised Word Sense Disambiguation," University of California, Berkeley, Department of EECS, Computer Science Division, Tech. Rep. 03–1227, Feb. 2003. R. Wilensky, Planning and Understanding: A Computational Approach to Human Reasoning, Advanced Book Program, Reading, MA: Addison-Wesley Publishing Co., 1983. R. Wilensky, "Understanding Goal-Based Stories," Yale University, Sep. 1978. B. Kahn and R. Wilensky, "A Framework for Distributed Digital Object Services", May 1995.
HFST
Helsinki Finite-State Technology (HFST) is a computer programming library and set of utilities for natural language processing with finite-state automata and finite-state transducers. It is free and open-source software, released under a mix of the GNU General Public License version 3 (GPLv3) and the Apache License. == Features == The library functions as an interchanging interface to multiple backends, such as OpenFST, foma and SFST. The utilities comprise various compilers, such as hfst-twolc (a compiler for morphological two-level rules), hfst-lexc (a compiler for lexicon definitions) and hfst-regexp2fst (a regular expression compiler). Functions from Xerox's proprietary scripting language xfst is duplicated in hfst-xfst, and the pattern matching utility pmatch in hfst-pmatch, which goes beyond the finite-state formalism in having recursive transition networks (RTNs). The library and utilities are written in C++, with an interface to the library in Python and a utility for looking up results from transducers ported to Java and Python. Transducers in HFST may incorporate weights depending on the backend. For performing FST operations, this is currently only possible via the OpenFST backend. HFST provides two native backends, one designed for fast lookup (hfst-optimized-lookup), the other for format interchange. Both of them can be weighted. == Uses == HFST has been used for writing various linguistic tools, such as spell-checkers, hyphenators, and morphologies. Morphological dictionaries written in other formalisms have also been converted to HFST's formats.
Network eavesdropping
Network eavesdropping, also known as eavesdropping attack, sniffing attack, or snooping attack, is a method that retrieves user information through the internet. This attack happens on electronic devices like computers and smartphones. This network attack typically happens under the usage of unsecured networks, such as public wifi connections or shared electronic devices. Eavesdropping attacks through the network is considered one of the most urgent threats in industries that rely on collecting and storing data. Internet users use eavesdropping via the Internet to improve information security. A typical network eavesdropper may be called a Black-hat hacker and is considered a low-level hacker as it is simple to network eavesdrop successfully. The threat of network eavesdroppers is a growing concern. Research and discussions are brought up in the public's eye, for instance, types of eavesdropping, open-source tools, and commercial tools to prevent eavesdropping. Models against network eavesdropping attempts are built and developed as privacy is increasingly valued. Sections on cases of successful network eavesdropping attempts and its laws and policies in the National Security Agency are mentioned. Some laws include the Electronic Communications Privacy Act and the Foreign Intelligence Surveillance Act. == Types of attacks == Types of network eavesdropping include intervening in the process of decryption of messages on communication systems, attempting to access documents stored in a network system, and listening on electronic devices. Types include electronic performance monitoring and control systems, keystroke logging, man-in-the-middle attacks, observing exit nodes on a network, and Skype & Type. === Electronic performance monitoring and control systems (EPMCSs) === Electronic performance monitoring and control systems are used by employees or companies and organizations to collect, store, analyze, and report actions or performances of employers when they are working. The beginning of this system is used to increase the efficiency of workers, but instances of unintentional eavesdropping can occur, for example, when employees' casual phone calls or conversations would be recorded. === Keystroke logging === Keystroke logging is a program that can oversee the writing process of the user. It can be used to analyze the user's typing activities, as keystroke logging provides detailed information on activities like typing speed, pausing, deletion of texts, and more behaviors. By monitoring the activities and sounds of the keyboard strikes, the message typed by the user can be translated. Although keystroke logging systems do not explain reasons for pauses or deletion of texts, it allows attackers to analyze text information. Keystroke logging can also be used with eye-tracking devices which monitor the movements of the user's eyes to determine patterns of the user's typing actions which can be used to explain the reasons for pauses or deletion of texts. === Man-in-the-middle attack (MitM) === A Man-in-the-middle attack is an active eavesdropping method that intrudes on the network system. It can retrieve and alter the information sent between two parties without anyone noticing. The attacker hijacks the communication systems and gains control over the transport of data, but cannot insert voice messages that sound or act like the actual users. Attackers also create independent communications through the system with the users acting as if the conversation between users is private. The "man-in-the-middle" can also be referred to as lurkers in a social context. A lurker is a person who rarely or never posts anything online, but the person stays online and observes other users' actions. Lurking can be valuable as it lets people gain knowledge from other users. However, like eavesdropping, lurking into other users' private information violates privacy and social norms. === Observing exit nodes === Distributed networks including communication networks are usually designed so that nodes can enter and exit the network freely. However, this poses a danger in which attacks can easily access the system and may cause serious consequences, for example, leakage of the user's phone number or credit card number. In many anonymous network pathways, the last node before exiting the network may contain actual information sent by users. Tor exit nodes are an example. Tor is an anonymous communication system that allows users to hide their IP addresses. It also has layers of encryption that protect information sent between users from eavesdropping attempts trying to observe the network traffic. However, Tor exit nodes are used to eavesdrop at the end of the network traffic. The last node in the network path flowing through the traffic, for instance, Tor exit nodes, can acquire original information or messages that were transmitted between different users. === Skype & Type (S&T) === Skype & Type (S&T) is a new keyboard acoustic eavesdropping attack that takes advantage of Voice-over IP (VoIP). S&T is practical and can be used in many applications in the real world, as it does not require attackers to be close to the victim and it can work with only some leaked keystrokes instead of every keystroke. With some knowledge of the victim's typing patterns, attackers can gain a 91.7% accuracy typed by the victim. Different recording devices including laptop microphones, smartphones, and headset microphones can be used for attackers to eavesdrop on the victim's style and speed of typing. It is especially dangerous when attackers know what language the victim is typing in. == Tools to prevent eavesdropping attacks == Computer programs where the source code of the system is shared with the public for free or for commercial use can be used to prevent network eavesdropping. They are often modified to cater to different network systems, and the tools are specific in what task it performs. In this case, Advanced Encryption Standard-256, Bro, Chaosreader, CommView, Firewalls, Security Agencies, Snort, Tcptrace, and Wireshark are tools that address network security and network eavesdropping. === Advanced encryption standard-256 (AES-256) === It is a cipher block chaining (CBC) mode for ciphered messages and hash-based message codes. The AES-256 contains 256 keys for identifying the actual user, and it represents the standard used for securing many layers on the internet. AES-256 is used by Zoom Phone apps that help encrypt chat messages sent by Zoom users. If this feature is used in the app, users will only see encrypted chats when they use the app, and notifications of an encrypted chat will be sent with no content involved. === Bro === Bro is a system that detects network attackers and abnormal traffic on the internet. It emerged at the University of California, Berkeley that detects invading network systems. The system does not apply to the detection of eavesdropping by default, but can be modified to an offline analyzing tool for eavesdropping attacks. Bro runs under Digital Unix, FreeBSD, IRIX, SunOS, and Solaris operating systems, with the implementation of approximately 22,000 lines of C++ and 1,900 lines of Bro. It is still in the process of development for real-world applications. === Chaosreader === Chaosreader is a simplified version of many open-source eavesdropping tools. It creates HTML pages on the content of when a network intrusion is detected. No actions are taken when an attack occurs and only information such as time, network location on which system or wall the user is trying to attack will be recorded. === CommView === CommView is specific to Windows systems which limits real-world applications because of its specific system usage. It captures network traffic and eavesdropping attempts by using packet analyzing and decoding. === Firewalls === Firewall technology filters network traffic and blocks malicious users from attacking the network system. It prevents users from intruding into private networks. Having a firewall in the entrance to a network system requires user authentications before allowing actions performed by users. There are different types of firewall technologies that can be applied to different types of networks. === Security agencies === A Secure Node Identification Agent is a mobile agent used to distinguish secure neighbor nodes and informs the Node Monitoring System (NMOA). The NMOA stays within nodes and monitors the energy exerted, and receives information about nodes including node ID, location, signal strength, hop counts, and more. It detects nodes nearby that are moving out of range by comparing signal strengths. The NMOA signals the Secure Node Identification Agent (SNIA) and updates each other on neighboring node information. The Node BlackBoard is a knowledge base that reads and updates the agents, acting as the brain of the security system. The Node Key Management agent is created when an encryption key is inserted to th
Katz's back-off model
Katz back-off is a generative n-gram language model that estimates the conditional probability of a word given its history in the n-gram. It accomplishes this estimation by backing off through progressively shorter history models under certain conditions. By doing so, the model with the most reliable information about a given history is used to provide the better results. The model was introduced in 1987 by Slava M. Katz. Prior to that, n-gram language models were constructed by training individual models for different n-gram orders using maximum likelihood estimation and then interpolating them together. == Method == The equation for Katz's back-off model is: P b o ( w i ∣ w i − n + 1 ⋯ w i − 1 ) = { d w i − n + 1 ⋯ w i C ( w i − n + 1 ⋯ w i − 1 w i ) C ( w i − n + 1 ⋯ w i − 1 ) if C ( w i − n + 1 ⋯ w i ) > k α w i − n + 1 ⋯ w i − 1 P b o ( w i ∣ w i − n + 2 ⋯ w i − 1 ) otherwise {\displaystyle {\begin{aligned}&P_{bo}(w_{i}\mid w_{i-n+1}\cdots w_{i-1})\\[4pt]={}&{\begin{cases}d_{w_{i-n+1}\cdots w_{i}}{\dfrac {C(w_{i-n+1}\cdots w_{i-1}w_{i})}{C(w_{i-n+1}\cdots w_{i-1})}}&{\text{if }}C(w_{i-n+1}\cdots w_{i})>k\\[10pt]\alpha _{w_{i-n+1}\cdots w_{i-1}}P_{bo}(w_{i}\mid w_{i-n+2}\cdots w_{i-1})&{\text{otherwise}}\end{cases}}\end{aligned}}} where C(x) = number of times x appears in training wi = ith word in the given context Essentially, this means that if the n-gram has been seen more than k times in training, the conditional probability of a word given its history is proportional to the maximum likelihood estimate of that n-gram. Otherwise, the conditional probability is equal to the back-off conditional probability of the (n − 1)-gram. The more difficult part is determining the values for k, d and α. k {\displaystyle k} is the least important of the parameters. It is usually chosen to be 0. However, empirical testing may find better values for k. d {\displaystyle d} is typically the amount of discounting found by Good–Turing estimation. In other words, if Good–Turing estimates C {\displaystyle C} as C ∗ {\displaystyle C^{}} , then d = C ∗ C {\displaystyle d={\frac {C^{}}{C}}} To compute α {\displaystyle \alpha } , it is useful to first define a quantity β, which is the left-over probability mass for the (n − 1)-gram: β w i − n + 1 ⋯ w i − 1 = 1 − ∑ { w i : C ( w i − n + 1 ⋯ w i ) > k } d w i − n + 1 ⋯ w i C ( w i − n + 1 ⋯ w i − 1 w i ) C ( w i − n + 1 ⋯ w i − 1 ) {\displaystyle \beta _{w_{i-n+1}\cdots w_{i-1}}=1-\sum _{\{w_{i}:C(w_{i-n+1}\cdots w_{i})>k\}}d_{w_{i-n+1}\cdots w_{i}}{\frac {C(w_{i-n+1}\cdots w_{i-1}w_{i})}{C(w_{i-n+1}\cdots w_{i-1})}}} Then the back-off weight, α, is computed as follows: α w i − n + 1 ⋯ w i − 1 = β w i − n + 1 ⋯ w i − 1 ∑ { w i : C ( w i − n + 1 ⋯ w i ) ≤ k } P b o ( w i ∣ w i − n + 2 ⋯ w i − 1 ) {\displaystyle \alpha _{w_{i-n+1}\cdots w_{i-1}}={\frac {\beta _{w_{i-n+1}\cdots w_{i-1}}}{\sum _{\{w_{i}:C(w_{i-n+1}\cdots w_{i})\leq k\}}P_{bo}(w_{i}\mid w_{i-n+2}\cdots w_{i-1})}}} The above formula only applies if there is data for the "(n − 1)-gram". If not, the algorithm skips n-1 entirely and uses the Katz estimate for n-2. (and so on until an n-gram with data is found) == Discussion == This model generally works well in practice, but fails in some circumstances. For example, suppose that the bigram "a b" and the unigram "c" are very common, but the trigram "a b c" is never seen. Since "a b" and "c" are very common, it may be significant (that is, not due to chance) that "a b c" is never seen. Perhaps it's not allowed by the rules of the grammar. Instead of assigning a more appropriate value of 0, the method will back off to the bigram and estimate P(c | b), which may be too high.