In statistics, naive (sometimes simple or idiot's) Bayes classifiers are a family of "probabilistic classifiers" which assume that the features are conditionally independent, given the target class. In other words, a naive Bayes model assumes the information about the class provided by each variable is unrelated to the information from the others, with no information shared between the predictors. The highly unrealistic nature of this assumption, called the naive independence assumption, is what gives the classifier its name. These classifiers are some of the simplest Bayesian network models. Naive Bayes classifiers generally perform worse than more advanced models like logistic regressions, especially at quantifying uncertainty (with naive Bayes models often producing wildly overconfident probabilities). However, they are highly scalable, requiring only one parameter for each feature or predictor in a learning problem. Maximum-likelihood training can be done by evaluating a closed-form expression (simply by counting observations in each group), rather than the expensive iterative approximation algorithms required by most other models. Despite the use of Bayes' theorem in the classifier's decision rule, naive Bayes is not (necessarily) a Bayesian method, and naive Bayes models can be fit to data using either Bayesian or frequentist methods. == Introduction == Naive Bayes is a simple technique for constructing classifiers: models that assign class labels to problem instances, represented as vectors of feature values, where the class labels are drawn from some finite set. There is not a single algorithm for training such classifiers, but a family of algorithms based on a common principle: all naive Bayes classifiers assume that the value of a particular feature is independent of the value of any other feature, given the class variable. For example, a fruit may be considered to be an apple if it is red, round, and about 10 cm in diameter. A naive Bayes classifier considers each of these features to contribute independently to the probability that this fruit is an apple, regardless of any possible correlations between the color, roundness, and diameter features. In many practical applications, parameter estimation for naive Bayes models uses the method of maximum likelihood; in other words, one can work with the naive Bayes model without accepting Bayesian probability or using any Bayesian methods. Despite their naive design and apparently oversimplified assumptions, naive Bayes classifiers have worked quite well in many complex real-world situations. In 2004, an analysis of the Bayesian classification problem showed that there are sound theoretical reasons for the apparently implausible efficacy of naive Bayes classifiers. Still, a comprehensive comparison with other classification algorithms in 2006 showed that Bayes classification is outperformed by other approaches, such as boosted trees or random forests. An advantage of naive Bayes is that it only requires a small amount of training data to estimate the parameters necessary for classification. == Probabilistic model == Abstractly, naive Bayes is a conditional probability model: it assigns probabilities p ( C k ∣ x 1 , … , x n ) {\displaystyle p(C_{k}\mid x_{1},\ldots ,x_{n})} for each of the K possible outcomes or classes C k {\displaystyle C_{k}} given a problem instance to be classified, represented by a vector x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})} encoding some n features (independent variables). The problem with the above formulation is that if the number of features n is large or if a feature can take on a large number of values, then basing such a model on probability tables is infeasible. The model must therefore be reformulated to make it more tractable. Using Bayes' theorem, the conditional probability can be decomposed as: p ( C k ∣ x ) = p ( C k ) p ( x ∣ C k ) p ( x ) {\displaystyle p(C_{k}\mid \mathbf {x} )={\frac {p(C_{k})\ p(\mathbf {x} \mid C_{k})}{p(\mathbf {x} )}}\,} In plain English, using Bayesian probability terminology, the above equation can be written as posterior = prior × likelihood evidence {\displaystyle {\text{posterior}}={\frac {{\text{prior}}\times {\text{likelihood}}}{\text{evidence}}}\,} In practice, there is interest only in the numerator of that fraction, because the denominator does not depend on C {\displaystyle C} and the values of the features x i {\displaystyle x_{i}} are given, so that the denominator is effectively constant. The numerator is equivalent to the joint probability model p ( C k , x 1 , … , x n ) {\displaystyle p(C_{k},x_{1},\ldots ,x_{n})\,} which can be rewritten as follows, using the chain rule for repeated applications of the definition of conditional probability: p ( C k , x 1 , … , x n ) = p ( x 1 , … , x n , C k ) = p ( x 1 ∣ x 2 , … , x n , C k ) p ( x 2 , … , x n , C k ) = p ( x 1 ∣ x 2 , … , x n , C k ) p ( x 2 ∣ x 3 , … , x n , C k ) p ( x 3 , … , x n , C k ) = ⋯ = p ( x 1 ∣ x 2 , … , x n , C k ) p ( x 2 ∣ x 3 , … , x n , C k ) ⋯ p ( x n − 1 ∣ x n , C k ) p ( x n ∣ C k ) p ( C k ) {\displaystyle {\begin{aligned}p(C_{k},x_{1},\ldots ,x_{n})&=p(x_{1},\ldots ,x_{n},C_{k})\\&=p(x_{1}\mid x_{2},\ldots ,x_{n},C_{k})\ p(x_{2},\ldots ,x_{n},C_{k})\\&=p(x_{1}\mid x_{2},\ldots ,x_{n},C_{k})\ p(x_{2}\mid x_{3},\ldots ,x_{n},C_{k})\ p(x_{3},\ldots ,x_{n},C_{k})\\&=\cdots \\&=p(x_{1}\mid x_{2},\ldots ,x_{n},C_{k})\ p(x_{2}\mid x_{3},\ldots ,x_{n},C_{k})\cdots p(x_{n-1}\mid x_{n},C_{k})\ p(x_{n}\mid C_{k})\ p(C_{k})\\\end{aligned}}} Now the "naive" conditional independence assumptions come into play: assume that all features in x {\displaystyle \mathbf {x} } are mutually independent, conditional on the category C k {\displaystyle C_{k}} . Under this assumption, p ( x i ∣ x i + 1 , … , x n , C k ) = p ( x i ∣ C k ) . {\displaystyle p(x_{i}\mid x_{i+1},\ldots ,x_{n},C_{k})=p(x_{i}\mid C_{k})\,.} Thus, the joint model can be expressed as p ( C k ∣ x 1 , … , x n ) ∝ p ( C k , x 1 , … , x n ) = p ( C k ) p ( x 1 ∣ C k ) p ( x 2 ∣ C k ) p ( x 3 ∣ C k ) ⋯ = p ( C k ) ∏ i = 1 n p ( x i ∣ C k ) , {\displaystyle {\begin{aligned}p(C_{k}\mid x_{1},\ldots ,x_{n})\varpropto \ &p(C_{k},x_{1},\ldots ,x_{n})\\&=p(C_{k})\ p(x_{1}\mid C_{k})\ p(x_{2}\mid C_{k})\ p(x_{3}\mid C_{k})\ \cdots \\&=p(C_{k})\prod _{i=1}^{n}p(x_{i}\mid C_{k})\,,\end{aligned}}} where ∝ {\displaystyle \varpropto } denotes proportionality since the denominator p ( x ) {\displaystyle p(\mathbf {x} )} is omitted. This means that under the above independence assumptions, the conditional distribution over the class variable C {\displaystyle C} is: p ( C k ∣ x 1 , … , x n ) = 1 Z p ( C k ) ∏ i = 1 n p ( x i ∣ C k ) {\displaystyle p(C_{k}\mid x_{1},\ldots ,x_{n})={\frac {1}{Z}}\ p(C_{k})\prod _{i=1}^{n}p(x_{i}\mid C_{k})} where the evidence Z = p ( x ) = ∑ k p ( C k ) p ( x ∣ C k ) {\displaystyle Z=p(\mathbf {x} )=\sum _{k}p(C_{k})\ p(\mathbf {x} \mid C_{k})} is a scaling factor dependent only on x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} , that is, a constant if the values of the feature variables are known. Often, it is only necessary to discriminate between classes. In that case, the scaling factor is irrelevant, and it is sufficient to calculate the log-probability up to a factor: ln p ( C k ∣ x 1 , … , x n ) = ln p ( C k ) + ∑ i = 1 n ln p ( x i ∣ C k ) − ln Z ⏟ irrelevant {\displaystyle \ln p(C_{k}\mid x_{1},\ldots ,x_{n})=\ln p(C_{k})+\sum _{i=1}^{n}\ln p(x_{i}\mid C_{k})\underbrace {-\ln Z} _{\text{irrelevant}}} The scaling factor is irrelevant, since discrimination subtracts it away: ln p ( C k ∣ x 1 , … , x n ) p ( C l ∣ x 1 , … , x n ) = ( ln p ( C k ) + ∑ i = 1 n ln p ( x i ∣ C k ) ) − ( ln p ( C l ) + ∑ i = 1 n ln p ( x i ∣ C l ) ) {\displaystyle \ln {\frac {p(C_{k}\mid x_{1},\ldots ,x_{n})}{p(C_{l}\mid x_{1},\ldots ,x_{n})}}=\left(\ln p(C_{k})+\sum _{i=1}^{n}\ln p(x_{i}\mid C_{k})\right)-\left(\ln p(C_{l})+\sum _{i=1}^{n}\ln p(x_{i}\mid C_{l})\right)} There are two benefits of using log-probability. One is that it allows an interpretation in information theory, where log-probabilities are units of information in nats. Another is that it avoids arithmetic underflow. === Constructing a classifier from the probability model === The discussion so far has derived the independent feature model, that is, the naive Bayes probability model. The naive Bayes classifier combines this model with a decision rule. One common rule is to pick the hypothesis that is most probable so as to minimize the probability of misclassification; this is known as the maximum a posteriori or MAP decision rule. The corresponding classifier, a Bayes classifier, is the function that assigns a class label y ^ = C k {\displaystyle {\hat {y}}=C_{k}} for some k as follows: y ^ = argmax k ∈ { 1 , … , K } p ( C k ) ∏ i = 1 n p ( x i ∣ C k ) . {\displaystyle {\hat {y}}={\underset {k\in \{1,\ldots ,K\}}{\operatorname {argmax} }}\ p(C_{k})\displays
AI-assisted software development
AI-assisted software development is the use of artificial intelligence (AI) to augment software development. It uses large language models (LLMs), AI agents and other AI technologies to assist software developers. It helps in a range of tasks of the software development life cycle, from code generation to debugging, editing, testing, UI design, understanding the code, and documentation. Agentic coding denotes the use of AI agents for software development. == Technologies == === Source code generation === Large language models trained or fine-tuned on source-code corpora can generate source code from natural-language descriptions, comments, or docstrings. Research on code-generation systems often evaluates generated programs by functional correctness, such as whether the output passes automated test cases, rather than by syntax alone. Such tools can be features or extensions of integrated development environments (IDEs). === Intelligent code completion === AI agents using pre-trained and fine-tuned LLMs can predict and suggest code completions based on context. According to Husein, Aburajouh & Catal in a 2025 literature review in Computer Standards & Interfaces, "LLMs significantly enhance code completion performance across several programming languages and contexts, and their capability to predict relevant code snippets based on context and partial input boosts developer productivity substantially." === Testing, debugging, code review and analysis === AI is used to automatically generate test cases, identify potential bugs and security vulnerabilities, and suggest fixes. AI can also be used to perform static code analysis and suggest potential performance improvements. == Limitations == Both ownership of and responsibility for AI-generated code is disputed. According to a report from the German Federal Office for Information Security, the use of AI coding assistants without careful oversight from experienced developers can introduce both minor and major security vulnerabilities, and any potential gain in productivity should be weighed against the cost of additional quality control and security measures. According to Deloitte, outputs from AI-assisted software development must be validated through a combination of automated testing, static analysis tools and human review, creating a governance layer to improve quality and accountability. == Vibe coding ==
IMazing
iMazing is mobile device management software that allows users to transfer files and data between iOS devices (iPhone, iPad and iPod Touch) and macOS or Windows computers, in addition to many other features beyond the scope of what Apple's own tools enable. == History == Developed by DigiDNA, iMazing was initially released in 2008 as DiskAid, enabling users to transfer data and files from the iPhone or iPod Touch to Mac or Windows computers. DiskAid was renamed iMazing in 2014. Version 2.0 was released on September 13, 2016. In August 2021, version 2.14 of iMazing added a spyware detection feature. The feature is based on Amnesty International’s Mobile Verification Toolkit to detect Pegasus Spyware following the publication of Pegasus Project. == Description == With iMazing, an iPhone or iPad can be used similarly to an external hard drive. It performs tasks that iTunes doesn’t offer, including incremental backups of iOS devices, browsing and exporting text and voicemail messages, managing apps, encryption, and migrating data from an old phone to a new one. The menu bar app iMazing Mini enables automatic, wireless and encrypted backups of iPhones. The iMazing HEIC Converter is a free desktop app for Mac and PC that lets users convert photos from HEIC format to JPG or PNG.
Fake nude photography
Fake nude photography is the creation of nude photographs designed to appear as genuine nudes of an individual. The motivations for the creation of these modified photographs include curiosity, sexual gratification, the stigmatization or embarrassment of the subject, and commercial gain, such as through the sale of the photographs via pornographic websites. Fakes can be created using image editing software or through machine learning. Fake images created using the latter method are called deepfakes. == History == Magazines such as Celebrity Skin published non-fake paparazzi shots and illicitly obtained nude photos, showing there was a market for such images. Subsequently, some websites hosted fake nude or pornographic photos of celebrities, which are sometimes referred to as celebrity fakes. In the 1990s and 2000s, fake nude images of celebrities proliferated on Usenet and on websites, leading to campaigns to take legal action against the creators of the images and websites dedicated to determining the veracity of nude photos. "Deepfakes", which use artificial neural networks to superimpose one person's face into an image or video of someone else, were popularized in the late 2010s, leading to concerns about the technology's use in fake news and revenge porn. Fake nude photography is sometimes confused with Deepfake pornography, but the two are distinct. Fake nude photography typically starts with human-made non-sexual images, and merely makes it appear that the people in them are nude (but not having sex). Deepfake pornography typically starts with human-made sexual (pornographic) images or videos, and alters the actors' facial features to make the participants in the sexual act look like someone else. === DeepNude === In June 2019, a downloadable Windows and Linux application called DeepNude was released which used a Generative Adversarial Network to remove clothing from images of women. The images it produced were typically not pornographic, merely nude. Because there were more images of nude women than men available to its creator, the images it produced were all female, even when the original was male. The app had both a paid and unpaid version. A few days later, on June 27, the creators removed the application and refunded consumers, although various copies of the app, both free and for charge, continue to exist. On GitHub, the open-source version of this program called "open-deepnude" was deleted. The open-source version had the advantage of allowing it to be trained on a larger dataset of nude images to increase the resulting nude image's accuracy level. A successor free software application, Dreamtime, was later released, and some copies of it remain available, though some have been suppressed. === Deepfake Telegram Bot === In July 2019 a deepfake bot service was launched on messaging app Telegram that used AI technology to create nude images of women. The service was free and enabled users to submit photos and receive manipulated nude images within minutes. The service was connected to seven Telegram channels, including the main channel that hosts the bot, technical support, and image sharing channels. While the total number of users was unknown, the main channel had over 45,000 members. As of July 2020, it is estimated that approximately 24,000 manipulated images had been shared across the image sharing channels. === Nudify websites === By late 2024, most ways to produce nude images from photographs of clothed people were accessible at websites rather than in apps, and required payment. == Purposes == The reasons for the creation of nude photos may range from a need to discredit the target publicly, personal hatred for the target, or the promise of pecuniary gains for such work on the part of the creator of such photos. Fake nude photos often target prominent figures such as businesspeople or politicians. == Notable cases == In 2010, 97 people were arrested in Korea after spreading fake nude pictures of the group Girls' Generation on the internet. In 2011, a 53-year-old Incheon man was arrested after spreading more fake pictures of the same group. In 2012, South Korean police identified 157 Korean artists of whom fake nudes were circulating. In 2012, when Liu Yifei's fake nude photography released on the network, Liu Yifei Red Star Land Company declared a legal search to find out who created and released the photos. In the same year, Chinese actor Huang Xiaoming released nude photos that sparked public controversy, but they were ultimately proven to be real pictures. In 2014, supermodel Kate Upton threatened to sue a website for posting her fake nude photos. Previously, in 2011, this page was threatened by Taylor Swift. In November 2014, singer Rain was angry because of a fake nude photo that spread throughout the internet. Information reveals that: "Rain's nude photo was released from Kim Tae-hee's lost phone." Rain's label, Cube Entertainment, stated that the person in the nude photo is not Rain and the company has since stated that it will take strict legal action against those who post photos together with false comments. In July 2018, Seoul police launched an investigation after a fake nude photo of President Moon Jae-in was posted on the website of the Korean radical feminist group WOMAD. In early 2019, Alexandria Ocasio-Cortez, a Democratic politician, was berated by other political parties over a fake nude photo of her in the bathroom. The picture created a huge wave of media controversy in the United States. == Methods == Fake nude images can be created using image editing software or neural network applications. There are two basic methods: Combine and superimpose existing images onto source images, adding the face of the subject onto a nude model. Remove clothes from the source image to make it look like a nude photo. == Impact == Images of this type may have a negative psychological impact on the victims and may be used for extortion purposes.
Deductive language
A deductive language is a computer programming language in which the program is a collection of predicates ('facts') and rules that connect them. Such a language is used to create knowledge based systems or expert systems which can deduce answers to problem sets by applying the rules to the facts they have been given. An example of a deductive language is Prolog, or its database-query cousin, Datalog. == History == As the name implies, deductive languages are rooted in the principles of deductive reasoning; making inferences based upon current knowledge. The first recommendation to use a clausal form of logic for representing computer programs was made by Cordell Green (1969) at Stanford Research Institute (now SRI International). This idea can also be linked back to the battle between procedural and declarative information representation in early artificial intelligence systems. Deductive languages and their use in logic programming can also be dated to the same year when Foster and Elcock introduced Absys, the first deductive/logical programming language. Shortly after, the first Prolog system was introduced in 1972 by Colmerauer through collaboration with Robert Kowalski. == Components == The components of a deductive language are a system of formal logic and a knowledge base upon which the logic is applied. === Formal Logic === Formal logic is the study of inference in regards to formal content. The distinguishing feature between formal and informal logic is that in the former case, the logical rule applied to the content is not specific to a situation. The laws hold regardless of a change in context. Although first-order logic is described in the example below to demonstrate the uses of a deductive language, no formal system is mandated and the use of a specific system is defined within the language rules or grammar. As input, a predicate takes any object(s) in the domain of interest and outputs either one of two Boolean values: true or false. For example, consider the sentences "Barack Obama is the 44th president" and "If it rains today, I will bring an umbrella". The first is a statement with an associated truth value. The second is a conditional statement relying on the value of some other statement. Either of these sentences can be broken down into predicates which can be compared and form the knowledge base of a deductive language. Moreover, variables such as 'Barack Obama' or 'president' can be quantified over. For example, take 'Barack Obama' as variable 'x'. In the sentence "There exists an 'x' such that if 'x' is the president, then 'x' is the commander in chief." This is an example of the existential quantifier in first order logic. Take 'president' to be the variable 'y'. In the sentence "For every 'y', 'y' is the leader of their nation." This is an example of the universal quantifier. === Knowledge Base === A collection of 'facts' or predicates and variables form the knowledge base of a deductive language. Depending on the language, the order of declaration of these predicates within the knowledge base may or may not influence the result of applying logical rules. Upon application of certain 'rules' or inferences, new predicates may be added to a knowledge base. As new facts are established or added, they form the basis for new inferences. As the core of early expert systems, artificial intelligence systems which can make decisions like an expert human, knowledge bases provided more information than databases. They contained structured data, with classes, subclasses, and instances. == Prolog == Prolog is an example of a deductive, declarative language that applies first- order logic to a knowledge base. To run a program in Prolog, a query is posed and based upon the inference engine and the specific facts in the knowledge base, a result is returned. The result can be anything appropriate from a new relation or predicate, to a literal such as a Boolean (true/false), depending on the engine and type system.
Facial age estimation
Facial age estimation is the use of artificial intelligence to estimate the age of a person based on their facial features. Computer vision techniques are used to analyse the facial features in the images of millions of people whose age is known and then deep learning is used to create an algorithm that tries to predict the age of an unknown person. The key use of the technology is to prevent access to age-restricted goods and services. Examples include restricting children from accessing internet pornography, checking that they meet a mandatory minimum age when registering for an account on social media, or preventing adults from accessing websites, online chat or games designed only for use by children. The technology is distinct from facial recognition systems as the software does not attempt to uniquely identify the individual. Researchers have applied neural networks for age estimation since at least 2010. == Evaluation == An ongoing study by the National Institute of Standards and Technology (NIST) entitled 'Face Analysis Technology Evaluation' seeks to establish the technical performance of prototype age estimation algorithms submitted by academic teams and software vendors including Brno University of Technology, Czech Technical University in Prague, Dermalog, IDEMIA, Incode Technologies Inc, Jumio, Nominder, Rank One Computing, Unissey and Yoti. == Public sector use == The UK government has explored using facial age estimation at the UK border as an alternative to bone X-rays and MRI scans when determining child status of asylum seekers. == Commercial use == Commercial users of facial age estimation include Instagram and OnlyFans. In January 2025, John Lewis & Partners announced that had started using the technology to check the age of people shopping for knives on its website, to comply with UK legislation to limit knife crime. In the UK, several supermarket chains have taken part in Home Office trials of the technology to automate the checking of a customer's age when buying age-restricted goods such as alcohol. UK legislation introduced in January 2025 mandates robust forms of age verification hosting adult content viewable in the UK by July 2025. Allowable methods include facial age estimation. == Criticism == Adam Schwartz, a lawyer for the Electronic Frontier Foundation, criticized the use of facial age estimation software, noting its inaccuracy especially in cases of minorities and women, as was found in NIST's 2024 report. Twenty organisations jointly under European Digital Rights called the practice a "systematic and invasive processing of young people's data" that risks discriminatory profiling.
Tandem (app)
Tandem is a mobile language exchange and language learning app. == History == Tandem was founded in Hannover, Germany in 2014 by Arnd Aschentrup, Tobias Dickmeis, and Matthias Kleimann. Prior to founding Tandem, the trio had launched Vive, a members-only mobile video chat platform. Tandem has been criticised for not accepting members into the community immediately, as opposed to competitors including HelloTalk, Speaky or Cafehub. In some countries, there is a waiting list and applicants can wait up to seven days for their application to be processed by human moderators. In 2015, Tandem completed its first funding round (seed funding) of €600,000. Participating investors included business angels such as Atlantic Labs (Christophe Maire), Hannover Beteiligungsfonds, Marcus Englert (Chairman of the Supervisory Board of Rocket Internet SE ), Catagonia, Ludwig zu Salm, Florian Langenscheidt, Heiko Hubertz, Martin Sinner, and Zehden Enterprises. In 2016, the company received a further €2 million from new investors Rubylight and Faber Ventures, as well as from existing investors Hannover Beteiligungsfonds, Atlantic Labs, and Zehden Enterprises. Since 2018, the premium membership Tandem Pro has been available, which offers members unlimited access to all language learning features of the app as well as the removal of advertising for a monthly fee.