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Inductive bias
The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered. Inductive bias is anything which makes the algorithm learn one pattern instead of another pattern (e.g., step-functions in decision trees instead of continuous functions in linear regression models). Learning involves searching a space of solutions for a solution that provides a good explanation of the data. However, in many cases, there may be multiple equally appropriate solutions. An inductive bias allows a learning algorithm to prioritize one solution (or interpretation) over another, independently of the observed data. In machine learning, the aim is to construct algorithms that are able to learn to predict a certain target output. To achieve this, the learning algorithm is presented some training examples that demonstrate the intended relation of input and output values. Then the learner is supposed to approximate the correct output, even for examples that have not been shown during training. Without any additional assumptions, this problem cannot be solved since unseen situations might have an arbitrary output value. The kind of necessary assumptions about the nature of the target function are subsumed in the phrase inductive bias. A classical example of an inductive bias is Occam's razor, assuming that the simplest consistent hypothesis about the target function is actually the best. Here, consistent means that the hypothesis of the learner yields correct outputs for all of the examples that have been given to the algorithm. Approaches to a more formal definition of inductive bias are based on mathematical logic. Here, the inductive bias is a logical formula that, together with the training data, logically entails the hypothesis generated by the learner. However, this strict formalism fails in many practical cases in which the inductive bias can only be given as a rough description (e.g., in the case of artificial neural networks), or not at all. == Types == The following is a list of common inductive biases in machine learning algorithms. Maximum conditional independence: if the hypothesis can be cast in a Bayesian framework, try to maximize conditional independence. This is the bias used in the Naive Bayes classifier. Minimum cross-validation error: when trying to choose among hypotheses, select the hypothesis with the lowest cross-validation error. Although cross-validation may seem to be free of bias, the "no free lunch" theorems show that cross-validation must be biased, for example assuming that there is no information encoded in the ordering of the data. Maximum margin: when drawing a boundary between two classes, attempt to maximize the width of the boundary. This is the bias used in support vector machines. The assumption is that distinct classes tend to be separated by wide boundaries. Minimum description length: when forming a hypothesis, attempt to minimize the length of the description of the hypothesis. Minimum features: unless there is good evidence that a feature is useful, it should be deleted. This is the assumption behind feature selection algorithms. Nearest neighbors: assume that most of the cases in a small neighborhood in feature space belong to the same class. Given a case for which the class is unknown, guess that it belongs to the same class as the majority in its immediate neighborhood. This is the bias used in the k-nearest neighbors algorithm. The assumption is that cases that are near each other tend to belong to the same class. == Shift of bias == Although most learning algorithms have a static bias, some algorithms are designed to shift their bias as they acquire more data. This does not avoid bias, since the bias shifting process itself must have a bias.
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CarPlay
CarPlay is an Apple standard that enables a car radio or automotive head unit to be a display and controller for an iOS device. It is available on iPhone 5 and later models running iOS 7.1 or later. More than 800 car and motorcycle models support CarPlay, according to Apple. Vehicle owners can add support by installing certain aftermarket vehicle audio products. Most CarPlay systems connect to iOS through USB, some are wireless, and wireless support can be added through aftermarket dongles. CarPlay Ultra, a more integrated version of CarPlay, was first announced on Aston Martin DBX707 in May 2025. == Software == Apple's CarPlay-enabled apps include: Phone Apple Music Apple Maps Calendar Messages Audiobooks (part of Apple Books) Podcasts Settings News Developers must obtain permission from Apple to develop CarPlay-enabled apps. Such apps fall into five categories: Audio: primarily provide audio content, such as music or podcasts. Examples: Amazon Music, Audible, Google Play Music, iHeartRadio, QQ Music, Spotify, and Overcast. Navigation: turn-by-turn guidance, including searching for points of interests and navigating to a destination. Examples: AutoNavi, Baidu Maps, Google Maps, ChargeFinder and Waze. Automaker-made apps allow a user to control vehicle-specific features such as climate controls, gas levels, or radio via CarPlay. Messaging/Voice over IP (VoIP): listen to new messages and reply using dictation in an audio-only interface. Messaging apps on CarPlay integrate with third-party Siri support (known as SiriKit), while VoIP apps integrate with the iOS calling interface using CallKit. Examples: Telegram, WhatsApp, and Zoom. Food-ordering and parking-services apps. To discourage distracted driving, Siri is used extensively, providing voice turn-by-turn navigation guidance and voice-input for text messages. Newscast-style weather and stock results are announced instead of displayed. Requests that bring up visual information may be blocked when the car is in gear, and most native CarPlay apps deliver audio content with minimal interaction. CarPlay-enabled apps installed on the device appear on the CarPlay home screen unless disabled by the user. The inclusion or exclusion and order of app appearance can be changed on a per-vehicle basis. == Hardware == Most of the CarPlay software runs on the connected iPhone. The CarPlay interface provides audio output and a visual display to the vehicle's infotainment system, while adapting to the vehicle's available control methods, including touch screens, rotary dials, physical buttons, steering-wheel controls, and hands-free microphones. Aftermarket head units may support CarPlay or Android Auto, and many support both platforms. === Wired CarPlay === In a wired CarPlay configuration, the iPhone connects to the vehicle or head unit via a USB cable. The USB connection supplies power to the iPhone and provides a stable data link for audio, video, and control input. Wired CarPlay is supported by a wide range of factory-installed infotainment systems and aftermarket head units. Some third-party devices marketed as wireless CarPlay adapters operate by emulating a wired CarPlay connection to the vehicle. These devices plug into the vehicle's USB port and present themselves as a wired CarPlay interface, while separately establishing a wireless connection to the iPhone. Such devices still require the vehicle or head unit to support standard (wired) CarPlay. === Wireless CarPlay === Wireless CarPlay allows the iPhone to connect to a compatible vehicle or head unit without a physical cable. During the initial pairing process, the iPhone exchanges network credentials with the CarPlay receiver over Bluetooth. Once paired, CarPlay data is transmitted over a two-way Wi-Fi connection between the phone and the vehicle. Wireless CarPlay support depends on both the vehicle or head unit hardware and the iPhone model, and is generally limited to newer factory systems and select aftermarket receivers. == History == === Predecessor === In 2008, one year after the release of the iPhone, Mercedes vehicles were first to sell an audio system incorporating both the iPod and iPhone, equipped with 30-pin iOS input jacks. The new 2008 Harman Kardon NTG 2.5 featured full audio streaming, syncing, charging and control integrated into the steering wheel controls, instrument panel, and head unit. Apple was working with Mercedes to develop iOS compatible audio systems into their cars first only a year after iPhone launch. With an Apple Lightning-to-30-pin adapter, iPhones/iPods remain backwards-compatible with the Harman Kardon 2.5 and later models. This is the earliest audio system specifically engineered for iPod/iPhone integration, which predated CarPlay and every other manufacturer incorporating iOS into vehicles. The concept of CarPlay was based on the iOS 4 feature called "iPod Out" which was produced through several years of joint development by Apple and the BMW Group's Technology Office USA. iPod Out enabled vehicles with the necessary infrastructure to "host" the analog video and audio from a supporting iOS device while receiving inputs, such as button presses and knob rotations, from a car's infotainment system, to drive the "hosted" user interface in the vehicle's built-in display. It was announced at WWDC 2010 and first shipped in BMW Group vehicles in early 2011. The BMW and Mini option was called "PlugIn" and paved the way for the first cross-OEM platforms, introducing the concept of requiring a car-specific interface for apps (as opposed to MirrorLink's simple and insufficient mirroring of what was shown on the smartphone's screen). === Development === CarPlay's codename was Stark. Apple's Eddy Cue announced it as iOS in the Car at WWDC 2013. In January 2014, it was reported that Apple's hardware-oriented corporate culture had led to release delays. iOS in the Car was then rebranded and launched as CarPlay with significant design changes at the Geneva Motor Show in March 2014 with Ferrari, Kia, Mercedes-Benz, and Volvo among the first car manufacturers. At WWDC 2022, Apple announced plans to release an all-new version of CarPlay, informally dubbed CarPlay 2. The new version was said to be able to control vehicle functions, access vehicle stats, and take over multiple vehicle screens. Officials said they planned to release it in late 2024 and that manufacturers that are planning to adopt the new CarPlay include: Audi, Acura, Ford, Honda, Infiniti, Jaguar, Land Rover, Lincoln, Mercedes-Benz, Nissan, Polestar, Porsche, Renault, and Volvo. In January 2025, amidst delays, Apple removed the planned released date from its website. On May 15, 2025, Apple announced that next-generation CarPlay, now called CarPlay Ultra, would be included with all new vehicles from Aston Martin. Existing vehicles will also be receiving CarPlay Ultra through a future software update. It is only available in the US and Canada. == Timeline == June 2013: Apple introduced iOS in the Car; an early version of CarPlay that was never publicly released, at WWDC 2013. June 2013: BMW officials announced their cars would not support iOS in the Car; they later changed their minds. November 2013: Siri Eyes Free mode was offered as a dealer-installed accessory in the US to some Honda Accord and Acura RDX & ILX models. In December, Honda offered additional integration, featuring new HondaLink services, on some US and Canada models of the Civic and the Fit. March 2014: Apple introduced CarPlay, which was renamed from iOS in the Car with significant design changes, at the 2014 Geneva Motor Show with automakers Ferrari, Mercedes-Benz and Volvo. September 2014: A Ferrari FF was the first car with a full version of CarPlay. November 2014: Hyundai announced the Sonata sedan would be their first model with available CarPlay by the end of the first quarter of 2015. January 2015: Volkswagen announced CarPlay support would be coming later in 2015 and would be either standard or available on the majority of their 2016 model year lineup. May 2015: General Motors announced CarPlay would be available starting with 14 different 2016 model year Chevrolet vehicles. July 2015: Honda announced CarPlay would be available in their vehicles starting with the 2016 Honda Accord. December 2015: Volvo implemented CarPlay in the 2016 Volvo XC90 as their first vehicle with CarPlay support. December 2015: Mercedes-Benz confirmed that CarPlay would be available starting with select 2016 model year vehicles. January 2016: Apple released a list detailing the car models which support CarPlay. January 2016: Ford announced CarPlay would be available on all 2017 Ford/Lincoln model year vehicles equipped with the Sync 3 infotainment system. January 2016: FCA (now a part of Stellantis) announced CarPlay would be available on their UConnect infotainment system starting with select 2016 model year vehicles. March 2016: Subaru announced the beginning of CarPlay and Android Auto support, st
Level set (data structures)
In computer science, a level set is a data structure designed to represent discretely sampled dynamic level sets of functions. A common use of this form of data structure is in efficient image rendering. The underlying method constructs a signed distance field that extends from the boundary, and can be used to solve the motion of the boundary in this field. == Chronological developments == The powerful level-set method is due to Osher and Sethian 1988. However, the straightforward implementation via a dense d-dimensional array of values, results in both time and storage complexity of O ( n d ) {\displaystyle O(n^{d})} , where n {\displaystyle n} is the cross sectional resolution of the spatial extents of the domain and d {\displaystyle d} is the number of spatial dimensions of the domain. === Narrow band === The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian, restricted most computations to a thin band of active voxels immediately surrounding the interface, thus reducing the time complexity in three dimensions to O ( n 2 ) {\displaystyle O(n^{2})} for most operations. Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an O ( n 3 ) {\displaystyle O(n^{3})} operation in which voxels over the entire volume were accessed. The storage complexity for this narrowband scheme was still O ( n 3 ) . {\displaystyle O(n^{3}).} Differential constructions over the narrow band domain edge require careful interpolation and domain alteration schemes to stabilise the solution. === Sparse field === This O ( n 3 ) {\displaystyle O(n^{3})} time complexity was eliminated in the approximate "sparse field" level set method introduced by Whitaker in 1998. The sparse field level set method employs a set of linked lists to track the active voxels around the interface. This allows incremental extension of the active region as needed without incurring any significant overhead. While consistently O ( n 2 ) {\displaystyle O(n^{2})} efficient in time, O ( n 3 ) {\displaystyle O(n^{3})} storage space is still required by the sparse field level set method. See for implementation details. === Sparse block grid === The sparse block grid method, introduced by Bridson in 2003, divides the entire bounding volume of size n 3 {\displaystyle n^{3}} into small cubic blocks of m 3 {\displaystyle m^{3}} voxels each. A coarse grid of size ( n / m ) 3 {\displaystyle (n/m)^{3}} then stores pointers only to those blocks that intersect the narrow band of the level set. Block allocation and deallocation occur as the surface propagates to accommodate to the deformations. This method has a suboptimal storage complexity of O ( ( n m ) 3 + m 3 n 2 ) {\displaystyle O\left((nm)3+m^{3}n^{2}\right)} , but retains the constant time access inherent to dense grids. === Octree === The octree level set method, introduced by Strain in 1999 and refined by Losasso, Gibou and Fedkiw, and more recently by Min and Gibou uses a tree of nested cubes of which the leaf nodes contain signed distance values. Octree level sets currently require uniform refinement along the interface (i.e. the narrow band) in order to obtain sufficient precision. This representation is efficient in terms of storage, O ( n 2 ) , {\displaystyle O(n^{2}),} and relatively efficient in terms of access queries, O ( log n ) . {\displaystyle O(\log \,n).} An advantage of the level method on octree data structures is that one can solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group has developed this line of work in computational materials, computational fluid dynamics, electrokinetics, image-guided surgery and controls. === Run-length encoded === The run-length encoding (RLE) level set method, introduced in 2004, applies the RLE scheme to compress regions away from the narrow band to just their sign representation while storing with full precision the narrow band. The sequential traversal of the narrow band is optimal and storage efficiency is further improved over the octree level set. The addition of an acceleration lookup table allows for fast O ( log r ) {\displaystyle O(\log r)} random access, where r is the number of runs per cross section. Additional efficiency is gained by applying the RLE scheme in a dimensional recursive fashion, a technique introduced by Nielsen & Museth's similar DT-Grid. === Hash Table Local Level Set === The Hash Table Local Level Set method was introduced in 2011 by Eyiyurekli and Breen and extended in 2012 by Brun, Guittet, and Gibou, only computes the level set data in a band around the interface, as in the Narrow Band Level-Set Method, but also only stores the data in that same band. A hash table data structure is used, which provides an O ( 1 ) {\displaystyle O(1)} access to the data. However, Brun et al. conclude that their method, while being easier to implement, performs worse than a quadtree implementation. They find that as it is, [...] a quadtree data structure seems more adapted than the hash table data structure for level-set algorithms. Three main reasons for worse efficiency are listed: to obtain accurate results, a rather large band is required close to the interface, which counterbalances the absence of grid nodes far from the interface; the performances are deteriorated by extrapolation procedures on the outer edges of the local grid and the width of the band restricts the time step and slows down the method. === Point-based === Corbett in 2005 introduced the point-based level set method. Instead of using a uniform sampling of the level set, the continuous level set function is reconstructed from a set of unorganized point samples via moving least squares.
Co-occurrence
In linguistics, co-occurrence or cooccurrence (in older texts often shown with diacritic as coöccurrence) is an above-chance frequency of ordered occurrence of two adjacent terms in a text corpus. Co-occurrence in this linguistic sense can be interpreted as an indicator of semantic proximity or an idiomatic expression. Corpus linguistics and its statistical analyses can reveal (regularity of) patterns of co-occurrences within a language and enable the working out of typical collocations for its lexical items. A co-occurrence restriction is identified when linguistic elements never occur together. Analysis of these restrictions can lead to discoveries about the structure and development of a language. Co-occurrence can be seen an extension of word counting in higher dimensions. Co-occurrence can be quantitatively described using measures like a massive correlation or mutual information. Co-occurrence information and knowledge of co-occurring words may be relevant in analysis of language for the purposes of large language models, part of the emerging field of artificial intelligence, and helpful in word games such as scrabble.