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Kernel embedding of distributions
In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which a probability distribution is represented as an element of a reproducing kernel Hilbert space (RKHS). A generalization of the individual data-point feature mapping done in classical kernel methods, the embedding of distributions into infinite-dimensional feature spaces can preserve all of the statistical features of arbitrary distributions, while allowing one to compare and manipulate distributions using Hilbert space operations such as inner products, distances, projections, linear transformations, and spectral analysis. This learning framework is very general and can be applied to distributions over any space Ω {\displaystyle \Omega } on which a sensible kernel function (measuring similarity between elements of Ω {\displaystyle \Omega } ) may be defined. For example, various kernels have been proposed for learning from data which are: vectors in R d {\displaystyle \mathbb {R} ^{d}} , discrete classes/categories, strings, graphs/networks, images, time series, manifolds, dynamical systems, and other structured objects. The theory behind kernel embeddings of distributions has been primarily developed by Alex Smola, Le Song, Arthur Gretton, and Bernhard Schölkopf. A review of recent works on kernel embedding of distributions can be found in. The analysis of distributions is fundamental in machine learning and statistics, and many algorithms in these fields rely on information theoretic approaches such as entropy, mutual information, or Kullback–Leibler divergence. However, to estimate these quantities, one must first either perform density estimation, or employ sophisticated space-partitioning/bias-correction strategies which are typically infeasible for high-dimensional data. Commonly, methods for modeling complex distributions rely on parametric assumptions that may be unfounded or computationally challenging (e.g. Gaussian mixture models), while nonparametric methods like kernel density estimation (Note: the smoothing kernels in this context have a different interpretation than the kernels discussed here) or characteristic function representation (via the Fourier transform of the distribution) break down in high-dimensional settings. Methods based on the kernel embedding of distributions sidestep these problems and also possess the following advantages: Data may be modeled without restrictive assumptions about the form of the distributions and relationships between variables Intermediate density estimation is not needed Practitioners may specify the properties of a distribution most relevant for their problem (incorporating prior knowledge via choice of the kernel) If a characteristic kernel is used, then the embedding can uniquely preserve all information about a distribution, while thanks to the kernel trick, computations on the potentially infinite-dimensional RKHS can be implemented in practice as simple Gram matrix operations Dimensionality-independent rates of convergence for the empirical kernel mean (estimated using samples from the distribution) to the kernel embedding of the true underlying distribution can be proven. Learning algorithms based on this framework exhibit good generalization ability and finite sample convergence, while often being simpler and more effective than information theoretic methods Thus, learning via the kernel embedding of distributions offers a principled drop-in replacement for information theoretic approaches and is a framework which not only subsumes many popular methods in machine learning and statistics as special cases, but also can lead to entirely new learning algorithms. == Definitions == Let X {\displaystyle X} denote a random variable with domain Ω {\displaystyle \Omega } and distribution P {\displaystyle P} . Given a symmetric, positive-definite kernel k : Ω × Ω → R {\displaystyle k:\Omega \times \Omega \rightarrow \mathbb {R} } the Moore–Aronszajn theorem asserts the existence of a unique RKHS H {\displaystyle {\mathcal {H}}} on Ω {\displaystyle \Omega } (a Hilbert space of functions f : Ω → R {\displaystyle f:\Omega \to \mathbb {R} } equipped with an inner product ⟨ ⋅ , ⋅ ⟩ H {\displaystyle \langle \cdot ,\cdot \rangle _{\mathcal {H}}} and a norm ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{\mathcal {H}}} ) for which k {\displaystyle k} is a reproducing kernel, i.e., in which the element k ( x , ⋅ ) {\displaystyle k(x,\cdot )} satisfies the reproducing property ⟨ f , k ( x , ⋅ ) ⟩ H = f ( x ) ∀ f ∈ H , ∀ x ∈ Ω . {\displaystyle \langle f,k(x,\cdot )\rangle _{\mathcal {H}}=f(x)\qquad \forall f\in {\mathcal {H}},\quad \forall x\in \Omega .} One may alternatively consider x ↦ k ( x , ⋅ ) {\displaystyle x\mapsto k(x,\cdot )} as an implicit feature mapping φ : Ω → H {\displaystyle \varphi :\Omega \rightarrow {\mathcal {H}}} (which is therefore also called the feature space), so that k ( x , x ′ ) = ⟨ φ ( x ) , φ ( x ′ ) ⟩ H {\displaystyle k(x,x')=\langle \varphi (x),\varphi (x')\rangle _{\mathcal {H}}} can be viewed as a measure of similarity between points x , x ′ ∈ Ω . {\displaystyle x,x'\in \Omega .} While the similarity measure is linear in the feature space, it may be highly nonlinear in the original space depending on the choice of kernel. === Kernel embedding === The kernel embedding of the distribution P {\displaystyle P} in H {\displaystyle {\mathcal {H}}} (also called the kernel mean or mean map) is given by: μ X := E [ k ( X , ⋅ ) ] = E [ φ ( X ) ] = ∫ Ω φ ( x ) d P ( x ) {\displaystyle \mu _{X}:=\mathbb {E} [k(X,\cdot )]=\mathbb {E} [\varphi (X)]=\int _{\Omega }\varphi (x)\ \mathrm {d} P(x)} If P {\displaystyle P} allows a square integrable density p {\displaystyle p} , then μ X = E k p {\displaystyle \mu _{X}={\mathcal {E}}_{k}p} , where E k {\displaystyle {\mathcal {E}}_{k}} is the Hilbert–Schmidt integral operator. A kernel is characteristic if the mean embedding μ : { family of distributions over Ω } → H {\displaystyle \mu :\{{\text{family of distributions over }}\Omega \}\to {\mathcal {H}}} is injective. Each distribution can thus be uniquely represented in the RKHS and all statistical features of distributions are preserved by the kernel embedding if a characteristic kernel is used. === Empirical kernel embedding === Given n {\displaystyle n} training examples { x 1 , … , x n } {\displaystyle \{x_{1},\ldots ,x_{n}\}} drawn independently and identically distributed (i.i.d.) from P , {\displaystyle P,} the kernel embedding of P {\displaystyle P} can be empirically estimated as μ ^ X = 1 n ∑ i = 1 n φ ( x i ) {\displaystyle {\widehat {\mu }}_{X}={\frac {1}{n}}\sum _{i=1}^{n}\varphi (x_{i})} === Joint distribution embedding === If Y {\displaystyle Y} denotes another random variable (for simplicity, assume the co-domain of Y {\displaystyle Y} is also Ω {\displaystyle \Omega } with the same kernel k {\displaystyle k} which satisfies ⟨ φ ( x ) ⊗ φ ( y ) , φ ( x ′ ) ⊗ φ ( y ′ ) ⟩ = k ( x , x ′ ) k ( y , y ′ ) {\displaystyle \langle \varphi (x)\otimes \varphi (y),\varphi (x')\otimes \varphi (y')\rangle =k(x,x')k(y,y')} ), then the joint distribution P ( x , y ) ) {\displaystyle P(x,y))} can be mapped into a tensor product feature space H ⊗ H {\displaystyle {\mathcal {H}}\otimes {\mathcal {H}}} via C X Y = E [ φ ( X ) ⊗ φ ( Y ) ] = ∫ Ω × Ω φ ( x ) ⊗ φ ( y ) d P ( x , y ) {\displaystyle {\mathcal {C}}_{XY}=\mathbb {E} [\varphi (X)\otimes \varphi (Y)]=\int _{\Omega \times \Omega }\varphi (x)\otimes \varphi (y)\ \mathrm {d} P(x,y)} By the equivalence between a tensor and a linear map, this joint embedding may be interpreted as an uncentered cross-covariance operator C X Y : H → H {\displaystyle {\mathcal {C}}_{XY}:{\mathcal {H}}\to {\mathcal {H}}} from which the cross-covariance of functions f , g ∈ H {\displaystyle f,g\in {\mathcal {H}}} can be computed as Cov ( f ( X ) , g ( Y ) ) := E [ f ( X ) g ( Y ) ] − E [ f ( X ) ] E [ g ( Y ) ] = ⟨ f , C X Y g ⟩ H = ⟨ f ⊗ g , C X Y ⟩ H ⊗ H {\displaystyle \operatorname {Cov} (f(X),g(Y)):=\mathbb {E} [f(X)g(Y)]-\mathbb {E} [f(X)]\mathbb {E} [g(Y)]=\langle f,{\mathcal {C}}_{XY}g\rangle _{\mathcal {H}}=\langle f\otimes g,{\mathcal {C}}_{XY}\rangle _{{\mathcal {H}}\otimes {\mathcal {H}}}} Given n {\displaystyle n} pairs of training examples { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle \{(x_{1},y_{1}),\dots ,(x_{n},y_{n})\}} drawn i.i.d. from P {\displaystyle P} , we can also empirically estimate the joint distribution kernel embedding via C ^ X Y = 1 n ∑ i = 1 n φ ( x i ) ⊗ φ ( y i ) {\displaystyle {\widehat {\mathcal {C}}}_{XY}={\frac {1}{n}}\sum _{i=1}^{n}\varphi (x_{i})\otimes \varphi (y_{i})} === Conditional distribution embedding === Given a conditional distribution P ( y ∣ x ) , {\displaystyle P(y\mid x),} one can define the corresponding RKHS embedding as μ Y ∣ x = E [ φ ( Y ) ∣ X ] = ∫ Ω φ ( y ) d P ( y ∣ x ) {\displaystyle \mu _{Y\mid x}=\mathbb {E} [\varphi (Y)\mid X]=\int _{\Omega
FactorDaily
FactorDaily is an Indian digital media publication founded in 2016 by Pankaj Mishra and Jayadevan PK. Mishra was formerly an Editor at TechCrunch and the Economic Times. The digital publication was launched with an intent to produce stories on the impact of technology on life in India. == History == FactorDaily began publishing in May 2016, with daily reported stories on technology, culture and life in India. Prior to its launch, the company had raised $1 million in seed funding from Accel India, Blume Ventures, Girish Mathrubootham of Freshdesk, Vijay Shekhar Sharma of PayTm, and Jay Vijayan of Tekion. Josey Puliyenthuruthel John, formerly Managing Editor at Business Today and National Corporate Editor at Mint, later joined the company as a Consulting Editor. In January 2017, FactorDaily launched its first Podcast called The Outliers. The inaugural episode featured a conversation with Manish Sharma of Printo on his journey starting up. == Awards == The FactorDaily team won the Bengaluru Editors Lab 2017, a journalism hackathon organised by the Global Editors Network (GEN). The story titled "India has 3,800 psychiatrists for 1.2bn people. Can tech step in to manage mental health?" won the first prize in the online category of the fifth Schizophrenia Research Foundation’s (SCARF) ‘Media for Mental Health’ awards. The story titled 'The dark hand of tech that stokes sex trafficking in India', won the Stop Slavery media Awards by the Thomson Reuters Foundation for the year 2020.
Mean opinion score
Mean opinion score (MOS) is a measure used in the domain of Quality of Experience and telecommunications engineering, representing overall quality of a stimulus or system. It is the arithmetic mean over all individual "values on a predefined scale that a subject assigns to his opinion of the performance of a system quality". Such ratings are usually gathered in a subjective quality evaluation test, but they can also be algorithmically estimated. MOS is a commonly used measure for video, audio, and audiovisual quality evaluation, but not restricted to those modalities. ITU-T has defined several ways of referring to a MOS in Recommendation ITU-T P.800.1, depending on whether the score was obtained from audiovisual, conversational, listening, talking, or video quality tests. == Rating scales and mathematical definition == The MOS is expressed as a single rational number, typically in the range 1–5, where 1 is lowest perceived quality, and 5 is the highest perceived quality. Other MOS ranges are also possible, depending on the rating scale that has been used in the underlying test. The Absolute Category Rating scale is very commonly used, which maps ratings between Bad and Excellent to numbers between 1 and 5, as seen in below table. Other standardized quality rating scales exist in ITU-T Recommendations (such as ITU-T P.800 or ITU-T P.910). For example, one could use a continuous scale ranging between 1–100. Which scale is used depends on the purpose of the test. In certain contexts there are no statistically significant differences between ratings for the same stimuli when they are obtained using different scales. The MOS is calculated as the arithmetic mean over single ratings performed by human subjects for a given stimulus in a subjective quality evaluation test. Thus: M O S = ∑ n = 1 N R n N {\displaystyle MOS={\frac {\sum _{n=1}^{N}{R_{n}}}{N}}} Where R {\displaystyle R} are the individual ratings for a given stimulus by N {\displaystyle N} subjects. == Properties of the MOS == The MOS is subject to certain mathematical properties and biases. In general, there is an ongoing debate on the usefulness of the MOS to quantify Quality of Experience in a single scalar value. When the MOS is acquired using a categorical rating scales, it is based on – similar to Likert scales – an ordinal scale. In this case, the ranking of the scale items is known, but their interval is not. Therefore, it is mathematically incorrect to calculate a mean over individual ratings in order to obtain the central tendency; the median should be used instead. However, in practice and in the definition of MOS, it is considered acceptable to calculate the arithmetic mean. It has been shown that for categorical rating scales (such as ACR), the individual items are not perceived equidistant by subjects. For example, there may be a larger "gap" between Good and Fair than there is between Good and Excellent. The perceived distance may also depend on the language into which the scale is translated. However, there exist studies that could not prove a significant impact of scale translation on the obtained results. Several other biases are present in the way MOS ratings are typically acquired. In addition to the above-mentioned issues with scales that are perceived non-linearly, there is a so-called "range-equalization bias": subjects, over the course of a subjective experiment, tend to give scores that span the entire rating scale. This makes it impossible to compare two different subjective tests if the range of presented quality differs. In other words, the MOS is never an absolute measure of quality, but only relative to the test in which it has been acquired. For the above reasons – and due to several other contextual factors influencing the perceived quality in a subjective test – a MOS value should only be reported if the context in which the values have been collected in is known and reported as well. MOS values gathered from different contexts and test designs therefore should not be directly compared. Recommendation ITU-T P.800.2 prescribes how MOS values should be reported. Specifically, P.800.2 says:it is not meaningful to directly compare MOS values produced from separate experiments, unless those experiments were explicitly designed to be compared, and even then the data should be statistically analysed to ensure that such a comparison is valid. == MOS for speech and audio quality estimation == MOS historically originates from subjective measurements where listeners would sit in a "quiet room" and score a telephone call quality as they perceived it. This kind of test methodology had been in use in the telephony industry for decades and was standardized in Recommendation ITU-T P.800. It specifies that "the talker should be seated in a quiet room with volume between 30 and 120 m³ and a reverberation time less than 500 ms (preferably in the range 200–300 ms). The room noise level must be below 30 dBA with no dominant peaks in the spectrum." Requirements for other modalities were similarly specified in later ITU-T Recommendations. == MOS estimation using quality models == Obtaining MOS ratings may be time-consuming and expensive as it requires the recruitment of human assessors. For various use cases such as codec development or service quality monitoring purposes – where quality should be estimated repeatedly and automatically – MOS scores can also be predicted by objective quality models, which typically have been developed and trained using human MOS ratings. A question that arises from using such models is whether the MOS differences produced are noticeable to the users. For example, when rating images on a five point MOS scale, an image with a MOS equal to 5 is expected to be noticeably better in quality than one with a MOS equal to 1. Contrary to that, it is not evident whether an image with a MOS equal to 3.8 is noticeably better in quality than one with a MOS equal to 3.6. Research conducted on determining the smallest MOS difference that is perceptible to users for digital photographs showed that a MOS difference of approximately 0.46 is required in order for 75% of the users to be able to detect the higher quality image. Nevertheless, image quality expectation, and hence MOS, changes over time with the change of user expectations. As a result, minimum noticeable MOS differences determined using analytical methods such as in may change over time.
CodePen
CodePen is an online community for testing and showcasing user-created HTML, CSS and JavaScript code snippets. It functions as an online code editor and open-source learning environment, where developers can create code snippets, called "pens," and test them. It was founded in 2012 by full-stack developers Alex Vazquez and Tim Sabat and front-end designer Chris Coyier. Its employees work remotely, rarely all meeting together in person. CodePen is a large community for web designers and developers to showcase their coding skills, with an estimated 330,000 registered users and 14.16 million monthly visitors.
EasyA
EasyA is a web3 technology company and education platform based in London (United Kingdom), founded in 2022 by Phil Kwok and Dom Kwok. EasyA was officially launched in 2022, focusing on web3 technologies. This community was influenced by the founders' experiences during the COVID-19 pandemic and early collaborations with universities and other educational institutions. Subsequently, the community was used as a foundation for developing Web3-related initiatives, including the organisation of EasyA's first Web3 hackathon in 2022. The EasyA app has over one million users and provides educational content on various blockchain technologies. EasyA Labs is a separate initiative focused on developing products intended to improve accessibility to cryptocurrency for a broader audience.
Telecommunications device for the deaf
A telecommunications device for the deaf (TDD) is a teleprinter, an electronic device for text communication over a telephone line, that is designed for use by persons with hearing or speech difficulties. Other names for the device include teletypewriter (TTY), textphone (common in Europe), and minicom (United Kingdom). The typical TDD is a device about the size of a typewriter or laptop computer with a QWERTY keyboard and small screen that uses an LED, LCD, or VFD screen to display typed text electronically. In addition, TDDs commonly have a small spool of paper on which text is also printed – old versions of the device had only a printer and no screen. The text is transmitted live, via a telephone line, to a compatible device, i.e. one that uses a similar communication protocol. Special telephone services have been developed to carry the TDD functionality even further. In certain countries, there are systems in place so that a deaf person can communicate with a hearing person on an ordinary voice phone using a human relay operator. There are also "carry-over" services, enabling people who can hear but cannot speak ("hearing carry-over", a.k.a. "HCO"), or people who cannot hear but are able to speak ("voice carry-over", a.k.a. "VCO") to use the telephone. The term TDD is sometimes discouraged because people who are deaf are increasingly using mainstream devices and technologies to carry out most of their communication. The devices described here were developed for use on the partially-analog Public Switched Telephone Network (PSTN). They do not work well on the new internet protocol (IP) networks. Thus as society increasingly moves toward IP based telecommunication, the telecommunication devices used by people who are deaf will not be TDDs. In the US and Canada, the devices are referred to as TTYs. Teletype Corporation, of Skokie, Illinois, made page printers for text, notably for news wire services and telegrams, but these used standards different from those for deaf communication, and although in quite widespread use, were technically incompatible. Furthermore, these were sometimes referred to by the "TTY" initialism, short for "Teletype". When computers had keyboard input mechanisms and page printer output, before CRT terminals came into use, Teletypes were the most widely used devices. They were called "console typewriters". (Telex used similar equipment, but was a separate international communication network.) == History == === APCOM acoustic coupler or MODEM device === The TDD concept was developed by James C. Marsters (1924–2009), a dentist and private airplane pilot who became deaf as an infant because of scarlet fever, and Robert Weitbrecht, a deaf physicist. In 1964, Marsters, Weitbrecht and Andrew Saks, an electrical engineer and grandson of the founder of the Saks Fifth Avenue department store chain, founded APCOM (Applied Communications Corp.), located in the San Francisco Bay area, to develop the acoustic coupler, or modem; their first product was named the PhoneType. APCOM collected old teleprinter machines (TTYs) from the Department of Defense and junkyards. Acoustic couplers were cabled to TTYs enabling the AT&T standard Model 500 telephone to couple, or fit, into the rubber cups on the coupler, thus allowing the device to transmit and receive a unique sequence of tones generated by the different corresponding TTY keys. The entire configuration of teleprinter machine, acoustic coupler, and telephone set became known as the TTY. Weitbrecht invented the acoustic coupler modem in 1964. The actual mechanism for TTY communications was accomplished electro-mechanically through frequency-shift keying (FSK) allowing only half-duplex communication, where only one person at a time can transmit. === Paul Taylor TTY device === During the late 1960s, Paul Taylor combined Western Union Teletype machines with modems to create teletypewriters, known as TTYs. He distributed these early, non-portable devices to the homes of many in the deaf community in St. Louis, Missouri. He worked with others to establish a local telephone wake-up service. In the early 1970s, these small successes in St. Louis evolved into the nation's first local telephone relay system for the deaf. === Micon Industries MCM device === In 1973, the Manual Communications Module (MCM), which was the world's first electronic portable TTY allowing two-way telecommunications, premiered at the California Association of the Deaf convention in Sacramento, California. The battery-powered MCM was invented and designed by a deaf news anchor and interpreter, Kit Patrick Corson, in conjunction with Michael Cannon and physicist Art Ogawa. It was manufactured by Michael Cannon's company, Micon Industries, and initially marketed by Kit Corson's company, Silent Communications. In order to be compatible with the existing TTY network, the MCM was designed around the five-bit Baudot code established by the older TTY machines instead of the ASCII code used by computers. The MCM was an instant success with the deaf community despite the drawback of a $599 cost. Within six months there were more MCMs in use by the deaf and hard of hearing than TTY machines. After a year Micon took over the marketing of the MCM and subsequently concluded a deal with Pacific Bell (who coined the term "TDD") to purchase MCMs and rent them to deaf telephone subscribers for $30 per month. After Micon formed an alliance with APCOM, Michael Cannon (Micon), Paul Conover (Micon), and Andrea Saks (APCOM) successfully petitioned the California Public Utilities Commission (CPUC), resulting in a tariff that paid for TTY devices to be distributed free of cost to deaf persons. Micon produced over 1,000 MCMs per month, resulting in approximately 50,000 MCMs being disseminated into the deaf community. Before he left Micon in 1980, Michael Cannon developed several computer compatible variations of the MCM and a portable, battery operated printing TTY, but they were never as popular as the original MCM. Newer model TTYs could communicate with selectable codes that allow communications at a higher bit rate on those models similarly equipped. However, the lack of true computer interface functionality spelled the demise of the original TTY and its clones. During the mid-1970s, other so-called portable telephone devices were being cloned by other companies, and this was the time period when the term "TDD" began being used largely by those outside the deaf community. === Text messaging and the Def-Tone System (DTS) === This relay system became known commonly as the Def-Tone System (DTS) because the tones representing letters of the alphabet were eventually carried in tones outside the range of human hearing. Today, this is commonly called multi-tap because you press a number 1, 2 or 3 times to get a corresponding letter. In 1994 Joseph Alan Poirier, a college student-worker, recommended using the system to send texts to forklifts to improve delivery of parts to the assembly line at GM Powertrain in Toledo, Ohio, and sending a text to pagers. He recommended taking pagers to alphanumeric displays incorporating the same system in discussions with the pager supplier for Outback Steakhouse and having relays put in the forklifts to ping alert messages to the pagers used in that system. He called it text messaging, coining the phrase. It is theorized that when Toyota forklift was allegedly hired by GM for this work, one of the subcontractors, Kyocera, utilized the work for the Toyota forklift company to create text messaging for cell phones. === Marsters Award === In 2009, AT&T received the James C. Marsters Promotion Award from TDI (formerly Telecommunications for the Deaf, Inc.) for its efforts to increase accessibility to communication for people with disabilities. The award holds some irony; it was AT&T that, in the 1960s, resisted efforts to implement TTY technology, claiming it would damage its communication equipment. In 1968, the Federal Communications Commission struck down AT&T's policy and forced it to offer TTY access to its network. == Protocols == There are many different standards for TDDs and textphones. === Original 5-bit Baudot code === The original standard used by TTYs is a variant of the Baudot code. The maximum speed of this protocol is 10 characters per second. This is a half-duplex protocol, which means that only one person at a time may transmit characters. If both try to transmit at the same time, the characters will be garbled on the other end. This protocol is commonly used in the United States. This is a variant of the Baudot code, implemented as 5-bits per character transmitted asynchronously using frequency-shift key-modulation at either 45.5 or 50 baud, 1 start bit, 5 data bits, and 1.5 stop bits. Details of the protocol implementation are available in TIA-825-A and also in T-REC V.18 Annex A "5-bit operational mode". === Turbo Code === The UltraTec company implements another protocol known as Enh