In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts x = ⟨ x 1 , x 2 , … , x d ⟩ {\displaystyle \mathbf {x} =\langle x_{1},x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts gives the estimator θ ^ i = x i + α N + α d ( i = 1 , … , d ) , {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\alpha }{N+\alpha d}}\qquad (i=1,\ldots ,d),} where the smoothed count x ^ i = N θ ^ i {\displaystyle {\hat {x}}_{i}=N{\hat {\theta }}_{i}} , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) x i / N {\displaystyle x_{i}/N} and the uniform probability 1 / d . {\displaystyle 1/d.} Common choices for α are 0 (no smoothing), +1⁄2 (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empirically based on the observed data. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution. == History == Laplace came up with this smoothing technique when he tried to estimate the chance that the sun will rise tomorrow. His rationale was that even given a large sample of days with the rising sun, we still can not be completely sure that the sun will still rise tomorrow (known as the sunrise problem). == Pseudocount == A pseudocount is an amount (not generally an integer, despite its name) added to the number of observed cases in order to change the expected probability in a model of those data, when not known to be zero. It is so named because, roughly speaking, a pseudo-count of value α {\displaystyle \alpha } weighs into the posterior distribution similarly to each category having an additional count of α {\displaystyle \alpha } . If the number of occurrences of each item i {\displaystyle i} is x i {\displaystyle x_{i}} out of N {\displaystyle N} samples, the empirical probability of event i {\displaystyle i} is p i , empirical = x i N , {\displaystyle p_{i,{\text{empirical}}}={\frac {x_{i}}{N}},} but the posterior probability when additively smoothed is p i , α -smoothed = x i + α N + α d , {\displaystyle p_{i,\alpha {\text{-smoothed}}}={\frac {x_{i}+\alpha }{N+\alpha d}},} as if to increase each count x i {\displaystyle x_{i}} by α {\displaystyle \alpha } a priori. Depending on the prior knowledge, which is sometimes a subjective value, a pseudocount may have any non-negative finite value. It may only be zero (or the possibility ignored) if impossible by definition, such as the possibility of a decimal digit of π being a letter, or a physical possibility that would be rejected and so not counted, such as a computer printing a letter when a valid program for π is run, or excluded and not counted because of no interest, such as if only interested in the zeros and ones. Generally, there is also a possibility that no value may be computable or observable in a finite time (see the halting problem). But at least one possibility must have a non-zero pseudocount, otherwise no prediction could be computed before the first observation. The relative values of pseudocounts represent the relative prior expected probabilities of their possibilities. The sum of the pseudocounts, which may be very large, represents the estimated weight of the prior knowledge compared with all the actual observations (one for each) when determining the expected probability. In any observed data set or sample there is the possibility, especially with low-probability events and with small data sets, of a possible event not occurring. Its observed frequency is therefore zero, apparently implying a probability of zero. This oversimplification is inaccurate and often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. By artificially adjusting the probability of rare (but not impossible) events so those probabilities are not exactly zero, zero-frequency problems are avoided. Also see Cromwell's rule. === Choice of pseudocount === ==== Weakly informative prior ==== One common approach is to add 1 to each observed number of events, including the zero-count possibilities. This is sometimes called Laplace's rule of succession. This approach is equivalent to assuming a uniform prior distribution over the probabilities for each possible event (spanning the simplex where each probability is between 0 and 1, and they all sum to 1). Using the Jeffreys prior approach, a pseudocount of one half should be added to each possible outcome. Pseudocounts should be set to one or one-half only when there is no prior knowledge at all – see the principle of indifference. However, given appropriate prior knowledge, the sum should be adjusted in proportion to the expectation that the prior probabilities should be considered correct, despite evidence to the contrary – see further analysis. Higher values are appropriate inasmuch as there is prior knowledge of the true values (for a mint-condition coin, say); lower values inasmuch as there is prior knowledge that there is probable bias, but of unknown degree (for a bent coin, say). ==== Frequentist interval ==== One way to motivate pseudocounts, particularly for binomial data, is via a formula for the midpoint of an interval estimate, particularly a binomial proportion confidence interval. The best-known is due to Edwin Bidwell Wilson, in Wilson (1927): the midpoint of the Wilson score interval corresponding to z {\displaystyle z} standard deviations on either side is n S + z n + 2 z {\displaystyle {\frac {n_{S}+z}{n+2z}}} Taking z = 2 {\displaystyle z=2} standard deviations to approximate a 95% confidence interval ( z ≈ 1.96 {\displaystyle z\approx 1.96} ) yields pseudocount of 2 for each outcome, so 4 in total, colloquially known as the "plus four rule": n S + 2 n + 4 {\displaystyle {\frac {n_{S}+2}{n+4}}} This is also the midpoint of the Agresti–Coull interval (Agresti & Coull 1998). ==== Known incidence rates ==== Often the bias of an unknown trial population is tested against a control population with known parameters (incidence rates) μ = ⟨ μ 1 , μ 2 , … , μ d ⟩ . {\displaystyle {\boldsymbol {\mu }}=\langle \mu _{1},\mu _{2},\ldots ,\mu _{d}\rangle .} In this case the uniform probability 1 / d {\displaystyle 1/d} should be replaced by the known incidence rate of the control population μ i {\displaystyle \mu _{i}} to calculate the smoothed estimator: θ ^ i = x i + μ i α d N + α d ( i = 1 , … , d ) . {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\mu _{i}\alpha d}{N+\alpha d}}\qquad (i=1,\ldots ,d).} As a consistency check, if the empirical estimator happens to equal the incidence rate, i.e. μ i = x i / N , {\displaystyle \mu _{i}=x_{i}/N,} the smoothed estimator is independent of α {\displaystyle \alpha } and also equals the incidence rate. == Applications == === Classification === Additive smoothing is commonly a component of naive Bayes classifiers. === Statistical language modelling === In a bag of words model of natural language processing and information retrieval, the data consists of the number of occurrences of each word in a document. Additive smoothing allows the assignment of non-zero probabilities to words which do not occur in the sample. Studies have shown that additive smoothing is more effective than other probability smoothing methods in several retrieval tasks such as language-model-based pseudo-relevance feedback and recommender systems.
Optical granulometry
Optical granulometry is the process of measuring the different grain sizes in a granular material, based on a photograph. Technology has been created to analyze a photograph and create statistics based on what the picture portrays. This information is vital in maintaining machinery in various trades worldwide. Mining companies can use optical granulometry to analyze inactive or moving rock to quantify the size of these fragments. Forestry companies can zero in on wood chip sizes without stopping the production process, and minimize sizing errors. With more photoanalysis technologies being produced, mining companies have shown an increased interest in these types of systems because of their ability to maintain efficiency throughout the mining process. Companies are saving millions of dollars annually because of this new technology, and are cutting back on maintenance costs on equipment. In order for optical granulometry to be completely successful, an accurate photo must be taken – under sufficient lighting, and using proper technology – to obtain quantified results. If these requirements are met, an image analysis system can be implemented. == The process == Software uses four basic steps in determining the average size of material: See the Wikipedia article on Photoanalysis to see how mining, forestry and agricultural companies are using this technology to improve quality control techniques. == Smartphone-based, segmentation-free estimation of grain size distribution == Recently, a methodology has emerged by which soil grain size distribution can be inferred from optical images acquired with commodity smartphones by training convolutional neural networks to predict parameters of the distribution curve directly from the image, without explicit image segmentation . In this approach, a standardized image of a soil surface is captured under controlled conditions, preprocessed to reduce device-specific variability, and passed to a regression model that outputs the parameters of a cumulative distribution function e.g., a two-parameter Weibull curve. The resulting distribution can be used to derive geotechnical descriptors and class boundaries.
Security.txt
security.txt is an accepted standard for website security information that allows security researchers to report security vulnerabilities easily. The standard prescribes a text file named security.txt in the well known location, similar in syntax to robots.txt but intended to be machine and human readable, for those wishing to contact a website's owner about security issues. security.txt files have been adopted by Google, GitHub, LinkedIn, and Facebook. == History == The Internet Draft was first submitted by Edwin Foudil in September 2017. At that time it covered four directives, "Contact", "Encryption", "Disclosure" and "Acknowledgement". Foudil expected to add further directives based on feedback. In addition, web security expert Scott Helme said he had seen positive feedback from the security community while use among the top 1 million websites was "as low as expected right now". In 2019, the Cybersecurity and Infrastructure Security Agency (CISA) published a draft binding operational directive that requires all US federal agencies to publish a security.txt file within 180 days. The Internet Engineering Steering Group (IESG) issued a Last Call for security.txt in December 2019 which ended on January 6, 2020. A study in 2021 found that over ten percent of top-100 websites published a security.txt file, with the percentage of sites publishing the file decreasing as more websites were considered. The study also noted a number of discrepancies between the standard and the content of the file. In April 2022 the security.txt file has been accepted by Internet Engineering Task Force (IETF) as RFC 9116. == File format == security.txt files can be served under the /.well-known/ directory (i.e. /.well-known/security.txt) or the top-level directory (i.e. /security.txt) of a website. The file must be served over HTTPS and in plaintext format.
Online service provider
An online service provider (OSP) can, for example, be an Internet service provider, an email provider, a news provider (press), an entertainment provider (music, movies), a search engine, an e-commerce site, an online banking site, a health site, an official government site, social media, a wiki, or a Usenet newsgroup. In its original more limited definition, it referred only to a commercial computer communication service in which paid members could dial via a computer modem the service's private computer network and access various services and information resources such as bulletin board systems, downloadable files and programs, news articles, chat rooms, and electronic mail services. The term "online service" was also used in references to these dial-up services. The traditional dial-up online service differed from the modern Internet service provider in that they provided a large degree of content that was only accessible by those who subscribed to the online service, while ISP mostly serves to provide access to the Internet and generally provides little if any exclusive content of its own. In the U.S., the Online Copyright Infringement Liability Limitation Act (OCILLA) portion of the U.S. Digital Millennium Copyright Act has expanded the legal definition of online service in two different ways for different portions of the law. It states in section 512(k)(1): (A) As used in subsection (a), the term "service provider" means an entity offering the transmission, routing, or providing of connections for digital online communications, between or among points specified by a user, of material of the user's choosing, without modification to the content of the material as sent or received. (B) As used in this section, other than subsection (a), the term "service provider" means a provider of online services or network access, or the operator of facilities therefore, and includes an entity described in subparagraph (A). These broad definitions make it possible for numerous web businesses to benefit from the OCILLA. == History == The first commercial online services went live in 1969. CompuServe (owned in the 1980s and 1990s by H&R Block) and The Source (for a time owned by The Reader's Digest) are considered the first major online services created to serve the market of personal computer users. Utilizing text-based interfaces and menus, these services allowed anyone with a modem and communications software to use email, chat, news, financial and stock information, bulletin boards, special interest groups (SIGs), forums and general information. Subscribers could exchange email only with other subscribers of the same service. (For a time a service called DASnet carried mail among several online services, and CompuServe, MCI Mail, and other services experimented with X.400 protocols to exchange email until the Internet rendered these outmoded.) Other text-based online services followed such as Delphi, GEnie and MCI Mail. The 1980s also saw the rise of independent Computer Bulletin Boards, or BBSes. (Online services are not BBSes. An online service may contain an electronic bulletin board, but the term "BBS" is reserved for independent dialup, microcomputer-based services that are usually single-user systems.) The commercial services used pre-existing packet-switched (X.25) data communications networks, or the services' own networks (as with CompuServe). In either case, users dialed into local access points and were connected to remote computer centers where information and services were located. As with telephone service, subscribers paid by the minute, with separate day-time and evening/weekend rates. As the use of computers that supported color and graphics, such the Atari 8-bit computers, Commodore 64, TI-99/4A, Apple II, and early IBM PC compatibles, increased, online services gradually developed framed or partially graphical information displays. Early services such as CompuServe added increasingly sophisticated graphics-based front end software to present their information, though they continued to offer text-based access for those who needed or preferred it. In 1985 Viewtron, which began as a Videotex service requiring a dedicated terminal, introduced software allowing home computer owners access. Beginning in the mid-1980s graphics based online services such as PlayNET, Prodigy, and Quantum Link (aka Q-Link) were developed. Quantum Link, which was based on Commodore-only Playnet software, later developed AppleLink Personal Edition, PC-Link (based on Tandy's DeskMate), and Promenade (for IBM), all of which (including Q-Link) were later combined as America Online. These online services presaged the web browser that would change global online life 10 years later. Before Quantum Link, Apple computer had developed its own service, called AppleLink, which was mostly a support network targeted at Apple dealers and developers. Later, Apple offered the short-lived eWorld, targeted at Mac consumers and based on the Mac version of the America Online software. Beginning in 1992, the Internet, which had previously been limited to government, academic, and corporate research settings, was opened to commercial entities. The first online service to offer Internet access was DELPHI, which had developed TCP/IP access much earlier, in connection with an environmental group that rated Internet access. The explosion of popularity of the World Wide Web in 1994 accelerated the development of the Internet as an information and communication resource for consumers and businesses. The sudden availability of low- to no-cost email and appearance of free independent web sites broke the business model that had supported the rise of the early online service industry. CompuServe, BIX, AOL, DELPHI, and Prodigy gradually added access to Internet e-mail, Usenet newsgroups, ftp, and to web sites. At the same time, they moved from usage-based billing to monthly subscriptions. Similarly, companies that paid to have AOL host their information or early online stores began to develop their own web sites, putting further stress on the economics of the online industry. Only the largest services like AOL (which later acquired CompuServe, just as CompuServe acquired The Source) were able to make the transition to the Internet-centric world. A new class of online service provider arose to provide access to the Internet, the internet service provider or ISP. Internet-only service providers like UUNET, The Pipeline, Panix, Netcom, the World, EarthLink, and MindSpring provided no content of their own, concentrating their efforts on making it easy for nontechnical users to install the various software required to "get online" before consumer operating systems came internet-enabled out of the box. In contrast to the online services' multitiered per-minute or per-hour rates, many ISPs offered flat-fee, unlimited access plans. Independent companies sprang up to offer access and packages to compete with the big networks (eg, the-wire.com, 1994 in Toronto and bway.net 1995 in New York). These providers first offered access through telephone and modem, just as did the early online services providers. By the early 2000s, these independent ISPs had largely been supplanted by high speed and broadband access through cable and phone companies, as well as wireless access. The importance of the online services industry was vital in "paving the road" for the information superhighway. When Mosaic and Netscape were released in 1994, they had a ready audience of more than 10 million people who were able to download their first web browser through an online service. Though ISPs quickly began offering software packages with setup to their customers, this brief period gave many users their first online experience. Two online services in particular, Prodigy and AOL, are often confused with the Internet, or the origins of the Internet. Prodigy's Chief Technical Officer said in 1999: "Eleven years ago, the Internet was just an intangible dream that Prodigy brought to life. Now it is a force to be reckoned with." Despite that statement, neither service provided the back bone for the Internet, nor did either start the Internet. == Online service interfaces == The first online service used a simple text-based interface in which content was largely text only and users made choices via a command prompt. This allowed just about any computer with a modem and terminal communications program the ability to access these text-based online services. CompuServe would later offer, with the advent of the Apple Macintosh and Microsoft Windows-based PCs, a GUI interface program for their service. This provided a very rudimentary GUI interface. CompuServe continued to offer text-only access for those needing it. Online services like Prodigy and AOL developed their online service around a GUI and thus unlike CompuServe's early GUI-based software, these online services provided a more robust GUI interface. Early GUI-base
Information schema
In relational databases, the information schema (information_schema) is an ANSI-standard set of read-only views that provide information about all of the tables, views, columns, and procedures in a database. It can be used as a source of the information that some databases make available through non-standard commands, such as: the SHOW command of MySQL the DESCRIBE command of Oracle's SQLPlus the \d command in psql (PostgreSQL's default command-line program). => SELECT count(table_name) FROM information_schema.tables; count ------- 99 (1 row) => SELECT column_name, data_type, column_default, is_nullable FROM information_schema.columns WHERE table_name='alpha'; column_name | data_type | column_default | is_nullable -------------+-----------+----------------+------------- foo | integer | | YES bar | character | | YES (2 rows) => SELECT FROM information_schema.information_schema_catalog_name; catalog_name -------------- johnd (1 row) == Implementation == As a notable exception among major database systems, Oracle does not as of 2015 implement the information schema. An open-source project exists to address this. RDBMSs that support information_schema include: Amazon Redshift Apache Hive Microsoft SQL Server MonetDB Snowflake MySQL PostgreSQL H2 Database HSQLDB InterSystems Caché MariaDB SingleStore (formerly MemSQL) Mimer SQL Snowflake Trino Presto CrateDB ClickHouse CockroachDB Kinetica DB TiDB RDBMSs that do not support information_schema include: Apache Derby Apache Ignite Firebird Microsoft Access IBM Informix Ingres IBM Db2 Oracle Database SAP HANA SQLite Sybase ASE Sybase SQL Anywhere Teradata Vertica
Baby Bundle (app)
Baby Bundle is a parenting mobile app for iPhone and iPad. It was designed to help new parents through pregnancy and the first two years of parenthood. Developed in collaboration with medical experts, it helps track and record the child's development and growth, offers parental advice, manages vaccinations and health check-ups, stores photos and provides baby monitoring services. == History == Baby Bundle was founded in the United Kingdom by brothers, Nick and Anthony von Christierson. Each worked in investment banking prior to developing Baby Bundle, Nick at Greenhill & Co., and Anthony at Goldman Sachs. The idea for the app came when a friend's wife voiced her frustration over having multiple parenting apps on her smartphone. Nick and Anthony left their jobs to create a single app that would include all those features. They conducted market research by interviewing more than 500 parents in the UK and US. It took them a year to build the app, which was named by their mother. Looking for endorsement, they first went to the US in 2013 and partnered with parenting expert and pediatrician Dr. Jennifer Trachtenberg. Baby Bundle was launched in the US and Canadian App Stores in April 2014. In the same month, it became the #1 parenting app in iTunes and was featured by Apple as the #1 Editor's pick across all categories. Mashable called it one of the "Top 5 Can’t Miss Apps." Baby Bundle raised $1.8m seed round in March 2015 to fund development. The money came from a range of angel investors from across the US, UK and Asia. The von Christierson brothers have signed a deal to co-brand the app in the Middle East and expect to launch in Europe and Africa. == Features == Baby Bundle is an app for both the iPhone or iPad and provides smart monitoring tools and trackers for pregnancy and child development. It acts as a growth and daily activity tracker and offers parental advice, manages vaccinations and health check-ups. It has a parenting guide with tips and advice on what to expect when the baby arrives. An interactive forum also lets parents ask questions from others in the community. The app is free and also include paid premium features like the ability to turn two iPhones running into a baby monitor, a cloud service to share the child's data with a spouse and the ability to store data on more than one baby.
TalkBack
TalkBack is an accessibility service for the Android operating system that helps blind and visually impaired users to interact with their devices. It uses spoken words, vibration and other audible feedback to allow the user to know what is happening on the screen allowing the user to better interact with their device. The service is pre-installed on many Android devices, and it became part of the Android Accessibility Suite in 2017. According to the Google Play Store, the Android Accessibility Suite has been downloaded over five billion times, including devices that have the suite preinstalled. == Open-source == Google releases the source code of TalkBack with some releases of the accessibility service to GitHub, with the latest of these changes being from May 6, 2021. The source for these versions of Google TalkBack have been released under the Apache License version 2.0. == Release history ==