Uncertain database

An uncertain database is a kind of database studied in database theory. The goal of uncertain databases is to manage information on which there is some uncertainty. Uncertain databases make it possible to explicitly represent and manage uncertainty on the data, usually in a succinct way. == Formal definition == At the basis of uncertain databases is the notion of possible world. Specifically, a possible world of an uncertain database is a (certain) database which is one of the possible realizations of the uncertain database. A given uncertain database typically has more than one, and potentially infinitely many, possible worlds. A formalism to represent uncertain databases then explains how to succinctly represent a set of possible worlds into one uncertain database. == Types of uncertain databases == Uncertain database models differ in how they represent and quantify these possible worlds: Incomplete databases are a compact representation of the set of possible worlds – the use of NULL in SQL, arguably the most commonplace instantiation of uncertain databases, is an example of incomplete database model. Probabilistic databases are a compact representation of a probability distribution over the set of possible worlds. Fuzzy databases are a compact representation of a fuzzy set of the possible worlds. Though mostly studied in the relational setting, uncertain database models can also be defined in other relational models such as graph databases or XML databases. === Incomplete database === The most common database model is the relational model. Multiple incomplete database models have been defined over the relational model, that form extensions to the relational algebra. These have been called Imieliński–Lipski algebras: Relations with NULL values, also called Codd tables c-tables v-tables === Example === The following table is a relation of an incomplete database, described in the formalism of NULL values: There are infinitely many possible worlds for this incomplete database, obtained by replacing the "NULL" values with concrete values. For instance, the following relation is a possible world:

Yahoo Mail

Yahoo! Mail (also written as Yahoo Mail) is a mailbox provider by Yahoo. It is one of the largest email services worldwide, with 225 million users. It is accessible via a web browser (webmail), mobile app, or through third-party email clients via the POP, SMTP, and IMAP protocols. Users can also connect non-Yahoo e-mail accounts to their Yahoo Mail inbox. The service was launched on October 8, 1997. The service is free for personal use, with an optional monthly fee for additional features. It is also available in several languages other than English. == History == === 1997–2002 === On October 8, 1997, Yahoo announced its acquisition of online communications company Four11 for $92 million in stock. As part of the purchase, Yahoo received Four11's RocketMail webmail service. Yahoo Mail, based on the RocketMail technology, launched at the same time. Yahoo! chose acquisition rather than internal platform development, because, as Healy said, "Hotmail was growing at thousands and thousands users per week. We did an analysis. For us to build, it would have taken four to six months, and by then, so many users would have taken an email account. The speed of the market was critical." On March 21, 2002, Yahoo! eliminated free software client access and introduced the $29.99 per year Mail Forwarding Service. Mary Osako, a Yahoo! Spokeswoman, told CNET, "For-pay services on Yahoo!, originally launched in February 1999, have experienced great acceptance from our base of active registered users, and we expect this adoption to continue to grow." === 2002–2010 === During 2002, the Yahoo network was gradually redesigned, including the company website, Yahoo Mail and other services. Along with the new design, new features were implemented, including drop-down menus in DHTML and keyboard shortcuts. On July 9, 2004, Yahoo! acquired Oddpost, a webmail service which simulated a desktop email client. Oddpost had features such as drag-and-drop support, right-click menus, RSS feeds, a preview pane, and increased speed using email caching to shorten response time. Many of the features were incorporated into an updated Yahoo! Mail service. ==== Competition ==== On April 1, 2004, Google announced its Gmail service with 1 GB of storage, although Gmail's invitation-only accounts kept the other webmail services at the forefront. Most major webmail providers, including Yahoo! Mail, increased their mailbox storage in response. Yahoo! first announced 100 MB of storage for basic accounts and 2 GB of storage for premium users. However, soon Yahoo Mail increased its free storage quota to 1 GB, before eventually allowing unlimited storage from March 27, 2007, until October 8, 2013. === 2011–2021 === In May 2011, Yahoo Mail rolled out a new interface. It included updated design, enhanced performance, and improved Facebook integration. In 2013, Yahoo! redesigned the site and removed several features, such as simultaneously opening multiple emails in tabs, sorting by sender name, and dragging mails to folders. The new email interface was geared to give an improved user-experience for mobile devices, but was criticized for having an inferior desktop interface. Many users objected to the unannounced nature of the changes through an online post asking Yahoo! to bring back mail tabs with one hundred thousand voting and nearly ten thousand commenting. The redesign produced a problem that caused an unknown number of users to lose access to their accounts for several weeks. In December 2013, Yahoo! Mail suffered a major outage where approximately one million users, one percent of the site's total users, could not access their emails for several days. Yahoo!'s then-CEO Marissa Mayer publicly apologized to the site's users. China Yahoo Mail announced in April 2013 that it would shut down that August as part of Yahoo ceasing services in China since acquiring a stake in Alibaba in 2005. Users with email address suffixes @yahoo.com.cn and @yahoo.cn could transfer their accounts to AliCloud to continue receiving messages through the end of 2014. In January 2014, an undisclosed number of usernames and passwords were released to hackers, following a security breach that Yahoo! believed had occurred through a third-party website. Yahoo! contacted affected users and requested that passwords be changed. In October 2015, Yahoo! updated the mail service with a "more subtle" redesign, as well as improved mobile features. The same release introduced the Yahoo! Account Key, a smartphone-based replacement for password logins. The app also added support for third-party mail accounts. In 2017, Yahoo! again redesigned the web interface with a "more minimal" look, and introduced the option to customize it with different color themes and layouts. In 2019, Yahoo released a redesigned Yahoo Mail app to organize user inboxes, introducing features including a one-tap unsubscribe tool, package tracking, and travel updates. In 2020, Yahoo Mail users were able to fill Walmart shopping carts directly from their inboxes, an industry first. Yahoo! also added a feature to view NFL matches. === 2022–present === In 2022, updates to the Yahoo Mail mobile app added tools to help manage receipts, gift cards, and subscriptions. AI-based additions in 2023 included a feature that automates tracking coupon codes and credits for online shopping, as well as updates to search suggestions, message summaries and AI writing assistance. In 2024, updates to the desktop interface added more AI-based features, including a "priority inbox" tab with automatically generated summaries of important messages and automated suggestions of next actions based on message contents. In February 2025, Yahoo aired its first Super Bowl ad since 2002, in which Bill Murray invited viewers to contact him at his Yahoo Mail email address ([email protected]). The address received nearly 150,000 emails in the first two hours after broadcast. In June 2025, Yahoo Mail introduced a "Catch Up" feature that provides AI-generated summaries and email previews and prompts users to choose to delete or retain each one. As part of the feature's launch, Yahoo Mail collaborated with streetwear brand Anti Social Social Club on an apparel release. == User interface == As many as three web interfaces were available at any given time. The traditional "Yahoo! Mail Classic" preserved the availability of their original 1997 interface until July 2013 in North America. A 2005 version included a new Ajax interface, drag-and-drop, improved search, keyboard shortcuts, address auto-completion, and tabs. However, other features were removed, such as column widths and one click delete-move-to-next. In October 2010, Yahoo! released a beta version of Yahoo! Mail, which included improvements to performance, search, and Facebook integration. In May 2011, this became the default interface. Their current Webmail interface was introduced in 2017. == Spam policy == Yahoo! Mail is often used by spammers to provide a "remove me" email address. Often, these addresses are used to verify the recipient's address, thus opening the door for more spam. Yahoo! does not tolerate this practice and terminates accounts connected with spam-related activities without warning, causing spammers to lose access to any other Yahoo! services connected with their ID under the Terms of Service. Additionally, Yahoo! stresses that its servers are based in California and any spam-related activity which uses its servers could potentially violate that state's anti-spam laws. In February 2006, Yahoo! announced its decision (along with AOL) to give some organizations the option to "certify" mail by paying up to one cent for each outgoing message, allowing the mail in question to bypass inbound spam filters. Few mailers used it and, Goodmail, the company running the certification process, shut down in 2011. === Filters === In order to prevent abuse, in 2002 Yahoo! Mail activated filters which changed certain words (that could trigger unwanted JavaScript events) and word fragments into other words. "mocha" was changed to "espresso", "expression" became "statement", and "eval" (short for "evaluation") became "review". This resulted in many unintended corrections, such as "prevent" (prevalent), "revalidation" (evaluation) and "media review" (medieval). When asked about these changes, Yahoo! explained that the changed words were common terms used in their privacy dashboard and were blacklisted to prevent hackers from sending damaging commands via the program's HTML function. Starting before February 7, 2006, Yahoo! Mail ended the practice, and began to add an underscore as a prefix to certain suspicious words and word fragments. === Greylisting === Incoming mail to Yahoo! addresses can be subjected to deferred delivery as part of Yahoo's incoming spam controls. This can delay delivery of mail sent to Yahoo! addresses without the sender or recipients being aware of it. The deferral is typically of short duration, but

Accumulated local effects

Accumulated local effects (ALE) is a machine learning interpretability method. == Concepts == ALE uses a conditional feature distribution as an input and generates augmented data, creating more realistic data than a marginal distribution. It ignores far out-of-distribution (outlier) values. Unlike partial dependence plots and marginal plots, ALE is not defeated in the presence of correlated predictors. It analyzes differences in predictions instead of averaging them by calculating the average of the differences in model predictions over the augmented data, instead of the average of the predictions themselves. == Example == Given a model that predicts house prices based on its distance from city center and size of the building area, ALE compares the differences of predictions of houses of different sizes. The result separates the impact of the size from otherwise correlated features. == Limitations == Defining evaluation windows is subjective. High correlations between features can defeat the technique. ALE requires more and more uniformly distributed observations than PDP so that the conditional distribution can be reliably determined. The technique may produce inadequate results if the data is highly sparse, which is more common with high-dimensional data (curse of dimensionality).

Genetic operator

A genetic operator is an operator used in evolutionary algorithms (EA) to guide the algorithm towards a solution to a given problem. There are three main types of operators (mutation, crossover and selection), which must work in conjunction with one another in order for the algorithm to be successful. Genetic operators are used to create and maintain genetic diversity (mutation operator), combine existing solutions (also known as chromosomes) into new solutions (crossover) and select between solutions (selection). The classic representatives of evolutionary algorithms include genetic algorithms, evolution strategies, genetic programming and evolutionary programming. In his book discussing the use of genetic programming for the optimization of complex problems, computer scientist John Koza has also identified an 'inversion' or 'permutation' operator; however, the effectiveness of this operator has never been conclusively demonstrated and this operator is rarely discussed in the field of genetic programming. For combinatorial problems, however, these and other operators tailored to permutations are frequently used by other EAs. Mutation (or mutation-like) operators are said to be unary operators, as they only operate on one chromosome at a time. In contrast, crossover operators are said to be binary operators, as they operate on two chromosomes at a time, combining two existing chromosomes into one new chromosome. == Operators == Genetic variation is a necessity for the process of evolution. Genetic operators used in evolutionary algorithms are analogous to those in the natural world: survival of the fittest, or selection; reproduction (crossover, also called recombination); and mutation. === Selection === Selection operators give preference to better candidate solutions (chromosomes), allowing them to pass on their 'genes' to the next generation (iteration) of the algorithm. The best solutions are determined using some form of objective function (also known as a 'fitness function' in evolutionary algorithms), before being passed to the crossover operator. Different methods for choosing the best solutions exist, for example, fitness proportionate selection and tournament selection. A further or the same selection operator is used to determine the individuals for being selected to form the next parental generation. The selection operator may also ensure that the best solution(s) from the current generation always become(s) a member of the next generation without being altered; this is known as elitism or elitist selection. === Crossover === Crossover is the process of taking more than one parent solutions (chromosomes) and producing a child solution from them. By recombining portions of good solutions, the evolutionary algorithm is more likely to create a better solution. As with selection, there are a number of different methods for combining the parent solutions, including the edge recombination operator (ERO) and the 'cut and splice crossover' and 'uniform crossover' methods. The crossover method is often chosen to closely match the chromosome's representation of the solution; this may become particularly important when variables are grouped together as building blocks, which might be disrupted by a non-respectful crossover operator. Similarly, crossover methods may be particularly suited to certain problems; the ERO is considered a good option for solving the travelling salesman problem. === Mutation === The mutation operator encourages genetic diversity amongst solutions and attempts to prevent the evolutionary algorithm converging to a local minimum by stopping the solutions becoming too close to one another. In mutating the current pool of solutions, a given solution may change between slightly and entirely from the previous solution. By mutating the solutions, an evolutionary algorithm can reach an improved solution solely through the mutation operator. Again, different methods of mutation may be used; these range from a simple bit mutation (flipping random bits in a binary string chromosome with some low probability) to more complex mutation methods in which genes in the solution are changed, for example by adding a random value from the Gaussian distribution to the current gene value. As with the crossover operator, the mutation method is usually chosen to match the representation of the solution within the chromosome. == Combining operators == While each operator acts to improve the solutions produced by the evolutionary algorithm working individually, the operators must work in conjunction with each other for the algorithm to be successful in finding a good solution. Using the selection operator on its own will tend to fill the solution population with copies of the best solution from the population. If the selection and crossover operators are used without the mutation operator, the algorithm will tend to converge to a local minimum, that is, a good but sub-optimal solution to the problem. Using the mutation operator on its own leads to a random walk through the search space. Only by using all three operators together can the evolutionary algorithm become a noise-tolerant global search algorithm, yielding good solutions to the problem at hand.

Hinge loss

In machine learning, the hinge loss is a loss function used for training classifiers. The hinge loss is used for "maximum-margin" classification, most notably for support vector machines (SVMs). For an intended output t = ±1 and a classifier score y, the hinge loss of the prediction y is defined as ℓ ( y ) = max ( 0 , 1 − t ⋅ y ) {\displaystyle \ell (y)=\max(0,1-t\cdot y)} Note that y {\displaystyle y} should be the "raw" output of the classifier's decision function, not the predicted class label. For instance, in linear SVMs, y = w ⋅ x + b {\displaystyle y=\mathbf {w} \cdot \mathbf {x} +b} , where ( w , b ) {\displaystyle (\mathbf {w} ,b)} are the parameters of the hyperplane and x {\displaystyle \mathbf {x} } is the input variable(s). When t and y have the same sign (meaning y predicts the right class) and | y | ≥ 1 {\displaystyle |y|\geq 1} , the hinge loss ℓ ( y ) = 0 {\displaystyle \ell (y)=0} . When they have opposite signs, ℓ ( y ) {\displaystyle \ell (y)} increases linearly with y, and similarly if | y | < 1 {\displaystyle |y|<1} , even if it has the same sign (correct prediction, but not by enough margin). The Hinge loss is not a proper scoring rule. == Extensions == While binary SVMs are commonly extended to multiclass classification in a one-vs.-all or one-vs.-one fashion, it is also possible to extend the hinge loss itself for such an end. Several different variations of multiclass hinge loss have been proposed. For example, Crammer and Singer defined it for a linear classifier as ℓ ( y ) = max ( 0 , 1 + max y ≠ t w y x − w t x ) {\displaystyle \ell (y)=\max(0,1+\max _{y\neq t}\mathbf {w} _{y}\mathbf {x} -\mathbf {w} _{t}\mathbf {x} )} , where t {\displaystyle t} is the target label, w t {\displaystyle \mathbf {w} _{t}} and w y {\displaystyle \mathbf {w} _{y}} are the model parameters. Weston and Watkins provided a similar definition, but with a sum rather than a max: ℓ ( y ) = ∑ y ≠ t max ( 0 , 1 + w y x − w t x ) {\displaystyle \ell (y)=\sum _{y\neq t}\max(0,1+\mathbf {w} _{y}\mathbf {x} -\mathbf {w} _{t}\mathbf {x} )} . In structured prediction, the hinge loss can be further extended to structured output spaces. Structured SVMs with margin rescaling use the following variant, where w denotes the SVM's parameters, y the SVM's predictions, φ the joint feature function, and Δ the Hamming loss: ℓ ( y ) = max ( 0 , Δ ( y , t ) + ⟨ w , ϕ ( x , y ) ⟩ − ⟨ w , ϕ ( x , t ) ⟩ ) = max ( 0 , max y ∈ Y ( Δ ( y , t ) + ⟨ w , ϕ ( x , y ) ⟩ ) − ⟨ w , ϕ ( x , t ) ⟩ ) {\displaystyle {\begin{aligned}\ell (\mathbf {y} )&=\max(0,\Delta (\mathbf {y} ,\mathbf {t} )+\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {y} )\rangle -\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {t} )\rangle )\\&=\max(0,\max _{y\in {\mathcal {Y}}}\left(\Delta (\mathbf {y} ,\mathbf {t} )+\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {y} )\rangle \right)-\langle \mathbf {w} ,\phi (\mathbf {x} ,\mathbf {t} )\rangle )\end{aligned}}} . == Optimization == The hinge loss is a convex function, so many of the usual convex optimizers used in machine learning can work with it. It is not differentiable, but has a subgradient with respect to model parameters w of a linear SVM with score function y = w ⋅ x {\displaystyle y=\mathbf {w} \cdot \mathbf {x} } that is given by ∂ ℓ ∂ w i = { − t ⋅ x i if t ⋅ y < 1 , 0 otherwise . {\displaystyle {\frac {\partial \ell }{\partial w_{i}}}={\begin{cases}-t\cdot x_{i}&{\text{if }}t\cdot y<1,\\0&{\text{otherwise}}.\end{cases}}} However, since the derivative of the hinge loss at t y = 1 {\displaystyle ty=1} is undefined, smoothed versions may be preferred for optimization, such as Rennie and Srebro's ℓ ( y ) = { 1 2 − t y if t y ≤ 0 , 1 2 ( 1 − t y ) 2 if 0 < t y < 1 , 0 if 1 ≤ t y {\displaystyle \ell (y)={\begin{cases}{\frac {1}{2}}-ty&{\text{if}}~~ty\leq 0,\\{\frac {1}{2}}(1-ty)^{2}&{\text{if}}~~0

Netomi

Netomi, formerly msg.ai, is an American artificial intelligence company and developer of chatbot technologies. == History == msg.ai was founded in May 2015 by Puneet Mehta. msg.ai worked with Sony Pictures to launch a chat bot on Facebook Messenger for a $100M film, Goosebumps and subsequently joined Y Combinator as a member of the Winter 2016 class. Later that year and in 2017, msg.ai completed two rounds of seed funding, led by Y Combinator and Index Ventures. In 2018, the company changed its name to Netomi. In 2019, the company raised $14.7 million in a Series A funding round also led by Index Ventures. In 2021, the company raised $30 million in a Series B funding round led by WndrCo LLC.

Bondy's theorem

In mathematics, Bondy's theorem is a bound on the number of elements needed to distinguish the sets in a family of sets from each other. It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published it in 1972. == Statement == The theorem is as follows: Let X be a set with n elements and let A1, A2, ..., An be distinct subsets of X. Then there exists a subset S of X with n − 1 elements such that the sets Ai ∩ S are all distinct. In other words, if we have a 0-1 matrix with n rows and n columns such that each row is distinct, we can remove one column such that the rows of the resulting n × (n − 1) matrix are distinct. == Example == Consider the 4 × 4 matrix [ 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 ] {\displaystyle {\begin{bmatrix}1&1&0&1\\0&1&0&1\\0&0&1&1\\0&1&1&0\end{bmatrix}}} where all rows are pairwise distinct. If we delete, for example, the first column, the resulting matrix [ 1 0 1 1 0 1 0 1 1 1 1 0 ] {\displaystyle {\begin{bmatrix}1&0&1\\1&0&1\\0&1&1\\1&1&0\end{bmatrix}}} no longer has this property: the first row is identical to the second row. Nevertheless, by Bondy's theorem we know that we can always find a column that can be deleted without introducing any identical rows. In this case, we can delete the third column: all rows of the 3 × 4 matrix [ 1 1 1 0 1 1 0 0 1 0 1 0 ] {\displaystyle {\begin{bmatrix}1&1&1\\0&1&1\\0&0&1\\0&1&0\end{bmatrix}}} are distinct. Another possibility would have been deleting the fourth column. == Learning theory application == From the perspective of computational learning theory, Bondy's theorem can be rephrased as follows: Let C be a concept class over a finite domain X. Then there exists a subset S of X with the size at most |C| − 1 such that S is a witness set for every concept in C. This implies that every finite concept class C has its teaching dimension bounded by |C| − 1.