Kubeflow is an open-source platform for machine learning and MLOps on Kubernetes introduced by Google. The different stages in a typical machine learning lifecycle are represented with different software components in Kubeflow, including model development (Kubeflow Notebooks), model training (Kubeflow Pipelines, Kubeflow Training Operator), model serving (KServe), and automated machine learning (Katib). Each component of Kubeflow can be deployed separately, and it is not a requirement to deploy every component. == History == The Kubeflow project was first announced at KubeCon + CloudNativeCon North America 2017 by Google engineers David Aronchick, Jeremy Lewi, and Vishnu Kannan to address a perceived lack of flexible options for building production-ready machine learning systems. The project has also stated it began as a way for Google to open-source how they ran TensorFlow internally. The first release of Kubeflow (Kubeflow 0.1) was announced at KubeCon + CloudNativeCon Europe 2018. Kubeflow 1.0 was released in March 2020 via a public blog post announcing that many Kubeflow components were graduating to a "stable status", indicating they were now ready for production usage. In October 2022, Google announced that the Kubeflow project had applied to join the Cloud Native Computing Foundation. In July 2023, the foundation voted to accept Kubeflow as an incubating stage project. == Components == === Kubeflow Notebooks for model development === Machine learning models are developed in the notebooks component called Kubeflow Notebooks. The component runs web-based development environments inside a Kubernetes cluster, with native support for Jupyter Notebook, Visual Studio Code, and RStudio. === Kubeflow Pipelines for model training === Once developed, models are trained in the Kubeflow Pipelines component. The component acts as a platform for building and deploying portable, scalable machine learning workflows based on Docker containers. Google Cloud Platform has adopted the Kubeflow Pipelines DSL within its Vertex AI Pipelines product. === Kubeflow Training Operator for model training === For certain machine learning models and libraries, the Kubeflow Training Operator component provides Kubernetes custom resources support. The component runs distributed or non-distributed TensorFlow, PyTorch, Apache MXNet, XGBoost, and MPI training jobs on Kubernetes. === KServe for model serving === The KServe component (previously named KFServing) provides Kubernetes custom resources for serving machine learning models on arbitrary frameworks including TensorFlow, XGBoost, scikit-learn, PyTorch, and ONNX. KServe was developed collaboratively by Google, IBM, Bloomberg, NVIDIA, and Seldon. Publicly disclosed adopters of KServe include Bloomberg, Gojek, the Wikimedia Foundation, and others. === Katib for automated machine learning === Lastly, Kubeflow includes a component for automated training and development of machine learning models, the Katib component. It is described as a Kubernetes-native project and features hyperparameter tuning, early stopping, and neural architecture search. == Release timeline ==
Unfold (app)
Unfold is a mobile application that allows users to create social media content using a variety of templates and other tools. It was founded in 2018 by Alfonso Cobo and Andy McCune. It enables users to add photos, video, and text with a variety of tools. In 2019, Unfold was acquired by Squarespace. == History == In January 2017, Alfonso Cobo was studying at Parsons School of Design when he realized there was no software or app that could create a portfolio of his work on an iPad. Cobo created an app called Portfolio, a basic version of a portfolio layout app, and the first one to exist for iPad. He launched it in 2017. After launching the first version of Portfolio, Cobo realized the more popular market and use case was on mobile. Around that time, Instagram was launching Stories. As a result, Cobo pivoted the app away from portfolios and instead focused on an app to showcase one's stories. Cobo later contacted Andy McCune, founder of social media account Earth, to collaborate with Unfold. Unfold also partnered with various companies to create custom templates. These include Equinox, Tommy Hilfiger, NARS, Billboard Music Awards, and Product Red. Unfold also launched a collection of Product Red templates to help eliminate HIV/AIDS in several African countries. In 2019, Squarespace acquired Unfold. The Unfold app has been downloaded over 60 million times and has been used to create over 1 billion Instagram stories. == Features == With Unfold, users can utilize hundreds of templates to make social content for social media platforms such as Instagram, Snapchat, and Facebook. The free app offers users basic templates and standard fonts, filters, and stickers, and there are also premium templates available for a monthly subscription. With Unfold+ and Unfold Pro (previously Unfold for Brands), users can access premium templates and tools, as well as upload custom brand assets and fonts. In 2020, Unfold launched Bio Sites, which allows users to link to multiple sites and platforms.
Critical data studies
Critical data studies is the exploration of and engagement with social, cultural, and ethical challenges that arise when working with big data. It is through various unique perspectives and taking a critical approach that this form of study can be practiced. As its name implies, critical data studies draws heavily on the influence of critical theory, which has a strong focus on addressing the organization of power structures. This idea is then applied to the study of data. Interest in this unique field of critical data studies began in 2011 with scholars danah boyd and Kate Crawford posing various questions for the critical study of big data and recognizing its potential threatening impacts on society and culture. It was not until 2014, and more exploration and conversations, that critical data studies was officially coined by scholars Craig Dalton and Jim Thatcher. They put a large emphasis on understanding the context of big data in order to approach it more critically. Researchers such as David Ribes, Robert Soden, Seyram Avle, Sarah E. Fox, and Phoebe Sengers focus on understanding data as a historical artifact and taking an interdisciplinary approach towards critical data studies. Other key scholars in this discipline include Rob Kitchin and Tracey P. Lauriault who focus on reevaluating data through different spheres. Various critical frameworks that can be applied to analyze big data include Feminist, Anti-Racist, Queer, Indigenous, Decolonial, Anti-Ableist, as well as Symbolic and Synthetic data science. These frameworks help to make sense of the data by addressing power, biases, privacy, consent, and underrepresentation or misrepresentation concerns that exist in data as well as how to approach and analyze this data with a more equitable mindset. == Motivation == In their article in which they coin the term 'critical data studies,' Dalton and Thatcher also provide several justifications as to why data studies is a discipline worthy of a critical approach. First, 'big data' is an important aspect of twenty-first century society, and the analysis of 'big data' allows for a deeper understanding of what is happening and for what reasons. Big data is important to critical data studies because it is the type of data used within this field. Big data does not necessarily refer to a large data set, it can have a data set with millions of rows, but also a data set that just has a wide variety and expansive scope of data with a smaller type of dataset. As well as having whole populations in the data set and not just sample sizes. Furthermore, big data as a technological tool and the information that it yields are not neutral, according to Dalton and Thatcher, making it worthy of critical analysis in order to identify and address its biases. Building off this idea, another justification for a critical approach is that the relationship between big data and society is an important one, and therefore worthy of study. Ribes et. al. argue there is a need for an interdisciplinary understanding of data as a historical artifact as a motivating aspect of critical data studies.The overarching consensus in the Computer-Supported Cooperative Work (CSCW) field, is that people should speak for the data, and not let the data speak for itself. The sources of big data and it’s relationship to varied metadata can be a complicated one, which leads to data disorder and a need for an ethical analysis. Additionally, Iliadis and Russo (2016) have called for studying data assemblages. This is to say, data has innate technological, political, social, and economic histories that should be taken into consideration. Kitchin argues data is almost never raw, and it is almost always cooked, meaning that it is always spoken for by the data scientists utilizing it. Thus, Big Data should be open to a variety of perspectives, especially those of cultural and philosophical nature. Further, data contains hidden histories, ideologies, and philosophies. Big data technology can cause significant changes in society's structure and in the everyday lives of people, and, being a product of society, big data technology is worthy of sociological investigation. Moreover, data sets are almost never completely without any influence. Rather, data are shaped by the vision or goals of those gathering the data, and during the data collection process, certain things are quantified, stored, sorted and even discarded by the research team. A critical approach is thus necessary in order to understand and reveal the intent behind the information being presented.One of these critical approaches has been through feminist data studies. This method applies feminist principles to critical studies and data collecting and analysis. The goal of this is to address the power imbalance in data science and society. According to Catherine D’Ignazio and Lauren F. Klein, a power analysis can be performed by examining power, challenging power, evaluating emotion and embodiment, rethinking binaries and hierarchies, embracing pluralism, considering context, and making labor visible. Feminist data studies is part of the movement towards making data to benefit everyone and not to increase existing inequalities. Moreover, data alone cannot speak for themselves; in order to possess any concrete meaning, data must be accompanied by theoretical insight or alternative quantitative or qualitative research measures. Based on different social topics such as anti-racist data studies, critical data studies give a focus on those social issues concerning data. Specifically in anti-racist data studies they use a classification approach to get representation for those within that community. Desmond Upton Patton and others used their own classification system in the communities of Chicago to help target and reduce violence with young teens on twitter. They had students in those communities help them to decipher the terminology and emojis of these teens to target the language used in tweets that followed with violence outside of the computer screens. This is just one real world example of critical data studies and its application. Dalton and Thatcher argue that if one were to only think of data in terms of its exploitative power, there is no possibility of using data for revolutionary, liberatory purposes. Finally, Dalton and Thatcher propose that a critical approach in studying data allows for 'big data' to be combined with older, 'small data,' and thus create more thorough research, opening up more opportunities, questions and topics to be explored. == Issues and concerns for critical data scholars == Data plays a pivotal role in the emerging knowledge economy, driving productivity, competitiveness, efficiency, sustainability, and capital accumulation. The ethical, political, and economic dimensions of data dynamically evolve across space and time, influenced by changing regimes, technologies, and priorities. Technically, the focus lies on handling, storing, and analyzing vast data sets, utilizing machine learning-based data mining and analytics. This technological advancement raises concerns about data quality, encompassing validity, reliability, authenticity, usability, and lineage. The use of data in modern society brings about new ways of understanding and measuring the world, but also brings with it certain concerns or issues. Data scholars attempt to bring some of these issues to light in their quest to be critical of data. Technical and organizational issues could include the scope of the data set, meaning there is too little or too much data to work with, leading to inaccurate results. It becomes crucial for critical data scholars to carefully consider the adequacy of data volume for their analyses. The quality of the data itself is another facet of concern. The data itself could be of poor quality, such as an incomplete or messy data set with missing or inaccurate data values. This would lead researchers to have to make edits and assumptions about the data itself. Addressing these issues often requires scholars to make edits and assumptions about the data to ensure its reliability and relevance. Data scientists could have improper access to the actual data set, limiting their abilities to analyze it. Linnet Taylor explains how gaps in data can arise when people of varying levels of power have certain rights to their data sources. These people in power can control what data is collected, how it is displayed and how it is analyzed. The capabilities of the research team also play a crucial role in the quality of data analytics. The research team may have inadequate skills or organizational capabilities which leads to the actual analytics performed on the dataset to be biased. This can also lead to ecological fallacies, meaning an assumption is made about an individual based on data or results from a larger group of people. These technical and organizational challenges highlight the complexity of working with data and
Private message
In computer networking, a private message (PM), or direct message (DM), refers to a private communication, often text-based, sent or received by a user of a private communication channel on any given platform. Unlike public posts, PMs are only viewable by the participants. Long a function present on IRCs and Internet forums, private channels for PMs have also been prevalent features on instant messaging (IM) and on social media networks. It may be either synchronous (e.g. on an IM) or asynchronous (e.g. on an Internet forum). The term private message (PM) originated as a feature on internet forums, while the term direct message (DM) originated as a feature on Twitter. Due to the popularity of the latter service, DM has since been appropriated by other platforms, such as Instagram, and is often genericized in popular usage. == Overview == There are two main types of private messages, and one obscure type: One type includes those found on IRCs and Internet forums, as well as on social media services like Twitter, Facebook, and Instagram, where the focus is public posting, PMs allow users to communicate privately without leaving the platform. The second type are those relayed through instant messaging platforms such as WhatsApp and Snapchat, where users join the networks primarily to exchange PMs. A third type, peer-to-peer messaging, occurs when users create and own the infrastructure used to transmit and store the messages; while features vary depending on application, they give the user full control over the data they transmit. An example of software that enables this kind of messaging is Classified-ads. Besides serving as a tool to connect privately with friends and family, PMs have gained momentum in the workplace. Working professionals use PMs to reach coworkers in other spaces and increase efficiency during meetings. Although useful, using PMs in the workplace may blur the boundary between work and private lives. Some common forms of private messaging today include Facebook messaging (sometimes referred to as "inboxing"), Twitter direct messaging, and Instagram direct messaging. These forms of private messaging provide a private space on a usually public site. For instance, most activity on Twitter is public, but Twitter DMs provide a private space for communication between two users. This differs from mediums like email, texting, and Snapchat, where most or all activity is always private. Modern forms of private messaging may include multimedia messages, such as pictures or videos. == History == Email was first developed to send messages between different computers on ARPANET in 1971. Access to ARPANET was primarily limited to universities and other research institutions. Starting in 1983 or 1984, FidoNet allowed home computer users to send and receive email via bulletin board systems. Information services such as CompuServe, America Online, and Prodigy also helped to popularizes online messaging. The advent of the public World Wide Web in 1993 increased access to email via internet service providers, and later via webmail. Instant messaging systems became popular in the mid 1990s, as Internet access improved and personal computers became more common. The introduction of Skype in 2003 popularized Internet-based voice and video messaging. Direct messaging is now a feature of all major social networking services. == Privacy concerns == In January 2014, Matthew Campbell and Michael Hurley filed a class-action lawsuit against Facebook for breaching the Electronic Communications Privacy Act. They alleged that private messages which contained URLs were being read and used to generate profit, through data mining and user profiling, and that it was misleading for Facebook to refer to the functionality as "private" with the implication that the communication was "free from surveillance". In 2012, some Facebook users misinterpreted a redesign of the Facebook wall as publicly sharing private messages from 2008–2009. These were found to be public wall posts from those years, made at a time when it was not possible to like or comment on a wall post, making the notes look like private messages.
Social media marketing
Social media marketing is the use of social media platforms and websites to promote a product or service. Although the terms e-marketing and digital marketing are still dominant in academia, social media marketing is becoming more popular for practitioners and researchers. Social media platforms such as Facebook, LinkedIn, Instagram, and Twitter, among others, have built-in data analytics tools that companies can use to track the progress, success, and engagement of social media marketing campaigns. Companies address a range of stakeholders through social media marketing, including current and potential customers, current and potential employees, journalists, bloggers, and the general public. On a strategic level, social media marketing includes the management of a marketing campaign, governance, setting the scope (e.g. more active or passive use) and the establishment of a firm's desired social media "culture" and "tone". Firms that use social media marketing can allow customers and Internet users to post user-generated content (e.g., online comments, product reviews, etc.), also known as "earned media", rather than use marketer-prepared advertising copy. == Purposes and tactics == Social media may be employed in marketing as a communications tool that makes companies accessible to those who are interested in their product and visible to those who are not familiar with their products. It is used by companies to create buzz, learn from customers, and target them. Of the top 10 factors that correlate with a strong Google organic search, seven are social media-dependent. This means that if brands with little to no social media presence tend to show up less on Google searches. While platforms such as Twitter, Facebook and—in the past—Google+ have a larger number of monthly users, the visual media-sharing-based mobile platforms garner a higher interaction rate in comparison, and have registered the fastest growth, and have changed the ways in which consumers engage with brand content. Instagram has an interaction rate of 1.46% with an average of 130 million users monthly as opposed to Twitter, which has a .03% interaction rate with an average of 210 million monthly users. Unlike traditional media that are often cost-prohibitive to many companies, a social media strategy does not require significant financial investment. To this end, companies make use of platforms such as Facebook, Twitter, YouTube, TikTok and Instagram to reach audiences much wider than through traditional print, television, or radio advertisements alone at a fraction of the cost, as most social networking sites can be used at little or no cost (however, some websites charge companies for premium services). This has changed the ways that companies approach and interact with customers, as a substantial percentage of consumer interactions are now being carried out over online platforms with much higher visibility. Customers can post reviews of products and services, rate customer service, and ask questions or voice concerns directly to companies through social media platforms. According to Measuring Success, over 80% of consumers use the web to research products and services. Thus social media marketing is also used by businesses in order to build relationships of trust with consumers. To this aim, companies may hire personnel to specifically handle these social media interactions, who usually report under the title of online community managers. Handling these interactions in a satisfactory manner can result in an increase of consumer trust. To both this aim and to fix the public's perception of a company, three steps are taken in order to address consumer concerns: Identifying the extent of the social chatter Engaging the influencers to help Developing a proportional response == Strategies == === Passive approach === Social media can be a useful source of market information and a way to hear customers' perspectives. Blogs, content communities, and forums are platforms where individuals share their reviews and recommendations of brands, products, and services. Businesses are able to tap into and analyze customer voices and feedback generated in social media for marketing purposes. In this sense, social media is a relatively inexpensive source of market intelligence which can be used by marketers and managers to track and respond to consumer-identified problems and detect market opportunities. === Active approach === Social media can be used as a public relations tool, a direct marketing tool, and a communication channel to target very specific audiences, with social media influencers and social media personalities as effective customer engagement tools. This tactic is widely known as influencer marketing, which gives brands the opportunity to reach their target audience via a group of selected influencers advertising their product or service. Brands were projected to spend up to $15 billion on influencer marketing by 2022, per Business Insider Intelligence estimates, based on Mediakix data. The use of customer influencers, such as popular bloggers, can be an efficient and cost-effective method to launch new products or services. == Engagement == Engagement with the social web means that customers and stakeholders are active participants rather than passive spectators. An example of these are consumer advocacy groups and groups that criticize companies (e.g., lobby groups or advocacy organizations). The use of Social media in a business or political context allows people to express and share opinions about a company's products, services or business practices, or a government's actions. On social media, each participant becomes part of the marketing department (or a challenge to the marketing effort) as other customers read their comments or reviews. The effectiveness of social media marketing campaigns is dependent on the promotion of online engagement. With the advent of social media marketing, it has become increasingly important to gain customer interest in products and services, which can eventually be translated into buying behavior, or voting and donating behavior in a political context. New online marketing concepts of engagement and loyalty have emerged which aim to build customer participation and brand reputation. Engagement in social media for the purpose of a social media strategy is divided into two parts. The first is proactive, regular posting of new online content, which can be seen through digital photos, digital videos, text, and conversations. It is also represented through sharing of content and information from others via weblinks. The second part is reactive conversations, with social media users responding to those who reach out to others' social media profiles through comments or messages. == Campaigns == === Local businesses === Small businesses use social networking sites as a promotional technique. Businesses can follow individuals' social media usage in their local area and advertise specials and deals, which can be exclusive and in the form of "get a free drink with a copy of this tweet". This type of message encourages other locals to follow the business on their official websites in order to obtain the promotional deal. The business's brand visibility is enhanced in the process. Social networking sites are also used by small businesses to develop their own market research on new products and services. By encouraging their customers to give feedback on new product ideas, businesses can gain insights on whether or not a product may be accepted by their target market enough to merit full production. In addition, customers will feel the company has engaged them in the process of co-creation—the process in which the business uses customer feedback to create or modify a product or service to fill a need of the target market. Such feedback can be presented in various forms, such as surveys, contests, and polls. Social networking sites such as LinkedIn, also provide opportunities for small businesses to find candidates to fill staff positions. Review sites such as Yelp help small businesses build their reputation beyond brand visibility. Positive customer peer reviews help influence new prospects to purchase goods and services more than company advertising. == Benefits == Social Media Marketing allows companies to promote themselves to large, diverse audiences that could not be reached through traditional marketing such as phone and email-based advertising. Marketing on most social media platforms also comes at little to no cost, making it accessible to virtually any size business. Social Media Marketing accommodates personalized and direct marketing that targets specific demographics and markets. Companies can engage with customers directly, allowing them to obtain feedback and resolve issues almost immediately. Another advantage of social media marketing is that it's an ideal environment for a company to conduct market research. It can be used
Uniform convergence in probability
Uniform convergence in probability is a form of convergence in probability in statistical asymptotic theory and probability theory. It means that, under certain conditions, the empirical frequencies of all events in a certain event-family uniformly converge to their theoretical probabilities. Uniform convergence in probability has applications to statistics as well as machine learning as part of statistical learning theory. Specifically, the Glivenko-Cantelli theorem and the homonymous classes of functions are fundamentally related to uniform convergence. The law of large numbers says that, for each single event A {\displaystyle A} , its empirical frequency in a sequence of independent trials converges (with high probability) to its theoretical probability. In many application however, the need arises to judge simultaneously the probabilities of events of an entire class S {\displaystyle S} from one and the same sample. Moreover, it, is required that the relative frequency of the events converge to the probability uniformly over the entire class of events S {\displaystyle S} . The Uniform Convergence Theorem gives a sufficient condition for this convergence to hold. Roughly, if the event-family is sufficiently simple (its VC dimension is sufficiently small) then uniform convergence holds. == Definitions == For a class of predicates H {\displaystyle H} defined on a set X {\displaystyle X} and a set of samples x = ( x 1 , x 2 , … , x m ) {\displaystyle x=(x_{1},x_{2},\dots ,x_{m})} , where x i ∈ X {\displaystyle x_{i}\in X} , the empirical frequency of h ∈ H {\displaystyle h\in H} on x {\displaystyle x} is Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | . {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|.} The theoretical probability of h ∈ H {\displaystyle h\in H} is defined as Q P ( h ) = P { y ∈ X : h ( y ) = 1 } . {\displaystyle Q_{P}(h)=P\{y\in X:h(y)=1\}.} The Uniform Convergence Theorem states, roughly, that if H {\displaystyle H} is "simple" and we draw samples independently (with replacement) from X {\displaystyle X} according to any distribution P {\displaystyle P} , then with high probability, the empirical frequency will be close to its expected value, which is the theoretical probability. Here "simple" means that the Vapnik–Chervonenkis dimension of the class H {\displaystyle H} is small relative to the size of the sample. In other words, a sufficiently simple collection of functions behaves roughly the same on a small random sample as it does on the distribution as a whole. The Uniform Convergence Theorem was first proved by Vapnik and Chervonenkis using the concept of growth function. == Uniform Convergence Theorem == The statement of the Uniform Convergence Theorem is as follows: If H {\displaystyle H} is a set of { 0 , 1 } {\displaystyle \{0,1\}} -valued functions defined on a set X {\displaystyle X} and P {\displaystyle P} is a probability distribution on X {\displaystyle X} then for ε > 0 {\displaystyle \varepsilon >0} and m {\displaystyle m} a positive integer, we have: P m { | Q P ( h ) − Q x ^ ( h ) | ≥ ε for some h ∈ H } ≤ 4 Π H ( 2 m ) e − ε 2 m / 8 . {\displaystyle P^{m}\{|Q_{P}(h)-{\widehat {Q_{x}}}(h)|\geq \varepsilon {\text{ for some }}h\in H\}\leq 4\Pi _{H}(2m)e^{-\varepsilon ^{2}m/8}.} In the above, for any x ∈ X m , {\displaystyle x\in X^{m},} Q P ( h ) = P { ( y ∈ X : h ( y ) = 1 } , {\displaystyle Q_{P}(h)=P\{(y\in X:h(y)=1\},} Q ^ x ( h ) = 1 m | { i : 1 ≤ i ≤ m , h ( x i ) = 1 } | {\displaystyle {\widehat {Q}}_{x}(h)={\frac {1}{m}}|\{i:1\leq i\leq m,h(x_{i})=1\}|} and | x | = m . {\displaystyle |x|=m.} P m {\displaystyle P^{m}} indicates that the probability is taken over x {\displaystyle x} consisting of m {\displaystyle m} i.i.d. draws from the distribution P . {\displaystyle P.} Finally, the growth function Π H {\displaystyle \Pi _{H}} is defined in the following way, for any { 0 , 1 } {\displaystyle \{0,1\}} -valued functions H {\displaystyle H} over X {\displaystyle X} and for any natural number m {\displaystyle m} : Π H ( m ) = max | { h ∩ D : D ⊆ X , | D | = m , h ∈ H } | . {\displaystyle \Pi _{H}(m)=\max |\{h\cap D:D\subseteq X,|D|=m,h\in H\}|.} From the point of view of Learning Theory one can consider H {\displaystyle H} to be the Concept/Hypothesis class defined over the instance set X {\displaystyle X} . Crucially, the Sauer–Shelah lemma implies that Π H ( m ) ≤ m d {\displaystyle \Pi _{H}(m)\leq m^{d}} , where d {\displaystyle d} is the VC dimension of H {\displaystyle H} . == Proof of the Uniform Convergence Theorem == and are the sources of the proof below. Before we get into the details of the proof of the Uniform Convergence Theorem we will present a high level overview of the proof. Symmetrization: We transform the problem of analyzing | Q P ( h ) − Q ^ x ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon } into the problem of analyzing | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} , where r {\displaystyle r} and s {\displaystyle s} are i.i.d samples of size m {\displaystyle m} drawn according to the distribution P {\displaystyle P} . One can view r {\displaystyle r} as the original randomly drawn sample of length m {\displaystyle m} , while s {\displaystyle s} may be thought as the testing sample which is used to estimate Q P ( h ) {\displaystyle Q_{P}(h)} . Permutation: Since r {\displaystyle r} and s {\displaystyle s} are picked identically and independently, so swapping elements between them will not change the probability distribution on r {\displaystyle r} and s {\displaystyle s} . So, we will try to bound the probability of | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} for some h ∈ H {\displaystyle h\in H} by considering the effect of a specific collection of permutations of the joint sample x = r | | s {\displaystyle x=r||s} . Specifically, we consider permutations σ ( x ) {\displaystyle \sigma (x)} which swap x i {\displaystyle x_{i}} and x m + i {\displaystyle x_{m+i}} in some subset of 1 , 2 , . . . , m {\displaystyle {1,2,...,m}} . The symbol r | | s {\displaystyle r||s} means the concatenation of r {\displaystyle r} and s {\displaystyle s} . Reduction to a finite class: We can now restrict the function class H {\displaystyle H} to a fixed joint sample and hence, if H {\displaystyle H} has finite VC Dimension, it reduces to the problem to one involving a finite function class. We present the technical details of the proof. It should be stressed that this proof glosses over details like the measurability of the events V {\displaystyle V} and R {\displaystyle R} ; measurability is granted in the case of H {\displaystyle H} being finite or countable, but this is not normally the case in standard applications of the theorem (e.g. for statistical learning theory or to prove the Glivenko-Cantelli theorem). To get measurability, one needs to use a notion of separability of the underlying space, possibly related to H {\displaystyle H} . === Symmetrization === Lemma: Let V = { x ∈ X m : | Q P ( h ) − Q ^ x ( h ) | ≥ ε for some h ∈ H } {\displaystyle V=\{x\in X^{m}:|Q_{P}(h)-{\widehat {Q}}_{x}(h)|\geq \varepsilon {\text{ for some }}h\in H\}} and R = { ( r , s ) ∈ X m × X m : | Q r ^ ( h ) − Q ^ s ( h ) | ≥ ε / 2 for some h ∈ H } . {\displaystyle R=\{(r,s)\in X^{m}\times X^{m}:|{\widehat {Q_{r}}}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2{\text{ for some }}h\in H\}.} Then for m ≥ 2 ε 2 {\displaystyle m\geq {\frac {2}{\varepsilon ^{2}}}} , P m ( V ) ≤ 2 P 2 m ( R ) {\displaystyle P^{m}(V)\leq 2P^{2m}(R)} . Proof: By the triangle inequality, if | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2} then | Q ^ r ( h ) − Q ^ s ( h ) | ≥ ε / 2 {\displaystyle |{\widehat {Q}}_{r}(h)-{\widehat {Q}}_{s}(h)|\geq \varepsilon /2} . Therefore, P 2 m ( R ) ≥ P 2 m { ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } = ∫ V P m { s : ∃ h ∈ H , | Q P ( h ) − Q ^ r ( h ) | ≥ ε and | Q P ( h ) − Q ^ s ( h ) | ≤ ε / 2 } d P m ( r ) = A {\displaystyle {\begin{aligned}&P^{2m}(R)\\[5pt]\geq {}&P^{2m}\{\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\\[5pt]={}&\int _{V}P^{m}\{s:\exists h\in H,|Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon {\text{ and }}|Q_{P}(h)-{\widehat {Q}}_{s}(h)|\leq \varepsilon /2\}\,dP^{m}(r)\\[5pt]={}&A\end{aligned}}} since r {\displaystyle r} and s {\displaystyle s} are independent. Now for r ∈ V {\displaystyle r\in V} fix an h ∈ H {\displaystyle h\in H} such that | Q P ( h ) − Q ^ r ( h ) | ≥ ε {\displaystyle |Q_{P}(h)-{\widehat {Q}}_{r}(h)|\geq \varepsilon } . For this h {\displaystyle h} , we shall
Social recruiting
Social recruiting (social hiring or social media recruitment) is recruiting candidates by using social platforms as talent databases or for advertising. Social recruiting uses social media profiles, blogs, and other Internet sites to find information on candidates. It also uses social media to advertise jobs either through HR vendors or through crowdsourcing where job seekers and others share job openings within their online social networks. Social recruiting's effectiveness and return on investment have been difficult to determine, since applicants do not usually apply through the social channels which first attracted them. In May 2013, Maximum Employment Marketing Group released the Social Recruitment Monitor, which ranks the reach, engagement, and interactivity of employers' social recruiting efforts around the world. == Social recruitment software == The social recruitment software market (a form of e-recruitment) is often included in the wider talent management software sector. Bersin & Associates valued the wider talent management market at over $2bn in 2007. Social recruitment increasingly sits at an intersection of a number of fast-moving areas including social networking, recruitment and now cloud computing. Additionally, mobile recruiting has become another hot topic, especially with the rise in tablet and smartphone usage. In 2012, there was a rise of tech companies using social recruiting applications to find and screen applicants. As more companies saw value in filling jobs by putting them on the social platforms where millions of people spend at least 37 minutes daily, there developed a much larger focus on social recruiting among the talent acquisition community. By mid-2013, many major enterprise companies such as Pepsi, Gap, AIG, and Oracle had begun effectively utilizing social recruiting software, making it clear that large corporations were open to automating or streamlining (and ultimately investing in) their social recruiting processes.