Anti-social Media Bill was introduced by the Senate of the Federal Republic of Nigeria on 5 November 2019 to criminalise the use of the social media in peddling false or malicious information. The original title of the bill is Protection from Internet Falsehood and Manipulations Bill 2019. It was sponsored by Senator Mohammed Sani Musa from the largely conservative northern Nigeria. After the bill passed second reading on the floor of the Nigeria Senate and its details were made public, information emerged on the social media accusing the sponsor of the bill of plagiarising a similar law in Singapore which is at the bottom of global ranking in the freedom of speech and of the press. But the senator denied that he plagiarised Singaporean law. == Opposition to the bill == Angry reactions trailed the introduction of the bill, and a number of civil society organisations, human rights activists, and Nigerian citizens unanimously opposed the bill. International rights group, Amnesty International and Human Rights Watch condemned the proposed legislation saying it is aimed at gagging freedom of speech which is a universal right in a country of over two hundred million people. Opposition political parties are very critical of the bill and accused the government of attempting to strip bare, Nigerian citizens of their rights to free speech and destroying same social media on whose power and influence the ruling All Progressives Congress, APC came to power in 2015. Nigeria Information Minister, Lai Mohammed has been at the center of public criticism because he is suspected to be the brain behind the proposed act. Lai was a former spokesman of then opposition All Progressives Congress. A "Stop the Social Media Bill! You can no longer take our rights from us" online petition campaign to force the Nigeria parliament to drop the bill received over 90,000 signatures within 24 hours. In November 2019, after the bill passed second reading in the senate, Akon Eyakenyi, a senator from Akwa Ibom State publicly said he would resist the bill. === Support for the bill === Those who support the proposed act especially Senators have often argued that the law would help curtail hate speech. President Muhammad Buhari who is seen as a beneficiary of the influence and power of the social media and free speech has been mute about it. But the president's senior aides and family members have publicly spoken in support of the bill. In November 2019, the wife of the president, Aisha Buhari, told a gathering at the Nigeria's National Mosque in the capital, Abuja that if China with over one billion people could regulate the social media, Nigeria should do same. But Nigerians reacted saying Nigeria is not a one-party communist state like China. Days later, a daughter to the president, Zahra Indimi told a gathering of young people in Abuja that social media had become a potent weapon for bullying those they thought were doing better than them in terms of social class and called for a critical regulation. == Key provisions of the bill == === Title === Protection from Internet Falsehoods, Manipulations and Other Related Matters Bill 2019. === Explanatory memorandum === This Act is to prevent Falsehoods and Manipulations in Internet transmission and correspondences in Nigeria. To suppress falsehoods and manipulations and counter the effects of such communications and transmissions and to sanction offenders with a view to encouraging and enhancing transparency by Social Media Platforms using the internet correspondences. === Objectives === One objective of the bill is to prevent the transmission of false statements or declaration of facts in Nigeria. Another objective of the bill is to end the financing of online mediums that transmit false statements. Measures will be taken to detect and control inauthentic behaviour and misuse of online accounts (parody accounts). When paid content is posted towards a political end, there will be measures to ensure the poster discloses such information. There will be sanction for offenders. === Transmission of false statement === According to the bill, a person must not: Transmit a statement that is false or, Transmit a statement that might: i. Affect the security or any part of Nigeria. ii. Affect public health, public safety or public finance. iii. Affect Nigeria's relationship with other countries. iv. influence the outcome of an election to any office in a general election. v. Cause enmity or hatred towards a person or group of persons. Anyone guilty of the above is liable to a fine of N300,000 or three years' imprisonment or both (for individual); and a fine not exceeding ten million naira (for corporate organisations). Same punishment applies for fake online accounts that transmit statements listed above. === Parody accounts === The bill says a person shall not open an account to transmit false statement. Anyone found guilty will be fined N200,000 or three years' imprisonment or both (for an individual) or five million naira (for corporate organisations). If such accounts transmit a statement that will affect security or influence the outcome of an election, such a person will be fined N300,000 or three years' imprisonment or both. If a person receives payment or reward to help another to transmit false statements knowingly, he/she is liable to a fine of N150,000 or three years' imprisonment or both. If a person receives payment or reward to help another to transmit a statement affects security or influence the outcome of an election, the fine is N300,000 or three years' imprisonment or both (for individual) and ten million naira for organisations. === Declaration === According to the bill, a law enforcement department can issue a "declaration" to offenders. And this declaration will be issued even if the "false statement" has been corrected or pulled down. The offender will be required to publish a "correction notice" in a specified newspaper, online location or other printed publication of Nigeria. Failure to comply, a person is liable to N200,000 or 12 months' imprisonment or both (for individual) and five million naira for organisations. === Access blocking order === The bill says the law enforcement department will also issue an access blocking order to offenders. The law enforcement department may direct the NCC to order the internet access service provider to disable access by users in Nigeria to the online location and the NCC must give the internet access service provider an access blocking order. An internet access service provider that does not comply with any access blocking order is liable on conviction to a fine not exceeding ten million naira for each day during any part of which that order is not fully complied with, up to a total of five million naira.
Decision tree pruning
Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. This problem is known as the horizon effect. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide additional information. Pruning should reduce the size of a learning tree without reducing predictive accuracy as measured by a cross-validation set. There are many techniques for tree pruning that differ in the measurement that is used to optimize performance. == Techniques == Pruning processes can be divided into two types (pre- and post-pruning). Pre-pruning procedures prevent a complete induction of the training set by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered to be more efficient because they do not induce an entire set, but rather trees remain small from the start. Prepruning methods share a common problem, the horizon effect. This is to be understood as the undesired premature termination of the induction by the stop () criterion. Post-pruning (or just pruning) is the most common way of simplifying trees. Here, nodes and subtrees are replaced with leaves to reduce complexity. Pruning can not only significantly reduce the size but also improve the classification accuracy of unseen objects. It may be the case that the accuracy of the assignment on the train set deteriorates, but the accuracy of the classification properties of the tree increases overall. The procedures are differentiated on the basis of their approach in the tree (top-down or bottom-up). === Bottom-up pruning === These procedures start at the last node in the tree (the lowest point). Following recursively upwards, they determine the relevance of each individual node. If the relevance for the classification is not given, the node is dropped or replaced by a leaf. The advantage is that no relevant sub-trees can be lost with this method. These methods include Reduced Error Pruning (REP), Minimum Cost Complexity Pruning (MCCP), or Minimum Error Pruning (MEP). === Top-down pruning === In contrast to the bottom-up method, this method starts at the root of the tree. Following the structure below, a relevance check is carried out which decides whether a node is relevant for the classification of all n items or not. By pruning the tree at an inner node, it can happen that an entire sub-tree (regardless of its relevance) is dropped. One of these representatives is pessimistic error pruning (PEP), which brings quite good results with unseen items. == Pruning algorithms == === Reduced error pruning === One of the simplest forms of pruning is reduced error pruning. Starting at the leaves, each node is replaced with its most popular class. If the prediction accuracy is not affected then the change is kept. While somewhat naive, reduced error pruning has the advantage of simplicity and speed. === Cost complexity pruning === Cost complexity pruning generates a series of trees T 0 … T m {\displaystyle T_{0}\dots T_{m}} where T 0 {\displaystyle T_{0}} is the initial tree and T m {\displaystyle T_{m}} is the root alone. At step i {\displaystyle i} , the tree is created by removing a subtree from tree i − 1 {\displaystyle i-1} and replacing it with a leaf node with value chosen as in the tree building algorithm. The subtree that is removed is chosen as follows: Define the error rate of tree T {\displaystyle T} over data set S {\displaystyle S} as err ( T , S ) {\displaystyle \operatorname {err} (T,S)} . The subtree t {\displaystyle t} that minimizes err ( prune ( T , t ) , S ) − err ( T , S ) | leaves ( T ) | − | leaves ( prune ( T , t ) ) | {\displaystyle {\frac {\operatorname {err} (\operatorname {prune} (T,t),S)-\operatorname {err} (T,S)}{\left\vert \operatorname {leaves} (T)\right\vert -\left\vert \operatorname {leaves} (\operatorname {prune} (T,t))\right\vert }}} is chosen for removal. The function prune ( T , t ) {\displaystyle \operatorname {prune} (T,t)} defines the tree obtained by pruning the subtrees t {\displaystyle t} from the tree T {\displaystyle T} . Once the series of trees has been created, the best tree is chosen by generalized accuracy as measured by a training set or cross-validation. == Examples == Pruning could be applied in a compression scheme of a learning algorithm to remove the redundant details without compromising the model's performances. In neural networks, pruning removes entire neurons or layers of neurons.
Cloud manufacturing
Cloud manufacturing (CMfg) is a new manufacturing paradigm developed from existing advanced manufacturing models (e.g., ASP, AM, NM, MGrid) and enterprise information technologies under the support of cloud computing, Internet of Things (IoT), virtualization and service-oriented technologies, and advanced computing technologies. It transforms manufacturing resources and manufacturing capabilities into manufacturing services, which can be managed and operated in an intelligent and unified way to enable the full sharing and circulating of manufacturing resources and manufacturing capabilities. CMfg can provide safe and reliable, high quality, cheap and on-demand manufacturing services for the whole lifecycle of manufacturing. The concept of manufacturing here refers to big manufacturing that includes the whole lifecycle of a product (e.g. design, simulation, production, test, maintenance). The concept of Cloud manufacturing was initially proposed by the research group led by Prof. Bo Hu Li and Prof. Lin Zhang in China in 2010. Related discussions and research were conducted hereafter, and some similar definitions (e.g. Cloud-Based Design and Manufacturing (CBDM). ) to cloud manufacturing were introduced. Cloud manufacturing is a type of parallel, networked, and distributed system consisting of an integrated and inter-connected virtualized service pool (manufacturing cloud) of manufacturing resources and capabilities as well as capabilities of intelligent management and on-demand use of services to provide solutions for all kinds of users involved in the whole lifecycle of manufacturing. == Types == Cloud Manufacturing can be divided into two categories. The first category concerns deploying manufacturing software on the Cloud, i.e. a “manufacturing version” of Computing. CAx software can be supplied as a service on the Manufacturing Cloud (MCloud). The second category has a broader scope, cutting across production, management, design and engineering abilities in a manufacturing business. Unlike with computing and data storage, manufacturing involves physical equipment, monitors, materials and so on. In this kind of Cloud Manufacturing system, both material and non-material facilities are implemented on the Manufacturing Cloud to support the whole supply chain. Costly resources are shared on the network. This means that the utilisation rate of rarely used equipment rises and the cost of expensive equipment is reduced. According to the concept of Cloud technology, there will not be direct interaction between Cloud Users and Service Providers. The Cloud User should neither manage nor control the infrastructure and manufacturing applications. As a matter of fact, the former can be considered part of the latter. In CMfg system, various manufacturing resources and abilities can be intelligently sensed and connected into wider Internet, and automatically managed and controlled using IoT technologies (e.g., RFID, wired and wireless sensor network, embedded system). Then the manufacturing resources and abilities are virtualized and encapsulated into different manufacturing cloud services (MCSs), that can be accessed, invoked, and deployed based on knowledge by using virtualization technologies, service-oriented technologies, and cloud computing technologies. The MCSs are classified and aggregated according to specific rules and algorithms, and different kinds of manufacturing clouds are constructed. Different users can search and invoke the qualified MCSs from related manufacturing cloud according to their needs, and assemble them to be a virtual manufacturing environment or solution to complete their manufacturing task involved in the whole life cycle of manufacturing processes under the support of cloud computing, service-oriented technologies, and advanced computing technologies. Four types of cloud deployment modes (public, private, community and hybrid clouds) are ubiquitous as a single point of access. Private cloud refers to a centralized management effort in which manufacturing services are shared within one company or its subsidiaries. Enterprises' mission-critical and core-business applications are often kept in a private cloud. Community cloud is a collaborative effort in which manufacturing services are shared between several organizations from a specific community with common concerns. Public cloud realizes the key concept of sharing services with the general public in a multi-tenant environment. Hybrid cloud is a composition of two or more clouds (private, community or public) that remain distinct entities but are also bound together, offering the benefits of multiple deployment modes. == Resources == From the resource’s perspective, each kind of manufacturing capability requires support from the related manufacturing resource. For each type of manufacturing capability, its related manufacturing resource comes in two forms, soft resources and hard resources. === Soft resources === Software: software applications throughout the product lifecycle including design, analysis, simulation, process planning, and are only beginning to be embraced by the electronics manufacturing industry. Knowledge: experience and know-how needed to complete a production task, i.e. engineering knowledge, product models, standards, evaluation procedures and results, customer feedback, and manufacturing in the cloud provides just as many solutions as the number of questions it also raises for manufacturing executives wanting to make the best possible decision. Skill: expertise in performing a specific manufacturing task. Personnel: human resource engaged in the manufacturing process, i.e. designers, operators, managers, technicians, project teams, customer service, etc. Experience: performance, quality, client evaluation, etc. Business Network: business relationships and business opportunity networks that exist in an enterprise. === Hard resources === Manufacturing Equipment: facilities needed for completing a manufacturing task, e.g. machine tools, cutters, test and monitoring equipment and other fabrication tools. Monitoring/Control Resource: devices used to identify and control other manufacturing resource, for instance, RFID (Radio-Frequency IDentification), WSN (Wireless Sensor Network), virtual managers and remote controllers. Computational Resource: computing devices to support production process, e.g. servers, computers, storage media, control devices, etc. Materials: inputs and outputs in a production system, e.g. raw material, product-in-progress, finished product, power, water, lubricants, etc. Storage: automated storage and retrieval systems, logic controllers, location of warehouses, volume capacity and schedule/optimization methods. Transportation: movement of manufacturing inputs/outputs from one location to another. It includes the modes of transport, e.g. air, rail, road, water, cable, pipeline and space, and the related price, and time taken.
Programming tool
A programming tool or software development tool is a computer program that is used to develop another computer program, usually by helping the developer manage computer files. For example, a programmer may use a tool called a source code editor to edit source code files, and then a compiler to convert the source code into machine code files. They may also use build tools that automatically package executable program and data files into shareable packages or install kits. A set of tools that are run one after another, with each tool feeding its output to the next one, is called a toolchain. An integrated development environment (IDE) integrates the function of several tools into a single program. Usually, an IDE provides a source code editor as well as other built-in or plug-in tools that help with compiling, debugging, and testing. Whether a program is considered a development tool can be subjective. Some programs, such as the GNU compiler collection, are used exclusively for software development while others, such as Notepad, are not meant specifically for development but are nevertheless often used for programming. == Categories == Notable categories of development tools: Assembler – Converts assembly language into machine code Bug tracking system – Software application that records software bugs Build automation – Building software via an unattended fashion Code review software – Activity where one or more people check a program's code Compiler – Software that translates code from one programming language to another Compiler-compiler – Program that generates parsers or compilers, a.k.a. parser generator Debugger – Software for debugging a computer program Decompiler – Program translating executable to source code Disassembler – Computer program to translate machine language into assembly language Documentation generator – Automation technology for creating software documentation Graphical user interface builder – Software development tool Linker – Program that combines intermediate build files into an executable file Loader – Loads executable files into memory and prepares them for execution by the CPU. Memory debugger – Software memory problem finder Minifier – Removal of unnecessary characters in code without changing its functionality Pretty-printer – Formatting to make code or markup easier to readPages displaying short descriptions of redirect targets Performance profiler – Measuring the time or resources used by a section of a computer program Static code analyzer – Analysis of computer programs without executing themPages displaying short descriptions of redirect targets Source code editor – Text editor specializing in software codePages displaying short descriptions of redirect targets Source code generation – Type of computer programmingPages displaying short descriptions of redirect targets Version control system – Stores and tracks versions of files
Autoscaling
Autoscaling, (also written as auto scaling, auto-scaling, or known as automatic scaling), is a method used in cloud computing that dynamically adjusts the amount of computational resources in a server farm - typically measured by the number of active servers - automatically based on the load on the farm. For example, the number of servers running behind a web application may be increased or decreased automatically based on the number of active users on the site. Since such metrics may change dramatically throughout the course of the day, and servers are a limited resource that cost money to run even while idle, there is often an incentive to run "just enough" servers to support the current load while still being able to support sudden and large spikes in activity. Autoscaling is helpful for such needs, as it can reduce the number of active servers when activity is low, and launch new servers when activity is high. Autoscaling is closely related to, and builds upon, the idea of load balancing. == Advantages == Autoscaling offers the following advantages: For companies running their own web server infrastructure, autoscaling typically means allowing some servers to go to sleep during times of low load, saving on electricity costs (as well as water costs if water is being used to cool the machines). For companies using infrastructure hosted in the cloud, autoscaling can mean lower bills, because most cloud providers charge based on total usage rather than maximum capacity. Even for companies that cannot reduce the total compute capacity they run or pay for at any given time, autoscaling can help by allowing the company to run less time-sensitive workloads on machines that get freed up by autoscaling during times of low traffic. Autoscaling solutions, such as the one offered by Amazon Web Services, can also take care of replacing unhealthy instances and therefore protecting somewhat against hardware, network, and application failures. Autoscaling can offer greater uptime and more availability in cases where production workloads are variable and unpredictable. Autoscaling differs from having a fixed daily, weekly, or yearly cycle of server use in that it is responsive to actual usage patterns, and thus reduces the potential downside of having too few or too many servers for the traffic load. For instance, if traffic is usually lower at midnight, then a static scaling solution might schedule some servers to sleep at night, but this might result in downtime on a night where people happen to use the Internet more (for instance, due to a viral news event). Autoscaling, on the other hand, can handle unexpected traffic spikes better. == Terminology == In the list below, we use the terminology used by Amazon Web Services (AWS). However, alternative names are noted and terminology that is specific to the names of Amazon services is not used for the names. == Practice == === Amazon Web Services (AWS) === Amazon Web Services launched the Amazon Elastic Compute Cloud (EC2) service in August 2006, that allowed developers to programmatically create and terminate instances (machines). At the time of initial launch, AWS did not offer autoscaling, but the ability to programmatically create and terminate instances gave developers the flexibility to write their own code for autoscaling. Third-party autoscaling software for AWS began appearing around April 2008. These included tools by Scalr and RightScale. RightScale was used by Animoto, which was able to handle Facebook traffic by adopting autoscaling. On May 18, 2009, Amazon launched its own autoscaling feature along with Elastic Load Balancing, as part of Amazon Elastic Compute Cloud. Autoscaling is now an integral component of Amazon's EC2 offering. Autoscaling on Amazon Web Services is done through a web browser or the command line tool. In May 2016 Autoscaling was also offered in AWS ECS Service. On-demand video provider Netflix documented their use of autoscaling with Amazon Web Services to meet their highly variable consumer needs. They found that aggressive scaling up and delayed and cautious scaling down served their goals of uptime and responsiveness best. In an article for TechCrunch, Zev Laderman, the co-founder and CEO of Newvem, a service that helps optimize AWS cloud infrastructure, recommended that startups use autoscaling in order to keep their Amazon Web Services costs low. Various best practice guides for AWS use suggest using its autoscaling feature even in cases where the load is not variable. That is because autoscaling offers two other advantages: automatic replacement of any instances that become unhealthy for any reason (such as hardware failure, network failure, or application error), and automatic replacement of spot instances that get interrupted for price or capacity reasons, making it more feasible to use spot instances for production purposes. Netflix's internal best practices require every instance to be in an autoscaling group, and its conformity monkey terminates any instance not in an autoscaling group in order to enforce this best practice. === Microsoft's Windows Azure === On June 27, 2013, Microsoft announced that it was adding autoscaling support to its Windows Azure cloud computing platform. Documentation for the feature is available on the Microsoft Developer Network. === Oracle Cloud === Oracle Cloud Platform allows server instances to automatically scale a cluster in or out by defining an auto-scaling rule. These rules are based on CPU and/or memory utilization and determine when to add or remove nodes. === Google Cloud Platform === On November 17, 2014, the Google Compute Engine announced a public beta of its autoscaling feature for use in Google Cloud Platform applications. As of March 2015, the autoscaling tool is still in Beta. === Facebook === In a blog post in August 2014, a Facebook engineer disclosed that the company had started using autoscaling to bring down its energy costs. The blog post reported a 27% decline in energy use for low traffic hours (around midnight) and a 10-15% decline in energy use over the typical 24-hour cycle. === Kubernetes Horizontal Pod Autoscaler === Kubernetes Horizontal Pod Autoscaler automatically scales the number of pods in a replication controller, deployment or replicaset based on observed CPU utilization (or, with beta support, on some other, application-provided metrics) == Alternative autoscaling decision approaches == Autoscaling by default uses reactive decision approach for dealing with traffic scaling: scaling only happens in response to real-time changes in metrics. In some cases, particularly when the changes occur very quickly, this reactive approach to scaling is insufficient. Two other kinds of autoscaling decision approaches are described below. === Scheduled autoscaling approach === This is an approach to autoscaling where changes are made to the minimum size, maximum size, or desired capacity of the autoscaling group at specific times of day. Scheduled scaling is useful, for instance, if there is a known traffic load increase or decrease at specific times of the day, but the change is too sudden for reactive approach based autoscaling to respond fast enough. AWS autoscaling groups support scheduled scaling. === Predictive autoscaling === This approach to autoscaling uses predictive analytics. The idea is to combine recent usage trends with historical usage data as well as other kinds of data to predict usage in the future, and autoscale based on these predictions. For parts of their infrastructure and specific workloads, Netflix found that Scryer, their predictive analytics engine, gave better results than Amazon's reactive autoscaling approach. In particular, it was better for: Identifying huge spikes in demand in the near future and getting capacity ready a little in advance Dealing with large-scale outages, such as failure of entire availability zones and regions Dealing with variable traffic patterns, providing more flexibility on the rate of scaling out or in based on the typical level and rate of change in demand at various times of day On November 20, 2018, AWS announced that predictive scaling would be available as part of its autoscaling offering.
Rademacher complexity
In computational learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with respect to a probability distribution. The concept can also be extended to real valued functions. == Definitions == === Rademacher complexity of a set === Given a set A ⊆ R m {\displaystyle A\subseteq \mathbb {R} ^{m}} , the Rademacher complexity of A is defined as follows: Rad ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] {\displaystyle \operatorname {Rad} (A):={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{a\in A}\sum _{i=1}^{m}\sigma _{i}a_{i}\right]} where σ 1 , σ 2 , … , σ m {\displaystyle \sigma _{1},\sigma _{2},\dots ,\sigma _{m}} are independent random variables drawn from the Rademacher distribution i.e. Pr ( σ i = + 1 ) = Pr ( σ i = − 1 ) = 1 / 2 {\displaystyle \Pr(\sigma _{i}=+1)=\Pr(\sigma _{i}=-1)=1/2} for i ∈ { 1 , 2 , … , m } {\displaystyle i\in \{1,2,\dots ,m\}} , and a = ( a 1 , … , a m ) ∈ A {\displaystyle a=(a_{1},\ldots ,a_{m})\in A} . Some authors take the absolute value of the sum before taking the supremum, but if A {\displaystyle A} is symmetric this makes no difference. === Rademacher complexity of a function class === Let S = { z 1 , z 2 , … , z m } ⊆ Z {\displaystyle S=\{z_{1},z_{2},\dots ,z_{m}\}\subseteq Z} be a sample of points and consider a function class F {\displaystyle {\mathcal {F}}} of real-valued functions over Z {\displaystyle Z} . Then, the empirical Rademacher complexity of F {\displaystyle {\mathcal {F}}} given S {\displaystyle S} is defined as: Rad S ( F ) = 1 m E σ [ sup f ∈ F | ∑ i = 1 m σ i f ( z i ) | ] {\displaystyle \operatorname {Rad} _{S}({\mathcal {F}})={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{f\in {\mathcal {F}}}\left|\sum _{i=1}^{m}\sigma _{i}f(z_{i})\right|\right]} This can also be written using the previous definition: Rad S ( F ) = Rad ( F ∘ S ) {\displaystyle \operatorname {Rad} _{S}({\mathcal {F}})=\operatorname {Rad} ({\mathcal {F}}\circ S)} where F ∘ S {\displaystyle {\mathcal {F}}\circ S} denotes function composition, i.e.: F ∘ S := { ( f ( z 1 ) , … , f ( z m ) ) ∣ f ∈ F } {\displaystyle {\mathcal {F}}\circ S:=\{(f(z_{1}),\ldots ,f(z_{m}))\mid f\in {\mathcal {F}}\}} The worst case empirical Rademacher complexity is Rad ¯ m ( F ) = sup S = { z 1 , … , z m } Rad S ( F ) {\displaystyle {\overline {\operatorname {Rad} }}_{m}({\mathcal {F}})=\sup _{S=\{z_{1},\dots ,z_{m}\}}\operatorname {Rad} _{S}({\mathcal {F}})} Let P {\displaystyle P} be a probability distribution over Z {\displaystyle Z} . The Rademacher complexity of the function class F {\displaystyle {\mathcal {F}}} with respect to P {\displaystyle P} for sample size m {\displaystyle m} is: Rad P , m ( F ) := E S ∼ P m [ Rad S ( F ) ] {\displaystyle \operatorname {Rad} _{P,m}({\mathcal {F}}):=\mathbb {E} _{S\sim P^{m}}\left[\operatorname {Rad} _{S}({\mathcal {F}})\right]} where the above expectation is taken over an identically independently distributed (i.i.d.) sample S = ( z 1 , z 2 , … , z m ) {\displaystyle S=(z_{1},z_{2},\dots ,z_{m})} generated according to P {\displaystyle P} . == Intuition == The Rademacher complexity is typically applied on a function class of models that are used for classification, with the goal of measuring their ability to classify points drawn from a probability space under arbitrary labellings. When the function class is rich enough, it contains functions that can appropriately adapt for each arrangement of labels, simulated by the random draw of σ i {\displaystyle \sigma _{i}} under the expectation, so that this quantity in the sum is maximized. The Rademacher complexity of a set A {\displaystyle A} can be rewritten as Rad ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] = 1 m 2 m ∑ σ ∈ { − 1 / m , + 1 / m } m [ sup a ∈ A ⟨ σ , a ⟩ ] . {\displaystyle \operatorname {Rad} (A):={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{a\in A}\sum _{i=1}^{m}\sigma _{i}a_{i}\right]={\frac {1}{{\sqrt {m}}2^{m}}}\sum _{\sigma \in \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}}\left[\sup _{a\in A}\langle \sigma ,a\rangle \right].} Each term in the summation is the farthest distance of the set A {\displaystyle A} from the origin, along a unit-length direction σ {\displaystyle \sigma } . The directions are along the vertices of a hypercube. Thus, we can also write it as Rad ( A ) = 1 2 m 1 2 m − 1 ∑ σ ∈ { − 1 / m , + 1 / m } m / { − 1 , + 1 } [ sup a ∈ A ⟨ σ , a ⟩ − inf a ∈ A ⟨ σ , a ⟩ ] {\displaystyle \operatorname {Rad} (A)={\frac {1}{2{\sqrt {m}}}}{\frac {1}{2^{m-1}}}\sum _{\sigma \in \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}/\{-1,+1\}}\left[\sup _{a\in A}\langle \sigma ,a\rangle -\inf _{a\in A}\langle \sigma ,a\rangle \right]} Here, the set { − 1 / m , + 1 / m } m / { − 1 , + 1 } {\displaystyle \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}/\{-1,+1\}} denotes half of the vertices of a hypercube, selected so that each diagonal has exactly one vertex selected. In words, this states that 2 m Rad ( A ) {\displaystyle 2{\sqrt {m}}\operatorname {Rad} (A)} is precisely the average width of the set A {\displaystyle A} along all diagonal directions of a hypercube. == Examples == A singleton set has 0 width in any direction, so it has Rademacher complexity 0. The set A = { ( 1 , 1 ) , ( 1 , 2 ) } ⊆ R 2 {\displaystyle A=\{(1,1),(1,2)\}\subseteq \mathbb {R} ^{2}} has average width 1 / 2 {\displaystyle 1/{\sqrt {2}}} along the two diagonal directions of the square, so it has Rademacher complexity 1 / 4 {\displaystyle 1/4} . The unit cube [ 0 , 1 ] m {\displaystyle [0,1]^{m}} has constant width m {\displaystyle {\sqrt {m}}} along the diagonal directions, so it has Rademacher complexity 1 / 2 {\displaystyle 1/2} . Similarly, the unit cross-polytope { x ∈ R m : ‖ x ‖ 1 ≤ 1 } {\displaystyle \{x\in \mathbb {R} ^{m}:\|x\|_{1}\leq 1\}} has constant width 2 / m {\displaystyle 2/{\sqrt {m}}} along the diagonal directions, so it has Rademacher complexity 1 / m {\displaystyle 1/m} . == Using the Rademacher complexity == The Rademacher complexity can be used to derive data-dependent upper-bounds on the learnability of function classes. Intuitively, a function-class with smaller Rademacher complexity is easier to learn. === Bounding the representativeness === In machine learning, it is desired to have a training set that represents the true distribution of some sample data S {\displaystyle S} . This can be quantified using the notion of representativeness. Denote by P {\displaystyle P} the probability distribution from which the samples are drawn. Denote by H {\displaystyle H} the set of hypotheses (potential classifiers) and denote by F {\displaystyle {\mathcal {F}}} the corresponding set of error functions, i.e., for every hypothesis h ∈ H {\displaystyle h\in H} , there is a function f h ∈ F {\displaystyle f_{h}\in F} , that maps each training sample (features,label) to the error of the classifier h {\displaystyle h} (note in this case hypothesis and classifier are used interchangeably). For example, in the case that h {\displaystyle h} represents a binary classifier, the error function is a 0–1 loss function, i.e. the error function f h {\displaystyle f_{h}} returns 0 if h {\displaystyle h} correctly classifies a sample and 1 else. We omit the index and write f {\displaystyle f} instead of f h {\displaystyle f_{h}} when the underlying hypothesis is irrelevant. Define: L P ( f ) := E z ∼ P [ f ( z ) ] {\displaystyle L_{P}(f):=\mathbb {E} _{z\sim P}[f(z)]} – the expected error of some error function f ∈ F {\displaystyle f\in {\mathcal {F}}} on the real distribution P {\displaystyle P} ; L S ( f ) := 1 m ∑ i = 1 m f ( z i ) {\displaystyle L_{S}(f):={1 \over m}\sum _{i=1}^{m}f(z_{i})} – the estimated error of some error function f ∈ F {\displaystyle f\in {\mathcal {F}}} on the sample S {\displaystyle S} . The representativeness of the sample S {\displaystyle S} , with respect to P {\displaystyle P} and F {\displaystyle {\mathcal {F}}} , is defined as: Rep P ( F , S ) := sup f ∈ F ( L P ( f ) − L S ( f ) ) {\displaystyle \operatorname {Rep} _{P}({\mathcal {F}},S):=\sup _{f\in F}(L_{P}(f)-L_{S}(f))} Smaller representativeness is better, since it provides a way to avoid overfitting: it means that the true error of a classifier is not much higher than its estimated error, and so selecting a classifier that has low estimated error will ensure that the true error is also low. Note however that the concept of representativeness is relative and hence can not be compared across distinct samples. The expected representativeness of a sample can be bounded above by the Rademacher complexity of the function class: If F {\displaystyle {\mathcal {F}}} is a set of functions with range within [ 0 , 1 ] {\displaystyle [0,1]} , then Rad P , m ( F ) − ln 2 2 m ≤ E S ∼ P m [ Rep P ( F , S ) ] ≤ 2 Rad P , m ( F ) {\displaystyle \operatorname {Rad} _{P,m}({\mathcal {F}})-{\sqrt {\frac {\ln 2}{2m}}}\leq \mathbb {E} _{S\sim P^{m}}[\operatorname {Rep} _{P}({\
Cloud printing
There are, in essence, three kinds of Cloud printing. == Benefits == 76% of IT teams have moved, or plan to move, their print workflows to the cloud due to its simplicity. Consumers can print easily to any printer from their PC, tablet or smartphone, while the Cloud print service monitors the supplies level. Many printer vendors such as Lexmark propose an automatic supplies shipment based on the real-time analysis of the printer supplies and user behavior to ensure printing will always be possible. For IT department, Cloud Printing eliminates the need for print servers and represents the only way to print from Cloud virtual desktops and servers. For consumers, cloud ready printers eliminate the need for PC connections and print drivers, enabling them to print from mobile devices. As for publishers and content owners, cloud printing allows them to "avoid the cost and complexity of buying and managing the underlying hardware, software and processes" required for the production of professional print products. Leveraging cloud print for print on demand also allows businesses to cut down on the costs associated with mass production. Moreover, cloud printing can be considered more eco-friendly, as it significantly reduces the amount of paper used (13% reduction in print jobs yearly) and lowers carbon emissions from transportation. As many companies move their IT to the Cloud, some adopting the Windows 365 and Azure Virtual Desktop services from Microsoft, the connection from the Cloud environment to the on-premise printers become an issue as opening ports for incoming print flow traffic is not an option. In 2020, at the exact same time Google discontinued its Google Print offer, Microsoft has announced its Universal Print service offer, aimed at making printing compatible with Cloud Desktop environments, making printing driver-free and simple with no client to install on PC. With Universal Print Microsoft has built a disrupting architecture with a value proposition commodifying printers, removing print servers and drivers, allowing to move printers to VLAN for security purpose and printing from anywhere. Clients are free to use any printer from any model as they all work the same, clients are not tied anymore to any printer brand and that gave a significant boost to the Cloud print market. That Microsoft Universal Print architecture provides APIs to third-party developers who can develop add-ons such as Celiveo 365 to extend Microsoft Cloud Print with added features such as access control on printers and copiers, follow-me pull print, data encryption, advanced usage reporting or charge back. == Providers of Consumer Cloud Printing Solutions == Before 2020 only a handful of providers used to work towards a professional cloud print solution, operating in their own niche or focus on mobile devices. In 2020 Microsoft has boosted that market by announcing its Universal Print Cloud printing service and since then many publishers have started to propose solutions for that growing market. The Covid pandemic also created the need for employees to be able to print at home when using the corporate IT software. Closed VPN often prevent accessing home network printers from corporate laptops and Full Public Cloud solutions are meant to be a solution to that problem. After the decision by Google to terminate Google Cloud Print service on 31 December 2020, most printer vendors released their own mobile cloud solution to fill the gap, while Hewlett-Packard implemented its own cloud print with their ePrint solution. Those solutions are often proprietary, only working on printers proposed by the vendor. Google has decided to let third-party developers develop Cloud Print solutions and to limit its scope to certifying the best Print Management offers compatible with its Chrome Enterprise Cloud ecosystem. == Providers of Corporate Cloud Printing solutions == While many print solutions claim to be "Cloud Printing", there are actually three categories: full Private Cloud, full Public Cloud, and Hybrid Cloud. Their differences are real and have an impact on the overall TCO as the more software there is on-site, the more hidden cost there are. In the Full Public Cloud category, independent SaaS vendors like Celiveo, ezeep , Printix , and Y Soft support a wide range of printer brands and models, allowing clients to buy the best printer without being locked on any brand. They are leveraging cloud computing technology to offer cloud-based print infrastructure and cloud-based printing software as a Service (SaaS). These solutions have integrations to cloud enabled printers or provide embedded printer agents. They feature allow users to print to any printer in any network, isolated network or not, even if that printer is otherwise not reachable from the user's computer. This also allows IT departments to move printers to VLAN for maximum security, like what they are doing with IP phones. Google Chrome Enterprise Cloud ecosystem has its own technical particularities and Google certifies Print Management solutions, ensuring they comply with Google technical requirement, yet letting each solution differentiate from others with specific features or security. Many of solutions for Chrome Enterprise are Hybrid, a few are Full Public Cloud. Industry experts believe that as these services become more popular, users will no longer consider printers as necessary assets but rather as devices that they can access on demand when the need to generate a printed page presents itself. == Caveats of Cloud Printing == == Security == Print jobs flow through Public Internet. It is therefore important to verify no Man-in-the-Middle attack can be performed. The only technical solution is to ensure each printer and PC uses a non-self-generated cryptographic token or certificate allowing TLS mutual authentication and specific data encryption. Self-generated printer certificates are unknown from the Cloud and prevent trusted authentication. Microsoft has implemented its Zero Trust Access security in its Universal Print service, it generates a unique certificate on printers compatible with its service. Other Cloud Printing SaaS providers have followed Microsoft on that High Security path. Print jobs data stored on the Cloud is sensitive as it contains user information as well as all information appearing on pages. Good practices require such data is encrypted at rest and in motion, using asymmetric PKI keys instead of fixed encryption keys. Some solutions require to open incoming traffic ports on the firewall to let Cloud services communicate with printers attached behind that firewall (most of the time for IPP/IPPS flows), some other solutions use a pull model where the communication is always initiated by the printer and no firewall port needs to be open. In terms of security the later is to be preferred.