XGBoost (eXtreme Gradient Boosting) is an open-source software library which provides a regularizing gradient boosting framework for C++, Java, Python, R, Julia, Perl, and Scala. It works on Linux, Microsoft Windows, and macOS. From the project description, it aims to provide a "Scalable, Portable and Distributed Gradient Boosting (GBM, GBRT, GBDT) Library". It runs on a single machine, as well as the distributed processing frameworks Apache Hadoop, Apache Spark, Apache Flink, and Dask. XGBoost gained much popularity and attention in the mid-2010s as the algorithm of choice for many winning teams of machine learning competitions. == History == XGBoost initially started as a research project by Tianqi Chen as part of the Distributed (Deep) Machine Learning Community (DMLC) group at the University of Washington. Initially, it began as a terminal application which could be configured using a libsvm configuration file. It became well known in the ML competition circles after its use in the winning solution of the Higgs Machine Learning Challenge. Soon after, the Python and R packages were built, and XGBoost now has package implementations for Java, Scala, Julia, Perl, and other languages. This brought the library to more developers and contributed to its popularity among the Kaggle community, where it has been used for a large number of competitions. It was soon integrated with a number of other packages making it easier to use in their respective communities. It has now been integrated with scikit-learn for Python users and with the caret package for R users. It can also be integrated into Data Flow frameworks like Apache Spark, Apache Hadoop, and Apache Flink using the abstracted Rabit and XGBoost4J. XGBoost is also available on OpenCL for FPGAs. An efficient, scalable implementation of XGBoost has been published by Tianqi Chen and Carlos Guestrin. While the XGBoost model often achieves higher accuracy than a single decision tree, it sacrifices the intrinsic interpretability of decision trees. For example, following the path that a decision tree takes to make its decision is trivial and self-explained, but following the paths of hundreds or thousands of trees is much harder. == Features == Salient features of XGBoost which make it different from other gradient boosting algorithms include: Clever penalization of trees A proportional shrinking of leaf nodes Newton Boosting Extra randomization parameter Implementation on single, distributed systems and out-of-core computation Automatic feature selection Theoretically justified weighted quantile sketching for efficient computation Parallel tree structure boosting with sparsity Efficient cacheable block structure for decision tree training == The algorithm == XGBoost works as Newton–Raphson in function space unlike gradient boosting that works as gradient descent in function space, a second order Taylor approximation is used in the loss function to make the connection to Newton–Raphson method. A generic unregularized XGBoost algorithm is: == Parameters == XGBoost has parameters which can be specified to affect how it functions and performs. Some parameters include: Learning rate (also known as the "step size" or “"shrinkage"), it is a number between 0 and 1 (default is 0.3), which determines the rate the algorithm learns from each iteration. n_estimators, sets the number of trees to be built in the ensemble, where more trees generally increases the complexity of the model, but can lead to overfitting with too many trees. Gamma (also known as Lagrange multiplier or the minimum loss reduction parameter), controls the minimum amount of loss reduction required to make a further split on a leaf node of the tree. The default in XGBoost is 0 . max_depth, represents how deeply each tree in the boosting process can grow during training, where the default is 6. == Awards == John Chambers Award (2016) High Energy Physics meets Machine Learning award (HEP meets ML) (2016)
Outline of automation
The following outline is provided as an overview of and topical guide to automation: Automation – use of control systems and information technologies to reduce the need for human work in the production of goods and services. In the scope of industrialization, automation is a step beyond mechanization. == Essence of automation == Control system – a device, or set of devices to manage, command, direct or regulate the behavior of other devices or systems. Industrial control system (ICS) – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed control systems (DCS), and other smaller control system configurations such as skid-mounted programmable logic controllers (PLC) often found in industrial sectors and critical infrastructures. Industrialization – period of social and economic change that transforms a human group from an agrarian society into an industrial one. Numerical control (NC) – refers to the automation of machine tools that are operated by abstractly programmed commands encoded on a storage medium, as opposed to controlled manually via handwheels or levers, or mechanically automated via cams alone. Robotics – the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots and computer systems for their control, sensory feedback, and information processing. == Branches of automation == === General purpose === Autonomous automation – autonomous software agents to adapt the controllers of computer controlled industrial machinery and processes Banking automation Broadcast automation Building automation – advanced functionality provided by the control system of a building. A building automation system (BAS) is an example of a distributed control system. Home automation – control system of a home. Office automation – the varied computer machinery and software used to digitally create, collect, store, manipulate, and relay office information needed for accomplishing basic tasks such as business process automation and robotic process automation. Console automation Database automation Integrated library system Laboratory automation === Specific purpose === Automated attendant Automated guided vehicle Autonomous mobile robot Automated highway system Automated pool cleaner Automated teller machine Automatic painting (robotic) Pop music automation Remotely operated vehicle Robotic lawn mower Telephone switchboard Vending machine == Fields contributing to automation == Cybernetics – the interdisciplinary study of the structure of regulatory systems. Cognitive science – interdisciplinary scientific study of the mind and its processes. It examines what cognition is, what it does and how it works. Robotics – the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots and computer systems for their control, sensory feedback, and information processing. == History of automation == History of mass production – Prerequisites of mass production were interchangeable parts, machine tools and power, especially in the form of electricity. Mass production was popularized in the 1910s and 1920s by Henry Ford's Ford Motor Company, which introduced electric motors to the then-well-known technique of chain or sequential production. History of home automation == Automated machines == Machine to Machine OLE for process control (OPC) Process control – a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range. Run Book Automation (RBA) Robot – a mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control. == Automated machine components == Artificial intelligence – the intelligence of machines and the branch of computer science that aims to create it. Friendly artificial intelligence – an artificial intelligence that has a positive rather than negative effect on humanity, and the field of knowledge required to build such an artificial intelligence. === Automation tools === Artificial neural network (ANN) – mathematical model or computational model that is inspired by the structure or functional aspects of biological neural networks. Human machine interface (HMI) – operator level local control panel that monitors field devices Laboratory information management system (LIMS) – software package that offers a set of key features that support a modern laboratory's operations. Industrial control system – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed control systems (DCS), and other smaller control system configurations such as skid-mounted programmable logic controllers (PLC) often found in the industrial sectors and critical infrastructures. Distributed control system (DCS) – control system usually of a manufacturing system, process or any kind of dynamic system, in which the controller elements are not central in location (like the brain) but are distributed throughout the system with each component sub-system controlled by one or more controllers. Manufacturing execution system (MES) – system that manages manufacturing operations in a factory, including management of resources, scheduling production processes, dispatching production orders, execution of production orders, etc. Programmable automation controller (PAC) – digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. Programmable logic controller (PLC)A Programmable Logic Controller, PLC or Programmable Controller is a digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. The abbreviation "PLC" and the term "Programmable Logic Controller" are registered trademarks of the Allen-Bradley Company (Rockwell Automation). PLCs are used in many industries and machines. Unlike general-purpose computers, the PLC is designed for multiple inputs and output arrangements, extended temperature ranges, immunity to electrical noise, and resistance to vibration and impact. Programs to control machine operation are typically stored in battery-backed-up or non-volatile memory. A PLC is an example of a hard real time system since output results must be produced in response to input conditions within a limited time, otherwise unintended operation will result. Supervisory control and data acquisition (SCADA) – generally refers to industrial control systems (ICS): computer systems that monitor and control industrial, infrastructure, or facility-based processes, as described below: Industrial processes include those of manufacturing, production, power generation, fabrication, and refining, and may run in continuous, batch, repetitive, or discrete modes. Simulation § Engineering Technology simulation or Process simulation == Social movements == Automation-related social movement – a movement that advocates semi- or fully automatic systems to provide for human needs globally. For example, automation of farming and food distribution throughout the world so that no one will go hungry. One goal is to automate all mundane labor, to free humans to engage in more creative activities (or less work). The Technocracy movement – social movement active from the Great Depression (1930s) to date that proposes replacing politicians and business people with scientists and engineers who have the technical expertise to manage the economy. The Zeitgeist Movement – movement advocating the replacement of the market economy with an economy in which all resources are equitably, commonly and sustainably shared. == Automation in the future == Android – a robot or synthetic organism designed to look and act like a human, and with a body having a flesh-like resemblance Technological singularity – the hypothetical future emergence of greater-than-human intelligence through technological means Semi-automation – using a centralized computer controller to orchestrate the activities of man and machine. == Automation-related publications == IEEE Spectrum – the flagship publication of the Institute of Electrical and Electronics Engineers (IEEE), explores the development, applications and implications of new technologies, and provides a forum for understanding, discussion and leadership in these areas. IEEE Transactions on Information Theory – peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE), focused on the study of information theory, the mathematics of communications, including computer communications, robotics communications, etc. IEEE Transactions on Control S
Site Security Handbook
The Site Security Handbook, RFC 2196, is a guide on setting computer security policies and procedures for sites that have systems on the Internet (however, the information provided should also be useful to sites not yet connected to the Internet). The guide lists issues and factors that a site must consider when setting their own policies. It makes a number of recommendations and provides discussions of relevant areas. This guide is only a framework for setting security policies and procedures. In order to have an effective set of policies and procedures, a site will have to make many decisions, gain agreement, and then communicate and implement these policies. The guide is a product of the IETF SSH working group, and was published in 1997, obsoleting the earlier RFC 1244 from 1991.
Automotive security
Automotive security refers to the branch of computer security focused on the cyber risks related to the automotive context. The increasingly high number of ECUs in vehicles and, alongside, the implementation of multiple different means of communication from and towards the vehicle in a remote and wireless manner led to the necessity of a branch of cybersecurity dedicated to the threats associated with vehicles. Not to be confused with automotive safety. == Causes == The implementation of multiple ECUs (Electronic Control Units) inside vehicles began in the early '70s thanks to the development of integrated circuits and microprocessors that made it economically feasible to produce the ECUs on a large scale. Since then the number of ECUs has increased to up to 100 per vehicle. These units nowadays control almost everything in the vehicle, from simple tasks such as activating the wipers to more safety-related ones like brake-by-wire or ABS (Anti-lock Braking System). Autonomous driving is also strongly reliant on the implementation of new, complex ECUs such as the ADAS, alongside sensors (lidars and radars) and their control units. Inside the vehicle, the ECUs are connected with each other through cabled or wireless communication networks, such as CAN bus (controller area network), MOST bus (Media Oriented System Transport), FlexRay (Automotive Network Communications Protocol) or RF (radio frequency) as in many implementations of TPMSs (tire-pressure monitoring systems). Many of these ECUs require data received through these networks that arrive from various sensors to operate and use such data to modify the behavior of the vehicle (e.g., the cruise control modifies the vehicle's speed depending on signals arriving from a button usually located on the steering wheel). Since the development of cheap wireless communication technologies such as Bluetooth, LTE, Wi-Fi, RFID and similar, automotive producers and OEMs have designed ECUs that implement such technologies with the goal of improving the experience of the driver and passengers. Safety-related systems such as the OnStar from General Motors, telematic units, communication between smartphones and the vehicle's speakers through Bluetooth, Android Auto and Apple CarPlay. == Threat model == Threat models of the automotive world are based on both real-world and theoretically possible attacks. Most real-world attacks aim at the safety of the people in and around the car, by modifying the cyber-physical capabilities of the vehicle (e.g., steering, braking, accelerating without requiring actions from the driver), while theoretical attacks have been supposed to focus also on privacy-related goals, such as obtaining GPS data on the vehicle, or capturing microphone signals and similar. Regarding the attack surfaces of the vehicle, they are usually divided in long-range, short-range, and local attack surfaces: LTE and DSRC can be considered long-range ones, while Bluetooth and Wi-Fi are usually considered short-range although still wireless. Finally, USB, OBD-II and all the attack surfaces that require physical access to the car are defined as local. An attacker that is able to implement the attack through a long-range surface is considered stronger and more dangerous than the one that requires physical access to the vehicle. In 2015 the possibility of attacks on vehicles already on the market has been proven possible by Miller and Valasek, that managed to disrupt the driving of a Jeep Cherokee while remotely connecting to it through remote wireless communication. === Controller area network attacks === The most common network used in vehicles and the one that is mainly used for safety-related communication is CAN, due to its real-time properties, simplicity, and cheapness. For this reason the majority of real-world attacks have been implemented against ECUs connected through this type of network. The majority of attacks demonstrated either against actual vehicles or in testbeds fall in one or more of the following categories: ==== Sniffing ==== Sniffing in the computer security field generally refers to the possibility of intercepting and logging packets or more generally data from a network. In the case of CAN, since it is a bus network, every node listens to all communication on the network. It is useful for the attacker to read data to learn the behavior of the other nodes of the network before implementing the actual attack. Usually, the final goal of the attacker is not to simply sniff the data on CAN, since the packets passing on this type of network are not usually valuable just to read. ==== Denial of service ==== Denial of service (DoS) in information security is usually described as an attack that has the objective of making a machine or a network unavailable. DoS attacks against ECUs connected to CAN buses can be done both against the network, by abusing the arbitration protocol used by CAN to always win the arbitration, and targeting the single ECU, by abusing the error handling protocol of CAN. In this second case the attacker flags the messages of the victim as faulty to convince the victim of being broken and therefore shut itself off the network. ==== Spoofing ==== Spoofing attacks comprise all cases in which an attacker, by falsifying data, sends messages pretending to be another node of the network. In automotive security usually spoofing attacks are divided into masquerade and replay attacks. Replay attacks are defined as all those where the attacker pretends to be the victim and sends sniffed data that the victim sent in a previous iteration of authentication. Masquerade attacks are, on the contrary, spoofing attacks where the data payload has been created by the attacker. == Real life automotive threat example == Security researchers Charlie Miller and Chris Valasek have successfully demonstrated remote access to a wide variety of vehicle controls using a Jeep Cherokee as the target. They were able to control the radio, environmental controls, windshield wipers, and certain engine and brake functions. The method used to hack the system was implementation of pre-programmed chip into the controller area network (CAN) bus. By inserting this chip into the CAN bus, he was able to send arbitrary message to CAN bus. One other thing that Miller has pointed out is the danger of the CAN bus, as it broadcasts the signal which the message can be caught by the hackers throughout the network. The control of the vehicle was all done remotely, manipulating the system without any physical interaction. Miller states that he could control any of some 1.4 million vehicles in the United States regardless of the location or distance, the only thing needed is for someone to turn on the vehicle to gain access. The work by Miller and Valasek replicated earlier work completed and published by academics in 2010 and 2011 on a different vehicle. The earlier work demonstrated the ability to compromise a vehicle remotely, over multiple wireless channels (including cellular), and the ability to remotely control critical components on the vehicle post-compromise, including the telematics unit and the car's brakes. While the earlier academic work was publicly visible, both in peer-reviewed scholarly publications and in the press, the Miller and Valesek work received even greater public visibility. == Security measures == The increasing complexity of devices and networks in the automotive context requires the application of security measures to limit the capabilities of a potential attacker. Since the early 2000 many different countermeasures have been proposed and, in some cases, applied. Following, a list of the most common security measures: Sub-networks: to limit the attacker capabilities even if he/she manages to access the vehicle from remote through a remotely connected ECU, the networks of the vehicle are divided in multiple sub-networks, and the most critical ECUs are not placed in the same sub-networks of the ECUs that can be accessed from remote. Gateways: the sub-networks are divided by secure gateways or firewalls that block messages from crossing from a sub-network to the other if they were not intended to. Intrusion Detection Systems (IDS): on each critical sub-network, one of the nodes (ECUs) connected to it has the goal of reading all data passing on the sub-network and detect messages that, given some rules, are considered malicious (made by an attacker). The arbitrary messages can be caught by the passenger by using IDS which will notify the owner regarding with unexpected message. Authentication protocols: in order to implement authentication on networks where it is not already implemented (such as CAN), it is possible to design an authentication protocol that works on the higher layers of the ISO OSI model, by using part of the data payload of a message to authenticate the message itself. Hardware Security Modules: since many ECUs are not powerful enough to keep real-time delays whi
Automotive security
Automotive security refers to the branch of computer security focused on the cyber risks related to the automotive context. The increasingly high number of ECUs in vehicles and, alongside, the implementation of multiple different means of communication from and towards the vehicle in a remote and wireless manner led to the necessity of a branch of cybersecurity dedicated to the threats associated with vehicles. Not to be confused with automotive safety. == Causes == The implementation of multiple ECUs (Electronic Control Units) inside vehicles began in the early '70s thanks to the development of integrated circuits and microprocessors that made it economically feasible to produce the ECUs on a large scale. Since then the number of ECUs has increased to up to 100 per vehicle. These units nowadays control almost everything in the vehicle, from simple tasks such as activating the wipers to more safety-related ones like brake-by-wire or ABS (Anti-lock Braking System). Autonomous driving is also strongly reliant on the implementation of new, complex ECUs such as the ADAS, alongside sensors (lidars and radars) and their control units. Inside the vehicle, the ECUs are connected with each other through cabled or wireless communication networks, such as CAN bus (controller area network), MOST bus (Media Oriented System Transport), FlexRay (Automotive Network Communications Protocol) or RF (radio frequency) as in many implementations of TPMSs (tire-pressure monitoring systems). Many of these ECUs require data received through these networks that arrive from various sensors to operate and use such data to modify the behavior of the vehicle (e.g., the cruise control modifies the vehicle's speed depending on signals arriving from a button usually located on the steering wheel). Since the development of cheap wireless communication technologies such as Bluetooth, LTE, Wi-Fi, RFID and similar, automotive producers and OEMs have designed ECUs that implement such technologies with the goal of improving the experience of the driver and passengers. Safety-related systems such as the OnStar from General Motors, telematic units, communication between smartphones and the vehicle's speakers through Bluetooth, Android Auto and Apple CarPlay. == Threat model == Threat models of the automotive world are based on both real-world and theoretically possible attacks. Most real-world attacks aim at the safety of the people in and around the car, by modifying the cyber-physical capabilities of the vehicle (e.g., steering, braking, accelerating without requiring actions from the driver), while theoretical attacks have been supposed to focus also on privacy-related goals, such as obtaining GPS data on the vehicle, or capturing microphone signals and similar. Regarding the attack surfaces of the vehicle, they are usually divided in long-range, short-range, and local attack surfaces: LTE and DSRC can be considered long-range ones, while Bluetooth and Wi-Fi are usually considered short-range although still wireless. Finally, USB, OBD-II and all the attack surfaces that require physical access to the car are defined as local. An attacker that is able to implement the attack through a long-range surface is considered stronger and more dangerous than the one that requires physical access to the vehicle. In 2015 the possibility of attacks on vehicles already on the market has been proven possible by Miller and Valasek, that managed to disrupt the driving of a Jeep Cherokee while remotely connecting to it through remote wireless communication. === Controller area network attacks === The most common network used in vehicles and the one that is mainly used for safety-related communication is CAN, due to its real-time properties, simplicity, and cheapness. For this reason the majority of real-world attacks have been implemented against ECUs connected through this type of network. The majority of attacks demonstrated either against actual vehicles or in testbeds fall in one or more of the following categories: ==== Sniffing ==== Sniffing in the computer security field generally refers to the possibility of intercepting and logging packets or more generally data from a network. In the case of CAN, since it is a bus network, every node listens to all communication on the network. It is useful for the attacker to read data to learn the behavior of the other nodes of the network before implementing the actual attack. Usually, the final goal of the attacker is not to simply sniff the data on CAN, since the packets passing on this type of network are not usually valuable just to read. ==== Denial of service ==== Denial of service (DoS) in information security is usually described as an attack that has the objective of making a machine or a network unavailable. DoS attacks against ECUs connected to CAN buses can be done both against the network, by abusing the arbitration protocol used by CAN to always win the arbitration, and targeting the single ECU, by abusing the error handling protocol of CAN. In this second case the attacker flags the messages of the victim as faulty to convince the victim of being broken and therefore shut itself off the network. ==== Spoofing ==== Spoofing attacks comprise all cases in which an attacker, by falsifying data, sends messages pretending to be another node of the network. In automotive security usually spoofing attacks are divided into masquerade and replay attacks. Replay attacks are defined as all those where the attacker pretends to be the victim and sends sniffed data that the victim sent in a previous iteration of authentication. Masquerade attacks are, on the contrary, spoofing attacks where the data payload has been created by the attacker. == Real life automotive threat example == Security researchers Charlie Miller and Chris Valasek have successfully demonstrated remote access to a wide variety of vehicle controls using a Jeep Cherokee as the target. They were able to control the radio, environmental controls, windshield wipers, and certain engine and brake functions. The method used to hack the system was implementation of pre-programmed chip into the controller area network (CAN) bus. By inserting this chip into the CAN bus, he was able to send arbitrary message to CAN bus. One other thing that Miller has pointed out is the danger of the CAN bus, as it broadcasts the signal which the message can be caught by the hackers throughout the network. The control of the vehicle was all done remotely, manipulating the system without any physical interaction. Miller states that he could control any of some 1.4 million vehicles in the United States regardless of the location or distance, the only thing needed is for someone to turn on the vehicle to gain access. The work by Miller and Valasek replicated earlier work completed and published by academics in 2010 and 2011 on a different vehicle. The earlier work demonstrated the ability to compromise a vehicle remotely, over multiple wireless channels (including cellular), and the ability to remotely control critical components on the vehicle post-compromise, including the telematics unit and the car's brakes. While the earlier academic work was publicly visible, both in peer-reviewed scholarly publications and in the press, the Miller and Valesek work received even greater public visibility. == Security measures == The increasing complexity of devices and networks in the automotive context requires the application of security measures to limit the capabilities of a potential attacker. Since the early 2000 many different countermeasures have been proposed and, in some cases, applied. Following, a list of the most common security measures: Sub-networks: to limit the attacker capabilities even if he/she manages to access the vehicle from remote through a remotely connected ECU, the networks of the vehicle are divided in multiple sub-networks, and the most critical ECUs are not placed in the same sub-networks of the ECUs that can be accessed from remote. Gateways: the sub-networks are divided by secure gateways or firewalls that block messages from crossing from a sub-network to the other if they were not intended to. Intrusion Detection Systems (IDS): on each critical sub-network, one of the nodes (ECUs) connected to it has the goal of reading all data passing on the sub-network and detect messages that, given some rules, are considered malicious (made by an attacker). The arbitrary messages can be caught by the passenger by using IDS which will notify the owner regarding with unexpected message. Authentication protocols: in order to implement authentication on networks where it is not already implemented (such as CAN), it is possible to design an authentication protocol that works on the higher layers of the ISO OSI model, by using part of the data payload of a message to authenticate the message itself. Hardware Security Modules: since many ECUs are not powerful enough to keep real-time delays whi
Solomonoff's theory of inductive inference
Solomonoff's theory of inductive inference proves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the programming language must be chosen prior to the data and that the environment being observed is generated by an unknown algorithm. This is also called a theory of induction. Due to its basis in the dynamical (state-space model) character of Algorithmic Information Theory, it encompasses statistical as well as dynamical information criteria for model selection. It was introduced by Ray Solomonoff, based on probability theory and theoretical computer science. In essence, Solomonoff's induction derives the posterior probability of any computable theory, given a sequence of observed data. This posterior probability is derived from Bayes' rule and some universal prior, that is, a prior that assigns a positive probability to any computable theory. Solomonoff proved that this induction is incomputable (or more precisely, lower semi-computable), but noted that "this incomputability is of a very benign kind", and that it "in no way inhibits its use for practical prediction" (as it can be approximated from below more accurately with more computational resources). It is only "incomputable" in the benign sense that no scientific consensus is able to prove that the best current scientific theory is the best of all possible theories. However, Solomonoff's theory does provide an objective criterion for deciding among the current scientific theories explaining a given set of observations. Solomonoff's induction naturally formalizes Occam's razor by assigning larger prior credences to theories that require a shorter algorithmic description. == Origin == === Philosophical === The theory is based in philosophical foundations, and was founded by Ray Solomonoff around 1960. It is a mathematically formalized combination of Occam's razor and the Principle of Multiple Explanations. All computable theories which perfectly describe previous observations are used to calculate the probability of the next observation, with more weight put on the shorter computable theories. Marcus Hutter's universal artificial intelligence builds upon this to calculate the expected value of an action. === Principle === Solomonoff's induction has been argued to be the computational formalization of pure Bayesianism. To understand, recall that Bayesianism derives the posterior probability P [ T | D ] {\displaystyle \mathbb {P} [T|D]} of a theory T {\displaystyle T} given data D {\displaystyle D} by applying Bayes rule, which yields P [ T | D ] = P [ D | T ] P [ T ] P [ D | T ] P [ T ] + ∑ A ≠ T P [ D | A ] P [ A ] {\displaystyle \mathbb {P} [T|D]={\frac {\mathbb {P} [D|T]\mathbb {P} [T]}{\mathbb {P} [D|T]\mathbb {P} [T]+\sum _{A\neq T}\mathbb {P} [D|A]\mathbb {P} [A]}}} where theories A {\displaystyle A} are alternatives to theory T {\displaystyle T} . For this equation to make sense, the quantities P [ D | T ] {\displaystyle \mathbb {P} [D|T]} and P [ D | A ] {\displaystyle \mathbb {P} [D|A]} must be well-defined for all theories T {\displaystyle T} and A {\displaystyle A} . In other words, any theory must define a probability distribution over observable data D {\displaystyle D} . Solomonoff's induction essentially boils down to demanding that all such probability distributions be computable. Interestingly, the set of computable probability distributions is a subset of the set of all programs, which is countable. Similarly, the sets of observable data considered by Solomonoff were finite. Without loss of generality, we can thus consider that any observable data is a finite bit string. As a result, Solomonoff's induction can be defined by only invoking discrete probability distributions. Solomonoff's induction then allows to make probabilistic predictions of future data F {\displaystyle F} , by simply obeying the laws of probability. Namely, we have P [ F | D ] = E T [ P [ F | T , D ] ] = ∑ T P [ F | T , D ] P [ T | D ] {\displaystyle \mathbb {P} [F|D]=\mathbb {E} _{T}[\mathbb {P} [F|T,D]]=\sum _{T}\mathbb {P} [F|T,D]\mathbb {P} [T|D]} . This quantity can be interpreted as the average predictions P [ F | T , D ] {\displaystyle \mathbb {P} [F|T,D]} of all theories T {\displaystyle T} given past data D {\displaystyle D} , weighted by their posterior credences P [ T | D ] {\displaystyle \mathbb {P} [T|D]} . === Mathematical === The proof of the "razor" is based on the known mathematical properties of a probability distribution over a countable set. These properties are relevant because the infinite set of all programs is a denumerable set. The sum S of the probabilities of all programs must be exactly equal to one (as per the definition of probability) thus the probabilities must roughly decrease as we enumerate the infinite set of all programs, otherwise S will be strictly greater than one. To be more precise, for every ϵ {\displaystyle \epsilon } > 0, there is some length l such that the probability of all programs longer than l is at most ϵ {\displaystyle \epsilon } . This does not, however, preclude very long programs from having very high probability. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The universal prior probability of any prefix p of a computable sequence x is the sum of the probabilities of all programs (for a universal computer) that compute something starting with p. Given some p and any computable but unknown probability distribution from which x is sampled, the universal prior and Bayes' theorem can be used to predict the yet unseen parts of x in optimal fashion. == Mathematical guarantees == === Solomonoff's completeness === The remarkable property of Solomonoff's induction is its completeness. In essence, the completeness theorem guarantees that the expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic) data generating process. The errors can be measured using the Kullback–Leibler divergence or the square of the difference between the induction's prediction and the probability assigned by the (stochastic) data generating process. === Solomonoff's uncomputability === Unfortunately, Solomonoff also proved that Solomonoff's induction is uncomputable. In fact, he showed that computability and completeness are mutually exclusive: any complete theory must be uncomputable. The proof of this is derived from a game between the induction and the environment. Essentially, any computable induction can be tricked by a computable environment, by choosing the computable environment that negates the computable induction's prediction. This fact can be regarded as an instance of the no free lunch theorem. == Modern applications == === Artificial intelligence === Though Solomonoff's inductive inference is not computable, several AIXI-derived algorithms approximate it in order to make it run on a modern computer. The more computing power they are given, the closer their predictions are to the predictions of inductive inference (their mathematical limit is Solomonoff's inductive inference). Another direction of inductive inference is based on E. Mark Gold's model of learning in the limit from 1967 and has developed since then more and more models of learning. The general scenario is the following: Given a class S of computable functions, is there a learner (that is, recursive functional) which for any input of the form (f(0),f(1),...,f(n)) outputs a hypothesis (an index e with respect to a previously agreed on acceptable numbering of all computable functions; the indexed function may be required consistent with the given values of f). A learner M learns a function f if almost all its hypotheses are the same index e, which generates the function f; M learns S if M learns every f in S. Basic results are that all recursively enumerable classes of functions are learnable while the class REC of all computable functions is not learnable. Many related models have been considered and also the learning of classes of recursively enumerable sets from positive data is a topic studied from Gold's pioneering paper in 1967 onwards. A far reaching extension of the Gold’s approach is developed by Schmidhuber's theory of generalized Kolmogorov complexities, which are kinds of super-recursive algorithms.
Zesta
Zesta is an online food ordering and delivery platform operating across the African region. Formerly known as Square Eats, the company rebranded to Zesta in 2025. Zesta connects customers with restaurants and stores, offering delivery services for food, groceries, parcel delivery and other essentials. == History == Zesta was originally founded as Square Eats in 2020 by twin brothers Henry Newman and Randall Newman when they were 21 years old. It was launched in Gaborone, Botswana, and quickly gained traction as a leading food delivery service in the country. The company halted operations and took a strategic decision to reinvent the business in 2022. In 2025, the company announced its rebranding to Zesta, highlighting its commitment to evolving beyond food delivery to become a super app. === COVID-19 initiative === During the COVID-19 pandemic, Zesta (then Square Eats) implemented measures to ensure safety and hygiene, including providing free gloves and hand sanitizer to drivers and introducing contactless delivery options. These efforts positioned the platform as a trusted service during the pandemic. == Service == Zesta facilitates delivery from a wide range of merchant partners via a smartphone app, available on iOS and Android platforms, or through its website. Customers can browse their favorite restaurants, place orders, and have meals delivered to their doorstep efficiently.