AI For Students Studying

AI For Students Studying — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Expectation propagation

Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.
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Intelligent decision support system

An intelligent decision support system (IDSS) is a decision support system that makes extensive use of artificial intelligence (AI) techniques. Use of AI techniques in management information systems has a long history – indeed terms such as "Knowledge-based systems" (KBS) and "intelligent systems" have been used since the early 1980s to describe components of management systems, but the term "Intelligent decision support system" is thought to originate with Clyde Holsapple and Andrew Whinston in the late 1970s. Examples of specialized intelligent decision support systems include Flexible manufacturing systems (FMS), intelligent marketing decision support systems and medical diagnosis systems. Ideally, an intelligent decision support system should behave like a human consultant: supporting decision makers by gathering and analysing evidence, identifying and diagnosing problems, proposing possible courses of action and evaluating such proposed actions. The aim of the AI techniques embedded in an intelligent decision support system is to enable these tasks to be performed by a computer, while emulating human capabilities as closely as possible. Many IDSS implementations are based on expert systems, a well established type of KBS that encode knowledge and emulate the cognitive behaviours of human experts using predicate logic rules, and have been shown to perform better than the original human experts in some circumstances. Expert systems emerged as practical applications in the 1980s based on research in artificial intelligence performed during the late 1960s and early 1970s. They typically combine knowledge of a particular application domain with an inference capability to enable the system to propose decisions or diagnoses. Accuracy and consistency can be comparable to (or even exceed) that of human experts when the decision parameters are well known (e.g. if a common disease is being diagnosed), but performance can be poor when novel or uncertain circumstances arise. Research in AI focused on enabling systems to respond to novelty and uncertainty in more flexible ways is starting to be used in IDSS. For example, intelligent agents that perform complex cognitive tasks without any need for human intervention have been used in a range of decision support applications. Capabilities of these intelligent agents include knowledge sharing, machine learning, data mining, and automated inference. A range of AI techniques such as case based reasoning, rough sets and fuzzy logic have also been used to enable decision support systems to perform better in uncertain conditions. A 2009 research about a multi-artificial system intelligence system named IILS is proposed to automate problem-solving processes within the logistics industry. The system involves integrating intelligence modules based on case-based reasoning, multi-agent systems, fuzzy logic, and artificial neural networks aiming to offer advanced logistics solutions and support in making well-informed, high-quality decisions to address a wide range of customer needs and challenges.
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Cost-sensitive machine learning

Cost-sensitive machine learning is an approach within machine learning that considers varying costs associated with different types of errors. This method diverges from traditional approaches by introducing a cost matrix, explicitly specifying the penalties or benefits for each type of prediction error. The inherent difficulty which cost-sensitive machine learning tackles is that minimizing different kinds of classification errors is a multi-objective optimization problem. == Overview == Cost-sensitive machine learning optimizes models based on the specific consequences of misclassifications, making it a valuable tool in various applications. It is especially useful in problems with a high imbalance in class distribution and a high imbalance in associated costs Cost-sensitive machine learning introduces a scalar cost function in order to find one (of multiple) Pareto optimal points in this multi-objective optimization problem (similar to the Weighted sum model) == Cost Matrix == The cost matrix is a crucial element within cost-sensitive modeling, explicitly defining the costs or benefits associated with different prediction errors in classification tasks. Represented as a table, the matrix aligns true and predicted classes, assigning a cost value to each combination. For instance, in binary classification, it may distinguish costs for false positives and false negatives. The utility of the cost matrix lies in its application to calculate the expected cost or loss. The formula, expressed as a double summation, utilizes joint probabilities: Expected Loss = ∑ i ∑ j P ( Actual i , Predicted j ) ⋅ Cost Actual i , Predicted j {\displaystyle {\text{Expected Loss}}=\sum _{i}\sum _{j}P({\text{Actual}}_{i},{\text{Predicted}}_{j})\cdot {\text{Cost}}_{{\text{Actual}}_{i},{\text{Predicted}}_{j}}} Here, P ( Actual i , Predicted j ) {\displaystyle P({\text{Actual}}_{i},{\text{Predicted}}_{j})} denotes the joint probability of actual class i {\displaystyle i} and predicted class j {\displaystyle j} , providing a nuanced measure that considers both the probabilities and associated costs. This approach allows practitioners to fine-tune models based on the specific consequences of misclassifications, adapting to scenarios where the impact of prediction errors varies across classes. == Applications == === Fraud Detection === In the realm of data science, particularly in finance, cost-sensitive machine learning is applied to fraud detection. By assigning different costs to false positives and false negatives, models can be fine-tuned to minimize the overall financial impact of misclassifications. === Medical Diagnostics === In healthcare, cost-sensitive machine learning plays a role in medical diagnostics. The approach allows for customization of models based on the potential harm associated with misdiagnoses, ensuring a more patient-centric application of machine learning algorithms. == Challenges == A typical challenge in cost-sensitive machine learning is the reliable determination of the cost matrix which may evolve over time. == Literature == Cost-Sensitive Machine Learning. USA, CRC Press, 2011. ISBN 9781439839287 Abhishek, K., Abdelaziz, D. M. (2023). Machine Learning for Imbalanced Data: Tackle Imbalanced Datasets Using Machine Learning and Deep Learning Techniques. (n.p.): Packt Publishing. ISBN 9781801070881
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Situated approach (artificial intelligence)

In artificial intelligence research, the situated approach builds agents that are designed to behave effectively successfully in their environment. This requires designing AI "from the bottom-up" by focussing on the basic perceptual and motor skills required to survive. The situated approach gives a much lower priority to abstract reasoning or problem-solving skills. The approach was originally proposed as an alternative to traditional approaches (that is, approaches popular before 1985 or so). After several decades, classical AI technologies started to face intractable issues (e.g. combinatorial explosion) when confronted with real-world modeling problems. All approaches to address these issues focus on modeling intelligences situated in an environment. They have become known as the situated approach to AI. == Emergence of a concept == === From traditional AI to Nouvelle AI === During the late 1980s, the approach now known as Nouvelle AI (Nouvelle means new in French) was pioneered at the MIT Artificial Intelligence Laboratory by Rodney Brooks. As opposed to classical or traditional artificial intelligence, Nouvelle AI purposely avoided the traditional goal of modeling human-level performance, but rather tries to create systems with intelligence at the level of insects, closer to real-world robots. But eventually, at least at MIT new AI did lead to an attempt for humanoid AI in the Cog Project. === From Nouvelle AI to behavior-based and situated AI === The conceptual shift introduced by nouvelle AI flourished in the robotics area, given way to behavior-based robotics (BBR), a methodology for developing AI based on a modular decomposition of intelligence. It was made famous by Rodney Brooks: his subsumption architecture was one of the earliest attempts to describe a mechanism for developing BBAI. It is extremely popular in robotics and to a lesser extent to implement intelligent virtual agents because it allows the successful creation of real-time dynamic systems that can run in complex environments. For example, it underlies the intelligence of the Sony Aibo and many RoboCup robot teams. Realizing that in fact all these approaches were aiming at building not an abstract intelligence, but rather an intelligence situated in a given environment, they have come to be known as the situated approach. In fact, this approach stems out from early insights of Alan Turing, describing the need to build machines equipped with sense organs to learn directly from the real-world instead of focusing on abstract activities, such as playing chess. == Definitions == Classically, a software entity is defined as a simulated element, able to act on itself and on its environment, and which has an internal representation of itself and of the outside world. An entity can communicate with other entities, and its behavior is the consequence of its perceptions, its representations, and its interactions with the other entities. === AI loop === Simulating entities in a virtual environment requires simulating the entire process that goes from a perception of the environment, or more generally from a stimulus, to an action on the environment. This process is called the AI loop and technology used to simulate it can be subdivided in two categories. Sensorimotor or low-level AI deals with either the perception problem (what is perceived?) or the animation problem (how are actions executed?). Decisional or high-level AI deals with the action selection problem (what is the most appropriate action in response to a given perception, i.e. what is the most appropriate behavior?). === Traditional or symbolic AI === There are two main approaches in decisional AI. The vast majority of the technologies available on the market, such as planning algorithms, finite-state machines (FSA), or expert systems, are based on the traditional or symbolic AI approach. Its main characteristics are: It is top-down: it subdivides, in a recursive manner, a given problem into a series of sub-problems that are supposedly easier to solve. It is knowledge-based: it relies on a symbolic description of the world, such as a set of rules. However, the limits of traditional AI, which goal is to build systems that mimic human intelligence, are well-known: inevitably, a combinatorial explosion of the number of rules occurs due to the complexity of the environment. In fact, it is impossible to predict all the situations that will be encountered by an autonomous entity. === Situated or behavioral AI === In order to address these issues, another approach to decisional AI, also known as situated or behavioral AI, has been proposed. It does not attempt to model systems that produce deductive reasoning processes, but rather systems that behave realistically in their environment. The main characteristics of this approach are the following: It is bottom-up: it relies on elementary behaviors, which can be combined to implement more complex behaviors. It is behavior-based: it does not rely on a symbolic description of the environment, but rather on a model of the interactions of the entities with their environment. The goal of situated AI is to model entities that are autonomous in their environment. This is achieved thanks to both the intrinsic robustness of the control architecture, and its adaptation capabilities to unforeseen situations. === Situated agents === In artificial intelligence and cognitive science, the term situated refers to an agent which is embedded in an environment. The term situated is commonly used to refer to robots, but some researchers argue that software agents can also be situated if: they exist in a dynamic (rapidly changing) environment, which they can manipulate or change through their actions, and which they can sense or perceive. Examples might include web-based agents, which can alter data or trigger processes (such as purchases) over the Internet, or virtual-reality bots which inhabit and change virtual worlds, such as Second Life. Being situated is generally considered to be part of being embodied, but it is useful to consider each perspective individually. The situated perspective emphasizes that intelligent behavior derives from the environment and the agent's interactions with it. The nature of these interactions are defined by an agent's embodiment. == Implementation principles == === Modular decomposition === The most important attribute of a system driven by situated AI is that the intelligence is controlled by a set of independent semi-autonomous modules. In the original systems, each module was actually a separate device or was at least conceived of as running on its own processing thread. Generally, though, the modules are just abstractions. In this respect, situated AI may be seen as a software engineering approach to AI, perhaps akin to object oriented design. Situated AI is often associated with reactive planning, but the two are not synonymous. Brooks advocated an extreme version of cognitive minimalism which required initially that the behavior modules were finite-state machines and thus contained no conventional memory or learning. This is associated with reactive AI because reactive AI requires reacting to the current state of the world, not to an agent's memory or preconception of that world. However, learning is obviously key to realistic strong AI, so this constraint has been relaxed, though not entirely abandoned. === Action selection mechanism === The situated AI community has presented several solutions to modeling decision-making processes, also known as action selection mechanisms. The first attempt to solve this problem goes back to subsumption architectures, which were in fact more an implementation technique than an algorithm. However, this attempt paved the way to several others, in particular the free-flow hierarchies and activation networks. A comparison of the structure and performances of these two mechanisms demonstrated the advantage of using free-flow hierarchies in solving the action selection problem. However, motor schemas and process description languages are two other approaches that have been used with success for autonomous robots. == Notes and references == Arsenio, Artur M. (2004) Towards an embodied and situated AI, In: Proceedings of the International FLAIRS conference, 2004. (online) The Artificial Life Route To Artificial Intelligence: Building Embodied, Situated Agents, Luc Steels and Rodney Brooks Eds., Lawrence Erlbaum Publishing, 1995. (ISBN 978-0805815184) Rodney A. Brooks Cambrian Intelligence (MIT Press, 1999) ISBN 0-262-52263-2; collection of early papers including "Intelligence without representation" and "Intelligence without reason", from 1986 & 1991 respectively. Ronald C. Arkin Behavior-Based Robotics (MIT Press, 1998) ISBN 0-262-01165-4 Hendriks-Jansen, Horst (1996) Catching Ourselves in the Act: Situated Activity, Interactive Emergence, Evolution, and Human Thought. Cambridge, Mass.: MIT Press.
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SmarterChild

SmarterChild was a chatbot available on AOL Instant Messenger and Windows Live Messenger (previously MSN Messenger) networks. == History == SmarterChild was an apparently intelligent agent or "bot" developed by ActiveBuddy, Inc., with offices in New York and Sunnyvale. It was widely distributed across global instant messaging networks. SmarterChild became very popular, attracting over 30 million Instant Messenger "buddies" on AIM (AOL), MSN and Yahoo Messenger over the course of its lifetime. Founded in 2000, ActiveBuddy was the brainchild of Robert Hoffer and Timothy Kay, who later brought seasoned advertising executive Peter Levitan on board as CEO. The concept for conversational instant messaging bots came from the founder's vision to add natural language comprehension functionality to the increasingly popular AIM instant messaging application. The original implementation took shape as a demo that Kay programmed in Perl in his Los Altos garage to connect a single buddy name, "ActiveBuddy", to look up stock symbols, and later allow AIM users to play Colossal Cave Adventure, a word-based adventure game, and MIT's Boris Katz Start Question Answering System but quickly grew to include a wide range of database applications the company called 'knowledge domains' including instant access to news, weather, stock information, movie times, yellow pages listings, and detailed sports data, as well as a variety of tools (personal assistant, calculators, translator, etc.). None of the individual domains which the company had named “stocksBuddy”, “sportsBuddy”, etc. ever launched publicly. When Stephen Klein came on board as COO — and eventually CEO — he insisted that all of the disparate test “buddies” be launched together with the company’s highly-developed colloquial chat domain. He suggested using “SmarterChild”, a username coined by Tim Kay which Tim was using to test various things. The bundled domains were launched publicly as SmarterChild (on AIM initially) in June 2001. SmarterChild provided information wrapped in fun and quirky conversation. The company generated no revenue from SmarterChild, but used it as a demonstration of the power of what Klein called “conversational computing”. The company subsequently marketed Automated Service Agents—delivering immediate answers to customer service inquiries—-to large corporations, like Comcast, Cingular, TimeWarner Cable, etc. SmarterChild's popularity spawned targeted marketing-oriented bots for Radiohead, Austin Powers, Intel, Keebler, The Sporting News and others. ActiveBuddy co-founders, Kay and Hoffer, as co-inventors, were issued two controversial U.S. patents in 2002. ActiveBuddy changed its name to Colloquis (briefly Conversagent) and targeted development of consumer-facing enterprise customer service agents, which the company marketed as Automated Service Agents. Microsoft acquired Colloquis in October 2006 and proceeded to de-commission SmarterChild and kill off the Automated Service Agent business as well. Robert Hoffer, ActiveBuddy co-founder, licensed the technology from Microsoft after Microsoft abandoned the Colloquis technology.
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Journal of Machine Learning Research

The Journal of Machine Learning Research is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). == History == The journal was established as an open-access alternative to the journal Machine Learning. In 2001, forty editorial board members of Machine Learning resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the Journal of Machine Learning Research allows authors to publish articles for free and retain copyright, while archives are freely available online. Print editions of the journal were published by MIT Press until 2004 and by Microtome Publishing thereafter. From its inception, the journal received no revenue from the print edition and paid no subvention to MIT Press or Microtome Publishing. In response to the prohibitive costs of arranging workshop and conference proceedings publication with traditional academic publishing companies, the journal launched a proceedings publication arm in 2007 and now publishes proceedings for several leading machine learning conferences, including the International Conference on Machine Learning, COLT, AISTATS, and workshops held at the Conference on Neural Information Processing Systems.
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Hello World: How to be Human in the Age of the Machine

Hello World: How to Be Human in the Age of the Machine (also titled Hello World: Being Human in the Age of Algorithms) is a book on the growing influence of algorithms and artificial intelligence (AI) on human life, authored by mathematician and science communicator Hannah Fry. The book examines how algorithms are increasingly shaping decisions in critical areas such as healthcare, transportation, justice, finance, and the arts. == Overview == Fry uses real-world examples, such as driverless cars and predictive policing, to illustrate her points. She emphasizes that algorithms are not inherently objective; they reflect biases embedded in their design and data inputs. While acknowledging their potential to improve efficiency and accuracy, Fry cautions against over-reliance on machines without human judgment. Fry explores moral questions surrounding algorithmic decision-making, such as whether machines can replace human empathy in critical situations. She advocates for greater scrutiny of algorithms to ensure fairness and avoid harmful biases. The book proposes a "cyborg future", where humans work alongside algorithms to enhance decision-making while retaining ultimate control. == Reception == Hello World has been praised for its clarity, engaging storytelling, and balanced perspective. Critics have highlighted Fry's ability to make complex topics accessible to general audiences while raising important questions about technology's impact on society. The book was shortlisted for awards such as the 2018 Baillie Gifford Prize and the Royal Society Science Book Prize.
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AIXI

AIXI is a theoretical mathematical formalism for artificial general intelligence. It combines Solomonoff induction with sequential decision theory. AIXI was first proposed by Marcus Hutter in 2000 and several results regarding AIXI are proved in Hutter's 2005 book Universal Artificial Intelligence. AIXI is a reinforcement learning (RL) agent. It maximizes the expected total rewards received from the environment. Intuitively, it simultaneously considers every computable hypothesis (or environment). In each time step, it looks at every possible program and evaluates how many rewards that program generates depending on the next action taken. The promised rewards are then weighted by the subjective belief that this program constitutes the true environment. This belief is computed from the length of the program: longer programs are considered less likely, in line with Occam's razor. AIXI then selects the action that has the highest expected total reward in the weighted sum of all these programs. == Etymology == According to Hutter, the word "AIXI" can have several interpretations. AIXI can stand for AI based on Solomonoff's distribution, denoted by ξ {\displaystyle \xi } (which is the Greek letter xi), or e.g. it can stand for AI "crossed" (X) with induction (I). There are other interpretations. == Definition == AIXI is a reinforcement learning agent that interacts with some stochastic and unknown but computable environment μ {\displaystyle \mu } . The interaction proceeds in time steps, from t = 1 {\displaystyle t=1} to t = m {\displaystyle t=m} , where m ∈ N {\displaystyle m\in \mathbb {N} } is the lifespan of the AIXI agent. At time step t, the agent chooses an action a t ∈ A {\displaystyle a_{t}\in {\mathcal {A}}} (e.g. a limb movement) and executes it in the environment, and the environment responds with a "percept" e t ∈ E = O × R {\displaystyle e_{t}\in {\mathcal {E}}={\mathcal {O}}\times \mathbb {R} } , which consists of an "observation" o t ∈ O {\displaystyle o_{t}\in {\mathcal {O}}} (e.g., a camera image) and a reward r t ∈ R {\displaystyle r_{t}\in \mathbb {R} } , distributed according to the conditional probability μ ( o t r t | a 1 o 1 r 1 . . . a t − 1 o t − 1 r t − 1 a t ) {\displaystyle \mu (o_{t}r_{t}|a_{1}o_{1}r_{1}...a_{t-1}o_{t-1}r_{t-1}a_{t})} , where a 1 o 1 r 1 . . . a t − 1 o t − 1 r t − 1 a t {\displaystyle a_{1}o_{1}r_{1}...a_{t-1}o_{t-1}r_{t-1}a_{t}} is the "history" of actions, observations and rewards. The environment μ {\displaystyle \mu } is thus mathematically represented as a probability distribution over "percepts" (observations and rewards) which depend on the full history, so there is no Markov assumption (as opposed to other RL algorithms). Note again that this probability distribution is unknown to the AIXI agent. Furthermore, note again that μ {\displaystyle \mu } is computable, that is, the observations and rewards received by the agent from the environment μ {\displaystyle \mu } can be computed by some program (which runs on a Turing machine), given the past actions of the AIXI agent. The only goal of the AIXI agent is to maximize ∑ t = 1 m r t {\displaystyle \sum _{t=1}^{m}r_{t}} , that is, the sum of rewards from time step 1 to m. The AIXI agent is associated with a stochastic policy π : ( A × E ) ∗ → A {\displaystyle \pi :({\mathcal {A}}\times {\mathcal {E}})^{}\rightarrow {\mathcal {A}}} , which is the function it uses to choose actions at every time step, where A {\displaystyle {\mathcal {A}}} is the space of all possible actions that AIXI can take and E {\displaystyle {\mathcal {E}}} is the space of all possible "percepts" that can be produced by the environment. The environment (or probability distribution) μ {\displaystyle \mu } can also be thought of as a stochastic policy (which is a function): μ : ( A × E ) ∗ × A → E {\displaystyle \mu :({\mathcal {A}}\times {\mathcal {E}})^{}\times {\mathcal {A}}\rightarrow {\mathcal {E}}} , where the ∗ {\displaystyle } is the Kleene star operation. In general, at time step t {\displaystyle t} (which ranges from 1 to m), AIXI, having previously executed actions a 1 … a t − 1 {\displaystyle a_{1}\dots a_{t-1}} (which is often abbreviated in the literature as a < t {\displaystyle a_{ Read more →
Patch management

Patch management (or patch management policy or patch policy or patch management process) is concerned with the identification, acquisition, distribution, testing and installation of patches to systems. Proper patch management can be a net productivity boost for an organization. Patches can be used to defend against and eliminate potential vulnerabilities of a system, so that no threats may exploit them. Problems can arise during patch management, including buggy patches that either fail to fix their problem or introduce new issues. Patch management tools help orchestrate all of the procedures involved in patch management. == Description == Patch management is defined as a sub-practice of various disciplines including vulnerability management (part of security management), lifecycle management (with further possible sub-classification into application lifecycle management and release management), change management, and systems management. The practice is broadly concerned with the identification, acquisition, distribution, and installation of patches to systems. Some definitions of patch management are as a software-level practice, while others are as a systems-level process: software, drivers, and firmware. == Cost–benefit analysis == While reserving time for patching takes up enterprise resources, there are balancing factors which can make proper patch management into a net productivity boost for an organization. Up-to-date systems often perform more efficiently, less costly, with less errors, less security risks, and better user workflow. Additionally, compliance with changing local and federal regulations are more likely to be satisfied. Patching security vulnerabilities has been one among many competing priorities for organizations, leading to longer periods before patching for some organizations. Equifax was too slow to implement its 2015 patch management plan to be able to mitigate or prevent the 2017 Equifax data breach, leading to scrutiny from regulators. == Relation to security management == Patches can be used to defend against and eliminate potential vulnerabilities of a system, so that no threats may exploit them; therefore, patch management can be considered a sub-discipline of vulnerability management. Every patchable device in a system presents an attack surface that must be secured. === Time plan === Automatic updates are where the patch is applied automatically with little to know actions or planning required. This approach is recommended for many individuals and organizations. Some organizations also have to prioritize which patches to prioritize given limited resources. Patch Tuesday is the most common process when major companies like Microsoft and Adobe release patches on a known date so that companies can plan resources around implementing the patches more quickly. Linux is open-sourced and patches can be released at any time, leading some to rely on mailing lists or other ways to be alerted to updates. === Inventory === Taking an inventory of software and hardware, including versions can make it easier to correlate with bugs or patches as they become known. Taking stock of how much education and support others in an organization need to install their patches can also help for planning how to implement the patch or design systems to begin with. Streamlining the process by using tools that can communicate with each other can also help to reduce the time of exposure to known vulnerabilities. == Challenges == There are a multitude of problems that can arise during patch management. A common issue is buggy patches, which either fail to fix their problem or introduce new issues. Another issue is deployment synchronization, since various subsystems may receive instructions to update at different times. Similarly, the difficulty of patch management across many devices may grow at an uncontrollable rate depending on organizational size. One prominent demonstration of the challenges facing proper patch management was the buggy Falcon Sensor patch by CrowdStrike which caused one of the worst IT outages of all time. == Implementations == A patch management tool (alternatively patch manager, patch management system, patch management software, or centralized patch management) help orchestrate all of the procedures involved in patch management. Tools can be in-house (applied locally by local administrators), or external, as with managed service providers (applied externally by a provider). === Patch management software === Windows Update for Business, System Center Configuration Manager, and Windows Server Update Services offer control over patch deployment, with features enabling testing, scheduling updates, and setting custom configurations on Windows platforms. === Managed service providers === == Regulatory requirements (United States) == Timely patching of software vulnerabilities is a requirement under multiple regulatory frameworks in the United States. The Health Insurance Portability and Accountability Act (HIPAA) Security Rule requires covered entities to protect electronic protected health information by implementing security measures sufficient to reduce risks to a reasonable and appropriate level, which industry guidance has long interpreted to include timely patch management. A proposed new HIPAA Security Rule would make patch management requirements explicit, mandating that covered entities and business associates deploy security patches and updates within a defined risk-based timeline and maintain written procedures for prioritizing, testing, and applying patches to systems that store, process, or transmit ePHI. The 2025 proposal continues to receive industry pushback as of December 2025. HIPAA was last updated in 2013. The Payment Card Industry Data Security Standard (PCI DSS) requires organizations to protect system components from known vulnerabilities by installing applicable security patches within one month of release for critical patches. The Cybersecurity and Infrastructure Security Agency (CISA) maintains a Known Exploited Vulnerabilities (KEV) catalog that compels U.S. federal agencies to remediate listed vulnerabilities within specified timelines. Agencies are typically required to patch within 3 weeks, though some vulnerabilities must be fixed within 24 hours.
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Hyperparameter optimization

In machine learning, hyperparameter optimization or tuning is the problem of choosing a set of optimal hyperparameters for a learning algorithm. A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set. The objective function takes a set of hyperparameters and returns the associated loss. Cross-validation is often used to estimate this generalization performance, and therefore choose the set of values for hyperparameters that maximize it. == Approaches == === Grid search === The traditional method for hyperparameter optimization has been grid search, or a parameter sweep, which is simply an exhaustive searching through a manually specified subset of the hyperparameter space of a learning algorithm. A grid search algorithm must be guided by some performance metric, typically measured by cross-validation on the training set or evaluation on a hold-out validation set. Since the parameter space of a machine learner may include real-valued or unbounded value spaces for certain parameters, manually set bounds and discretization may be necessary before applying grid search. For example, a typical soft-margin SVM classifier equipped with an RBF kernel has at least two hyperparameters that need to be tuned for good performance on unseen data: a regularization constant C and a kernel hyperparameter γ. Both parameters are continuous, so to perform grid search, one selects a finite set of "reasonable" values for each, say C ∈ { 10 , 100 , 1000 } {\displaystyle C\in \{10,100,1000\}} γ ∈ { 0.1 , 0.2 , 0.5 , 1.0 } {\displaystyle \gamma \in \{0.1,0.2,0.5,1.0\}} Grid search then trains an SVM with each pair (C, γ) in the Cartesian product of these two sets and evaluates their performance on a held-out validation set (or by internal cross-validation on the training set, in which case multiple SVMs are trained per pair). Finally, the grid search algorithm outputs the settings that achieved the highest score in the validation procedure. Grid search suffers from the curse of dimensionality, but is often embarrassingly parallel because the hyperparameter settings it evaluates are typically independent of each other. === Random search === Random Search replaces the exhaustive enumeration of all combinations by selecting them randomly. This can be simply applied to the discrete setting described above, but also generalizes to continuous and mixed spaces. A benefit over grid search is that random search can explore many more values than grid search could for continuous hyperparameters. It can outperform Grid search, especially when only a small number of hyperparameters affects the final performance of the machine learning algorithm. In this case, the optimization problem is said to have a low intrinsic dimensionality. Random Search is also embarrassingly parallel, and additionally allows the inclusion of prior knowledge by specifying the distribution from which to sample. Despite its simplicity, random search remains one of the important base-lines against which to compare the performance of new hyperparameter optimization methods. === Bayesian optimization === Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian optimization builds a probabilistic model of the function mapping from hyperparameter values to the objective evaluated on a validation set. By iteratively evaluating a promising hyperparameter configuration based on the current model, and then updating it, Bayesian optimization aims to gather observations revealing as much information as possible about this function and, in particular, the location of the optimum. It tries to balance exploration (hyperparameters for which the outcome is most uncertain) and exploitation (hyperparameters expected close to the optimum). In practice, Bayesian optimization has been shown to obtain better results in fewer evaluations compared to grid search and random search, due to the ability to reason about the quality of experiments before they are run. === Gradient-based optimization === For specific learning algorithms, it is possible to compute the gradient with respect to hyperparameters and then optimize the hyperparameters using gradient descent. The first usage of these techniques was focused on neural networks. Since then, these methods have been extended to other models such as support vector machines or logistic regression. A different approach in order to obtain a gradient with respect to hyperparameters consists in differentiating the steps of an iterative optimization algorithm using automatic differentiation. A more recent work along this direction uses the implicit function theorem to calculate hypergradients and proposes a stable approximation of the inverse Hessian. The method scales to millions of hyperparameters and requires constant memory. In a different approach, a hypernetwork is trained to approximate the best response function. One of the advantages of this method is that it can handle discrete hyperparameters as well. Self-tuning networks offer a memory efficient version of this approach by choosing a compact representation for the hypernetwork. More recently, Δ-STN has improved this method further by a slight reparameterization of the hypernetwork which speeds up training. Δ-STN also yields a better approximation of the best-response Jacobian by linearizing the network in the weights, hence removing unnecessary nonlinear effects of large changes in the weights. Apart from hypernetwork approaches, gradient-based methods can be used to optimize discrete hyperparameters also by adopting a continuous relaxation of the parameters. Such methods have been extensively used for the optimization of architecture hyperparameters in neural architecture search. === Evolutionary optimization === Evolutionary optimization is a methodology for the global optimization of noisy black-box functions. In hyperparameter optimization, evolutionary optimization uses evolutionary algorithms to search the space of hyperparameters for a given algorithm. Evolutionary hyperparameter optimization follows a process inspired by the biological concept of evolution: Create an initial population of random solutions (i.e., randomly generate tuples of hyperparameters, typically 100+) Evaluate the hyperparameter tuples and acquire their fitness function (e.g., 10-fold cross-validation accuracy of the machine learning algorithm with those hyperparameters) Rank the hyperparameter tuples by their relative fitness Replace the worst-performing hyperparameter tuples with new ones generated via crossover and mutation Repeat steps 2-4 until satisfactory algorithm performance is reached or is no longer improving. Evolutionary optimization has been used in hyperparameter optimization for statistical machine learning algorithms, automated machine learning, typical neural network and deep neural network architecture search, as well as training of the weights in deep neural networks. === Population-based === Population Based Training (PBT) learns both hyperparameter values and network weights. Multiple learning processes operate independently, using different hyperparameters. As with evolutionary methods, poorly performing models are iteratively replaced with models that adopt modified hyperparameter values and weights based on the better performers. This replacement model warm starting is the primary differentiator between PBT and other evolutionary methods. PBT thus allows the hyperparameters to evolve and eliminates the need for manual hypertuning. The process makes no assumptions regarding model architecture, loss functions or training procedures. PBT and its variants are adaptive methods: they update hyperparameters during the training of the models. On the contrary, non-adaptive methods have the sub-optimal strategy to assign a constant set of hyperparameters for the whole training. === Early stopping-based === A class of early stopping-based hyperparameter optimization algorithms is purpose-built for large search spaces of continuous and discrete hyperparameters, particularly when the computational cost to evaluate the performance of a set of hyperparameters is high. Irace implements the iterated racing algorithm, that focuses the search around the most promising configurations, using statistical tests to discard the ones that perform poorly. Another early stopping hyperparameter optimization algorithm is successive halving (SHA), which begins as a random search but periodically prunes low-performing models, thereby focusing computational resources on more promising models. Asynchronous successive halving (ASHA) further improves upon SHA's resource utilization profile by removing the need to synchronously evaluate a
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Audio inpainting

Audio inpainting (also known as audio interpolation) is an audio restoration task which deals with the reconstruction of missing or corrupted portions of a digital audio signal. Inpainting techniques are employed when parts of the audio have been lost due to various factors such as transmission errors, data corruption or errors during recording. The goal of audio inpainting is to fill in the gaps (i.e., the missing portions) in the audio signal seamlessly, making the reconstructed portions indistinguishable from the original content and avoiding the introduction of audible distortions or alterations. Many techniques have been proposed to solve the audio inpainting problem and this is usually achieved by analyzing the temporal and spectral information surrounding each missing portion of the considered audio signal. Classic methods employ statistical models or digital signal processing algorithms to predict and synthesize the missing or damaged sections. Recent solutions, instead, take advantage of deep learning models, thanks to the growing trend of exploiting data-driven methods in the context of audio restoration. Depending on the extent of the lost information, the inpainting task can be divided in three categories. Short inpainting refers to the reconstruction of few milliseconds (approximately less than 10) of missing signal, that occurs in the case of short distortions such as clicks or clipping. In this case, the goal of the reconstruction is to recover the lost information exactly. In long inpainting instead, with gaps in the order of hundreds of milliseconds or even seconds, this goal becomes unrealistic, since restoration techniques cannot rely on local information. Therefore, besides providing a coherent reconstruction, the algorithms need to generate new information that has to be semantically compatible with the surrounding context (i.e., the audio signal surrounding the gaps). The case of medium duration gaps lays between short and long inpainting. It refers to the reconstruction of tens of millisecond of missing data, a scale where the non-stationary characteristic of audio already becomes important. == Definition == Consider a digital audio signal x {\displaystyle \mathbf {x} } . A corrupted version of x {\displaystyle \mathbf {x} } , which is the audio signal presenting missing gaps to be reconstructed, can be defined as x ~ = m ∘ x {\displaystyle \mathbf {\tilde {x}} =\mathbf {m} \circ \mathbf {x} } , where m {\displaystyle \mathbf {m} } is a binary mask encoding the reliable or missing samples of x {\displaystyle \mathbf {x} } , and ∘ {\displaystyle \circ } represents the element-wise product. Audio inpainting aims at finding x ^ {\displaystyle \mathbf {\hat {x}} } (i.e., the reconstruction), which is an estimation of x {\displaystyle \mathbf {x} } . This is an ill-posed inverse problem, which is characterized by a non-unique set of solutions. For this reason, similarly to the formulation used for the inpainting problem in other domains, the reconstructed audio signal can be found through an optimization problem that is formally expressed as x ^ ∗ = argmin X ^ L ( m ∘ x ^ , x ~ ) + R ( x ^ ) {\displaystyle \mathbf {\hat {x}} ^{}={\underset {\hat {\mathbf {X} }}{\text{argmin}}}~L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )+R(\mathbf {\hat {x}} )} . In particular, x ^ ∗ {\displaystyle \mathbf {\hat {x}} ^{}} is the optimal reconstructed audio signal and L {\displaystyle L} is a distance measure term that computes the reconstruction accuracy between the corrupted audio signal and the estimated one. For example, this term can be expressed with a mean squared error or similar metrics. Since L {\displaystyle L} is computed only on the reliable frames, there are many solutions that can minimize L ( m ∘ x ^ , x ~ ) {\displaystyle L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )} . It is thus necessary to add a constraint to the minimization, in order to restrict the results only to the valid solutions. This is expressed through the regularization term R {\displaystyle R} that is computed on the reconstructed audio signal x ^ {\displaystyle \mathbf {\hat {x}} } . This term encodes some kind of a-priori information on the audio data. For example, R {\displaystyle R} can express assumptions on the stationarity of the signal, on the sparsity of its representation or can be learned from data. == Techniques == There exist various techniques to perform audio inpainting. These can vary significantly, influenced by factors such as the specific application requirements, the length of the gaps and the available data. In the literature, these techniques are broadly divided in model-based techniques (sometimes also referred as signal processing techniques) and data-driven techniques. === Model-based techniques === Model-based techniques involve the exploitation of mathematical models or assumptions about the underlying structure of the audio signal. These models can be based on prior knowledge of the audio content or statistical properties observed in the data. By leveraging these models, missing or corrupted portions of the audio signal can be inferred or estimated. An example of a model-based techniques are autoregressive models. These methods interpolate or extrapolate the missing samples based on the neighboring values, by using mathematical functions to approximate the missing data. In particular, in autoregressive models the missing samples are completed through linear prediction. The autoregressive coefficients necessary for this prediction are learned from the surrounding audio data, specifically from the data adjacent to each gap. Some more recent techniques approach audio inpainting by representing audio signals as sparse linear combinations of a limited number of basis functions (as for example in the Short Time Fourier Transform). In this context, the aim is to find the sparse representation of the missing section of the signal that most accurately matches the surrounding, unaffected signal. The aforementioned methods exhibit optimal performance when applied to filling in relatively short gaps, lasting only a few tens of milliseconds, and thus they can be included in the context of short inpainting. However, these signal-processing techniques tend to struggle when dealing with longer gaps. The reason behind this limitation lies in the violation of the stationarity condition, as the signal often undergoes significant changes after the gap, making it substantially different from the signal preceding the gap. As a way to overcome these limitations, some approaches add strong assumptions also about the fundamental structure of the gap itself, exploiting sinusoidal modeling or similarity graphs to perform inpainting of longer missing portions of audio signals. === Data-driven techniques === Data-driven techniques rely on the analysis and exploitation of the available audio data. These techniques often employ deep learning algorithms that learn patterns and relationships directly from the provided data. They involve training models on large datasets of audio examples, allowing them to capture the statistical regularities present in the audio signals. Once trained, these models can be used to generate missing portions of the audio signal based on the learned representations, without being restricted by stationarity assumptions. Data-driven techniques also offer the advantage of adaptability and flexibility, as they can learn from diverse audio datasets and potentially handle complex inpainting scenarios. As of today, such techniques constitute the state-of-the-art of audio inpainting, being able to reconstruct gaps of hundreds of milliseconds or even seconds. These performances are made possible by the use of generative models that have the capability to generate novel content to fill in the missing portions. For example, generative adversarial networks, which are the state-of-the-art of generative models in many areas, rely on two competing neural networks trained simultaneously in a two-player minmax game: the generator produces new data from samples of a random variable, the discriminator attempts to distinguish between generated and real data. During the training, the generator's objective is to fool the discriminator, while the discriminator attempts to learn to better classify real and fake data. In GAN-based inpainting methods the generator acts as a context encoder and produces a plausible completion for the gap only given the available information surrounding it. The discriminator is used to train the generator and tests the consistency of the produced inpainted audio. Recently, also diffusion models have established themselves as the state-of-the-art of generative models in many fields, often beating even GAN-based solutions. For this reason they have also been used to solve the audio inpainting problem, obtaining valid results. These models generate new data instances by inverting the
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Anna Becker

Anna Becker is an Israeli researcher known in the field of artificial intelligence and computer science within the financial field. == Early life and education == Becker was born in Russia and immigrated to Israel at 16 after graduating from a school in Moscow. At 17, she began her studies at Technion – Israel Institute of Technology. During her master's degree in computer science, she taught first-year students of the same course, and at 27, Becker completed her PhD in Computer Science and Artificial Intelligence. == Career == While pursuing her PhD, Becker resolved an NP-complete approximation algorithm that had been unresolved for over twenty years. This made her a recognized scholar in the field. After completing her PhD, she developed an approximation technique by a factor of two. This technique is widely used today in operating systems, database systems, and VLSI chip designs. She then founded and sold Strategy Runner, a fintech software. After this, she founded EndoTech, an algorithmic trading platform based on artificial intelligence and machine learning. EndoTech's trading strategies have been operating in live cryptocurrency markets since 2017. The platform's BTC Alpha strategy has reported an average annual return of 163% on fixed capital over eight years of live operation, with a maximum drawdown of 14% and a trade accuracy rate of approximately 83%. In 2026, EndoTech entered a partnership with Bit1 Exchange to make its BTC Alpha and ETH Alpha copy trading strategies accessible to retail investors with no minimum deposit requirement, through a full-custody model in which user funds remain in their own exchange wallets at all times.As of 2023, Becker is working on Fianchetto Fund, an AI-based investing analysis platform. Becker has also co-authored a book on Bayesian networks, which has been published widely in the field of computer science and artificial intelligence.
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Quantexa

Quantexa is a UK-based software company that develops artificial intelligence-based applications for data analytics and decision-making. The company was founded in 2016 and is headquartered in London, with operations in North America, Europe, and the Asia-Pacific region. As of 2025, Quantexa reported a valuation of $2.6 billion and provides services to organizations in over 70 countries. Investors include Warburg Pincus, HSBC, and the Ontario Teachers’ Pension Plan. == History == Quantexa was founded in London in 2016 by several co-founders, including Jamie Hutton, Richard Seewald, Imam Hoque, Felix Hoddinott, and Vishal Marria, who also serves as the company's chief executive officer. The company was established to develop tools intended to address limitations in traditional data analysis methods, particularly those related to identifying hidden connections across large datasets. The name "Quantexa" is derived from the company's focus on quantitative methods and data analysis. In 2023, Quantexa acquired Dublin-based AI firm Aylien. In April 2023, the company completed a Series E funding round, raising $129 million at a valuation of approximately $1.8 billion, marking its entry into "unicorn" status. In October 2024, the company reported annual recurring revenue (ARR) exceeding $100 million. In early 2025, Quantexa participated in the World Economic Forum's Unicorn Program, which supports high-growth technology companies. In March 2025, Quantexa completed a Series F funding round of $175 million, led by Teachers' Venture Growth, the venture arm of the Ontario Teachers' Pension Plan. That August, the company was reported to be considering a 2026 IPO. The company formed a partnership with Zurich in October 2025, the first insurer to add its AI-based Decision Intelligence platform to enhance fraud detection.
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Highway network

In machine learning, the Highway Network was the first working very deep feedforward neural network with hundreds of layers, much deeper than previous neural networks. It uses skip connections modulated by learned gating mechanisms to regulate information flow, inspired by long short-term memory (LSTM) recurrent neural networks. The advantage of the Highway Network over other deep learning architectures is its ability to overcome or partially prevent the vanishing gradient problem, thus improving its optimization. Gating mechanisms are used to facilitate information flow across the many layers ("information highways"). Highway Networks have found use in text sequence labeling and speech recognition tasks. In 2014, the state of the art was training deep neural networks with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In 2015, two techniques were developed to train such networks: the Highway Network (published in May), and the residual neural network, or ResNet (December). ResNet behaves like an open-gated Highway Net. == Model == The model has two gates in addition to the H ( W H , x ) {\displaystyle H(W_{H},x)} gate: the transform gate T ( W T , x ) {\displaystyle T(W_{T},x)} and the carry gate C ( W C , x ) {\displaystyle C(W_{C},x)} . The latter two gates are non-linear transfer functions (specifically sigmoid by convention). The function H {\displaystyle H} can be any desired transfer function. The carry gate is defined as: C ( W C , x ) = 1 − T ( W T , x ) {\displaystyle C(W_{C},x)=1-T(W_{T},x)} while the transform gate is just a gate with a sigmoid transfer function. == Structure == The structure of a hidden layer in the Highway Network follows the equation: y = H ( x , W H ) ⋅ T ( x , W T ) + x ⋅ C ( x , W C ) = H ( x , W H ) ⋅ T ( x , W T ) + x ⋅ ( 1 − T ( x , W T ) ) {\displaystyle {\begin{aligned}y=H(x,W_{H})\cdot T(x,W_{T})+x\cdot C(x,W_{C})\\=H(x,W_{H})\cdot T(x,W_{T})+x\cdot (1-T(x,W_{T}))\end{aligned}}} == Related work == Sepp Hochreiter analyzed the vanishing gradient problem in 1991 and attributed to it the reason why deep learning did not work well. To overcome this problem, Long Short-Term Memory (LSTM) recurrent neural networks have residual connections with a weight of 1.0 in every LSTM cell (called the constant error carrousel) to compute y t + 1 = F ( x t ) + x t {\textstyle y_{t+1}=F(x_{t})+x_{t}} . During backpropagation through time, this becomes the residual formula y = F ( x ) + x {\textstyle y=F(x)+x} for feedforward neural networks. This enables training very deep recurrent neural networks with a very long time span t. A later LSTM version published in 2000 modulates the identity LSTM connections by so-called "forget gates" such that their weights are not fixed to 1.0 but can be learned. In experiments, the forget gates were initialized with positive bias weights, thus being opened, addressing the vanishing gradient problem. As long as the forget gates of the 2000 LSTM are open, it behaves like the 1997 LSTM. The Highway Network of May 2015 applies these principles to feedforward neural networks. It was reported to be "the first very deep feedforward network with hundreds of layers". It is like a 2000 LSTM with forget gates unfolded in time, while the later Residual Nets have no equivalent of forget gates and are like the unfolded original 1997 LSTM. If the skip connections in Highway Networks are "without gates," or if their gates are kept open (activation 1.0), they become Residual Networks. The residual connection is a special case of the "short-cut connection" or "skip connection" by Rosenblatt (1961) and Lang & Witbrock (1988) which has the form x ↦ F ( x ) + A x {\displaystyle x\mapsto F(x)+Ax} . Here the randomly initialized weight matrix A does not have to be the identity mapping. Every residual connection is a skip connection, but almost all skip connections are not residual connections. The original Highway Network paper not only introduced the basic principle for very deep feedforward networks, but also included experimental results with 20, 50, and 100 layers networks, and mentioned ongoing experiments with up to 900 layers. Networks with 50 or 100 layers had lower training error than their plain network counterparts, but no lower training error than their 20 layers counterpart (on the MNIST dataset, Figure 1 in ). No improvement on test accuracy was reported with networks deeper than 19 layers (on the CIFAR-10 dataset; Table 1 in ). The ResNet paper, however, provided strong experimental evidence of the benefits of going deeper than 20 layers. It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in ). This is also why the forget gates of the 2000 LSTM were initially opened through positive bias weights: as long as the gates are open, it behaves like the 1997 LSTM. Similarly, a Highway Net whose gates are opened through strongly positive bias weights behaves like a ResNet. The skip connections used in modern neural networks (e.g., Transformers) are dominantly identity mappings.
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Surrogate model

A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (e.g., length, curvature, material, etc.). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheaper to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting. Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations. == Goals == The scientific challenge of surrogate modeling is the generation of a surrogate that is as accurate as possible, using as few simulation evaluations as possible. The process comprises three major steps which may be interleaved iteratively: Sample selection (also known as sequential design, optimal experimental design (OED) or active learning) Construction of the surrogate model and optimizing the model parameters (i.e., bias-variance tradeoff) Appraisal of the accuracy of the surrogate. The accuracy of the surrogate depends on the number and location of samples (expensive experiments or simulations) in the design space. A systematic data representation during training can improve model scalability, thereby reducing the need for expensive simulations. Various design of experiments (DOE) techniques cater to different sources of errors, in particular, errors due to noise in the data or errors due to an improper surrogate model. == Types of surrogate models == Popular surrogate modeling approaches are: polynomial response surfaces; kriging; more generalized Bayesian approaches; gradient-enhanced kriging (GEK); radial basis function; support vector machines; space mapping; artificial neural networks and Bayesian networks. Other methods recently explored include Fourier surrogate modeling , random forests, convolutional neural networks, and generative adversarial networks. For some problems, the nature of the true function is not known a priori, and therefore it is not clear which surrogate model will be the most accurate one. In addition, there is no consensus on how to obtain the most reliable estimates of the accuracy of a given surrogate. Many other problems have known physics properties. In these cases, physics-based surrogates such as space-mapping based models are commonly used. == Invariance properties == Recently proposed comparison-based surrogate models (e.g., ranking support vector machines) for evolutionary algorithms, such as CMA-ES, allow preservation of some invariance properties of surrogate-assisted optimizers: Invariance with respect to monotonic transformations of the function (scaling) Invariance with respect to orthogonal transformations of the search space (rotation) == Applications == An important distinction can be made between two different applications of surrogate models: design optimization and design space approximation (also known as emulation). In surrogate model-based optimization, an initial surrogate is constructed using some of the available budgets of expensive experiments and/or simulations. The remaining experiments/simulations are run for designs which the surrogate model predicts may have promising performance. The process usually takes the form of the following search/update procedure. Initial sample selection (the experiments and/or simulations to be run) Construct surrogate model Search surrogate model (the model can be searched extensively, e.g., using a genetic algorithm, as it is cheap to evaluate) Run and update experiment/simulation at new location(s) found by search and add to sample Iterate steps 2 to 4 until out of time or design is "good enough" Depending on the type of surrogate used and the complexity of the problem, the process may converge on a local or global optimum, or perhaps none at all. In design space approximation, one is not interested in finding the optimal parameter vector, but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above), the optimum found cannot be validated. == Surrogate modeling software == Surrogate Modeling Toolbox (SMT: https://github.com/SMTorg/smt) is a Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to the training data. It also includes new surrogate models that are not available elsewhere: kriging by partial-least squares reduction and energy-minimizing spline interpolation. Python library SAMBO Optimization supports sequential optimization with arbitrary models, with tree-based models and Gaussian process models built in. Surrogates.jl is a Julia packages which offers tools like random forests, radial basis methods and kriging. == Surrogate-Assisted Evolutionary Algorithms (SAEAs) == SAEAs are an advanced class of optimization techniques that integrate evolutionary algorithms (EAs) with surrogate models. In traditional EAs, evaluating the fitness of candidate solutions often requires computationally expensive simulations or experiments. SAEAs address this challenge by building a surrogate model, which is a computationally inexpensive approximation of the objective function or constraint functions. The surrogate model serves as a substitute for the actual evaluation process during the evolutionary search. It allows the algorithm to quickly estimate the fitness of new candidate solutions, thereby reducing the number of expensive evaluations needed. This significantly speeds up the optimization process, especially in cases where the objective function evaluations are time-consuming or resource-intensive. SAEAs typically involve three main steps: (1) building the surrogate model using a set of initial sampled data points, (2) performing the evolutionary search using the surrogate model to guide the selection, crossover, and mutation operations, and (3) periodically updating the surrogate model with new data points generated during the evolutionary process to improve its accuracy. By balancing exploration (searching new areas in the solution space) and exploitation (refining known promising areas), SAEAs can efficiently find high-quality solutions to complex optimization problems. They have been successfully applied in various fields, including engineering design, machine learning, and computational finance, where traditional optimization methods may struggle due to the high computational cost of fitness evaluations.
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