In computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed in 1984 by Leslie Valiant. In this framework, the learner receives samples and must select a generalization function (called the hypothesis) from a certain class of possible functions. The goal is that, with high probability (the "probably" part), the selected function will have low generalization error (the "approximately correct" part). The learner must be able to learn the concept given any arbitrary approximation ratio, probability of success, or distribution of the samples. The model was later extended to treat noise (misclassified samples). An important innovation of the PAC framework is the introduction of computational complexity theory concepts to machine learning. In particular, the learner is expected to find efficient functions (time and space requirements bounded to a polynomial of the example size), and the learner itself must implement an efficient procedure (requiring an example count bounded to a polynomial of the concept size, modified by the approximation and likelihood bounds). == Definitions and terminology == In order to give the definition for something that is PAC-learnable, we first have to introduce some terminology. For the following definitions, two examples will be used. The first is the problem of character recognition given an array of n {\displaystyle n} bits encoding a binary-valued image. The other example is the problem of finding an interval that will correctly classify points within the interval as positive and the points outside of the range as negative. Let X {\displaystyle X} be a set called the instance space or the encoding of all the samples. In the character recognition problem, the instance space is X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} . In the interval problem the instance space, X {\displaystyle X} , is the set of all bounded intervals in R {\displaystyle \mathbb {R} } , where R {\displaystyle \mathbb {R} } denotes the set of all real numbers. A concept is a subset c ⊂ X {\displaystyle c\subset X} . One concept is the set of all patterns of bits in X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} that encode a picture of the letter "P". An example concept from the second example is the set of open intervals, { ( a , b ) ∣ 0 ≤ a ≤ π / 2 , π ≤ b ≤ 13 } {\displaystyle \{(a,b)\mid 0\leq a\leq \pi /2,\pi \leq b\leq {\sqrt {13}}\}} , each of which contains only the positive points. A concept class C {\displaystyle C} is a collection of concepts over X {\displaystyle X} . This could be the set of all subsets of the array of bits that are skeletonized 4-connected (width of the font is 1). Let EX ( c , D ) {\displaystyle \operatorname {EX} (c,D)} be a procedure that draws an example, x {\displaystyle x} , using a probability distribution D {\displaystyle D} and gives the correct label c ( x ) {\displaystyle c(x)} , that is 1 if x ∈ c {\displaystyle x\in c} and 0 otherwise. Now, given 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} , assume there is an algorithm A {\displaystyle A} and a polynomial p {\displaystyle p} in 1 / ϵ , 1 / δ {\displaystyle 1/\epsilon ,1/\delta } (and other relevant parameters of the class C {\displaystyle C} ) such that, given a sample of size p {\displaystyle p} drawn according to EX ( c , D ) {\displaystyle \operatorname {EX} (c,D)} , then, with probability of at least 1 − δ {\displaystyle 1-\delta } , A {\displaystyle A} outputs a hypothesis h ∈ C {\displaystyle h\in C} that has an average error less than or equal to ϵ {\displaystyle \epsilon } on X {\displaystyle X} with the same distribution D {\displaystyle D} . Further if the above statement for algorithm A {\displaystyle A} is true for every concept c ∈ C {\displaystyle c\in C} and for every distribution D {\displaystyle D} over X {\displaystyle X} , and for all 0 < ϵ , δ < 1 {\displaystyle 0<\epsilon ,\delta <1} then C {\displaystyle C} is (efficiently) PAC learnable (or distribution-free PAC learnable). We can also say that A {\displaystyle A} is a PAC learning algorithm for C {\displaystyle C} . == Equivalence == Under some regularity conditions these conditions are equivalent: The concept class C is PAC learnable. The VC dimension of C is finite. C is a uniformly Glivenko-Cantelli class. C is compressible in the sense of Littlestone and Warmuth
Couchbase Server
Couchbase Server, originally known as Membase, is a source-available, distributed (shared-nothing architecture) multi-model NoSQL document-oriented database software package optimized for interactive applications. These applications may serve many concurrent users by creating, storing, retrieving, aggregating, manipulating and presenting data. In support of these kinds of application needs, Couchbase Server is designed to provide easy-to-scale key-value, or JSON document access, with low latency and high sustainability throughput. It is designed to be clustered from a single machine to very large-scale deployments spanning many machines. Couchbase Server provided client protocol compatibility with memcached, but added disk persistence, data replication, live cluster reconfiguration, rebalancing and multitenancy with data partitioning. == Product history == Membase was developed by several leaders of the memcached project, who had founded a company, NorthScale, to develop a key-value store with the simplicity, speed, and scalability of memcached, but also the storage, persistence and querying capabilities of a database. The original membase source code was contributed by NorthScale, and project co-sponsors Zynga and Naver Corporation (then known as NHN) to a new project on membase.org in June 2010. On February 8, 2011, the Membase project founders and Membase, Inc. announced a merger with CouchOne (a company with many of the principal players behind CouchDB) with an associated project merger. The merged company was called Couchbase, Inc. In January 2012, Couchbase released Couchbase Server 1.8. In September of 2012, Orbitz said it had changed some of its systems to use Couchbase. In December of 2012, Couchbase Server 2.0 (announced in July 2011) was released and included a new JSON document store, indexing and querying, incremental MapReduce and replication across data centers. == Architecture == Every Couchbase node consists of a data service, index service, query service, and cluster manager component. Starting with the 4.0 release, the three services can be distributed to run on separate nodes of the cluster if needed. In the parlance of Eric Brewer's CAP theorem, Couchbase is normally a CP type system meaning it provides consistency and partition tolerance, or it can be set up as an AP system with multiple clusters. === Cluster manager === The cluster manager supervises the configuration and behavior of all the servers in a Couchbase cluster. It configures and supervises inter-node behavior like managing replication streams and re-balancing operations. It also provides metric aggregation and consensus functions for the cluster, and a RESTful cluster management interface. The cluster manager uses the Erlang programming language and the Open Telecom Platform. ==== Replication and fail-over ==== Data replication within the nodes of a cluster can be controlled with several parameters. In December of 2012, support was added for replication between different data centers. === Data manager === The data manager stores and retrieves documents in response to data operations from applications. It asynchronously writes data to disk after acknowledging to the client. In version 1.7 and later, applications can optionally ensure data is written to more than one server or to disk before acknowledging a write to the client. Parameters define item ages that affect when data is persisted, and how max memory and migration from main-memory to disk is handled. It supports working sets greater than a memory quota per "node" or "bucket". External systems can subscribe to filtered data streams, supporting, for example, full text search indexing, data analytics or archiving. ==== Data format ==== A document is the most basic unit of data manipulation in Couchbase Server. Documents are stored in JSON document format with no predefined schemas. Non-JSON documents can also be stored in Couchbase Server (binary, serialized values, XML, etc.) ==== Object-managed cache ==== Couchbase Server includes a built-in multi-threaded object-managed cache that implements memcached compatible APIs such as get, set, delete, append, prepend etc. ==== Storage engine ==== Couchbase Server has a tail-append storage design that is immune to data corruption, OOM killers or sudden loss of power. Data is written to the data file in an append-only manner, which enables Couchbase to do mostly sequential writes for update, and provide an optimized access patterns for disk I/O. === Performance === A performance benchmark done by Altoros in 2012, compared Couchbase Server with other technologies. Cisco Systems published a benchmark that measured the latency and throughput of Couchbase Server with a mixed workload in 2012. == Licensing and support == Couchbase Server is a packaged version of Couchbase's open source software technology and is available in a community edition without recent bug fixes with an Apache 2.0 license and an edition for commercial use. Couchbase Server builds are available for Ubuntu, Debian, Red Hat, SUSE, Oracle Linux, Microsoft Windows and macOS operating systems. Couchbase has supported software developers' kits for the programming languages .NET, PHP, Ruby, Python, C, Node.js, Java, Go, and Scala. == SQL++ == A query language called SQL++ (formerly called N1QL), is used for manipulating the JSON data in Couchbase, just like SQL manipulates data in RDBMS. It has SELECT, INSERT, UPDATE, DELETE, MERGE statements to operate on JSON data. It was initially announced in March 2015 as "SQL for documents". The SQL++ data model is non-first normal form (N1NF) with support for nested attributes and domain-oriented normalization. The SQL++ data model is also a proper superset and generalization of the relational model. === Example === Like query SELECT FROM `bucket` WHERE email LIKE "%@example.org"; Array query SELECT FROM `bucket` WHERE ANY x IN friends SATISFIES x.name = "Pavan" END; == Couchbase Mobile == Couchbase Mobile / Couchbase Lite is a mobile database providing data replication. Couchbase Lite (originally TouchDB) provides native libraries for offline-first NoSQL databases with built-in peer-to-peer or client-server replication mechanisms. Sync Gateway manages secure access and synchronization of data between Couchbase Lite and Couchbase Server. Couchbase Lite added support for Vector Search in version 3.2, allowing cloud to edge support for vector search in mobile applications. == Uses == Couchbase began as an evolution of Memcached, a high-speed data cache, and can be used as a drop-in replacement for Memcached, providing high availability for memcached application without code changes. Couchbase is used to support applications where a flexible data model, easy scalability, and consistent high performance are required, such as tracking real-time user activity or providing a store of user preferences or online applications. Couchbase Mobile, which stores data locally on devices (usually mobile devices) is used to create “offline-first” applications that can operate when a device is not connected to a network and synchronize with Couchbase Server once a network connection is re-established. The Catalyst Lab at Northwestern University uses Couchbase Mobile to support the Evo application, a healthy lifestyle research program where data is used to help participants improve dietary quality, physical activity, stress, or sleep. Amadeus uses Couchbase with Apache Kafka to support their “open, simple, and agile” strategy to consume and integrate data on loyalty programs for airline and other travel partners. High scalability is needed when disruptive travel events create a need to recognize and compensate high value customers. Starting in 2012, it played a role in LinkedIn's caching systems, including backend caching for recruiter and jobs products, counters for security defense mechanisms, for internal applications. == Alternatives == For caching, Couchbase competes with Memcached and Redis. For document databases, Couchbase competes with other document-oriented database systems. It is commonly compared with MongoDB, Amazon DynamoDB, Oracle RDBMS, DataStax, Google Bigtable, MariaDB, IBM Cloudant, Redis Enterprise, SingleStore, and MarkLogic.
Top 10 AI Pair Programmers Compared (2026)
Looking for the best AI pair programmer? An AI pair programmer is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI pair programmer slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Chelsea Finn
Chelsea Finn (born October 8, 1992) is an American computer scientist and assistant professor at Stanford University. Her research investigates intelligence through the interactions of robots, with the hope to create robotic systems that can learn how to learn. She previously worked for Google and currently is a co-founder of the startup Physical Intelligence. == Early life and education == Finn was an undergraduate student in electrical engineering and computer science at Massachusetts Institute of Technology. She then moved to the University of California, Berkeley, where she earned her Ph.D. in 2018 under Pieter Abbeel and Sergey Levine. Her work in the Berkeley Artificial Intelligence Lab (BAIR) focused on gradient based algorithms . Such algorithms allow machines to 'learn to learn', more akin to human learning than traditional machine learning systems. These “meta-learning” techniques train machines to quickly adapt, such that when they encounter new scenarios they can learn quickly. As a doctoral student she worked as an intern at Google Brain, where she worked on robot learning algorithms from deep predictive models. She delivered a massive open online course on deep reinforcement learning. She was the first woman to win the C.V. & Daulat Ramamoorthy Distinguished Research Award. == Research and career == Finn investigates the capabilities of robots to develop intelligence through learning and interaction. She has made use of deep learning algorithms to simultaneously learn visual perception and control robotic skills. She developed meta-learning approaches to train neural networks to take in student code and output useful feedback. She showed that the system could quickly adapt without too much input from the instructor. She trialled the programme on Code in Place, a 12,000 student course delivered by Stanford University every year. She found that 97.9% of the time the students agreed with the feedback being given. == Awards and honors == 2016 C.V. & Daulat Ramamoorthy Distinguished Research Award 2017 Electrical engineering and computer science rising star 2018 MIT Technology Review 35 Under 35 2018 ACM Doctoral Dissertation Award 2020 Samsung Advanced Institute of Technology AI Researcher of the Year 2020 Intel Rising Star Faculty Award 2021 Office of Naval Research Young Investigator Award 2022 IEEE Robotics and Automation Society Early Academic Career Award == Select publications == Finn, Chelsea; Abbeel, Pieter; Levine, Sergey (2017-07-17). "Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks". International Conference on Machine Learning. PMLR: 1126–1135. arXiv:1703.03400. Sergey Levine; Chelsea Finn; Trevor Darrell; Pieter Abbeel (2016). "End-to-End Training of Deep Visuomotor Policies". Journal of Machine Learning Research. 17 (39): 1–40. arXiv:1504.00702. ISSN 1533-7928. Wikidata Q90313375. Chelsea Finn; Ian Goodfellow; Sergey Levine (2016). "Unsupervised Learning for Physical Interaction through Video Prediction" (PDF). Advances in Neural Information Processing Systems 29. Advances in Neural Information Processing Systems. Wikidata Q46993574.
Best AI Paraphrasing Tools in 2026
Curious about the best AI paraphrasing tool? An AI paraphrasing tool is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI paraphrasing tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
List of artificial intelligence journals
This is a list of notable peer-reviewed academic journals that publish research in the field of artificial intelligence (AI), including areas such as machine learning, computer vision, natural language processing, robotics, and intelligent systems. == General artificial intelligence == Artificial Intelligence (journal) – Elsevier Journal of Artificial Intelligence Research (JAIR) – AI Access Foundation Knowledge-Based Systems – Elsevier == Machine learning == Data Mining and Knowledge Discovery – Springer Machine Learning (journal) – Springer Journal of Machine Learning Research – Microtome Pattern Recognition (journal) – Elsevier Neural Networks (journal) – Elsevier Neural Computation (journal) – MIT Press Neurocomputing (journal) - Elsevier == Deep learning and neural computation == IEEE Transactions on Evolutionary Computation – IEEE IEEE Transactions on Neural Networks and Learning Systems – IEEE Nature Machine Intelligence – Springer Nature == Computer vision == International Journal of Computer Vision – Springer IEEE Transactions on Pattern Analysis and Machine Intelligence – IEEE Machine Vision and Applications – Springer == Natural language processing == Computational Linguistics (journal) – MIT Press Natural Language Processing Transactions of the Association for Computational Linguistics – ACL == Robotics and intelligent systems == IEEE Transactions on Robotics – IEEE Autonomous Robots – Springer Journal of Intelligent & Robotic Systems – Springer == Interdisciplinary and ethics in AI == AI & Society – Springer Artificial Life – MIT Press Philosophy & Technology – Springer Minds and Machines – Springer
Best AI Sales Assistants in 2026
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