Selmer Bringsjord (born November 24, 1958) is a professor of computer science and cognitive science and a former chair of the Department of Cognitive Science at Rensselaer Polytechnic Institute. He also holds an appointment in the Lally School of Management & Technology and teaches artificial Intelligence (AI), formal logic, human and machine reasoning, and philosophy of AI. == Biography == Bringsjord's education includes a B.A. in philosophy from the University of Pennsylvania and a Ph.D. in philosophy from Brown University, where he studied under Roderick Chisholm. He conducts research in AI as the director of the Rensselaer AI & Reasoning (RAIR) Laboratory. He specializes in the logico-mathematical and philosophical foundations of AI and cognitive science, and in collaboratively building AI systems on the basis of computational logic. Bringsjord believes that "the human mind will forever be superior to AI", and that "much of what many humans do for a living will be better done by indefatigable machines who require not a cent in pay". Bringsjord has stated that the "ultimate growth industry will be building smarter and smarter such machines on the one hand, and philosophizing about whether they are truly conscious and free on the other". Bringsjord has an argument for P = NP using digital physics. Other research includes developing a new computational-logic framework allowing the formalization of deliberative multi-agent "mindreading" as applied to the realm of nuclear strategy, with the goal of creating a model and simulation to enable reliable prediction. He has published an opinion piece advocating for counter-terrorism security ensured by pervasive, all-seeing sensors; automated reasoners; and autonomous, lethal robots. Bringsjord received a National Science Foundation award to research Social Robotics and the Covey Award for the advancement of philosophy of computing awarded by the International Association for Computing And Philosophy, among several others prizes. == Books authored == with Yang, Y. Mental Metalogic: A New, Unifying Theory of Human and Machine Reasoning (Mahwah, NJ: Lawrence Erlbaum).(2007) with Zenzen, M. Superminds: People Harness Hypercomputation, and More (Dordrecht, The Netherlands: Kluwer). (2003) ISBN 978-1402010958 with Ferrucci, D. Artificial Intelligence and Literary Creativity: Inside the Mind of Brutus, A Storytelling Machine (Mahwah, NJ: Lawrence Erlbaum).(2000) Abortion: A Dialogue (Indianapolis, IN: Hackett).(1997) What Robots Can and Can’t Be (Dordrecht, The Netherlands: Kluwer).(1992) Soft Wars (New York, NY: Penguin USA). A novel.(1991)
Neighborhood operation
In computer vision and image processing a neighborhood operation is a commonly used class of computations on image data which implies that it is processed according to the following pseudo code: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N) } This general procedure can be applied to image data of arbitrary dimensionality. Also, the image data on which the operation is applied does not have to be defined in terms of intensity or color, it can be any type of information which is organized as a function of spatial (and possibly temporal) variables in p. The result of applying a neighborhood operation on an image is again something which can be interpreted as an image, it has the same dimension as the original data. The value at each image point, however, does not have to be directly related to intensity or color. Instead it is an element in the range of the function f, which can be of arbitrary type. Normally the neighborhood N is of fixed size and is a square (or a cube, depending on the dimensionality of the image data) centered on the point p. Also the function f is fixed, but may in some cases have parameters which can vary with p, see below. In the simplest case, the neighborhood N may be only a single point. This type of operation is often referred to as a point-wise operation. == Examples == The most common examples of a neighborhood operation use a fixed function f which in addition is linear, that is, the computation consists of a linear shift invariant operation. In this case, the neighborhood operation corresponds to the convolution operation. A typical example is convolution with a low-pass filter, where the result can be interpreted in terms of local averages of the image data around each image point. Other examples are computation of local derivatives of the image data. It is also rather common to use a fixed but non-linear function f. This includes median filtering, and computation of local variances. The Nagao-Matsuyama filter is an example of a complex local neighbourhood operation that uses variance as an indicator of the uniformity within a pixel group. The result is similar to a convolution with a low-pass filter with the added effect of preserving sharp edges. There is also a class of neighborhood operations in which the function f has additional parameters which can vary with p: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N, parameters(p)) } This implies that the result is not shift invariant. Examples are adaptive Wiener filters. == Implementation aspects == The pseudo code given above suggests that a neighborhood operation is implemented in terms of an outer loop over all image points. However, since the results are independent, the image points can be visited in arbitrary order, or can even be processed in parallel. Furthermore, in the case of linear shift-invariant operations, the computation of f at each point implies a summation of products between the image data and the filter coefficients. The implementation of this neighborhood operation can then be made by having the summation loop outside the loop over all image points. An important issue related to neighborhood operation is how to deal with the fact that the neighborhood N becomes more or less undefined for points p close to the edge or border of the image data. Several strategies have been proposed: Compute result only for points p for which the corresponding neighborhood is well-defined. This implies that the output image will be somewhat smaller than the input image. Zero padding: Extend the input image sufficiently by adding extra points outside the original image which are set to zero. The loops over the image points described above visit only the original image points. Border extension: Extend the input image sufficiently by adding extra points outside the original image which are set to the image value at the closest image point. The loops over the image points described above visit only the original image points. Mirror extension: Extend the image sufficiently much by mirroring the image at the image boundaries. This method is less sensitive to local variations at the image boundary than border extension. Wrapping: The image is tiled, so that going off one edge wraps around to the opposite side of the image. This method assumes that the image is largely homogeneous, for example a stochastic image texture without large textons.
Peanut App
Peanut, a product of Peanut App Ltd. is an online community for women who are planning to become pregnant, women who are pregnant, women who have had children, and women who are experiencing menopause. Profiles of potential friends are displayed to users who can swipe up to show intent to connect. Users can also connect via discussion threads, groups, and live audio conversations. The app allows users to select their stage of life (trying to conceive, pregnancy, motherhood, or menopause), so as to meet women at a similar life stage, and to discover relevant content. Peanut was founded by Michelle Kennedy shortly after she left Bumble, a female-first dating app. She has described Peanut as, "the app she wishes she had when she first became a mother". == History == Peanut was initially launched in 2017 for mothers and pregnant women. The app focuses on helping users find others with shared interests, such as spoken languages, occupations, and hobbies. It also displays a woman's life stage, such as the age of her children, or the stage of pregnancy. In 2018, it launched a community discussion feature that intended to give women an "alternative to other social platforms". In 2019, it started to serve women who are trying to conceive. In April 2021, it integrated live audio, in response to the COVID-19 pandemic, and the restrictions around in-person socializing. in September 2021, it started to include women who are navigating perimenopause, menopause, and postmenopausal. Although it had initially catered for younger women navigating into new families, a large number of users had undergone surgically or chemically induced menopause due to medical conditions. In July 2021, Peanut launched an investment micro fund, Peanut StartHER, focused on investing in women-owned businesses, as well as other historically excluded founders. == Operation == The Peanut app is a social network exclusively for women, focusing on topics of pregnancy, motherhood, fertility, and menopause. It is available on iOS and Android devices. Users must prove their identity, in keeping with the primary function of in-app safety, and then they can create a profile to interact with other users. For pregnant users, the “Bump Buddies” feature helps connect them with other Peanut users who have a similar due date, which aimed to help expecting mothers combat loneliness during the COVID-19 pandemic. Peanut users also have the option to join “Groups” ‒ sub-sections of users focused on specific topics, including (but not limited to) location, life stage, pregnancy due date, and interests or hobbies. The live voice chat feature “Pods”, enables Peanut users to socialize without the pressure of photos or video chat. It offers features such as a muted audience of listeners who need to virtually raise their hand to speak, emoji reactions, and hosts who can moderate the conversations and invite people to speak.
Biomedical data science
Biomedical data science is a multidisciplinary field which leverages large volumes of data to promote biomedical innovation and discovery. Biomedical data science draws from various fields including Biostatistics, Biomedical informatics, and machine learning, with the goal of understanding biological and medical data. It can be viewed as the study and application of data science to solve biomedical problems. Modern biomedical datasets often have specific features which make their analyses difficult, including: Large numbers of feature (sometimes billions), typically far larger than the number of samples (typically tens or hundreds) Noisy and missing data Privacy concerns (e.g., electronic health record confidentiality) Requirement of interpretability from decision makers and regulatory bodies Many biomedical data science projects apply machine learning to such datasets. These characteristics, while also present in many data science applications more generally, make biomedical data science a specific field. Examples of biomedical data science research include: Computational genomics Computational imaging Electronic health records data mining Biomedical network science Clinical Natural Language Processing (NLP) == Computational Imaging and Deep Learning == Computational imaging is a cornerstone of biomedical data science, focusing on the development of algorithms to enhance, analyze, and interpret medical imagery. In recent years, the field has been transformed by the integration of deep learning, particularly through the use of Convolutional Neural Networks. Deep learning started from researchers manually defining characteristics like edge detection or texture representation learning. In a more modern approach of computational imaging, models automatically learn a hierarchy of features directly from raw pixel data. This overlap between data science and deep learning is applied across several key tasks: Classification: Identifying the presence of specific diseases, such as distinguishing between benign and malignant tumors in histopathology slides or detecting pneumonia in chest X-rays. Segmentation: The precise delineation of anatomical structures or lesions. A notable example is the U-Net architecture, which is widely used for biomedical image segmentation to help clinicians quantify organ volume or track tumor growth. Detection: Automating the localization of small objects, such as identifying microcalcifications in mammograms or polyps during colonoscopies. Registration: The process of aligning multiple images to provide a comprehensive view of the patient's anatomy. Even with all of these enhancements, the application of deep learning in medical imaging requires accomplishing vigorous challenges. An example of these changes is building large, annotated datasets and creating the imperative for model interpretability in clinical decision-making. == Electronic Health Records == Electronic Health Records (EHRs) are a digital alternative to patient paper charts, usually including individual records or population health information. EHRs can be used in a wide variety of applications, including research and analysation as they often include demographics, diagnoses, medications, test results, and personal statistics. === History === ==== 1960s ==== The earliest precursor is considered Dr. Lawrence Weed's problem-oriented medical record (POMR) published in the 1968 which sorts and groups medical records by medical diagnoses and symptoms. The POMR was the first system to organize based off of patient information rather than the source (doctors, nurses, attendings, etc.). In 1969, the Regenstrief Institute developed and published the Regenstrief Medical Record System which established electronic writing, storage, and retrieval of records which served as the basis for modern EHR systems. ==== 2000s ==== In 2009, the Health Information Technology for Economic and Clinical Health Act (HITECH Act) was passed in the United States. This act standardized privacy and distribution of EHRs and increased the acceptance and utilization of EHRs within medical and academic settings. == Artificial Intelligence and Machine Learning Applications == Machine Learning and Artificial Intelligence have become central tools in biomedical data science. Recent advances in large language models (LLMs) have expanded their role beyond text, with models trained directly on genomic sequences enabling tasks such as gene function prediction, variant effect analysis, and drug discovery. In clinical settings, Natural Language Processing (NLP) models are applied to electronic health records to extract structured insights from unstructured clinical notes and data, supporting diagnosis and treatment planning. Beyond genomics, AI models have been applied to protein structure prediction. AlphaFold, developed by Google DeepMind, uses deep learning to predict three-dimensional protein structures from amino acid sequences with high accuracy. These predictions have been used to support drug target identification and the study of disease mechanisms. == Knowledge Graphs == Knowledge graphs (KGs) are widely used in biomedical data science to represent and analyze complex relationships among biological and medical entities. By structuring data as nodes (e.g., genes, diseases, drugs) and edges (relationships), KGs enable computational methods to extract insights and support decision-making. These biomedical relationships can be efficiently modeled and queried using technologies such as Neo4j. === Biomedical Research Applications === KGs provide biomedical researchers with a way to model complex biological systems. They have been used to identify the relationships between diseases and biomolecules, support drug repurposing, and to uncover new biological insights. Additional applications include: Identification of novel antibiotic resistance genes through graph-based link prediction. Finding associations between miRNA and diseases. Prediction of protein-protein interactions. === Clinical Applications === In clinical settings, KGs can be used to make visual representations of a patient's electronic health records. The data obtained from these graphs can assist healthcare providers in improving patient diagnoses and prescribing more effective drugs. Additionally, embeddings derived from resources like the Unified Medical Language System (UMLS) enable natural language processing of clinical text and similarity analysis between medical concepts. === Limitations === Despite their advantages, knowledge graphs face several challenges. Some of these include: High algorithmic complexity and large biological datasets make the process computationally expensive. KG construction can be a time-consuming process that requires careful attention to assign appropriate node types and vocabularies. Using data from a wide range of datasets in one KG requires them to be effectively integrated. == Privacy == A primary challenge in biomedical data science is maintaining medical privacy. Conducting research requires that data be collected on a number of people for training and testing purposes and is stored within biomedical datasets. This poses a risk for violating patient confidentiality and may dissuade people from participating in studies. The main sources of health statistics are surveys administrative and medical records health care claims data, vital records surveillance disease registries grey literature and peer-reviewed literature. Large data collection is a useful tool for researching various medical conditions. Researchers use these large datasets of information to identify factors that may make people more susceptible to certain diseases. Large amounts of collected data can help researchers identify patterns for disease probabilities. The findings can show a person is more likely for a condition, or identify environmental, social, and personal habits that may lead to adverse health issues. Institutions researching using personal medical information come with a moral and legal responsibility to protect the use of that information. Protection of the collected information has become a big concern. Sophisticated and coordinated attacks on certain medical systems happen more frequently. Medical companies, medical insurance and private businesses have invested a great deal into the protection of personal data. Despite this, data breaches continue to be documented. The chart below shows the top healthcare breaches in 2025. For these reasons, many people have reservations about giving up their personal data. Aside from the legitimate use of personal data there have been instances where companies have found methods to profit from brokering medical information. Concerns exist regarding unauthorized use of sensitive information within these data companies. If a person is identified within a dataset, then sensitive data can be used to discriminate against them. For example, insurance companies may charge a hi
Systems development life cycle
The systems development life cycle (SDLC) describes the typical phases and progression between phases during the development of a computer-based system. These phases progress from inception to retirement. At base, there is just one life cycle, but the taxonomy used to describe it may vary; the cycle may be classified into different numbers of phases and various names may be used for those phases. The SDLC is analogous to the life cycle of a living organism from its birth to its death. In particular, the SDLC varies by system in much the same way that each living organism has a unique path through its life. The SDLC does not prescribe how engineers should go about their work to move the system through its life cycle. Prescriptive techniques are referred to using various terms such as methodology, model, framework, and formal process. Other terms are used for the same concept as SDLC, including software development life cycle (also SDLC), application development life cycle (ADLC), and system design life cycle (also SDLC). These other terms focus on a different scope of development and are associated with different prescriptive techniques, but are about the same essential life cycle. The term "life cycle" is often written without a space, as "lifecycle", with the former more popular in the past and in non-engineering contexts. The acronym SDLC was coined when the longer form was more popular and has remained associated with the expansion, even though the shorter form is popular in engineering. Also, SDLC is relatively unique as opposed to the TLA SDL, which is highly overloaded. == Phases == Depending on the source, the SDLC is described as having different phases and using different terms. Even so, there are common aspects. The following attempts to describe notable phases using notable terminology. The phases are somewhat ordered by the natural sequence of development, although they can be overlapping and iterative. === Conceptualization === During conceptualization (a.k.a. conceptual design, system investigation, feasibility), options and priorities are considered. A feasibility study can determine whether the development effort is worthwhile via activities such as understanding user needs, cost estimation, benefit analysis, and resource analysis. A study should address operational, financial, technical, human factors, and legal/political concerns. === Requirements analysis === Requirements analysis (a.k.a. preliminary design) involves understanding the problem and determining what is needed. Often this involves engaging users to define the requirements and recording them in a document known as a requirements specification. === Design === During the design phase (a.k.a. detail design), a solution is planned. The plan can include relatively high-level information such as describing the major components of the system. The plan can include relatively low-level information such as describing functions, screen layout, business rules, and process flow. The design phase is informed by the requirements of the system. The design must satisfy each requirement. The design may be recorded in textual documents as well as functional hierarchy diagrams, example screen images, business rules, process diagrams, pseudo-code, and data models. === Construction === During construction (a.k.a. implementation, production), the system is realized. Based on the design, hardware and software components are created and integrated. This phase includes testing sub-components, components and the integration of some components, but typically does not include testing at the complete system level. This phase may include the development of training materials, including user manuals and help files. === Acceptance === The acceptance phase (a.k.a. system testing) is about testing the complete system to ensure that it meets customer expectations (requirements). === Deployment === The deployment phase (a.k.a. implementation) involves the logistics of delivery to the customer. Some systems are deployed as a single instance (i.e. in the cloud), and deployment may be ad hoc and manual. Some systems are built in quantity and are associated with manufacturing process and commissioning. This phase may include training users to use the system. It may include transitioning future development to support staff. === Maintenance === During the maintenance phase (a.k.a. operation, utilization, support) development is largely inactive, although this phase does include customer support for resolving user issues and recording suggestions for improvement. Fixes and enhancements are handled by returning to the first phase, conceptualization. For minor changes, the cycle may be significantly abbreviated compared to initial development. === Decommission === Decommission (a.k.a. disposition, retirement, phase-out) is when the system is removed from use, i.e., when it reaches end-of-life. == Practices == === Management and control === SDLC phase objectives are described in this section with key deliverables, a description of recommended tasks, and a summary of related control objectives for effective management. It is critical for the project manager to establish and monitor control objectives while executing projects. Control objectives are clear statements of the desired result or purpose and should be defined and monitored throughout a project. Control objectives can be grouped into major categories (domains), and relate to the SDLC phases as shown in the figure. To manage and control a substantial SDLC initiative, a work breakdown structure (WBS) captures and schedules the work. The WBS and all programmatic material should be kept in the "project description" section of the project notebook. The project manager chooses a WBS format that best describes the project. The diagram shows that coverage spans numerous phases of the SDLC, but the associated MCD (Management Control Domains) shows mappings to SDLC phases. For example, Analysis and Design is primarily performed as part of the Acquisition and Implementation Domain, and System Build and Prototype is primarily performed as part of delivery and support. === Work breakdown structured organization === The upper section of the WBS provides an overview of the project scope and timeline. It should also summarize the major phases and milestones. The middle section is based on the SDLC phases. WBS elements consist of milestones and tasks to be completed rather than activities to be undertaken, and have a deadline. Each task has a measurable output (e.g., an analysis document). A WBS task may rely on one or more activities (e.g., coding). Parts of the project needing support from contractors should have a statement of work (SOW). The development of an SOW does not occur during a specific phase of SDLC but is developed to include the work from the SDLC process that may be conducted by contractors. === Baselines === Baselines are established after four of the five phases of the SDLC, and are critical to the iterative nature of the model. Baselines become milestones. functional baseline: established after the conceptual design phase. allocated baseline: established after the preliminary design phase. product baseline: established after the detailed design and development phase. updated product baseline: established after the production construction phase. In the following diagram, these stages are divided into ten steps, from definition to creation and modification of IT work products:
Sample complexity
The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g., only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. == Definition == Let X {\displaystyle X} be a space which we call the input space, and Y {\displaystyle Y} be a space which we call the output space, and let Z {\displaystyle Z} denote the product X × Y {\displaystyle X\times Y} . For example, in the setting of binary classification, X {\displaystyle X} is typically a finite-dimensional vector space and Y {\displaystyle Y} is the set { − 1 , 1 } {\displaystyle \{-1,1\}} . Fix a hypothesis space H {\displaystyle {\mathcal {H}}} of functions h : X → Y {\displaystyle h\colon X\to Y} . A learning algorithm over H {\displaystyle {\mathcal {H}}} is a computable map from Z {\displaystyle Z} to H {\displaystyle {\mathcal {H}}} . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} . Typical learning algorithms include empirical risk minimization, without or with Tikhonov regularization. Fix a loss function L : Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X × Y {\displaystyle X\times Y} , the expected risk of a hypothesis (a function) h ∈ H {\displaystyle h\in {\mathcal {H}}} is E ( h ) := E ρ [ L ( h ( x ) , y ) ] = ∫ X × Y L ( h ( x ) , y ) d ρ ( x , y ) {\displaystyle {\mathcal {E}}(h):=\mathbb {E} _{\rho }[{\mathcal {L}}(h(x),y)]=\int _{X\times Y}{\mathcal {L}}(h(x),y)\,d\rho (x,y)} In our setting, we have h = A ( S n ) {\displaystyle h={\mathcal {A}}(S_{n})} , where A {\displaystyle {\mathcal {A}}} is a learning algorithm and S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} is a sequence of vectors which are all drawn independently from ρ {\displaystyle \rho } . Define the optimal risk E H ∗ = inf h ∈ H E ( h ) . {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}={\underset {h\in {\mathcal {H}}}{\inf }}{\mathcal {E}}(h).} Set h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , for each sample size n {\displaystyle n} . h n {\displaystyle h_{n}} is a random variable and depends on the random variable S n {\displaystyle S_{n}} , which is drawn from the distribution ρ n {\displaystyle \rho ^{n}} . The algorithm A {\displaystyle {\mathcal {A}}} is called consistent if E ( h n ) {\displaystyle {\mathcal {E}}(h_{n})} probabilistically converges to E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} . In other words, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} , such that, for all sample sizes n ≥ N {\displaystyle n\geq N} , we have Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] < δ . {\displaystyle \Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]<\delta .} The sample complexity of A {\displaystyle {\mathcal {A}}} is then the minimum N {\displaystyle N} for which this holds, as a function of ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . We write the sample complexity as N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} to emphasize that this value of N {\displaystyle N} depends on ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . If A {\displaystyle {\mathcal {A}}} is not consistent, then we set N ( ρ , ϵ , δ ) = ∞ {\displaystyle N(\rho ,\epsilon ,\delta )=\infty } . If there exists an algorithm for which N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is finite, then we say that the hypothesis space H {\displaystyle {\mathcal {H}}} is learnable. In others words, the sample complexity N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} defines the rate of consistency of the algorithm: given a desired accuracy ϵ {\displaystyle \epsilon } and confidence δ {\displaystyle \delta } , one needs to sample N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} data points to guarantee that the risk of the output function is within ϵ {\displaystyle \epsilon } of the best possible, with probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity is polynomial, that is, whether N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is bounded by a polynomial in 1 / ϵ {\displaystyle 1/\epsilon } and 1 / δ {\displaystyle 1/\delta } . If N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is polynomial for some learning algorithm, then one says that the hypothesis space H {\displaystyle {\mathcal {H}}} is PAC-learnable. This is a stronger notion than being learnable. == Unrestricted hypothesis space: infinite sample complexity == One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) < δ , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right)<\delta ,} where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large. Thus, in order to make statements about the rate of convergence of the quantity sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right),} one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. == Restricted hypothesis space: finite sample-complexity == The latter approach leads to concepts such as VC dimension and Rademacher complexity which control the complexity of the space H {\displaystyle {\mathcal {H}}} . A smaller hypothesis space introduces more bias into the inference process, meaning that E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} may be greater than the best possible risk in a larger space. However, by restricting the complexity of the hypothesis space it becomes possible for an algorithm to produce more uniformly consistent functions. This trade-off leads to the concept of regularization. It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}} : H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class. This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. === An example of a PAC-learnable hypothesis space === X = R d , Y = { − 1 , 1 } {\displaystyle X=\mathbb {R} ^{d},Y=\{-1,1\}} , and let H {\displaystyle {\mathcal {H}}} be the space of affine functions on X {\displaystyle X} , that is, functions of the form x ↦ ⟨ w , x ⟩ + b {\displaystyle x\mapsto \langl
D4Science
D4Science is a Data Infrastructure offering services by community-driven virtual research environments. In particular, it supports communities of practice willing to implement open science practices, thus it is an Open Science Infrastructure. The infrastructure follows the system of systems approach, where the constituent systems (Service providers) offer "resources" (namely services and by them data, computing, storage) assembled together to implement the overall set of D4Science services. In particular, D4Science aggregates "domain agnostic" service providers as well as community-specific ones to build a unifying space where the aggregated resources can be exploited via Virtual research Environments and their services. It is spread across several sites, the primary one is hosted by the Istituto di Scienza e Tecnologie dell'Informazione of National Research Council (Italy). At the earth of this infrastructure there is an Open Source Software named gCube system. == Services == D4Science offers: Virtual Research Environment as a Service providing any community of practice with a dedicated working environment supporting any knowledge production process in a collaborative way, in fact every VRE enables computer-supported cooperative work by design. D4Science-based VREs are web-based, community-oriented, collaborative, user-friendly, open-science-enabler working environments for scientists and practitioners willing to work together to perform a set of (research) task. From the end-user perspective, each VRE manifests in a unifying web application (and a set of application programming interfaces (APIs)): (a) comprising several applications organised in specific menu items and (b) running in a plain web browser. Every application is providing VRE users with facilities implemented by relying on one or more services provisioned by diverse providers. Among the basic services every VRE is equipped with there are a Social Networking area enabling collaborative and open discussions on any topic and disseminating information of interest for the community, for example, the availability of a research outcome; a Workspace for storing, organizing and sharing any version of a research artifact, including dataset and model implementation; a User Management dashboard for managing membership and roles; a Catalogue Service recording the assets worth being published thus to make it possible for others to be informed and make use of these assets. Science Gateway as a Service providing a community of practice with a dedicated science gateway hosting a selected set of virtual research environments. Data Analytics at scale for data analytics including: a proprietary data analytics platform (DataMiner) to execute analytics tasks either by relying on methods provided by the user or by others. It is endowed with importing and sharing facilities for analytics methods implemented in heterogeneous forms including R, Java, Python, and KNIME. The platform enacts tasks execution by a distributed and hybrid computing infrastructure. Moreover, one of the worth highlighting feature of this platform is its open science-friendliness. All the analytics methods integrated in it are exposed by a standard protocol (the OGC WPS protocol) clients can use to get informed on available methods as well as to start processes, monitor their execution and access results. Every analytics task performed by the platform automatically produces a provenance record catering for the reproducibility of the task; an RStudio-based development environment for R enabling to perform statistical computing tasks in the cloud. This RStudio environment is (i) preconfigured with libraries and packages to ease the execution of common data analytics tasks, and (ii) provides seamless access to the VRE Workspace enabling sharing of resources with other members of the same working environment. a Jupyter-based notebook environment for developing and executing interactive computing by JupyterLab instances. Each JupyterLab is (i) preconfigured with libraries and packages to ease the execution of common data analytics tasks, and (ii) provides access to the VRE Workspace enabling sharing of resources with other members of the same working environment. == Community == The D4Science Infrastructure serves more than 24,000 registered users (August 2024) through 177 active VREs offered via 20 Science gateways. This extensive infrastructure not only supports a diverse range of scientific communities but also fosters significant engagement and collaboration among researchers worldwide. Engagement within the D4Science community is robust, with users benefiting from user-friendly application environments tailored to their specific needs. The platform allows users to securely preserve, access, and share their data from anywhere, fostering a collaborative and inclusive research environment. Additionally, groups of users can create their own virtual environments and customise them with the applications they need, further enhancing the platform's flexibility and usability. Supported communities and cases range from Agri-food to Social Data Science, Earth Science and Marine Science. These diverse applications demonstrate the versatility and broad applicability of the D4Science Infrastructure, making it an invaluable resource for researchers across various scientific domains. == History == The D4Science development has been supported by several European-funded projects. DILIGENT (2004-2007) in the Sixth Framework Programme for Research and Technological Development was the forerunner where a testbed infrastructure built by integrating digital library and grid computing technologies and resources was conceived and developed to serve the needs of communities of practice involved in knowledge development. In the context of the Seventh Framework Programme for research, technological development and demonstration the development of the D4Science initiative. In this period the infrastructure was established and developed to serve communities of practices from domains ranging from Earth Science to Marine Science with worldwide scope In the context of the H2020 research and innovation programme the maturity level of the D4Science infrastructure was high enough to allow a large and very diverse set of communities of practice to benefit from it and its services and further contribute to its development. Moreover, the services offered by the infrastructure have been developed to support open science practices. The operation and improvement of the D4Science infrastructure facilities are still ongoing while its exploitation is progressively growing.