AI Face Animator

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Scikit-learn

scikit-learn (formerly scikits.learn and also known as sklearn) is a free and open-source machine learning library for the Python programming language. It features various classification, regression and clustering algorithms including support-vector machines, random forests, gradient boosting, k-means and DBSCAN, and is designed to interoperate with the Python numerical and scientific libraries NumPy and SciPy. Scikit-learn is a NumFOCUS fiscally sponsored project. == Overview == The scikit-learn project started as scikits.learn, a Google Summer of Code project by French data scientist David Cournapeau. The name of the project derives from its role as a "scientific toolkit for machine learning", originally developed and distributed as a third-party extension to SciPy. The original codebase was later rewritten by other developers. In 2010, contributors Fabian Pedregosa, Gaël Varoquaux, Alexandre Gramfort and Vincent Michel, from the French Institute for Research in Computer Science and Automation in Saclay, France, took leadership of the project and released the first public version of the library on February 1, 2010. In November 2012, scikit-learn as well as scikit-image were described as two of the "well-maintained and popular" scikits libraries. In 2019, it was noted that scikit-learn is one of the most popular machine learning libraries on GitHub. At that time, the project had over 1,400 contributors and the documentation received 42 million visits in 2018. According to a 2022 Kaggle survey of nearly 24,000 respondents from 173 countries, scikit-learn was identified as the most widely used machine learning framework. == Features == Large catalogue of well-established machine learning algorithms and data pre-processing methods (i.e. feature engineering) Utility methods for common data-science tasks, such as splitting data into train and test sets, cross-validation and grid search Consistent way of running machine learning models (estimator.fit() and estimator.predict()), which libraries can implement Declarative way of structuring a data science process (the Pipeline), including data pre-processing and model fitting == Examples == Fitting a random forest classifier: == Implementation == scikit-learn is largely written in Python, and uses NumPy extensively for high-performance linear algebra and array operations. Furthermore, some core algorithms are written in Cython to improve performance. Support vector machines are implemented by a Cython wrapper around LIBSVM; logistic regression and linear support vector machines by a similar wrapper around LIBLINEAR. In such cases, extending these methods with Python may not be possible. scikit-learn integrates well with many other Python libraries, such as Matplotlib and plotly for plotting, NumPy for array vectorization, Pandas dataframes, SciPy, and many more. == History == scikit-learn was initially developed by David Cournapeau as a Google Summer of Code project in 2007. Later that year, Matthieu Brucher joined the project and started to use it as a part of his thesis work. In 2010, INRIA, the French Institute for Research in Computer Science and Automation, got involved and the first public release (v0.1 beta) was published in late January 2010. The project released its first stable version, 1.0.0, on September 24, 2021. The release was the result of over 2,100 merged pull requests, approximately 800 of which were dedicated to improving documentation. Development continues to focus on bug fixes, efficiency and feature expansion. The latest version, 1.8, was released on December 10, 2025. This update introduced native Array API support, enabling the library to perform GPU computations by directly using PyTorch and CuPy arrays. This version also included bug fixes, improvements and new features, such as efficiency improvements to the fit time of linear models. == Applications == Scikit-learn is widely used across industries for a variety of machine learning tasks such as classification, regression, clustering, and model selection. The following are real-world applications of the library: === Finance and Insurance === AXA uses scikit-learn to speed up the compensation process for car accidents and to detect insurance fraud. Zopa, a peer-to-peer lending platform, employs scikit-learn for credit risk modelling, fraud detection, marketing segmentation, and loan pricing. BNP Paribas Cardif uses scikit-learn to improve the dispatching of incoming mail and manage internal model risk governance through pipelines that reduce operational and overfitting risks. J.P. Morgan reports broad usage of scikit-learn across the bank for classification tasks and predictive analytics in financial decision-making. === Retail and E-Commerce === Booking.com uses scikit-learn for hotel and destination recommendation systems, fraudulent reservation detection, and workforce scheduling for customer support agents. HowAboutWe uses it to predict user engagement and preferences on a dating platform. Lovely leverages the library to understand user behaviour and detect fraudulent activity on its platform. Data Publica uses it for customer segmentation based on the success of past partnerships. Otto Group integrates scikit-learn throughout its data science stack, particularly in logistics optimization and product recommendations. === Media, Marketing, and Social Platforms === Spotify applies scikit-learn in its recommendation systems. Betaworks uses the library for both recommendation systems (e.g., for Digg) and dynamic subspace clustering applied to weather forecasting data. PeerIndex used scikit-learn for missing data imputation, tweet classification, and community clustering in social media analytics. Bestofmedia Group employs it for spam detection and ad click prediction. Machinalis utilizes scikit-learn for click-through rate prediction and relational information extraction for content classification and advertising optimization. Change.org applies scikit-learn for targeted email outreach based on user behaviour. === Technology === AWeber uses scikit-learn to extract features from emails and build pipelines for managing large-scale email campaigns. Solido applies it to semiconductor design tasks such as rare-event estimation and worst-case verification using statistical learning. Evernote, Dataiku, and other tech companies employ scikit-learn in prototyping and production workflows due to its consistent API and integration with the Python ecosystem. === Academia === Télécom ParisTech integrates scikit-learn in hands-on coursework and assignments as part of its machine learning curriculum. == Awards == 2019 Inria-French Academy of Sciences-Dassault Systèmes Innovation Prize: Awarded in recognition of scikit-learn's impact as a major free software breakthrough in machine learning and its role in the digital transformation of science and industry. 2022 Open Science Award for Open Source Research Software: Awarded by the French Ministry of Higher Education and Research as part of the second National Plan for Open Science. The project was recognized in the "Community" category for its technical quality, its large international contributor network, and the quality of its documentation.
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Reciprocal human machine learning

Reciprocal Human Machine Learning (RHML) is an interdisciplinary approach to designing human-AI interaction systems. RHML aims to enable continual learning between humans and machine learning models by having them learn from each other. This approach keeps the human expert "in the loop" to oversee and enhance machine learning performance and simultaneously support the human expert continue learning. == Background == RHML emerged in the context of the rise of big data analytics and artificial intelligence for intelligent tasks like sense-making and decision-making. As machine learning advanced to take on more roles, researchers realized fully autonomous systems had limitations and needed human guidance. RHML extends the concept of human-in-the-loop systems by promoting reciprocal learning. Humans learn from their interactions with machine learning models, staying up-to-date on evolving technology. The models also learn from human feedback and oversight. This amplification of learning on both sides is a key focus of RHML. The approach draws on theories of learning in dyads from education and psychology. It also builds on human-computer interaction and human-centered design principles. Implementing RHML requires developing specialized tools and interfaces tailored to the application == Applications == RHML has been explored across diverse domains including: Cybersecurity - Software to enable reciprocal learning between experts and AI models for social media threat detection. Organizational decision-making - RHML to structure collaboration between humans and AI systems. Workplace training - Using RHML for workers to learn from AI technologies on the job. Open science - Using human and AI collaboration to promote open science. Production and logistics - turning workers and intelligent machines into teammates. RHML maintains human oversight and control over AI systems, while enabling cutting-edge machine learning performance. This collaborative approach highlights the importance of keeping the human expert involved in the loop. An example of RHML in application is Free Spirit (AFSFCV), an open-source architecture first published in early 2025 as a whitepaper, proposing a visually structured approach to intent-based human–AI interaction.
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Human-in-the-loop

Human-in-the-loop (HITL) is used in multiple contexts. It can be defined as a model requiring human interaction. HITL is associated with modeling and simulation (M&S) in the live, virtual, and constructive taxonomy. HITL, along with the related human-on-the-loop, are also used in relation to lethal autonomous weapons. Further, HITL is used in the context of machine learning.It is also used in conversational AI to manage complex interactions that require human empathy. == Machine learning == In machine learning, HITL is used in the sense of humans aiding the computer in making the correct decisions in building a model. HITL improves machine learning over random sampling by selecting the most critical data needed to refine the model. == Simulation == In simulation, HITL models may conform to human factors requirements as in the case of a mockup. In this type of simulation, a human is always part of the simulation and consequently influences the outcome in such a way that is difficult if not impossible to reproduce exactly. HITL also readily allows for the identification of problems and requirements that may not be easily identified by other means of simulation. HITL is often referred to as an interactive simulation, which is a special kind of physical simulation in which physical simulations include human operators, such as in a flight or a driving simulator. === Benefits === Human-in-the-loop allows the user to change the outcome of an event or process. The immersion effectively contributes to a positive transfer of acquired skills into the real world. This can be demonstrated by trainees utilizing flight simulators in preparation to become pilots. HITL also allows for the acquisition of knowledge regarding how a new process may affect a particular event. Utilizing HITL allows participants to interact with realistic models and attempt to perform as they would in an actual scenario. HITL simulations bring to the surface issues that would not otherwise be apparent until after a new process has been deployed. A real-world example of HITL simulation as an evaluation tool is its usage by the Federal Aviation Administration (FAA) to allow air traffic controllers to test new automation procedures by directing the activities of simulated air traffic while monitoring the effect of the newly implemented procedures. As with most processes, there is always the possibility of human error, which can only be reproduced using HITL simulation. Although much can be done to automate systems, humans typically still need to take the information provided by a system to determine the next course of action based on their judgment and experience. Intelligent systems can only go so far in certain circumstances to automate a process; only humans in the simulation can accurately judge the final design. Tabletop simulation may be useful in the very early stages of project development for the purpose of collecting data to set broad parameters, but the important decisions require human-in-the-loop simulation. HITL reflects scenarios where human input remains essential despite advances in automation. === Within the virtual simulation taxonomy === Virtual simulations inject HITL in a central role by exercising motor control skills (e.g. flying an airplane), decision making skills (e.g. committing fire control resources to action), or communication skills (e.g. as members of a C4I team). === Examples === Flight simulators Driving simulators Marine simulators Video games Supply chain management simulators Digital puppetry === Misconceptions === Although human-in-the-loop simulation can include a computer simulation in the form of a synthetic environment, computer simulation is not necessarily a form of human-in-the-loop simulation, and is often considered as human-out-of-the loop simulation. In this particular case, a computer model’s behavior is modified according to a set of initial parameters. The results of the model differ from the results stemming from a true human-in-the-loop simulation because the results can easily be replicated time and time again, by simply providing identical parameters. == Weapons == === Taxonomy === Three classifications of the degree of human control of autonomous weapon systems were laid out by Bonnie Docherty in a 2012 Human Rights Watch report. human-in-the-loop: a human must instigate the action of the weapon (in other words not fully autonomous) human-on-the-loop: a human may abort an action human-out-of-the-loop: no human action is involved === Positive human action === In discussions of autonomous weapons and nuclear command and control, the phrase positive human action has been used alongside "human-in-the-loop" to emphasize that a human operator must affirmatively authorize the use of force. Descriptions of the United States Navy's Aegis Combat System have used the phrase in characterizing a requirement for affirmative human action to initiate live firing. A survey of autonomous weapons systems described the Aegis "Auto SM" mode as one in which "the system fully develops the engagement process however engagement requires positive human action". The phrase entered United States federal law in the National Defense Authorization Act for Fiscal Year 2025, which stipulates that artificial intelligence systems not compromise "the principle of requiring positive human actions in execution of decisions by the President with respect to the employment of nuclear weapons".
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Learnable function class

In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.
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NHS COVID-19

NHS COVID-19 was a voluntary contact tracing app for monitoring the spread of the COVID-19 pandemic in England and Wales, in use from 24 September 2020 until 27 April 2023. It was available for Android and iOS smartphones, and could be used by anyone aged 16 or over. Two versions of the app were created. The first was commissioned by NHSX and developed by the Pivotal division of American software company VMware. A pilot deployment began in May 2020, but on 18 June development of the app was abandoned in favour of a second design using the Apple/Google Exposure Notification system. Scotland and Northern Ireland had separate contact tracing apps. A 2023 study estimated that in its first year of use, the app's contact tracing function prevented an estimated 1 million cases, and 9,600 deaths. == Description == The app allowed users to: See the alert level of their local authority area (in Wales) or information about restrictions (in England); to enable this, the user must enter the first half of their postcode "Check in" at places displaying an NHS QR code poster (no longer required by legislation after 26 January 2022, removed from the app the next month) Be notified when they have been in close contact with someone who has tested positive for the virus Be notified when local health protection teams determine that people with the virus had attended a business or other venue around the same time as the user Check their symptoms, and book a coronavirus test if necessary If asked to self-isolate, receive information and a daily "countdown". At first, "close contact" was defined as being within 2 metres for 15 minutes, or within 4 metres for a longer time. These time durations were reduced from 29 October 2020, to as little as three minutes when the other person is at their most infectious, i.e. soon after they begin showing symptoms. === Implementation === The Android app was coded in Kotlin, and the iOS app in Swift. The backend used Java and is deployed to Amazon Web Services using Terraform. The code of the app and back-end is open-source and available on GitHub. == Context == The app was part of the UK's test and trace programme which was chaired by Dido Harding; from 12 May 2020 Tom Riordan, chief executive of Leeds City Council, led the tracing effort. == First phase and cancellation == === Description === In March 2020, NHSX commissioned a contact tracing app to monitor the spread in the United Kingdom of the coronavirus disease 2019 (COVID-19) in the 2020 pandemic, developed by the Pivotal division of American software company VMware. The app used a centralised approach, in contrast to the Google / Apple contact tracing project. NHSX consulted ethicists and GCHQ's National Cyber Security Centre (NCSC) about the privacy aspects. The app recorded the make and model of the phone and asked the user for their postcode area. It generated a unique installation identification number and also a daily identification number. It then used Bluetooth Low Energy (BLE) to record the daily identification number of other users nearby. If a user was unwell, they could tell the app about symptoms which are characteristic of COVID-19, such as a fever and cough. These details were then passed to a central NHS server. This would assess the information and notify other users that have been in contact, giving them appropriate advice such as physical distancing. The NHS would also arrange for a swab test of the unwell user and the outcome would determine further notifications to contacts: if the test confirmed infection with COVID-19, the contacts would be asked to isolate. By June 2020, £11.8 million had been spent on the app; in 2020–21, £35 million was spent on the app. === Deployment === The first public trial of the app began on the Isle of Wight on 5 May 2020 and by 11 May it had been downloaded 55,000 times. When the first national contact tracing schemes were launched – Test, Trace, Protect in Wales on 13 May, then on 28 May NHS Test and Trace in England, and Test and Protect in Scotland – the app was not ready to be included. Replying to a question at the government's daily briefing on 8 June, Hancock was unable to give a date for rollout of the app in England, saying it would be brought in "when it's right to do so". On 17 June, Lord Bethell, junior minister for Innovation at the Department of Health and Social Care, said "we're seeking to get something going before the winter ... it isn't a priority for us at the moment". On 18 June, Health Secretary Matt Hancock announced development would switch to the Apple/Google system after admitting that Apple's restrictions on usage of Bluetooth prevented the app from working effectively. At the same press briefing Dido Harding, leader of the UK's test and trace programme, said "What we've done in really rigorously testing both our own Covid-19 app and the Google-Apple version is demonstrate that none of them are working sufficiently well enough to be actually reliable to determine whether any of us should self-isolate for two weeks [and] that's true across the world". === Concerns === The first, ultimately rejected, version of the app was subject to privacy concerns, the government backtracking on initial statements that the data collected from the app would not be shared outside the NHS. Matthew Gould, CEO of NHSX, the government department responsible for the app, said the data would be accessible to other organisations, but did not disclose which. Data collected would not necessarily be anonymised and would be held in a centralised repository. Over 150 of the UK's security and privacy experts warned the app's data could be used by 'a bad actor (state, private sector, or hacker)' to spy on citizens. Fears were discussed by the House of Commons' Human Rights Select Committee about plans for the app to record user location data. Parliament's Joint Committee on Human Rights said this version of the app should not be released without proper privacy protections. The second version of the app, released nationwide, addressed these concerns by employing a decentralised framework, the Apple/Google Exposure Notification system. Under this system, users remain pseudonymous: a person diagnosed with COVID-19 does not know which people are informed about an encounter, and contacted persons do not receive any information about the person diagnosed with COVID-19. The functionality of the app was also questioned in late April and early May 2020, as the software's use of Bluetooth required the app to be constantly running, meaning users could not use other apps or lock their device if the app was to function properly. The developers of the app were said to have found a way of working around this restriction. === Related contracts === Faculty – a company linked to Cambridge Analytica – provided research and modelling to NHSX in support of the response to the pandemic. Palantir, also linked to Cambridge Analytica, provided their data management platform. These contracts began in February and March respectively. == Second phase == As outlined on cancellation of the first app on 18 June 2020, the Department of Health and Social Care published on 30 July a brief description of the "next phase" app. Users would be able to scan a QR code at venues they visit, and later be notified if they had visited a place which was the source of a number of infections; the app would also assist with identifying symptoms and ordering a test. By using the Exposure Notification system from Apple and Google, personal data would be decentralised. Zuhlke Engineering Ltd, the UK branch of Swiss-based Zühlke Group, used 70 staff to complete the development of the app in 12 weeks. Zuhlke Engineering was awarded "Development Team of the Year" title at UK IT Industry awards in November 2021 for development of NHS COVID-19 application. === Timeline === Testing of the app by NHS volunteer responders, and selected residents of the Isle of Wight and the London Borough of Newham, began around 13 August. The app was made available to the public (aged 16 or over) in England and Wales on 24 September. An updated app released on 29 October, in part from collaboration with the Alan Turing Institute, improved the accuracy of measurements of the distance between the user's phone and other phones. At the same time, the duration threshold for determining exposure was reduced; this was expected to lead to an increase in the number of users told to self-isolate. An update to the app in April 2021, timed to coincide with easing of restrictions on hospitality businesses, was blocked by Apple and Google. It was intended that users who tested positive would be asked to share their history of visited venues, to assist in warning others, but this would have contravened assurances by Apple and Google that location data from devices would not be shared. === Statistics and effectiveness === The app was downloaded six million times on the first day it was generally availa
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Hierarchical Risk Parity

Hierarchical Risk Parity (HRP) is an advanced investment portfolio optimization framework developed in 2016 by Marcos López de Prado at Guggenheim Partners and Cornell University. HRP is a probabilistic graph-based alternative to the prevailing mean-variance optimization (MVO) framework developed by Harry Markowitz in 1952, and for which he received the Nobel Prize in economic sciences. HRP algorithms apply discrete mathematics and machine learning techniques to create diversified and robust investment portfolios that outperform MVO methods out-of-sample. HRP aims to address the limitations of traditional portfolio construction methods, particularly when dealing with highly correlated assets. Following its publication, HRP has been implemented in numerous open-source libraries, and received multiple extensions. == Key features == HRP portfolios have been proposed as a robust alternative to traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated with quadratic optimizers: numerical instability, excessive concentration in a small number of assets, and poor out-of-sample performance. HRP leverages techniques from graph theory and machine learning to construct diversified portfolios using only the information embedded in the covariance matrix. Unlike quadratic programming methods, HRP does not require the covariance matrix to be invertible. Consequently, HRP remains applicable even in cases where the covariance matrix is ill-conditioned or singular—conditions under which standard optimizers fail. Monte Carlo simulations indicate that HRP achieves lower out-of-sample variance than CLA, despite the fact that minimizing variance is the explicit optimization objective of CLA. Furthermore, HRP portfolios exhibit lower realized risk compared to those generated by traditional risk parity methodologies. Empirical backtests have demonstrated that HRP would have historically outperformed conventional portfolio construction techniques. Algorithms within the HRP framework are characterized by the following features: Machine Learning Approach: HRP employs hierarchical clustering, a machine learning technique, to group similar assets based on their correlations. This allows the algorithm to identify the underlying hierarchical structure of the portfolio, and avoid that errors spread through the entire network. Risk-Based Allocation: The algorithm allocates capital based on risk, ensuring that assets only compete with similar assets for representation in the portfolio. This approach leads to better diversification across different risk sources, while avoiding the instability associated with noisy returns estimates. Covariance Matrix Handling: Unlike traditional methods like Mean-Variance Optimization, HRP does not require inverting the covariance matrix. This makes it more stable and applicable to portfolios with a large number of assets, particularly when the covariance matrix's condition number is high. == The problem: Markowitz's Curse == Portfolio construction is perhaps the most recurrent financial problem. On a daily basis, investment managers must build portfolios that incorporate their views and forecasts on risks and returns. Despite the theoretical elegance of Markowitz's mean-variance framework, its practical implementation is hindered by several limitations that undermine the reliability of solutions derived from the Critical Line Algorithm (CLA). A principal concern is the high sensitivity of optimal portfolios to small perturbations in expected returns: even minor forecasting errors can result in significantly different allocations (Michaud, 1998). Given the inherent difficulty of producing accurate return forecasts, numerous researchers have advocated for approaches that forgo expected returns entirely and instead rely solely on the covariance structure of asset returns. This has given rise to risk-based allocation methods, among which risk parity is a widely cited example (Jurczenko, 2015). While eliminating return forecasts mitigates some instability, it does not eliminate it. Quadratic programming techniques employed in portfolio optimization require the inversion of a positive-definite covariance matrix, meaning all eigenvalues must be strictly positive. When the matrix is numerically ill-conditioned—that is, when the ratio of its largest to smallest eigenvalue (its condition number) is large—matrix inversion becomes unreliable and prone to significant numerical errors (Bailey and López de Prado, 2012). The condition number of a covariance, correlation, or any symmetric (and thus diagonalizable) matrix is defined as the absolute value of the ratio between its largest and smallest eigenvalues in modulus. The figure on the right presents the sorted eigenvalues of several correlation matrices; the condition number is represented by the ratio of the first to last eigenvalues in each sequence. A diagonal correlation matrix, which is equal to its own inverse, exhibits the minimum possible condition number. As the number of correlated (or multicollinear) assets in a portfolio increases, the condition number rises. At high levels, this leads to severe numerical instability, whereby slight modifications in any matrix entry may result in drastically different inverses. This phenomenon, often referred to as Markowitz’s curse, encapsulates the paradox wherein increased correlation among assets heightens the theoretical need for diversification, yet simultaneously increases the likelihood of unstable optimization outcomes. Consequently, the potential benefits of diversification are frequently overshadowed by estimation errors. These problems are exacerbated as the dimensionality of the covariance matrix increases. The estimation of each covariance term consumes degrees of freedom, and in general, a minimum of 1 2 N ( N + 1 ) {\displaystyle {\frac {1}{2}}N(N+1)} independent and identically distributed (IID) observations is required to estimate a non-singular covariance matrix of dimension N {\displaystyle N} . For example, constructing an invertible covariance matrix of dimension 50 necessitates at least five years of daily IID observations. However, empirical evidence suggests that the correlation structure of financial assets is highly unstable over such extended periods. These difficulties are highlighted by the observation that even naïve allocation strategies—such as equally weighted portfolios—have frequently outperformed both mean-variance and risk-based optimizations in out-of-sample tests (De Miguel et al., 2009). == The solution: Hierarchical Risk Parity == The HRP algorithm addresses Markowitz's curse in three steps: Hierarchical Clustering: Assets are grouped into clusters based on their correlations, forming a hierarchical tree structure. Quasi-Diagonalization: The correlation matrix is reordered based on the clustering results, revealing a block diagonal structure. Recursive Bisection: Weights are assigned to assets through a top-down approach, splitting the portfolio into smaller sub-portfolios and allocating capital based on inverse variance. === Step 1: Hierarchical clustering === Given a T × N {\displaystyle T\times N} matrix of asset returns X {\displaystyle X} , where each column represents a time series of returns for one of N {\displaystyle N} assets over T {\displaystyle T} time periods, a hierarchical clustering process can be used to construct a tree-based representation of asset relationships. First, we compute the N × N {\displaystyle N\times N} correlation matrix ρ = ρ i , j i , j = 1 . . . N {\displaystyle \rho ={\rho _{i,j}}\;{i,j=1\;...\;N}} , where ρ i , j = c o r r ( X i , X j ) {\displaystyle \rho _{i,j}=\mathrm {corr} (X_{i},X_{j})} . From this, a pairwise distance matrix D = d i , j {\displaystyle D={d_{i,j}}} is defined using the transformation: d i , j = 1 2 ( 1 − ρ i , j ) {\displaystyle d_{i,j}={\sqrt {{\frac {1}{2}}(1-\rho _{i,j})}}} This distance function defines a proper metric space, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Next, a secondary distance matrix D ~ = d ~ i , j {\displaystyle {\tilde {D}}={{\tilde {d}}_{i,j}}} is computed, where each entry measures the Euclidean distance between the distance profiles of two assets: d ~ i , j = ∑ n = 1 N ( d n , i − d n , j ) 2 {\displaystyle {\tilde {d}}_{i,j}={\sqrt {\sum _{n=1}^{N}(d_{n,i}-d_{n,j})^{2}}}} While d i , j {\displaystyle d_{i,j}} reflects correlation-based proximity between two assets, d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} quantifies dissimilarity across the entire system, as it depends on all pairwise distances. Hierarchical clustering proceeds by identifying the pair ( i , j ) {\displaystyle (i,j)} with the smallest value of d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} (for i ≠ j {\displaystyle i\neq j} ), and forming a new cluster u [ 1 ] = ( i , j ) {\displaystyle u[1]=(i,j)} .
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Spike-and-slab regression

Spike-and-slab regression is a type of Bayesian linear regression in which a particular hierarchical prior distribution for the regression coefficients is chosen such that only a subset of the possible regressors is retained. The technique is particularly useful when the number of possible predictors is larger than the number of observations. The idea of the spike-and-slab model was originally proposed by Mitchell & Beauchamp (1988). The approach was further significantly developed by Madigan & Raftery (1994) and George & McCulloch (1997). A recent and important contribution to this literature is Ishwaran & Rao (2005). == Model description == Suppose we have P possible predictors in some model. Vector γ has a length equal to P and consists of zeros and ones. This vector indicates whether a particular variable is included in the regression or not. If no specific prior information on initial inclusion probabilities of particular variables is available, a Bernoulli prior distribution is a common default choice. Conditional on a predictor being in the regression, we identify a prior distribution for the model coefficient, which corresponds to that variable (β). A common choice on that step is to use a normal prior with a mean equal to zero and a large variance calculated based on ( X T X ) − 1 {\displaystyle (X^{T}X)^{-1}} (where X {\displaystyle X} is a design matrix of explanatory variables of the model). A draw of γ from its prior distribution is a list of the variables included in the regression. Conditional on this set of selected variables, we take a draw from the prior distribution of the regression coefficients (if γi = 1 then βi ≠ 0 and if γi = 0 then βi = 0). βγ denotes the subset of β for which γi = 1. In the next step, we calculate a posterior probability for both inclusion and coefficients by applying a standard statistical procedure. All steps of the described algorithm are repeated thousands of times using the Markov chain Monte Carlo (MCMC) technique. As a result, we obtain a posterior distribution of γ (variable inclusion in the model), β (regression coefficient values) and the corresponding prediction of y. The model got its name (spike-and-slab) due to the shape of the two prior distributions. The "spike" is the probability of a particular coefficient in the model to be zero. The "slab" is the prior distribution for the regression coefficient values. An advantage of Bayesian variable selection techniques is that they are able to make use of prior knowledge about the model. In the absence of such knowledge, some reasonable default values can be used; to quote Scott and Varian (2013): "For the analyst who prefers simplicity at the cost of some reasonable assumptions, useful prior information can be reduced to an expected model size, an expected R2, and a sample size ν determining the weight given to the guess at R2." Some researchers suggest the following default values: R2 = 0.5, ν = 0.01, and π = 0.5 (parameter of a prior Bernoulli distribution).
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Slopaganda

Slopaganda is a portmanteau of "AI slop" and "propaganda", referring to AI-generated content designed to manipulate beliefs, emotions, and political decision-making at scale. The term is credited to Michał Klincewicz, an assistant professor in the Department of Computational Cognitive Science at Tilburg University, in 2025. == Definition == Slopaganda is distinguished from traditional propaganda by three features: scale, scope, and speed. Generative AI makes it possible to produce large volumes of content quickly and at low cost, allows for highly personalised and targeted messaging to specific sub-audiences, and leverages the hyper-connectivity of social networks to accelerate dissemination beyond what conventional media could achieve. Unlike traditional propaganda, which delivers a uniform message to all recipients, slopaganda can be micro-targeted — tailored to individuals based on estimated prior beliefs to reinforce political biases or emotional associations. The authors note that it need not aim at literal deception: much slopaganda is expressive rather than truth-apt, designed to create emotional associations rather than false factual beliefs. == Relation to AI slop == Slopaganda is a subset of AI slop — low-quality, mass-produced AI-generated content — distinguished by intent. Where AI slop may be produced indifferently for commercial or engagement-farming purposes, slopaganda is deployed with a deliberate political or ideological goal. == Notable examples == Examples discussed by the term's originators include Donald Trump's prolific use of AI in Truth Social posts and Iranian Lego-themed music videos. AI-generated videos posted by the White House mixing real military footage with clips from films and video games; and deepfake audio imitating political candidates during the 2024 US presidential campaign have also been given the label slopaganda.
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Motor theory of speech perception

The motor theory of speech perception is the hypothesis that people perceive spoken words by identifying the vocal tract gestures with which they are pronounced rather than by identifying the sound patterns that speech generates. It originally claimed that speech perception is done through a specialized module that is innate and human-specific. Though the idea of a module has been qualified in more recent versions of the theory, the idea remains that the role of the speech motor system is not only to produce speech articulations but also to detect them. The hypothesis has gained more interest outside the field of speech perception than inside. This has increased particularly since the discovery of mirror neurons that link the production and perception of motor movements, including those made by the vocal tract. The theory was initially proposed in the Haskins Laboratories in the 1950s by Alvin Liberman and Franklin S. Cooper, and developed further by Donald Shankweiler, Michael Studdert-Kennedy, Ignatius Mattingly, Carol Fowler and Douglas Whalen. == Origins and development == The hypothesis has its origins in research using pattern playback to create reading machines for the blind that would substitute sounds for orthographic letters. This led to a close examination of how spoken sounds correspond to the acoustic spectrogram of them as a sequence of auditory sounds. This found that successive consonants and vowels overlap in time with one another (a phenomenon known as coarticulation). This suggested that speech is not heard like an acoustic "alphabet" or "cipher," but as a "code" of overlapping speech gestures. === Associationist approach === Initially, the theory was associationist: infants mimic the speech they hear and that this leads to behavioristic associations between articulation and its sensory consequences. Later, this overt mimicry would be short-circuited and become speech perception. This aspect of the theory was dropped, however, with the discovery that prelinguistic infants could already detect most of the phonetic contrasts used to separate different speech sounds. === Cognitivist approach === The behavioristic approach was replaced by a cognitivist one in which there was a speech module. The module detected speech in terms of hidden distal objects rather than at the proximal or immediate level of their input. The evidence for this was the research finding that speech processing was special such as duplex perception. === Changing distal objects === Initially, speech perception was assumed to link to speech objects that were both the invariant movements of speech articulators the invariant motor commands sent to muscles to move the vocal tract articulators This was later revised to include the phonetic gestures rather than motor commands, and then the gestures intended by the speaker at a prevocal, linguistic level, rather than actual movements. === Modern revision === The "speech is special" claim has been dropped, as it was found that speech perception could occur for nonspeech sounds (for example, slamming doors for duplex perception). === Mirror neurons === The discovery of mirror neurons has led to renewed interest in the motor theory of speech perception, and the theory still has its advocates, although there are also critics. == Support == === Nonauditory gesture information === If speech is identified in terms of how it is physically made, then nonauditory information should be incorporated into speech percepts even if it is still subjectively heard as "sounds". This is, in fact, the case. The McGurk effect shows that seeing the production of a spoken syllable that differs from an auditory cue synchronized with it affects the perception of the auditory one. In other words, if someone hears "ba" but sees a video of someone pronouncing "ga", what they hear is different—some people believe they hear "da". People find it easier to hear speech in noise if they can see the speaker. People can hear syllables better when their production can be felt haptically. === Categorical perception === Using a speech synthesizer, speech sounds can be varied in place of articulation along a continuum from /bɑ/ to /dɑ/ to /ɡɑ/, or in voice onset time on a continuum from /dɑ/ to /tɑ/ (for example). When listeners are asked to discriminate between two different sounds, they perceive sounds as belonging to discrete categories, even though the sounds vary continuously. In other words, 10 sounds (with the sound on one extreme being /dɑ/ and the sound on the other extreme being /tɑ/, and the ones in the middle varying on a scale) may all be acoustically different from one another, but the listener will hear all of them as either /dɑ/ or /tɑ/. Likewise, the English consonant /d/ may vary in its acoustic details across different phonetic contexts (the /d/ in /du/ does not technically sound the same as the one in /di/, for example), but all /d/'s as perceived by a listener fall within one category (voiced alveolar plosive) and that is because "linguistic representations are abstract, canonical, phonetic segments or the gestures that underlie these segments." This suggests that humans identify speech using categorical perception, and thus that a specialized module, such as that proposed by the motor theory of speech perception, may be on the right track. === Speech imitation === If people can hear the gestures in speech, then the imitation of speech should be very fast, as in when words are repeated that are heard in headphones as in speech shadowing. People can repeat heard syllables more quickly than they would be able to produce them normally. === Speech production === Hearing speech activates vocal tract muscles, and the motor cortex and premotor cortex. The integration of auditory and visual input in speech perception also involves such areas. Disrupting the premotor cortex disrupts the perception of speech units such as plosives. The activation of the motor areas occurs in terms of the phonemic features which link with the vocal track articulators that create speech gestures. The perception of a speech sound is aided by pre-emptively stimulating the motor representation of the articulators responsible for its pronunciation . Auditory and motor cortical coupling is restricted to a specific range of neuronal firing frequency. === Perception-action meshing === Evidence exists that perception and production are generally coupled in the motor system. This is supported by the existence of mirror neurons that are activated both by seeing (or hearing) an action and when that action is carried out. Another source of evidence is that for common coding theory between the representations used for perception and action. == Criticisms == The motor theory of speech perception is not widely held in the field of speech perception, though it is more popular in other fields, such as theoretical linguistics. As three of its advocates have noted, "it has few proponents within the field of speech perception, and many authors cite it primarily to offer critical commentary".p. 361 Several critiques of it exist. === Multiple sources === Speech perception is affected by nonproduction sources of information, such as context. Individual words are hard to understand in isolation but easy when heard in sentence context. It therefore seems that speech perception uses multiple sources that are integrated together in an optimal way. === Production === The motor theory of speech perception would predict that speech motor abilities in infants predict their speech perception abilities, but in actuality it is the other way around. It would also predict that defects in speech production would impair speech perception, but they do not. However, this only affects the first and already superseded behaviorist version of the theory, where infants were supposed to learn all production-perception patterns by imitation early in childhood. This is no longer the mainstream view of motor-speech theorists. === Speech module === Several sources of evidence for a specialized speech module have failed to be supported. Duplex perception can be observed with door slams. The McGurk effect can also be achieved with nonlinguistic stimuli, such as showing someone a video of a basketball bouncing but playing the sound of a ping-pong ball bouncing. As for categorical perception, listeners can be sensitive to acoustic differences within single phonetic categories. As a result, this part of the theory has been dropped by some researchers. === Sublexical tasks === The evidence provided for the motor theory of speech perception is limited to tasks such as syllable discrimination that use speech units not full spoken words or spoken sentences. As a result, "speech perception is sometimes interpreted as referring to the perception of speech at the sublexical level. However, the ultimate goal of these studies is presumably to understand the neural processes supporting the ability to process spee
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TensorFlow Hub

TensorFlow Hub (also styled TF Hub) is an open-source machine learning library and online repository that provides TensorFlow model components, called modules. It is maintained by Google as part of the TensorFlow ecosystem and allows developers to discover, publish, and reuse pretrained models for tasks such as computer vision, natural language processing, and transfer learning. == Overview == TensorFlow Hub provides a central platform where developers and researchers can access pre-trained models and integrate them directly into TensorFlow workflows. Each module encapsulates a computation graph and its trained weights, with standardized input and output signatures. Modules can be loaded using the hub.load() function or through Keras integration via hub.KerasLayer, enabling users to perform transfer learning or feature extraction. == History == TensorFlow Hub was announced by Google in March 2018, with the first public version released shortly after. Its introduction coincided with the growing adoption of transfer learning techniques and the need for standardized model packaging. Over time, the hub expanded to include models such as the BERT family, MobileNet, EfficientNet, and the Universal Sentence Encoder. In 2020, research on “Regret selection in TensorFlow Hub” explored the problem of identifying optimal models for downstream tasks given a large repository of alternatives. == Applications == TensorFlow Hub hosts a variety of models across machine learning domains: Natural language processing: BERT, ALBERT language model, and Universal Sentence Encoder. Computer vision: ResNet, Inception (deep learning), MobileNet, EfficientNet. Speech and audio: spectrogram feature extractors and automatic speech recognition models. Multilingual embeddings: cross-lingual and sentence-level representations for machine translation and semantic similarity. Modules are widely used in education, academic research, and industry for prototyping and production deployment.
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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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AI browser

An AI browser is a web browser with integrated artificial intelligence capabilities, such as automatically summarizing web page content or answering questions about it. A more specialized type is an agentic browser, based on the concept of agentic AI, which can take actions – such as navigating webpages or filling out forms – on behalf of the user. Several agentic browsers emerged in 2025, including ChatGPT Atlas (macOS only), Comet, and Dia. As of 2025, this is a recent development in the browser market, including new entrants from OpenAI, Opera and Perplexity. The designation of 'AI browser' also includes established browsers that later added non-agentic AI features, such as Microsoft Edge with the Copilot chatbot, Google Chrome with the Gemini chatbot (for Windows desktop users in the US with their language set to English), and Firefox with multiple chatbot providers (such as ChatGPT, Claude, Copilot, Gemini, and Le Chat). AI browsers have been noted to be susceptible to prompt injection attacks. == Browser extensions and integrations == Rather than creating entirely new browsers, some AI browsing solutions integrate with existing browsers through extensions or companion applications. These tools add agentic capabilities to established browsers without requiring users to switch platforms. Examples include Composite, which functions as a cross-browser agent that works with Chrome, Edge, and other browsers to automate web-based tasks for workers. == Cloud-based implementations == Cloud-based implementations of AI browsers allow users to run automated browsing agents without local installation. These systems operate on remote servers using frameworks such as Puppeteer or Playwright. Examples include Browserbase, Browser-use and AI Browser. The AI typically parses the Document Object Model (DOM) to locate and interact with page elements, and may also analyze browser screenshots to interpret layout and structure. == Criticisms and dangers == AI browsers have been noted to be susceptible to being vulnerable to prompt injection attacks, in which the content of websites can be used to hijack the control of the browser. Multiple organisations have argued against using AI browsers due to this vulnerability. The United Kingdom national cyber security centre and Gartner consider them to be too risky for adoption by most organisations. A study by the CISPA Helmholtz Center and Saarland University concluded that this vulnerability makes them easy targets for malware, fraud, automated defamation, disinformation and biased outputs.
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Glow (app)

Glow is a fertility awareness and period-tracking app. It is part of a suite of mobile apps focused on women's reproductive health and childcare, which includes Eve by Glow (a dedicated period tracker), Glow Nurture (a pregnancy tracker), and Glow Baby (a baby development tracker). The Glow company also operates an online shop that sells several fertility-related products, including ovulation test strips, pregnancy tests, and wearable breast pumps. In 2024, Glow was reported to have approximately 25 million users across its various apps and community message boards. == History == Glow debuted in August 2013 as an iOS app. It was founded by Michael Huang and Max Levchin and launched with $6 million in Series A funding from venture capital firms Founders Fund and Andreesen Horowitz. In 2014, Glow raised an additional $17 million in Series B funding, with Formation 8 joining existing investors. In 2015, Glow launched Ruby, an app dedicated to sexual health. That year, Wired reported that the company had added features to their apps allowing men to monitor their fertility. Glow subsequently released an additional set of apps focused on pregnancy tracking and infant development. In 2016, Glow reported that it had a total of approximately 3 million users; by 2018, this had grown to 15 million. Vox described it as one of the “big two” period and fertility tracking apps and the one that had started the “boom” in the femtech space. == Application and features == Glow was initially described as a fertility application that applied data-driven methods to menstrual and ovulation tracking. Core features include cycle logging, ovulation prediction, and symptom tracking. The app also provides educational content related to reproductive health and childcare, as well as a set of online message boards that allow individuals to share experiences and seek peer support. == Privacy and legal issues == Glow has received significant media attention for its privacy and security practices. In 2016, Consumer Reports identified potential exploits in the Glow app that they claimed could have exposed private user data to hackers. Glow subsequently reported that it had fixed the vulnerabilities and told The Washington Post they had no evidence that user data had been compromised. In September 2020, the California Attorney General announced a settlement with Glow related to Consumer Reports’ findings, which included a $250,000 civil penalty. Following the US Supreme Court's 2022 Dobbs v. Jackson ruling, which legalized state-level bans on abortion, Glow (and other fertility trackers, such as Clue and Flo) came under additional scrutiny over concerns that user data on abortions could be reported to law enforcement. After this surge of media interest, a research team affiliated with the University of New South Wales conducted an investigation into the privacy practices of several popular fertility apps, including Glow. Their review of Glow was mixed, noting that they provided several privacy settings and de-identified sensitive data, but that user information could still be disclosed in the future if the app was sold. Glow rejected that claim, telling the Australian Associated Press that it "did not share" personal data. The company also cited several internal security measures it had implemented and its apps' offline data protection setting, which allows users to permanently delete their health-related data. == Reception == In 2014, Fast Company reported that 20,000 women had used Glow to conceive. Later that year, The Guardian included Glow Nurture on its list of the best iPhone apps of 2014. Media coverage often praised Glow's array of menstrual tracking options, although some reviews also noted that fertility apps are not birth control tools and cautioned against relying on them for that purpose. In 2019, Cosmopolitan singled Glow's community of users as one of its standout features.
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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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Random feature

Random features (RF) are a technique used in machine learning to approximate kernel methods, introduced by Ali Rahimi and Ben Recht in their 2007 paper "Random Features for Large-Scale Kernel Machines", and extended by. RF uses a Monte Carlo approximation to kernel functions by randomly sampled feature maps. It is used for datasets that are too large for traditional kernel methods like support vector machine, kernel ridge regression, and gaussian process. == Mathematics == === Kernel method === Given a feature map ϕ : R d → V {\textstyle \phi :\mathbb {R} ^{d}\to V} , where V {\textstyle V} is a Hilbert space (more specifically, a reproducing kernel Hilbert space), the kernel trick replaces inner products in feature space ⟨ ϕ ( x i ) , ϕ ( x j ) ⟩ V {\displaystyle \langle \phi (x_{i}),\phi (x_{j})\rangle _{V}} by a kernel function k ( x i , x j ) : R d × R d → R {\displaystyle k(x_{i},x_{j}):\mathbb {R} ^{d}\times \mathbb {R} ^{d}\to \mathbb {R} } Kernel methods replaces linear operations in high-dimensional space by operations on the kernel matrix: K X := [ k ( x i , x j ) ] i , j ∈ 1 : N {\displaystyle K_{X}:=[k(x_{i},x_{j})]_{i,j\in 1:N}} where N {\textstyle N} is the number of data points. === Random kernel method === The problem with kernel methods is that the kernel matrix K X {\textstyle K_{X}} has size N × N {\textstyle N\times N} . This becomes computationally infeasible when N {\textstyle N} reaches the order of a million. The random kernel method replaces the kernel function k {\textstyle k} by an inner product in low-dimensional feature space R D {\textstyle \mathbb {R} ^{D}} : k ( x , y ) ≈ ⟨ z ( x ) , z ( y ) ⟩ {\displaystyle k(x,y)\approx \langle z(x),z(y)\rangle } where z {\textstyle z} is a randomly sampled feature map z : R d → R D {\textstyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{D}} . This converts kernel linear regression into linear regression in feature space, kernel SVM into SVM in feature space, etc. Since we have K X ≈ Z X T Z X {\displaystyle K_{X}\approx Z_{X}^{T}Z_{X}} where Z X = [ z ( x 1 ) , … , z ( x N ) ] {\displaystyle Z_{X}=[z(x_{1}),\dots ,z(x_{N})]} , these methods no longer involve matrices of size O ( N 2 ) {\textstyle O(N^{2})} , but only random feature matrices of size O ( D N ) {\textstyle O(DN)} . == Random Fourier feature == === Radial basis function kernel === The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} is defined as k ( x i , x j ) = exp ⁡ ( − ‖ x i − x j ‖ 2 2 σ 2 ) {\displaystyle k(x_{i},x_{j})=\exp \left(-{\frac {\|x_{i}-x_{j}\|^{2}}{2\sigma ^{2}}}\right)} where ‖ x i − x j ‖ 2 {\displaystyle \|x_{i}-x_{j}\|^{2}} is the squared Euclidean distance and σ {\displaystyle \sigma } is a free parameter defining the shape of the kernel. It can be approximated by a random Fourier feature map z : R d → R 2 D {\displaystyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{2D}} : z ( x ) := 1 D [ cos ⁡ ⟨ ω 1 , x ⟩ , sin ⁡ ⟨ ω 1 , x ⟩ , … , cos ⁡ ⟨ ω D , x ⟩ , sin ⁡ ⟨ ω D , x ⟩ ] T {\displaystyle z(x):={\frac {1}{\sqrt {D}}}[\cos \langle \omega _{1},x\rangle ,\sin \langle \omega _{1},x\rangle ,\ldots ,\cos \langle \omega _{D},x\rangle ,\sin \langle \omega _{D},x\rangle ]^{T}} where ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are IID samples from the multidimensional normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Since cos , sin {\displaystyle \cos ,\sin } are bounded, there is a stronger convergence guarantee by Hoeffding's inequality. === Random Fourier features === By Bochner's theorem, the above construction can be generalized to arbitrary positive definite shift-invariant kernel k ( x , y ) = k ( x − y ) {\displaystyle k(x,y)=k(x-y)} . Define its Fourier transform p ( ω ) = 1 2 π ∫ R d e − j ⟨ ω , Δ ⟩ k ( Δ ) d Δ {\displaystyle p(\omega )={\frac {1}{2\pi }}\int _{\mathbb {R} ^{d}}e^{-j\langle \omega ,\Delta \rangle }k(\Delta )d\Delta } then ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are sampled IID from the probability distribution with probability density p {\displaystyle p} . This applies for other kernels like the Laplace kernel and the Cauchy kernel. === Neural network interpretation === Given a random Fourier feature map z {\displaystyle z} , training the feature on a dataset by featurized linear regression is equivalent to fitting complex parameters θ 1 , … , θ D ∈ C {\displaystyle \theta _{1},\dots ,\theta _{D}\in \mathbb {C} } such that f θ ( x ) = R e ( ∑ k θ k e i ⟨ ω k , x ⟩ ) {\displaystyle f_{\theta }(x)=\mathrm {Re} \left(\sum _{k}\theta _{k}e^{i\langle \omega _{k},x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and the parameters in the first layer frozen. In the overparameterized case, when 2 D ≥ N {\displaystyle 2D\geq N} , the network linearly interpolates the dataset { ( x i , y i ) } i ∈ 1 : N {\displaystyle \{(x_{i},y_{i})\}_{i\in 1:N}} , and the network parameters is the least-norm solution: θ ^ = arg ⁡ min θ ∈ C D , f θ ( x k ) = y k ∀ k ∈ 1 : N ‖ θ ‖ {\displaystyle {\hat {\theta }}=\arg \min _{\theta \in \mathbb {C} ^{D},f_{\theta }(x_{k})=y_{k}\forall k\in 1:N}\|\theta \|} At the limit of D → ∞ {\displaystyle D\to \infty } , the L2 norm ‖ θ ^ ‖ → ‖ f K ‖ H {\displaystyle \|{\hat {\theta }}\|\to \|f_{K}\|_{H}} where f K {\displaystyle f_{K}} is the interpolating function obtained by the kernel regression with the original kernel, and ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{H}} is the norm in the reproducing kernel Hilbert space for the kernel. == Other examples == === Random binning features === A random binning features map partitions the input space using randomly shifted grids at randomly chosen resolutions and assigns to an input point a binary bit string that corresponds to the bins in which it falls. The grids are constructed so that the probability that two points x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} are assigned to the same bin is proportional to K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . The inner product between a pair of transformed points is proportional to the number of times the two points are binned together, and is therefore an unbiased estimate of K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . Since this mapping is not smooth and uses the proximity between input points, Random Binning Features works well for approximating kernels that depend only on the L 1 {\displaystyle L_{1}} distance between datapoints. === Orthogonal random features === Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. == Historical context == In NIPS 2006, deep learning had just become competitive with linear models like PCA and linear SVMs for large datasets, and people speculated about whether it could compete with kernel SVMs. However, there was no way to train kernel SVM on large datasets. The two authors developed the random feature method to train those. It was then found that the O ( 1 / D ) {\displaystyle O(1/D)} variance bound did not match practice: the variance bound predicts that approximation to within 0.01 {\displaystyle 0.01} requires D ∼ 10 4 {\displaystyle D\sim 10^{4}} , but in practice required only ∼ 10 2 {\displaystyle \sim 10^{2}} . Attempting to discover what caused this led to the subsequent two papers.
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