The P4 metric (also known as FS or Symmetric F ) enables performance evaluation of a binary classifier. The P4 metric is calculated from precision, recall, specificity, and NPV (negative predictive value). The definition of the P4 metric is similar to that of the F1 metric, however the P4 metric definition addresses criticisms leveled against the definition of the F1 metric. The definition of the P4 metric may, therefore, be understood as an extension of the F1 metric. Like the other known metrics, the P4 metric is a function of: TP (true positives), TN (true negatives), FP (false positives), FN (false negatives). == Justification == The key concept of the P4 metric is to leverage the four key conditional probabilities: P ( + ∣ C + ) {\displaystyle P(+\mid C{+})} — the probability that the sample is positive, provided the classifier result was positive. P ( C + ∣ + ) {\displaystyle P(C{+}\mid +)} — the probability that the classifier result will be positive, provided the sample is positive. P ( C − ∣ − ) {\displaystyle P(C{-}\mid -)} — the probability that the classifier result will be negative, provided the sample is negative. P ( − ∣ C − ) {\displaystyle P(-\mid C{-})} — the probability the sample is negative, provided the classifier result was negative. The main assumption behind this metric is that all the probabilities mentioned above are close to 1 for a properly designed binary classifier. Indeed, P 4 = 1 {\displaystyle \mathrm {P} _{4}=1} if, and only if, all of the probabilities above are equal to 1. Another important feature is that P 4 {\displaystyle \mathrm {P} _{4}} tends to zero any of the above probabilities tend to zero. == Definition == P4 is defined as a harmonic mean of four key conditional probabilities: P 4 = 4 1 P ( + ∣ C + ) + 1 P ( C + ∣ + ) + 1 P ( C − ∣ − ) + 1 P ( − ∣ C − ) = 4 1 p r e c i s i o n + 1 r e c a l l + 1 s p e c i f i c i t y + 1 N P V . {\displaystyle \mathrm {P} _{4}={\frac {4}{{\frac {1}{P(+\mid C{+})}}+{\frac {1}{P(C{+}\mid +)}}+{\frac {1}{P(C{-}\mid -)}}+{\frac {1}{P(-\mid C{-})}}}}={\frac {4}{{\frac {1}{\mathit {precision}}}+{\frac {1}{\mathit {recall}}}+{\frac {1}{\mathit {specificity}}}+{\frac {1}{\mathit {NPV}}}}}.} In terms of TP,TN,FP,FN it can be calculated as follows: P 4 = 4 ⋅ T P ⋅ T N 4 ⋅ T P ⋅ T N + ( T P + T N ) ⋅ ( F P + F N ) . {\displaystyle \mathrm {P} _{4}={\frac {4\cdot \mathrm {TP} \cdot \mathrm {TN} }{4\cdot \mathrm {TP} \cdot \mathrm {TN} +(\mathrm {TP} +\mathrm {TN} )\cdot (\mathrm {FP} +\mathrm {FN} )}}.} == Evaluation of the binary classifier performance == Evaluating the performance of binary classifiers is a multidisciplinary concept. It spans from the evaluation of medical tests, psychiatric tests to machine learning classifiers from a variety of fields. Thus, many of the metrics in use exist under several names, some defined independently. == Properties of P4 metric == Symmetry — contrasting to the F1 metric, P4 is symmetrical. It means - it does not change its value when dataset labeling is changed - positives named negatives and negatives named positives. Range: P 4 ∈ [ 0 , 1 ] {\displaystyle \mathrm {P} _{4}\in [0,1]} . Achieving P 4 ≈ 1 {\displaystyle \mathrm {P} _{4}\approx 1} requires all the key four conditional probabilities being close to 1. For P 4 ≈ 0 {\displaystyle \mathrm {P} _{4}\approx 0} it is sufficient that one of the key four conditional probabilities is close to 0. == Examples, comparing with the other metrics == Dependency table for selected metrics ("true" means depends, "false" - does not depend): Metrics that do not depend on a given probability are prone to misrepresentation when the probability approaches 0. === Example 1: Rare disease detection test === Let us consider a medical test used to detect a rare disease. Suppose a population size of 100000 and 0.05% of the population is infected. Further suppose the following test performance: 95% of all positive individuals are classified correctly (TPR=0.95) and 95% of all negative individuals are classified correctly (TNR=0.95). In such a case, due to high population imbalance and in spite of having high test accuracy (0.95), the probability that an individual who has been classified as positive is in fact positive is very low: P ( + ∣ C + ) = 0.0095. {\displaystyle P(+\mid C{+})=0.0095.} We can observe how this low probability is reflected in some of the metrics: P 4 = 0.0370 {\displaystyle \mathrm {P} _{4}=0.0370} , F 1 = 0.0188 {\displaystyle \mathrm {F} _{1}=0.0188} , J = 0.9100 {\displaystyle \mathrm {J} =\mathbf {0.9100} } (Informedness / Youden index), M K = 0.0095 {\displaystyle \mathrm {MK} =0.0095} (Markedness). === Example 2: Image recognition — cats vs dogs === Consider the problem of training a neural network based image classifier with only two types of images: those containing dogs (labeled as 0) and those containing cats (labeled as 1). Thus, the goal is to distinguish between the cats and dogs. Suppose that the classifier overpredicts in favour of cats ("positive" samples): 99.99% of cats are classified correctly and only 1% of dogs are classified correctly. Further, suppose that the image dataset consists of 100000 images, 90% of which are pictures of cats and 10% are pictures of dogs. In this situation, the probability that the picture containing dog will be classified correctly is pretty low: P ( C − | − ) = 0.01. {\displaystyle P(C-|-)=0.01.} Not all metrics are notice this low probability: P 4 = 0.0388 {\displaystyle \mathrm {P} _{4}=0.0388} , F 1 = 0.9478 {\displaystyle \mathrm {F} _{1}=\mathbf {0.9478} } , J = 0.0099 {\displaystyle \mathrm {J} =0.0099} (Informedness / Youden index), M K = 0.8183 {\displaystyle \mathrm {MK} =\mathbf {0.8183} } (Markedness).
Dave's Redistricting
Dave's Redistricting App (DRA) is an online web app originally created by Dave Bradlee that allows anyone to simulate redistricting a U.S. state's congressional and legislative districts. == Purpose == According to Bradlee, the software was designed to "put power in people's hands," and so that they "can see how the process works, so it's a little less mysterious than it was 10 years ago." Bradlee has noticed that many citizens are taking this process seriously and using his app to create legitimate redistricting maps that could be put in place. Some websites have called Bradlee the pioneer and cause of the rise of do-it-yourself redistricting. States such as Montana in 2021 allowed the general population to use it to submit redistricting proposals following the 2020 United States Census. Dave's Redistricting has frequently been mentioned as a resource that can be used to combat gerrymandering, given that the public has free access to it. Political science firms such as FiveThirtyEight have used the website to draw examples of gerrymandered districts, including on their famous Atlas of Redistricting. Dave Bradlee built the first generation of DRA. DRA 2020 is built by a small team of volunteers—Dave Bradlee, Terry Crowley, Alec Ramsay, and David Rinn—all with a shared passion for technology & democracy and all Microsoft veterans. Their mission is to empower civic organizations and citizen activists to advocate for fair congressional and legislative districts and increased transparency in the redistricting process. == Functions == Users can redraw the congressional and state legislative districts for all 50 states, the District of Columbia, and Puerto Rico using a variety of census and election datasets including Cook PVI. Maps can be optimized for different criteria. DRA 2020 added several major features to the first generation app: Sharing & collaborative editing of maps, like Google Docs Multiple statewide elections for all 50 states including the ability to import your own data Comprehensive analytics for evaluating and comparing maps Custom overlays, and Block-level editing DRA remains free to use. == Versions == 2.2: This uses Bing Maps, an outdated software that projects the districts of a single state onto a map of the United States. 2.5: After Bing Maps announced that it would no longer be updating for the foreseen future, the U.S. Map feature was removed. DRA 2020: At the end of 2018, a beta version of 2020 was released. This version that did not require Microsoft Silverlight and could be used in any web browser. DRA 2020 has been under continuous development since and is built using React (JavaScript library), Mapbox, OpenStreetMap, TypeScript, Node.js, Amazon Web Services, as well as many open source components, tools, and icons.
Mark Heimann
Mark A. Heimann is an American chess grandmaster and machine learning researcher. == Chess career == Heimann began playing chess at the age of 5 after his father bought him and his twin brother Alexander a chess set. He then won several national grade-level championships as well as the Pennsylvania and Ohio state championships in middle school and high school. In October 2007, he was ranked as the national #2 under-14 player, only behind future grandmaster Marc Tyler Arnold. In the February 2008 national rankings, he moved up to being the top-ranked under-14 player. In December 2012, he played for Washington University St. Louis' "A" team in the Pan-American Intercollegiate Chess Championships, where he was the second-most successful player, recording 4 wins, 1 draw, and 1 loss. The university's team also won the Division II championship title. In three tournaments between September and December 2022, Heimann earned three international master title norms, earning the international master title at the age of 29. In November 2024, he scored a GM norm at the U.S. Masters Chess Championship. He finished the event in joint-6th place. The following week, at the Saint Louis Masters tournament, he earned his final grandmaster norm and crossed 2500 in live rating, achieving the Grandmaster title. It was formally awarded to him in April 2025. == Research career == He obtained a bachelor's degree from Washington University in St. Louis in the School of Arts and Sciences and got his PhD from the University of Michigan. He is a machine learning researcher at Lawrence Livermore National Laboratory. == Personal life == Outside of chess and research, he also plays several instruments and is a competitive powerlifter.
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Zoubin Ghahramani
Zoubin Ghahramani FRS (Persian: زوبین قهرمانی; born 8 February 1970) is a British-Iranian machine learning and AI researcher, Vice President of Research at Google DeepMind and Professor of Information Engineering at the University of Cambridge. He has been a Fellow of St John's College, Cambridge since 2009. He held appointments at University College London from 1998 to 2005 and was Associate Research Professor in the Machine Learning Department at Carnegie Mellon University from 2003 to 2012. He was the Chief Scientist of Uber from 2016 until 2020. He joined Google Brain in 2020 as Senior Research Director, becoming a VP of Research in 2021, and heading Google Brain until its merger with DeepMind to form Google DeepMind. He was a founding Cambridge Liaison Director of the Alan Turing Institute and also founding Deputy Director of the Leverhulme Centre for the Future of Intelligence. Ghahramani contributed to the Royal Society's Machine Learning Report in 2017 and led the UK's Future of Compute Review, in 2023. == Education == Ghahramani was educated at the American School of Madrid in Spain and the University of Pennsylvania where he was awarded a dual degree in Cognitive Science and Computer Science in 1990. He obtained his Ph.D. in Cognitive Neuroscience from the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology, supervised by Michael I. Jordan and Tomaso Poggio. == Research and career == Following his Ph.D., Ghahramani moved to the University of Toronto in 1995 as a Postdoctoral Fellow in the Artificial Intelligence Lab, working with Geoffrey Hinton. From 1998 to 2005, he was a member of the faculty at the Gatsby Computational Neuroscience Unit, University College London. Ghahramani has made significant contributions in the areas of Bayesian machine learning (particularly variational methods for approximate Bayesian inference), as well as graphical models and computational neuroscience. His current research focuses on nonparametric Bayesian modelling and statistical machine learning. He has also worked on artificial intelligence, information retrieval, bioinformatics and statistics which provide the mathematical foundations for handling uncertainty, making decisions, and designing learning systems. He has published over 300 papers, receiving over 100,000 citations (an h-index of 132). He co-founded Geometric Intelligence in 2014, with Gary Marcus, Doug Bemis, and Ken Stanley, which was acquired by Uber in 2016. Afterwards, he transferred to Uber's AI Labs in 2016, and later became VP of AI and Chief Scientist at Uber. In 2020 he joined Google and became VP of Research and head of Google Brain in 2021 until its merger with DeepMind in April 2023. == Awards and honors == Ghahramani was elected Fellow of the Royal Society (FRS) in 2015. His certificate of election reads: Zoubin Ghahramani is a world leader in the field of machine learning, significantly advancing the state-of-the-art in algorithms that can learn from data. He is known in particular for fundamental contributions to probabilistic modeling and Bayesian nonparametric approaches to machine learning systems, and to the development of approximate variational inference algorithms for scalable learning. He is one of the pioneers of semi-supervised learning methods, active learning algorithms, and sparse Gaussian processes. His development of novel infinite dimensional nonparametric models, such as the infinite latent feature model, has been highly influential.He was awarded the Royal Society Milner Award in 2021 in recognition of 'his fundamental contributions to probabilistic machine learning'.
Prequel (mobile application)
Prequel, Inc. is an American technology company and mobile app developer known for developing the Prequel mobile application, which enables editing photos and videos with filters and effects generated using artificial intelligence. Prequel was founded in 2018 by Serge Aliseenko and Timur Khabirov, who currently serves as the company's CEO. It is headquartered in New York City. As of August 2022, it had been downloaded more than 100 million times. == History == In 2016, entrepreneur Timur Khabirov and investor Serge Aliseenko registered a US corporation named AIAR Labs Inc, which was developing AR solutions as an outsourced contractor. Of several proprietary products, Prequel was selected for beta-testing as a product focused on editing photos and videos. In 2018, Prequel was released on the Apple App Store. The launch cost $3 million USD, financed with the founders’ personal funds. The first release included approximately 10 filters for photos and the same amount of effects that augmented images with rose petals, rain and snow, VHS and film reel simulations, glitch, grain, sun puddles, and lomography. By June 2020, the app had also been released for Android. In 2021, Prequel founders Timur Khabirov and Serge Aliseenko launched a venture studio for startups working with artificial, computer vision, and AR-based visual art. In December 2022, Prequel reached the number 14 slot on the global rankings for Apple App Store’s Top Charts and the number 5 slot on the App Store’s U.S. charts. In March 2023, Prequel launched a new app called Artique, which is an AI-powered image editing app for businesses. Artique provides advertising and marketing graphic design using ready-made templates that users can customize, while giving suggestions and visual cues through artificial intelligence. Prequel was also one of the companies participating in discussions about artificial intelligence at SXSW 2023. == Features == Prequel describes its app as an "Aesthetic Pic Editor. The app uses artificial intelligence to create and edit content. Prequel can be used to touch up faces on images and videos and can also tie various decorative elements to certain points on the human body and face. Prequel filters include the "Cartoon" filter, which converts selfies into cartoon-style pictures. Other filters include Kidcore, Dust, Grain, Fisheye, Retro Style, Miami, Disco, and VHS-style filters, as well as the ability to create Renaissance-style pictures. Prequel also gives users the ability to apply color correction tools and to make moving images with 3D effects out of 2D images. Prequel allows users to take photos and videos directly through the app and apply filters and effects in real time. The app also comes with manual editing options for photos, such as adjusting the brightness and/or exposure and cropping photos, as well as an option to automatically apply adjustments. The Prequel app uses the Core ML, MNN, and TFLight frameworks to work with its neural networks. Some AI solutions are launched server-side, and some on the user's mobile device. A resulting photo or video edited with the app is called "a prequel." The app daily generates over 2 million such prequels, which are published by users in Instagram, TikTok, and other social media. As of 2022, the app has more than 800 filters and effects, along with video templates and support for GIFs and stickers. Prequel is free-to-use, but has a premium version that gives users access to more effects, filters, and beauty tools. Since its launch in 2018, Prequel has been downloaded more than 100 million times.
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