Rada Mihalcea is the Janice M. Jenkins Collegiate Professor of Computer Science and Engineering at the University of Michigan. She has made significant contributions to natural language processing, multimodal processing, computational social science, and AI for Social Good. With Paul Tarau, she invented the TextRank Algorithm, which is a classic algorithm widely used for text summarization. == Career == Mihalcea has a Ph.D. in Computer Science and Engineering from Southern Methodist University (2001) and a Ph.D. in Linguistics, Oxford University (2010). In 2017 she was named Director of the Artificial Intelligence Laboratory at University of Michigan, Computer Science and Engineering. In 2018, Mihalcea was elected as vice president for the Association for Computational Linguistics (ACL). In 2021, she was elected the president for ACL. She is a professor of Computer Science and Engineering at the University of Michigan, where she also leads the Language and Information Technologies (LIT) Lab. Before joining UofM, she was a professor at North Texas University between 2002-2013. A prolific researcher, Mihalcea has authored or coauthored over 500 articles since 1998 on topics ranging from semantic analysis of text to lie detection. Her work has been cited over 50,000 times on Google Scholar, which made her one of the most cited scholars in Multimodal Interaction and Computational Social Science. In 2008, Mihalcea received the Presidential Early Career Award for Scientists and Engineers (PECASE) She is an ACM Fellow (since 2019), AAAI Fellow (since 2021), and ACL Fellow (since 2025). Mihalcea is an outspoken promoter of diversity in computer science. She also supports an expansion of the traditional analysis of educational success, which tends to focus on academic behaviour, to include student life, personality and background outside of the classroom. Mihalcea leads Girls Encoded, a program designed to develop the pipeline of women in computer science as well as to retain the women who have entered into the program. == Awards == Elected to American Academy of Arts & Sciences, 2026 ACL Fellow, 2025 "for significant contributions to graph-based language processing, computational social science, and the advancement of NLP for social good." AAAI Fellow, 2021 "for significant contributions to natural language processing and computational social science". ACM Fellow, 2019 "for contributions to natural language processing, with innovations in data-driven and graph-based language processing". Sarah Goddard Power Award, 2019. Carol Hollenshead Award, 2018. Presidential Early Career Award for Scientists and Engineers (PECASE), 2009. Awarded by President Barack Obama. == Research == Mihalcea is known for her research in natural language processing, multimodal processing, computational social sciences. In a collaboration she leads at the University of Michigan, Mihalcea has created software that can detect human lying. In a study of video clips of high profile court cases, a computer was more accurate at detecting deception than human judges. Mihalcea's lie-detection software uses machine learning techniques to analyze video clips of actual trials. In her 2015 study, the team used clips from The Innocence Project, a national organization that works to reexamine cases where individuals were tried without the benefit of DNA testing with the aim of exonerating wrongfully convicted individuals. After identifying common human gestures, they transcribed the audio from the video clips of trials and analyzed how often subjects labeled deceptive used various words and phrases. The system was 75% accurate in identifying which subjects were deceptive among 120 videos. That puts Mihalcea's algorithm on par with the most commonly accepted form of lie detection, polygraph tests, which are roughly 85 percent accurate when testing guilty people and 56 percent accurate when testing the innocent. She notes there are still improvements to be made — in particular to account for cultural and demographic differences. A possibly unique advantage of Mihalcea's study was the real world, high stakes nature of the footage analyzed in the study. In laboratory experiments, it is difficult to create a setting that motivates people to truly lie. In 2018, Mihalcea and her collaborators worked on an algorithm-based system that identifies linguistic cues in fake news stories. It successfully found fakes up to 76% of the time, compared to a human success rate of 70%. == Publications == === Books === Rada Mihalcea and Dragomir Radev, Graph-based Natural Language Processing and Information Retrieval, Cambridge U. Press, 2011. Gabe Ignatow and Rada Mihalcea, Text Mining: A Guidebook for the Social Sciences, SAGE, 2016. Gabe Ignatow and Rada Mihalcea, An Introduction to Text Mining: Research Design, Data Collection, and Analysis, SAGE, 2017. === Journals and conferences === Textrank: Bringing order into text. R. Mihalcea, P. Tarau. Proceedings of the 2004 conference on empirical methods in natural language processing. 2004 Corpus-based and knowledge-based measures of text semantic similarity. R. Mihalcea, C. Corley, C. Strapparava. AAAI 6, 775-780. 2006 Wikify!: linking documents to encyclopedic knowledge. R. Mihalcea, A. Csomai. Proceedings of the sixteenth ACM conference on Conference on information and information management. 2007 Learning to identify emotions in text. C. Strapparava, R. Mihalcea. Proceedings of the 2008 ACM symposium on Applied computing, 1556-1560. 2008 Semeval-2007 task 14: Affective text. C. Strapparava, R. Mihalcea. Proceedings of the Fourth International Workshop on Semantic Evaluations. 2007 Learning multilingual subjective language via cross-lingual projections. R. Mihalcea, C. Banea, J. Wiebe. Proceedings of the 45th annual meeting of the association of computational linguistics. 2007 Graph-based ranking algorithms for sentence extraction, applied to text summarization. R. Mihalcea. Proceedings of the ACL Interactive Poster and Demonstration Sessions. 2004 Falcon: Boosting knowledge for answer engines. S. Harabagiu, D. Moldovan, M. Pasca, R. Mihalcea, M. Surdeanu, Razvan Bunescu, Roxana Girju, Vasile Rus, Paul Morarescu. TREC 9, 479-488. 2000 Measuring the semantic similarity of texts. C. Corley, R. Mihalcea. Proceedings of the ACL workshop on empirical modeling of semantic equivalence and entailment. 2005 R Mihalcea (2007). "Using wikipedia for automatic word-sense disambiguation". Human Language Technologies 2007: The Conference of the North American Chapter of the Association for Computational Linguistics; Proceedings of the Main Conference. CiteSeerX 10.1.1.74.3561. - see also Word-sense disambiguation Unsupervised graph-based word sense disambiguation using measures of word semantic similarity. R. Sinha, R. Mihalcea. International Conference on Semantic Computing (ICSC 2007), 363-369. 2007 == Personal life == Mihalcea was born in Cluj-Napoca, Romania, where she attended the Technical University of Cluj-Napoca. She can speak Romanian, English, Italian, and French. Mihalcea has two children - Zara (b. 2009) and Caius (b. 2013). They were both born in Dallas, Texas. She is married to an associate professor of engineering at the University of Michigan–Flint - Mihai Burzo. They met while they were both completing Ph.D.s at Southern Methodist University in 2001 and have often collaborated on research, such as the 2015 study on lie detection.
INDECT
INDECT is a research project in the area of intelligent security systems performed by several European universities since 2009 and funded by the European Union. The purpose of the project is to involve European scientists and researchers in the development of solutions to and tools for automatic threat detection through e.g. processing of CCTV camera data streams, standardization of video sequence quality for user applications, threat detection in computer networks as well as data and privacy protection. The area of research, applied methods, and techniques are described in the public deliverables which are available to the public on the project's website. Practically, all information related to the research is public. Only documents that comprise information related to financial data or information that could negatively influence the competitiveness and law enforcement capabilities of parties involved in the project are not published. This follows regulations and practices applied in EU research projects. == Application and target users == The main end-user of INDECT solutions are police forces and security services. The principle of operation of the project is detecting threats and identifying sources of threats, without monitoring and searching for particular citizens or groups of citizens. Then, the system operator (i.e. police officer) decides whether an intervention of services responsible for public security are required or not. Further investigation eventually leading to persons related to threats is performed, preserving the presumption of innocence, based on existing procedures already used by police services and prosecutors. As it can be found in the project deliverables, INDECT does not involve storage of personal data (such as names, addresses, identity document numbers, etc.). A similar, behavior-based surveillance program was SAMURAI (Suspicious and Abnormal behavior Monitoring Using a netwoRk of cAmeras & sensors for sItuation awareness enhancement). == Expected results == The main expected results of the INDECT project are: Trial of intelligent analysis of video and audio data for threat detection in urban environments Creation of tools and technology for privacy and data protection during storage and transmission of information using quantum cryptography and new methods of digital watermarking Performing computer-aided detection of threats and targeted crimes in Internet resources with privacy-protecting solutions Construction of a search engine for rapid semantic search based on watermarking of content related to child pornography and human organ trafficking Implementation of a distributed computer system that is capable of effective intelligent processing == Controversy == Some media and other sources accuse INDECT of privacy abuse, collecting personal data, and keeping information from the public. Consequently, these issues have been commented and discussed by some Members of the European Parliament. As seen in the project's documentation, INDECT does not involve mobile phone tracking or call interception. The rumors about testing INDECT during 2012 UEFA European Football Championship also turned out to be false. The mid-term review of the Seventh Framework Programme to the European Parliament strongly urges the European Commission to immediately make all documents available and to define a clear and strict mandate for the research goal, the application, and the end users of INDECT, and stresses a thorough investigation of the possible impact on fundamental rights. Nevertheless, according to Mr. Paweł Kowal, MEP, the project had the ethical review on 15 March 2011 in Brussels with the participation of ethics experts from Austria, France, Netherlands, Germany and Great Britain.
Outline of the Python programming language
The following outline is provided as an overview of and topical guide to Python: Python is a general-purpose, interpreted, object-oriented, functional, multi-paradigm, and dynamically typed programming language known for its emphasis on code readability and broad standard library. Python was created by Guido van Rossum and first released in 1991. It emphasizes code readability and developer productivity. == What type of language is Python? == Programming language — artificial language designed to communicate instructions to a machine. Object-oriented programming — built primarily around objects and classes. Functional programming — supports functions as first-class objects. Scripting language — often used for automation and small programs. General-purpose programming language — designed for a wide variety of application domains. Dynamically typed — type checking occurs at runtime. Interpreted language — code is executed by an interpreter. Multi-paradigm — supports procedural, object-oriented, and functional programming. == History of Python == ABC (programming language) – precursor to Python Python was started by Guido van Rossum in 1989 and first released in 1991. Python 2 — major version released in 2000, officially retired in 2020. Python 3 — released in 2008 == General Python concepts == == Issues and limitations == Performance — generally slower than many compiled languages such as C or Java can be mitigated by C extensions or JIT compilers (PyPy). Global interpreter lock — limits parallel CPU-bound threads in CPython Memory consumption — high memory use compared to some lower-level languages Version compatibility — Python 2 vs Python 3 differences caused migration issues == Python implementations == CPython — reference implementation in C IronPython — Python for .NET Jython — Python for the JVM MicroPython — Python for microcontrollers and embedded systems Nuitka — compiler that packages user code with CPython into a static binary PyPy — JIT-compiled Python interpreter for speed PythonAnywhere — freemium hosted Python installation that runs in the browser Stackless Python — Python with lightweight concurrency features == Python toolchain == List of Python software Comparison of Python IDEs Comparison of server-side web frameworks for Python List of Python frameworks List of Python libraries List of unit testing frameworks for Python Python Package Index == Notable projects using Python == YouTube (backend) Instagram (backend) Dropbox Reddit OpenStack Blender (scripting and plugins) SageMath NumPy Pandas TensorFlow == Python development communities == ActiveState — commercial Python distributions and support Anaconda, Inc. — Python data science ecosystem GitHub Python Software Foundation Python Package Index (PyPI) — third-party software repository for Python == Example source code == Articles with example Python code == Python publications == === Books about Python === Automate the Boring Stuff with Python – Creative Commons Python book Alex Martelli — Python in a Nutshell and Python Cookbook Mark Pilgrim – Dive into Python Naomi Ceder — The Quick Python Book Wes McKinney — Python for Data Analysis Zed Shaw – Learn Python the Hard Way === Textbooks === Core Python Programming == Python programmers == == Python conferences == EuroPython – annual Python conference in Europe PyCon – the largest annual convention for the Python community PyData – conference series focused on data analysis, machine learning, and scientific computing with Python SciPy Conferences – focused on the use of Python in scientific computing and research DjangoCon – a conference dedicated to the Django web framework PyOhio – a free regional Python conference held in Ohio == Python learning resources == Codecademy – interactive Python programming lessons GeeksforGeeks – tutorials, coding examples, and interactive programming for Python concepts and data structures. Kaggle – free Python courses focused on data science and machine learning. Python.org Tutorial – the official Python tutorial from the Python Software Foundation. Real Python – articles, tutorials, and courses for Python developers. W3Schools – beginner-friendly Python tutorials. Wikibooks Python Programming – free open-content textbook on Python. === Competitive programming === Codeforces – an online platform for programming contests that supports Python submissions Codewars – gamified coding challenges supporting Python HackerRank – competitive programming and interview preparation site with Python challenges Kaggle – while focused on data science competitions, it also includes Python-based problem solving. LeetCode – online judge and problem-solving platform where Python is widely used
Cloudlet
A cloudlet is a mobility-enhanced small-scale cloud datacenter that is located at the edge of the Internet. The main purpose of the cloudlet is supporting resource-intensive and interactive mobile applications by providing powerful computing resources to mobile devices with lower latency. It is a new architectural element that extends today's cloud computing infrastructure. It represents the middle tier of a 3-tier hierarchy: mobile device - cloudlet - cloud. A cloudlet can be viewed as a data center in a box whose goal is to bring the cloud closer. The cloudlet term was first coined by M. Satyanarayanan, Victor Bahl, Ramón Cáceres, and Nigel Davies, and a prototype implementation is developed by Carnegie Mellon University as a research project. The concept of cloudlet is also known as follow me cloud, and mobile micro-cloud. == Motivation == Many mobile services split the application into a front-end client program and a back-end server program following the traditional client-server model. The front-end mobile application offloads its functionality to the back-end servers for various reasons such as speeding up processing. With the advent of cloud computing, the back-end server is typically hosted at the cloud datacenter. Though the use of a cloud datacenter offers various benefits such as scalability and elasticity, its consolidation and centralization lead to a large separation between a mobile device and its associated datacenter. End-to-end communication then involves many network hops and results in high latencies and low bandwidth. For the reasons of latency, some emerging mobile applications require cloud offload infrastructure to be close to the mobile device to achieve low response time. In the ideal case, it is just one wireless hop away. For example, the offload infrastructure could be located in a cellular base station or it could be LAN-connected to a set of Wi-Fi base stations. The individual elements of this offload infrastructure are referred to as cloudlets. == Applications == Cloudlets aim to support mobile applications that are both resource-intensive and interactive. Augmented reality applications that use head-tracked systems require end-to-end latencies of less than 16 ms. Cloud games with remote rendering also require low latencies and high bandwidth. Wearable cognitive assistance systems combine devices such as Google Glass with cloud-based processing to guide users through complex tasks. This futuristic genre of applications is characterized as “astonishingly transformative” by the report of the 2013 NSF Workshop on Future Directions in Wireless Networking. These applications use cloud resources in the critical path of real-time user interaction. Consequently, they cannot tolerate end-to-end operation latencies of more than a few tens of milliseconds. Apple Siri and Google Now which perform compute-intensive speech recognition in the cloud, are further examples in this emerging space. == Cloudlet vs Cloud == There is significant overlap in the requirements for cloud and cloudlet. At both levels, there is the need for: (a) strong isolation between untrusted user-level computations; (b) mechanisms for authentication, access control, and metering; (c) dynamic resource allocation for user-level computations; and, (d) the ability to support a very wide range of user-level computations, with minimal restrictions on their process structure, programming languages or operating systems. At a cloud datacenter, these requirements are met today using the virtual machine (VM) abstraction. For the same reasons they are used in cloud computing today, VMs are used as an abstraction for cloudlets. Meanwhile, there are a few but important differentiators between cloud and cloudlet. === Rapid provisioning === Different from cloud data centers that are optimized for launching existing VM images in their storage tier, cloudlets need to be much more agile in their provisioning. Their association with mobile devices is highly dynamic, with considerable churn due to user mobility. A user from far away may unexpectedly show up at a cloudlet (e.g., if he just got off an international flight) and try to use it for an application such as a personalized language translator. For that user, the provisioning delay before he is able to use the application impacts usability. === VM handoff across cloudlets === If a mobile device user moves away from the cloudlet he is currently using, the interactive response will degrade as the logical network distance increases. To address this effect of user mobility, the offloaded services on the first cloudlet need to be transferred to the second cloudlet maintaining end-to-end network quality. This resembles live migration in cloud computing but differs considerably in a sense that the VM handoff happens in Wide Area Network (WAN). == OpenStack++ == Since the cloudlet model requires reconfiguration or additional deployment of hardware/software, it is important to provide a systematic way to incentivise the deployment. However, it can face a classic bootstrapping problem. Cloudlets need practical applications to incentivize cloudlet deployment. However, developers cannot heavily rely on cloudlet infrastructure until it is widely deployed. To break this deadlock and bootstrap the cloudlet deployment, researchers at Carnegie Mellon University proposed OpenStack++ that extends OpenStack to leverage its open ecosystem. OpenStack++ provides a set of cloudlet-specific APIs as OpenStack extensions. == Commercial implementations and standardization effort == By 2015 cloudlet based applications were commercially available. In 2017 the National Institute of Standards and Technology published draft standards for fog computing in which cloudlets were defined as nodes on the fog architecture.
LiveChat
LiveChat is an AI customer service software with chatbot, online chat, help desk software, and web analytics capabilities. LiveChat is used by over 76,000 companies. It was first launched in 2002 and is offered via a SaaS (software as a service) business model by Text. Organizations use LiveChat as a single point of contact to manage customer service and online sales activities with a single program. == Product == LiveChat is proprietary software. LiveChat's website chat widget can be embedded on customers' websites as a small chat box, often displayed in the bottom right corner of the web browser. It can be used to conduct chats, share files and save transcripts. The agent application is used by company employees to respond to questions asked by the customers. This is available through both web-based application, desktop applications, and mobile apps. Web chat sessions can be initiated by the visiting customer, or by the agent, either manually or automatically by the LiveChat system when the visitor meets the predefined criteria (i.e. searched keyword, time on website, encountered error, etc.). LiveChat's system attempts to identify the best prospects visiting a website based on data gathered from past purchasing decisions. Other features include real-time website traffic monitoring, built-in ticketing system and agents' efficiency analytics. LiveChat is available in 48 languages. == Research and reception == Reviewing LiveChat's usefulness for online learning in 2020, psychologist Jaclyn Broadbent said "LiveChat occurs as a real-time conversation, it can be time-consuming for staff and disruptive to other tasks." However, using it has resulted in reduced communication traffic from other channels, such as the discussion boards or email. As a teacher, the best time to be available on LiveChat is when you are doing other administrative jobs." Since 2014 LiveChat has been publishing Customer Service Report - an annual study of customer satisfaction and analysis of online business communication trends. It includes research of thousands of companies and millions of customer service email and live support interactions.
Kernel density estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. == Definition == Let x = ( x 1 , x 2 , x 3 , . . . ) {\displaystyle \mathbf {x} =\left(x_{1},x_{2},x_{3},...\right)} be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\left({\frac {x-x_{i}}{h}}\right)},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth or simply width. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov (parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. The kernel density estimator then becomes f ^ h ( x ) = 1 n ∑ i = 1 n 1 h 2 π exp ( − ( x − x i ) 2 2 h 2 ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {1}{h{\sqrt {2\pi }}}}\exp \left({\frac {-(x-x_{i})^{2}}{2h^{2}}}\right),} where h {\displaystyle h} is the standard deviation of the sample x {\displaystyle \mathbf {x} } . The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). == Example == Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. For the kernel density estimate, normal kernels with a standard deviation of 1.5 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. == Bandwidth selection == The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left[\int \!{\left({\hat {f}}\!_{h}(x)-f(x)\right)}^{2}dx\right]} Under weak assumptions on f and K, (f is the, generally unknown, real density function), MISE ( h ) = AMISE ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}{\left((nh)^{-1}+h^{4}\right)}} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\textstyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\textstyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big O notation. It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. === A rule-of-thumb bandwidth estimator === If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 / 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h={\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)}^{1/5}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {\mathrm {IQR} }{1.34}}\right)} where IQR is the
AirPair
AirPair is a service and eponymous company that connects people who need help with programming issues (usually, programmers at small technology companies or at finance companies that use technology products) and people who can help them. Unlike services such as oDesk and Elance, AirPair is not a service for outsourcing programming tasks, but rather a service that facilitates one-off knowledge transfers from people with highly specialized knowledge of particular technology stacks or programming issues to people who are in need of specialized help. == History == AirPair launched in March 2013, with founder Jonathon Kresner, who hails from Australia, working full-time, and it soon hired three other part-time developers to work alongside him. Kresner had previously founded two other startups: Preparty, a social invitation and event-booking service based in Australia, and ClimbFind, an online rock-climbing community that reached a million users. Kresner was inspired to work on AirPair because he saw the need for outside expert assistance with programming issues arise regularly at these startups. In November 2013, founder Kresner describes the company's initial success at bootstrapping itself to "Ramen profitability" in a blog post. In December 2013, AirPair was accepted into the Winter 2014 Y Combinator batch. In March 2014, AirPair announced it would launch partnerships with Stripe, Twilio, and other companies that had their own application programming interfaces, allowing developers having trouble with the APIs to seek help over AirPair from experts on the APIs. AirPair presented at the Y Combinator Winter 2014 Demo Day on March 25, 2014, and successfully raised over $1 million within the next 48 hours. == Reception == A review of AirPair by Will Lam stressed that because payment was based on time rather than results, it was important to use it for clearly thought-out questions where one had high confidence that the session would help. Dennis Beatty, who met AirPair founder Jonathon Kresner in March 2014, wrote in April 2014 a glowing review of AirPair's vision of connecting people and its business success. AirPair has been compared with other peer-to-peer coding help sites such as Codementor and HackHands.