AI Chatbot Creator

AI Chatbot Creator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

IT operations analytics

In the fields of information technology (IT) and systems management, IT operations analytics (ITOA) is an approach or method to retrieve, analyze, and report data for IT operations. ITOA may apply big data analytics to large datasets to produce business insights. In 2014, Gartner predicted its use might increase revenue or reduce costs. By 2017, it predicted that 15% of enterprises will use IT operations analytics technologies. == Definition == IT operations analytics (ITOA) (also known as advanced operational analytics, or IT data analytics) technologies are primarily used to discover complex patterns in high volumes of often "noisy" IT system availability and performance data. Forrester Research defined IT analytics as "The use of mathematical algorithms and other innovations to extract meaningful information from the sea of raw data collected by management and monitoring technologies." Note, ITOA is different than AIOps, which focuses on applying artificial intelligence and machine learning to the applications of ITOA. == History == Operations research as a discipline emerged from the Second World War to improve military efficiency and decision-making on the battlefield. However, only with the emergence of machine learning tech in the early 2000s could an artificially intelligent operational analytics platform actually begin to engage in the high-level pattern recognition that could adequately serve business needs. A critical catalyst towards ITOA development was the rise of Google, which pioneered a predictive analytics model that represented the first attempt to read into patterns of human behavior on the Internet. IT specialists then applied predictive analytics to the IT Industry, coming forward with platforms that can sift through data to generate insights without the need for human intervention. Due to the mainstream embrace of cloud computing and the increasing desire for businesses to adopt more big data practices, the ITOA industry has grown significantly since 2010. A 2016 ExtraHop survey of large and mid-size corporations indicates that 65 percent of the businesses surveyed will seek to integrate their data silos either this year or the next. The current goals of ITOA platforms are to improve the accuracy of their APM services, facilitate better integration with the data, and to enhance their predictive analytics capabilities. == Applications == ITOA systems tend to be used by IT operations teams, and Gartner describes seven applications of ITOA systems: Root cause analysis: The models, structures and pattern descriptions of IT infrastructure or application stack being monitored can help users pinpoint fine-grained and previously unknown root causes of overall system behavior pathologies. Proactive control of service performance and availability: Predicts future system states and the impact of those states on performance. Problem assignment: Determines how problems may be resolved or, at least, direct the results of inferences to the most appropriate individuals, or communities in the enterprise for problem resolution. Service impact analysis: When multiple root causes are known, the analytics system's output is used to determine and rank the relative impact, so that resources can be devoted to correcting the fault in the most timely and cost-effective way possible. Complement best-of-breed technology: The models, structures and pattern descriptions of IT infrastructure or application stack being monitored are used to correct or extend the outputs of other discovery-oriented tools to improve the fidelity of information used in operational tasks (e.g., service dependency maps, application runtime architecture topologies, network topologies). Real time application behavior learning: Learns & correlates the behavior of Application based on user pattern and underlying Infrastructure on various application patterns, create metrics of such correlated patterns and store it for further analysis. Dynamically baselines threshold: Learns behavior of Infrastructure on various application user patterns and determines the Optimal behavior of the Infra and technological components, bench marks and baselines the low and high water mark for the specific environments and dynamically changes the bench mark baselines with the changing infra and user patterns without any manual intervention. == Types == In their Data Growth Demands a Single, Architected IT Operations Analytics Platform, Gartner Research describes five types of analytics technologies: Log analysis Unstructured text indexing, search and inference (UTISI) Topological analysis (TA) Multidimensional database search and analysis (MDSA) Complex operations event processing (COEP) Statistical pattern discovery and recognition (SPDR) == Tools and ITOA platforms == A number of vendors operate in the ITOA space:
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Regularization perspectives on support vector machines

Within mathematical analysis, Regularization perspectives on support-vector machines provide a way of interpreting support-vector machines (SVMs) in the context of other regularization-based machine-learning algorithms. SVM algorithms categorize binary data, with the goal of fitting the training set data in a way that minimizes the average of the hinge-loss function and L2 norm of the learned weights. This strategy avoids overfitting via Tikhonov regularization and in the L2 norm sense and also corresponds to minimizing the bias and variance of our estimator of the weights. Estimators with lower Mean squared error predict better or generalize better when given unseen data. Specifically, Tikhonov regularization algorithms produce a decision boundary that minimizes the average training-set error and constrain the Decision boundary not to be excessively complicated or overfit the training data via a L2 norm of the weights term. The training and test-set errors can be measured without bias and in a fair way using accuracy, precision, Auc-Roc, precision-recall, and other metrics. Regularization perspectives on support-vector machines interpret SVM as a special case of Tikhonov regularization, specifically Tikhonov regularization with the hinge loss for a loss function. This provides a theoretical framework with which to analyze SVM algorithms and compare them to other algorithms with the same goals: to generalize without overfitting. SVM was first proposed in 1995 by Corinna Cortes and Vladimir Vapnik, and framed geometrically as a method for finding hyperplanes that can separate multidimensional data into two categories. This traditional geometric interpretation of SVMs provides useful intuition about how SVMs work, but is difficult to relate to other machine-learning techniques for avoiding overfitting, like regularization, early stopping, sparsity and Bayesian inference. However, once it was discovered that SVM is also a special case of Tikhonov regularization, regularization perspectives on SVM provided the theory necessary to fit SVM within a broader class of algorithms. This has enabled detailed comparisons between SVM and other forms of Tikhonov regularization, and theoretical grounding for why it is beneficial to use SVM's loss function, the hinge loss. == Theoretical background == In the statistical learning theory framework, an algorithm is a strategy for choosing a function f : X → Y {\displaystyle f\colon \mathbf {X} \to \mathbf {Y} } given a training set S = { ( x 1 , y 1 ) , … , ( x n , y n ) } {\displaystyle S=\{(x_{1},y_{1}),\ldots ,(x_{n},y_{n})\}} of inputs x i {\displaystyle x_{i}} and their labels y i {\displaystyle y_{i}} (the labels are usually ± 1 {\displaystyle \pm 1} ). Regularization strategies avoid overfitting by choosing a function that fits the data, but is not too complex. Specifically: f = argmin f ∈ H { 1 n ∑ i = 1 n V ( y i , f ( x i ) ) + λ ‖ f ‖ H 2 } , {\displaystyle f={\underset {f\in {\mathcal {H}}}{\operatorname {argmin} }}\left\{{\frac {1}{n}}\sum _{i=1}^{n}V(y_{i},f(x_{i}))+\lambda \|f\|_{\mathcal {H}}^{2}\right\},} where H {\displaystyle {\mathcal {H}}} is a hypothesis space of functions, V : Y × Y → R {\displaystyle V\colon \mathbf {Y} \times \mathbf {Y} \to \mathbb {R} } is the loss function, ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{\mathcal {H}}} is a norm on the hypothesis space of functions, and λ ∈ R {\displaystyle \lambda \in \mathbb {R} } is the regularization parameter. When H {\displaystyle {\mathcal {H}}} is a reproducing kernel Hilbert space, there exists a kernel function K : X × X → R {\displaystyle K\colon \mathbf {X} \times \mathbf {X} \to \mathbb {R} } that can be written as an n × n {\displaystyle n\times n} symmetric positive-definite matrix K {\displaystyle \mathbf {K} } . By the representer theorem, f ( x i ) = ∑ j = 1 n c j K i j , and ‖ f ‖ H 2 = ⟨ f , f ⟩ H = ∑ i = 1 n ∑ j = 1 n c i c j K ( x i , x j ) = c T K c . {\displaystyle f(x_{i})=\sum _{j=1}^{n}c_{j}\mathbf {K} _{ij},{\text{ and }}\|f\|_{\mathcal {H}}^{2}=\langle f,f\rangle _{\mathcal {H}}=\sum _{i=1}^{n}\sum _{j=1}^{n}c_{i}c_{j}K(x_{i},x_{j})=c^{T}\mathbf {K} c.} == Special properties of the hinge loss == The simplest and most intuitive loss function for categorization is the misclassification loss, or 0–1 loss, which is 0 if f ( x i ) = y i {\displaystyle f(x_{i})=y_{i}} and 1 if f ( x i ) ≠ y i {\displaystyle f(x_{i})\neq y_{i}} , i.e. the Heaviside step function on − y i f ( x i ) {\displaystyle -y_{i}f(x_{i})} . However, this loss function is not convex, which makes the regularization problem very difficult to minimize computationally. Therefore, we look for convex substitutes for the 0–1 loss. The hinge loss, V ( y i , f ( x i ) ) = ( 1 − y f ( x ) ) + {\displaystyle V{\big (}y_{i},f(x_{i}){\big )}={\big (}1-yf(x){\big )}_{+}} , where ( s ) + = max ( s , 0 ) {\displaystyle (s)_{+}=\max(s,0)} , provides such a convex relaxation. In fact, the hinge loss is the tightest convex upper bound to the 0–1 misclassification loss function, and with infinite data returns the Bayes-optimal solution: f b ( x ) = { 1 , p ( 1 ∣ x ) > p ( − 1 ∣ x ) , − 1 , p ( 1 ∣ x ) < p ( − 1 ∣ x ) . {\displaystyle f_{b}(x)={\begin{cases}1,&p(1\mid x)>p(-1\mid x),\\-1,&p(1\mid x) Read more →
Top 10 AI Chatbots Compared (2026)

Shopping for the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI chatbot slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Writer invariant

Writer invariant, also called authorial invariant or author's invariant, is a property of a text which is invariant of its author, that is, it will be similar in all texts of a given author and different in texts of different authors. It can be used to find plagiarism or discover who is real author of anonymously published text. Writer invariant is also an author's pattern of writing a letter in handwritten text recognition. While it is generally recognised that writer invariants exist, it is not agreed what properties of a text should be used. Among the first ones used was distribution of word lengths; other proposed invariants include average sentence length, average word length, noun, verb or adjective usage frequency, vocabulary richness, and frequency of function words, or specific function words. Of these, average sentence lengths can be very similar in works of different authors or vary significantly even within a single work; average word lengths likewise turn out to be very similar in works of different authors. Analysis of function words shows promise because they are used by authors unconsciously.
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Voice search

Voice search, also called voice-enabled search, allows the user to use a voice to search the Internet, a website, or an app. In a broader definition, voice search includes open-domain keyword query on any information on the Internet, for example in Google Voice Search, Cortana, Siri and Amazon Echo. Voice search is often interactive, involving several rounds of interaction that allows a system to ask for clarification. Voice search is a type of dialog system. Voice search is not a replacement for typed search. Rather the search terms, experience and use cases can differ heavily depending on the input type. == Supported language == Language is the most essential factor for a system to understand, and provide the most accurate results of what the user searches. This covers across languages, dialects, and accents, as users want a voice assistant that both understands them and speaks to them understandably. While spoken and written languages differ, voice search should support natural spoken language instead of only transforming voice into text and doing a regular text search with the help speech recognition. For example, in typed search an eCommerce user can easily copy and paste an alphanumeric product code to search field, but when speaking the search terms can be very different, such as "show me the new Bluetooth headphones by Samsung". == How it works == The difference between text and voice search is not only the input type. The mechanism must include an automatic speech recognition (ASR) for input, but it can also include natural language understanding for natural spoken search queries such as "What's the population for the United States" It can include text-to-speech (TTS) or a regular display for output modalities. Users might sometimes be required to activate the search by using a wake word. Then, the search system will detect the language spoken by the user. It will then detect the keywords and context of the sentence. Lastly, the device will return results depending on its output. A device with a screen might display the results, while a device without a screen will speak them back to the searcher.
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The Best Free AI Subtitle Generator for Beginners

In search of the best AI subtitle generator? An AI subtitle generator is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI subtitle generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Kaiming He

Kaiming He (Chinese: 何恺明; pinyin: Hé Kǎimíng) is a Chinese computer scientist who primarily researches computer vision and deep learning. He is an associate professor at Massachusetts Institute of Technology and works part-time as a Distinguished Scientist at Google DeepMind. He is known as one of the creators of the residual neural network (ResNet) architecture. == Early life and education == He attended the public Guangzhou Zhixin High School in Guangzhou, Guangdong, China. He scored first place for the total scores in the 2003 Guangdong provincial undergraduate admissions exam. He went to Tsinghua University for undergraduate education and received a Bachelor of Science degree in 2007. In 2007 to 2011, he pursued doctoral studies in information engineering at the Chinese University of Hong Kong at its Multimedia Laboratory, receiving a PhD degree in 2011. His doctoral dissertation was titled Single image haze removal using dark channel prior (2011), and his doctoral adviser was Tang Xiao'ou. == Career == He worked at Microsoft Research Asia from 2011 to 2016 and at Facebook Artificial Intelligence Research from 2016 to 2024. In 2024, he became an associate professor at the Department of Electrical Engineering and Computer Science of the Massachusetts Institute of Technology. His 2016 paper Deep Residual Learning for Image Recognition is the most cited research paper in 5 years according to Google Scholar's reports in 2020 and 2021. == Awards and recognitions == He won ICCV's best paper award (Marr Prize) in 2017 and CVPR's best paper award in 2009 and 2016. He was awarded the 2023 Future Science Prize along with 3 collaborators for "fundamental contribution to artificial intelligence by introducing deep residual learning".
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Best AI Logo Makers in 2026

Looking for the best AI logo maker? An AI logo maker is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI logo maker slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Light scanning photomacrography

Light Scanning Photomacrography (LSP), also known as Scanning Light Photomacrography (SLP) or Deep-Field Photomacrography, is a photographic film technique that allows for high magnification light imaging with exceptional depth of field (DOF). This method overcomes the limitations of conventional macro photography, which typically only keeps a portion of the subject in acceptable focus at high magnifications. == Historical background == The principles of LSP were first documented in the early 1960s by Dan McLachlan Jr., who highlighted its capability for extreme focal depth in microscopy and in 1968 patented the process. The technique was revived and further developed in the 1980s by photographers such as Darwin Dale and Nile Root, a faculty member at the Rochester Institute of Technology. In the early 1990s, William Sharp and Charles Kazilek, both researchers at Arizona State University, also published articles describing their technique and system setup for capturing SLP images. == Predecessor to stack image photography == Light Scanning Photomacrography offered a powerful analog tool for high-detail imaging in the age of film photography. It provided a comprehensive depth of field, making it invaluable in scientific and biomedical photography. As technology and techniques continue to evolve, LSP has been replaced by digital image focus stacking. This technique uses a collection of images captured in series at different focal depths, which are then processed using computer software to create a single image with a greater focus depth than any single image. == LSP technique and results == LSP involves the use of a thin plane of light that scans across the subject, which is mounted on a stage moving perpendicular to the film plane. The technique utilizes traditional optics and is governed by the physical laws of depth of field. By moving the subject through a narrow band of illumination, the entire subject can be recorded in sharp focus from the nearest details to the farthest ones. This analog process produces sharp and detailed images by slowly recording the image on film as the specimen passes through the sheet of light that is thinner than the effective DOF. Because the image is captured at the same relative distance from the camera lens, the resulting images are axonometric rather than perspective projection, which is what the human eye sees and is typically captured by a film camera. Because all parts of an LSP image are captured at the same distance from the lens, relative measurements can be taken from an LSP photograph and can be used for comparison. == Equipment and setup == A typical LSP setup includes: A stage that can move the subject perpendicular to the film plane. Light sources, in some cases modified projectors, are used to project a thin plane of light. A camera mounted on a stable stand such as a tabletop copy stand. In 1991, Sharp and Kazilek described their SLP system that used three Kodak Ektagraphic slide projectors with zoom lenses to create a thin plane of light. The projectors each had a slide mount with two razor blades placed edge-to-edge to create a thin slit for the light to pass through. The image was captured using a Nikon FE-2 SLR camera mounted above the specimen. Kodachrome 25 slide film was used to record the image and to minimize film grain size and maximize image sharpness == Commercial systems == A commercial SLP instrument was produced by the Irvine Optical Corp. Their DYNAPHOT system was based on a photomacroscope and could capture images on 4x5 film. The instrument came with two or three illumination sources and a motorized specimen stage. The system advertised a 2X – 40X magnification range and the ability to capture images in black and white and color. Other systems have been developed by Nile Root and Theodore Clarke and reported higher magnification (up to 100X). == LSP process == Alignment and Focusing: The light sources are aligned and focused to project a thin, consistent plane of light across the subject. Stage Movement: The subject stage moves at a controlled speed, scanning through the plane of light. Image Capture: The camera shutter is set to a long exposure or can be opened and closed manually. As the subject moves through the illuminated plane, it is recorded on the film. This process is very much like painting an image onto the film using photons instead of paint. == Applications == LSP was particularly useful in biomedical photography, where it was used to document magnified subjects with increased depth of field over traditional macro and micro photography. It has been employed to capture detailed images of biological specimens, such as imaging small insects and their parts. SLP has been used to document shell collections for scientific documentation and research. Other applications include forensic science, mineralogy, and the imaging of fractured surfaces and parts == Advantages and challenges of LSP imaging == === Advantages === Exceptional depth of field: Subjects are rendered in sharp focus throughout. High magnification: Detailed images at significant magnification without sacrificing DOF. Analog precision: Provides a non-digital solution with accurate image representation. Versatility: Can be used for a range of subject sizes, from macro to non-macro scales. === Challenges === Technical complexity: Requires precise setup and alignment. Exposure time: Typically requires long exposure times due to the scanning process. Contrast control: The highly directional lighting can create harsh shadows and high contrast, which may need to be managed. Digital competition: Focus stacking has largely replaced LSP in the digital era due to convenience and flexibility. == DIY contributions == Enthusiasts and researchers have contributed to the development and accessibility of LSP by creating and sharing DIY guides. These contributions have enabled others to build their own LSP systems using readily available materials and components. Nile Root's publications provide detailed instructions and recommendations for constructing an LSP setup. These DIY systems have allowed a wider audience to explore and utilize the benefits of LSP imaging in various fields.
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Additive smoothing

In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts x = ⟨ x 1 , x 2 , … , x d ⟩ {\displaystyle \mathbf {x} =\langle x_{1},x_{2},\ldots ,x_{d}\rangle } from a d {\displaystyle d} -dimensional multinomial distribution with N {\displaystyle N} trials, a "smoothed" version of the counts gives the estimator θ ^ i = x i + α N + α d ( i = 1 , … , d ) , {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\alpha }{N+\alpha d}}\qquad (i=1,\ldots ,d),} where the smoothed count x ^ i = N θ ^ i {\displaystyle {\hat {x}}_{i}=N{\hat {\theta }}_{i}} , and the "pseudocount" α > 0 is a smoothing parameter, with α = 0 corresponding to no smoothing (this parameter is explained in § Pseudocount below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) x i / N {\displaystyle x_{i}/N} and the uniform probability 1 / d . {\displaystyle 1/d.} Common choices for α are 0 (no smoothing), +1⁄2 (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empirically based on the observed data. From a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter α as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a beta distribution as the conjugate prior for the parameters of the binomial distribution. == History == Laplace came up with this smoothing technique when he tried to estimate the chance that the sun will rise tomorrow. His rationale was that even given a large sample of days with the rising sun, we still can not be completely sure that the sun will still rise tomorrow (known as the sunrise problem). == Pseudocount == A pseudocount is an amount (not generally an integer, despite its name) added to the number of observed cases in order to change the expected probability in a model of those data, when not known to be zero. It is so named because, roughly speaking, a pseudo-count of value α {\displaystyle \alpha } weighs into the posterior distribution similarly to each category having an additional count of α {\displaystyle \alpha } . If the number of occurrences of each item i {\displaystyle i} is x i {\displaystyle x_{i}} out of N {\displaystyle N} samples, the empirical probability of event i {\displaystyle i} is p i , empirical = x i N , {\displaystyle p_{i,{\text{empirical}}}={\frac {x_{i}}{N}},} but the posterior probability when additively smoothed is p i , α -smoothed = x i + α N + α d , {\displaystyle p_{i,\alpha {\text{-smoothed}}}={\frac {x_{i}+\alpha }{N+\alpha d}},} as if to increase each count x i {\displaystyle x_{i}} by α {\displaystyle \alpha } a priori. Depending on the prior knowledge, which is sometimes a subjective value, a pseudocount may have any non-negative finite value. It may only be zero (or the possibility ignored) if impossible by definition, such as the possibility of a decimal digit of π being a letter, or a physical possibility that would be rejected and so not counted, such as a computer printing a letter when a valid program for π is run, or excluded and not counted because of no interest, such as if only interested in the zeros and ones. Generally, there is also a possibility that no value may be computable or observable in a finite time (see the halting problem). But at least one possibility must have a non-zero pseudocount, otherwise no prediction could be computed before the first observation. The relative values of pseudocounts represent the relative prior expected probabilities of their possibilities. The sum of the pseudocounts, which may be very large, represents the estimated weight of the prior knowledge compared with all the actual observations (one for each) when determining the expected probability. In any observed data set or sample there is the possibility, especially with low-probability events and with small data sets, of a possible event not occurring. Its observed frequency is therefore zero, apparently implying a probability of zero. This oversimplification is inaccurate and often unhelpful, particularly in probability-based machine learning techniques such as artificial neural networks and hidden Markov models. By artificially adjusting the probability of rare (but not impossible) events so those probabilities are not exactly zero, zero-frequency problems are avoided. Also see Cromwell's rule. === Choice of pseudocount === ==== Weakly informative prior ==== One common approach is to add 1 to each observed number of events, including the zero-count possibilities. This is sometimes called Laplace's rule of succession. This approach is equivalent to assuming a uniform prior distribution over the probabilities for each possible event (spanning the simplex where each probability is between 0 and 1, and they all sum to 1). Using the Jeffreys prior approach, a pseudocount of one half should be added to each possible outcome. Pseudocounts should be set to one or one-half only when there is no prior knowledge at all – see the principle of indifference. However, given appropriate prior knowledge, the sum should be adjusted in proportion to the expectation that the prior probabilities should be considered correct, despite evidence to the contrary – see further analysis. Higher values are appropriate inasmuch as there is prior knowledge of the true values (for a mint-condition coin, say); lower values inasmuch as there is prior knowledge that there is probable bias, but of unknown degree (for a bent coin, say). ==== Frequentist interval ==== One way to motivate pseudocounts, particularly for binomial data, is via a formula for the midpoint of an interval estimate, particularly a binomial proportion confidence interval. The best-known is due to Edwin Bidwell Wilson, in Wilson (1927): the midpoint of the Wilson score interval corresponding to ⁠ z {\displaystyle z} ⁠ standard deviations on either side is n S + z n + 2 z {\displaystyle {\frac {n_{S}+z}{n+2z}}} Taking z = 2 {\displaystyle z=2} standard deviations to approximate a 95% confidence interval (⁠ z ≈ 1.96 {\displaystyle z\approx 1.96} ⁠) yields pseudocount of 2 for each outcome, so 4 in total, colloquially known as the "plus four rule": n S + 2 n + 4 {\displaystyle {\frac {n_{S}+2}{n+4}}} This is also the midpoint of the Agresti–Coull interval (Agresti & Coull 1998). ==== Known incidence rates ==== Often the bias of an unknown trial population is tested against a control population with known parameters (incidence rates) μ = ⟨ μ 1 , μ 2 , … , μ d ⟩ . {\displaystyle {\boldsymbol {\mu }}=\langle \mu _{1},\mu _{2},\ldots ,\mu _{d}\rangle .} In this case the uniform probability 1 / d {\displaystyle 1/d} should be replaced by the known incidence rate of the control population μ i {\displaystyle \mu _{i}} to calculate the smoothed estimator: θ ^ i = x i + μ i α d N + α d ( i = 1 , … , d ) . {\displaystyle {\hat {\theta }}_{i}={\frac {x_{i}+\mu _{i}\alpha d}{N+\alpha d}}\qquad (i=1,\ldots ,d).} As a consistency check, if the empirical estimator happens to equal the incidence rate, i.e. μ i = x i / N , {\displaystyle \mu _{i}=x_{i}/N,} the smoothed estimator is independent of α {\displaystyle \alpha } and also equals the incidence rate. == Applications == === Classification === Additive smoothing is commonly a component of naive Bayes classifiers. === Statistical language modelling === In a bag of words model of natural language processing and information retrieval, the data consists of the number of occurrences of each word in a document. Additive smoothing allows the assignment of non-zero probabilities to words which do not occur in the sample. Studies have shown that additive smoothing is more effective than other probability smoothing methods in several retrieval tasks such as language-model-based pseudo-relevance feedback and recommender systems.
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Katie Bouman

Katherine Louise Bouman (; born 1989) is an American engineer and computer scientist working in the field of computational imaging. She led the development of an algorithm for imaging black holes, known as Continuous High-resolution Image Reconstruction using Patch priors (CHIRP), and was a member of the Event Horizon Telescope team that captured the first image of a black hole. The California Institute of Technology, which hired Bouman as an assistant professor in June 2019, awarded her a named professorship in 2020. In 2021, asteroid 291387 Katiebouman was named after her. In 2024, she became an associate professor. == Early life and education == Bouman grew up in West Lafayette, Indiana. Her father, Charles Bouman, is a professor of electrical and computer engineering and biomedical engineering at Purdue University. As a high school student, Bouman conducted imaging research at Purdue University. She graduated from West Lafayette Junior-Senior High School in 2007. Bouman studied electrical engineering at the University of Michigan and graduated summa cum laude in 2011. She earned her master's degree in 2013 and obtained a doctoral degree in electrical engineering and computer science in 2017 from the Massachusetts Institute of Technology (MIT). At MIT, she was a member of the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL). This group also worked closely with MIT's Haystack Observatory and with the Event Horizon Telescope. She was supported by a National Science Foundation Graduate Fellowship. Her master's thesis, Estimating Material Properties of Fabric through the Observation of Motion, was awarded the Ernst Guillemin Award for best Master's Thesis in electrical engineering. Her Ph.D. dissertation, Extreme imaging via physical model inversion: seeing around corners and imaging black holes, was supervised by William T. Freeman. Prior to receiving her doctoral degree, Bouman delivered a TEDx talk, How to Take a Picture of a Black Hole, which explained algorithms that could be used to capture the first image of a black hole. == Research and career == After earning her doctorate, Bouman joined Harvard University as a postdoctoral fellow on the Event Horizon Telescope Imaging team. Bouman joined Event Horizon Telescope project in 2013. She led the development of an algorithm for imaging black holes, known as Continuous High-resolution Image Reconstruction using Patch priors (CHIRP). CHIRP inspired image validation procedures used in acquiring the first image of a black hole in April 2019, and Bouman played a significant role in the project by verifying images, selecting parameters for filtering images taken by the Event Horizon Telescope, and participating in the development of a robust imaging framework that compared the results of different image reconstruction techniques. Her group is analyzing the Event Horizon Telescope's images to learn more about general relativity in a strong gravitational field. Bouman received significant media attention after a photo, showing her reaction to the detection of the black hole shadow in the EHT images, went viral. Some people in the media and on the Internet misleadingly implied that Bouman was a "lone genius" behind the image. However, Bouman herself repeatedly noted that the result came from the work of a large collaboration, showing the importance of teamwork in science. Bouman also became the target of online harassment, to the extent that her colleague Andrew Chael made a statement on Twitter criticizing "awful and sexist attacks on my colleague and friend", including attempts to undermine her contributions by crediting him solely with work accomplished by the team. Bouman joined the California Institute of Technology (Caltech) as an assistant professor in June 2019, where she works on new systems for computational imaging using computer vision and machine learning. In 2024, she was promoted to associate professor of computing and mathematical sciences, electrical engineering and astronomy as well as a Rosenberg Scholar. Bouman received a named professorship at Caltech in 2020. In 2021, Bouman was awarded the Royal Photographic Society Progress Medal and Honorary Fellowship. == Recognition == She was recognized as one of the BBC's 100 women of 2019. In 2024, Bouman was awarded a Sloan Research Fellowship.
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Isabelle Guyon

Isabelle Guyon (French pronunciation: [izabɛl ɡɥijɔ̃]; born August 15, 1961) is a French-born researcher in machine learning known for her work on support-vector machines, artificial neural networks and bioinformatics. She is a Chair Professor at the University of Paris-Saclay. Guyon serves as the Director of Research at Google DeepMind since October 2022. She is considered to be a pioneer in the field, with her contribution to the support-vector machines with Vladimir Vapnik and Bernhard Boser. == Biography == After graduating from the French engineering school ESPCI Paris in 1985, she joined the group of Gerard Dreyfus at the Université Pierre-et-Marie-Curie to do a PhD on neural networks architectures and training. Guyon defended her thesis in 1988 and was hired the year after at AT&T Bell Laboratories, first as a post-doc, then as a group leader. She worked at Bell Labs for six years, where she explored several research areas, from neural networks to pattern recognition and computational learning theory, with application to handwriting recognition. She collaborated with Yann LeCun, Léon Bottou, Vladimir Vapnik, Corinna Cortes, Yoshua Bengio, Patrice Simard, and met her future husband, Bernhard Boser. In 1996, Guyon left Bell Labs and raised her children at Berkeley, California. In Berkeley, she created her own machine learning consulting company, Clopinet. She became interested in medical applications, and used her previous work to classify the genes responsible for different types of cancers. Since 2003, Guyon has organized many challenges in data science, in order to stimulate research in this field. She founded ChaLearn in 2011, a non-profit organization aimed at creating machine learning challenges open to everyone. She was Program Chair of NeurIPS 2016 and became General Chair of NeurIPS in 2017. She is also Action Editor for the Journal of Machine Learning Research and Series Editor for Series: Challenges in Machine Learning. She is a member of the European Laboratory for Learning and Intelligent Systems. In 2016, Guyon came back to France to take the Chair Professorship in Big data between the University of Paris-Saclay and INRIA. She works in TAU (TAckling the Underspecified), a research collaboration of the Laboratoire de recherche en informatique. Together with Bernhard Schölkopf and Vladimir Vapnik, she received in 2020 the BBVA Foundation Frontiers of Knowledge Awards for her work in machine learning. == Scientific work == Guyon has worked in many subfields of machine learning, including neural networks, support-vector machines, feature selection and applications of machine learning to biology. === Support-vector machines === Among her most notable contributions, Guyon co-invented support-vector machines (SVM) in 1992, with Bernhard Boser and Vladimir Vapnik. SVM is a supervised machine learning algorithm, comparable to neural networks or decision trees, which has quickly become a classical technique in machine learning. SVMs have especially contributed to the popularization of kernel methods. === Neural networks === During her years at Bell Labs, Guyon took part of numerous projects involving neural networks. In particular, she wrote some of the first papers on the use of neural network for handwriting recognition using the MNIST database. She is also a co-inventor of the siamese neural networks, a neural network architecture used to learn similarities, with applications to signature, face or object recognition. === Machine learning for biology === Guyon is the author of many publications at the intersection of biology (cancer research and genomics) and artificial intelligence. She has notably introduced the use of support-vector machines to detect cancer using genes. === Machine learning challenges === Through her non-profit organization ChaLearn, Guyon has organized and directed challenges open to everyone in order to solve open problems in machine learning, including computer vision, neurosciences, particle physics, feature selection, causality and automated machine learning. Most of the challenges organized by ChaLearn have resulted in publications. Among the most cited ones are: Guyon et al., Result analysis of the NIPS 2003 feature selection challenge, Advances in neural information processing systems, 2005, link Escalera et al., ChaLearn Looking at People Challenge 2014: Dataset and Results, Computer Vision - ECCV 2014 Workshops, Springer International Publishing, 2014, link Guyon et al., A brief Review of the ChaLearn AutoML Challenge, JMLR: Workshop and Conference Proceedings 64:21-30, 2016, link Adam-Bourdario et al., The Higgs boson machine learning challenge, JMLR: Workshop and Conference Proceedings 42:19-55, 2015, link == Private life == She is married to Bernhard Boser, a professor at UC Berkeley. She has twins and one daughter, all three of whom have completed a science degree. Guyon has three citizenships: French by birth, Swiss by marriage and American by naturalization. == Awards and honors == Nomination at the French Academy of technologies (2024) Recipient of the BBVA Foundation Frontiers of Knowledge Awards (2020) American Medical Informatics Association Fellow (2011) == Publications == Bernhard Boser, Isabelle Guyon and Vladmir Vapnik, A training algorithm for optimal margin classifiers, Proceedings of the fifth annual workshop on Computational learning theory, 1992, doi:10.1145/130385.130401 Jane Bromley, Isabelle Guyon, Yann LeCun, Eduard Säckinger and Roopak Shah, Signature verification using a" siamese" time delay neural network, Advances in Neural Information Processing Systems, 1994. Isabelle Guyon and André Elisseeff, An introduction to variable and feature selection, Journal of Machine Learning Research, 2003. Isabelle Guyon, Jason Weston, Stephen Barnhill and Vladimir Vapnik, Gene selection for cancer classification using support vector machines, Machine Learning, Kluwer Academic Publishers, 2002, doi:10.1023/A:1012487302797
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Deep Instinct

Deep Instinct is a cybersecurity company that applies deep learning to cybersecurity. The company implements artificial intelligence to the task of preventing and detecting malware. The company was the recipient of the Technology Pioneer by The World Economic Forum in 2017. Lane Bess has been CEO of the company since 2022. == Overview == In 2015, Deep Instinct was founded by Guy Caspi, Dr. Eli David, and Nadav Maman. The headquarters of the company is located in New York City. In July 2017, NVIDIA became an investor. According to Tom's Hardware, NVIDIA’s investment enabled access to a GPU-based neural network and CUDA platform, which they were using to achieve maximum vulnerability detection rates. As of February 2020, the company had raised $43 million in Series C funding round. In April 2021, Deep Instinct raised $100 million in Series D funding to accelerate growth. == Partnerships == In April 2019, Deep Instinct partnered with Chinese artist, Guo O. Dong on an art project titled, The Persistence of Chaos, consisting of a laptop infected with 6 pieces of malware that represented $95 billion in damages. The art was auctioned with a final bid of $1,345,000. In the same year, Globes reported that, HP Inc partnered with Deep Instinct to launch their security solution HP SureSense, which has been applied to the EliteBook and Zbook devices.
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András Kornai

András Kornai (born 1957 in Budapest) is a mathematical linguist. == Education == Kornai is the son of economist János Kornai. He earned two PhDs with the first being in mathematics in 1983 from Eötvös Loránd University in Budapest, where his advisor was Miklós Ajtai. His second was in linguistics in 1991 from Stanford University, where his advisor was Paul Kiparsky. == Career == He is a professor in the Department of Algebra at the Budapest Institute of Technology, where he works on an open source Hungarian morphological analyzer. He was Chief Scientist at MetaCarta, where he worked on information extraction before the company was acquired by Nokia. Prior to MetaCarta, he was Chief Scientist at Northern Light. He is on the board of the journal Grammars and YourAmigo PLC. His research interests include all mathematical aspects of natural language processing, speech recognition, and OCR. As area editor he was responsible for the Mathematical Linguistics area of the Oxford International Encyclopedia of Linguistics, and his joint work with Geoffrey Pullum, "The X-bar Theory of Phrase Structure", formally reconstructed that then-popular linguistic theory. == Awards and honors == 2009: ACM Distinguished Member == Monographs == Semantics. Springer Nature, 2020. ISBN 978-3-319-65644-1 Mathematical Linguistics. Springer Verlag, in the series Advanced Information and Knowledge Processing, November 2007. ISBN 978-1-84628-985-9 Hardbound, approximately 300 pages. See description. Formal Phonology. In the series Outstanding Dissertations in Linguistics, Garland Publishing, 1994, ISBN 0-8153-1730-1, hardbound, 240 pages Contents, Preface, Introduction (20 pages) On Hungarian Morphology. In the series Linguistica, Hungarian Academy of Sciences, 1994, ISBN 963-8461-73-X, paperbound, 174 pages Contents, Preface, Introduction (10 pages) == Books edited == Oxford International Encyclopedia of Linguistics (Mathematical Linguistics Area Editor under Editor in Chief William Frawley). 4 volumes, Oxford University Press, 2003, ISBN 978-0-19-513977-8. Proceedings of the HLT-NAACL Workshop on the Analysis of Geographic References. Jointly with Beth Sundheim. Association for Computational Linguistics, 2003, ISBN 1-932432-04-3 (WS9), paperbound, vi+81 pages. See related material. Extended Finite State Models of Language (editor). In the series Studies in Natural Language Processing, Cambridge University Press, 1999, ISBN 0-521-63198-X, hardbound, x+278 pages Contents, Introduction (7 pages). == Selected papers == Digital Language Death. PLoS ONE 8(10): e77056, 2012. [1] Hunmorph: open source word analysis (Jointly with V. Tron, Gy. Gyepesi, P. Halacsy, L. Nemeth, and D. Varga). In Proc. ACL 2005 Software Workshop 77-85 [2] Leveraging the open source ispell codebase for minority language analysis (Jointly with P. Halacsy, L. Nemeth, A. Rung, I. Szakadat, and V. Tron). In J. Carson-Berndsen (ed): Proc. SALTMIL 2004 56-59 [3] Explicit Finitism, International Journal of Theoretical Physics 2003/2 301-307 [4] Mathematical Linguistics (Jointly with G.K. Pullum) In W. Frawley (ed): Oxford International Encyclopedia of Linguistics, Oxford University Press 2003, v3 17-20 [5] Optical Character Recognition, In W. Frawley (ed): Oxford International Encyclopedia of Linguistics, Oxford University Press 2003, v3 33-34 [6] How many words are there? Glottometrics 2002/4 61-86 [7] Zipf's law outside the middle range Proc. Sixth Meeting on Mathematics of Language University of Central Florida, 1999 347-356 [8] A Robust, Language-Independent OCR System. (Jointly with Z. Lu, I. Bazzi, J. Makhoul, P. Natarajan, and R. Schwartz) In: Robert J. Mericsko (ed): Proc. 27th AIPR Workshop: Advances in Computer-Assisted Recognition SPIE Proceedings 3584 1999 [9] Quantitative Comparison of Languages. Grammars 1998/2 155-165 [10] The generative power of feature geometry. Annals of Mathematics and Artificial Intelligence 8 1993 37-46 [11] The X-bar Theory of Phrase Structure. (Jointly with G.K. Pullum) Language 66 1990 24-50 [12]
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Best AI Chatbots in 2026

Curious about the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI chatbot slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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