AI Tools For Ecommerce

AI Tools For Ecommerce — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Final Cut Express

  Final Cut Express was a video editing software suite created by Apple Inc. It was the consumer version of Final Cut Pro and was designed for advanced editing of digital video as well as high-definition video, which was used by many amateur and professional videographers. Final Cut Express was considered a step above iMovie in terms of capabilities, but a step underneath Final Cut Pro and its suite of applications. As of June 21, 2011, Final Cut Express was discontinued in favor of Final Cut Pro X. == History == Final Cut Express 1.0, based on Final Cut Pro 3, was released at Macworld Conference and Expo in San Francisco in 2003. The second version, based on Final Cut Pro 4, was released at Macworld San Francisco in 2004. The third version, capable of editing high definition video, was also announced at Macworld San Francisco a year later, and was released as Final Cut Express HD in February 2005. It was based on Final Cut Pro HD (version 4.5) and included LiveType 1.2 and Soundtrack 1.2. Final Cut Express version 3.5 was released with little fanfare in May 2006 as a Universal Binary. In addition to improving real-time rendering with Dynamic RT, version 3.5 upgraded LiveType to version 2.0 and Soundtrack to version 1.5. In November 2007, Apple released Final Cut Express 4, which although it did not support real-time editing in the AVCHD format (it only allowed for transcoding AVCHD to Apple Intermediate Codec (AIC) provided that the camera was actually attached to the computer - it did not convert AVCHD files stored elsewhere and is currently for Intel processors only), imported iMovie '08 projects and included 50 new filters. It did not include Soundtrack 1.5, but it still included LiveType which enables users to create advanced text for the movies they created in Final Cut. The price was dropped from $299 for version 3.5 to $199 for version 4.0. In June 2011, Final Cut Express was officially discontinued, in favor of Final Cut Pro X. == Features == Final Cut Express' interface was identical to that of Final Cut Pro, but lacks some film-specific features, including Cinema Tools, multi-cam editing, batch capture, and a time code view. The program performed 32 undo operations, while Final Cut Pro did 99 [2]. Features the program did include were: The ability to keyframe filters Dynamic RT, which changes real-time settings on-the-fly Motion path keyframing Opacity keyframing Ripple, roll, slip, slide and blade edits Picture-in-picture and split-screen effects Up to 99 video tracks and 12 compositing modes Up to 99 audio tracks Motion project import Two-way color correction. Chroma key One feature of Final Cut Express that was not available in Final Cut Pro is the ability to import iMovie '08 projects (though transitions are not preserved). === RT Extreme === Inherited from Final Cut Pro, Final Cut Express features RT Extreme, which allows previews of some video filters and transitions without rendering. Audio that is not in the native AIFF file format needs rendering before it can be played back. RT Extreme has three modes: 'Safe', for seeing multiple video layers at a quality that more or less guarantees a smooth playback; 'Unlimited', which allows the maximum number of composited video layers to be viewed at the same time; and 'Dynamic', which alternates between these settings depending on how many simultaneous video tracks are present. Frame dropping may result from using 'Unlimited' on low-resource machines. === Boris Calligraphy === Like Final Cut Pro, Express also comes with Boris Calligraphy, a plugin for advanced titling and scrolling/crawling titles more sophisticated than the ones that can be created with the built-in title overlays. Calligraphy has a WYSIWYG interface and features wrapping, alignment, leading, kerning and tracking features, as well as allowing up to five custom outlines and five custom drop shadows to be defined for a selected portion of the title. == Soundtrack == Prior to version 4, Final Cut Express included Soundtrack 1.5, a music program similar to the consumer-level GarageBand, but designed for videographers who wish to add music to their films. Soundtrack comes with around 4,000 professionally recorded instrument loops and sound effects that can be arranged in multiple tracks beneath the video track. To use Soundtrack, users export their Final Cut Express sequence, or a marked portion thereof, as a reference file, which can include scoring markers defined in the timeline. This reference file can be imported as the video track in Soundtrack. Soundtrack is functionally and visually identical to Soundtrack Pro's multitrack editing mode, but includes fewer Logic plugins and lacks the highly regarded noise removal tool. Soundtrack was removed from Final Cut Express 4, which lowered its price and may have encouraged people to buy Logic Express.

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  Statistical classification

  When classification is performed by a computer, statistical methods are normally used to develop the algorithm. Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g. "A", "B", "AB" or "O", for blood type), ordinal (e.g. "large", "medium" or "small"), integer-valued (e.g. the number of occurrences of a particular word in an email) or real-valued (e.g. a measurement of blood pressure). Other classifiers work by comparing observations to previous observations by means of a similarity or distance function. An algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term "classifier" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category. Terminology across fields is quite varied. In statistics, where classification is often done with logistic regression or a similar procedure, the properties of observations are termed explanatory variables (or independent variables, regressors, etc.), and the categories to be predicted are known as outcomes, which are considered to be possible values of the dependent variable. In machine learning, the observations are often known as instances, the explanatory variables are termed features (grouped into a feature vector), and the possible categories to be predicted are classes. Other fields may use different terminology: e.g. in community ecology, the term "classification" normally refers to cluster analysis. == Relation to other problems == Classification and clustering are examples of the more general problem of pattern recognition, which is the assignment of some sort of output value to a given input value. Other examples are regression, which assigns a real-valued output to each input; sequence labeling, which assigns a class to each member of a sequence of values (for example, part of speech tagging, which assigns a part of speech to each word in an input sentence); parsing, which assigns a parse tree to an input sentence, describing the syntactic structure of the sentence; etc. A common subclass of classification is probabilistic classification. Algorithms of this nature use statistical inference to find the best class for a given instance. Unlike other algorithms, which simply output a "best" class, probabilistic algorithms output a probability of the instance being a member of each of the possible classes. The best class is normally then selected as the one with the highest probability. However, such an algorithm has numerous advantages over non-probabilistic classifiers: It can output a confidence value associated with its choice (in general, a classifier that can do this is known as a confidence-weighted classifier). Correspondingly, it can abstain when its confidence of choosing any particular output is too low. Because of the probabilities which are generated, probabilistic classifiers can be more effectively incorporated into larger machine-learning tasks, in a way that partially or completely avoids the problem of error propagation. == Frequentist procedures == Early work on statistical classification was undertaken by Fisher, in the context of two-group problems, leading to Fisher's linear discriminant function as the rule for assigning a group to a new observation. This early work assumed that data-values within each of the two groups had a multivariate normal distribution. The extension of this same context to more than two groups has also been considered with a restriction imposed that the classification rule should be linear. Later work for the multivariate normal distribution allowed the classifier to be nonlinear: several classification rules can be derived based on different adjustments of the Mahalanobis distance, with a new observation being assigned to the group whose centre has the lowest adjusted distance from the observation. == Bayesian procedures == Unlike frequentist procedures, Bayesian classification procedures provide a natural way of taking into account any available information about the relative sizes of the different groups within the overall population. Bayesian procedures tend to be computationally expensive and, in the days before Markov chain Monte Carlo computations were developed, approximations for Bayesian clustering rules were devised. Some Bayesian procedures involve the calculation of group-membership probabilities: these provide a more informative outcome than a simple attribution of a single group-label to each new observation. == Binary and multiclass classification == Classification can be thought of as two separate problems – binary classification and multiclass classification. In binary classification, a better understood task, only two classes are involved, whereas multiclass classification involves assigning an object to one of several classes. Since many classification methods have been developed specifically for binary classification, multiclass classification often requires the combined use of multiple binary classifiers. == Feature vectors == Most algorithms describe an individual instance whose category is to be predicted using a feature vector of individual, measurable properties of the instance. Each property is termed a feature, also known in statistics as an explanatory variable (or independent variable, although features may or may not be statistically independent). Features may variously be binary (e.g. "on" or "off"); categorical (e.g. "A", "B", "AB" or "O", for blood type); ordinal (e.g. "large", "medium" or "small"); integer-valued (e.g. the number of occurrences of a particular word in an email); or real-valued (e.g. a measurement of blood pressure). If the instance is an image, the feature values might correspond to the pixels of an image; if the instance is a piece of text, the feature values might be occurrence frequencies of different words. Some algorithms work only in terms of discrete data and require that real-valued or integer-valued data be discretized into groups (e.g. less than 5, between 5 and 10, or greater than 10). == Linear classifiers == A large number of algorithms for classification can be phrased in terms of a linear function that assigns a score to each possible category k by combining the feature vector of an instance with a vector of weights, using a dot product. The predicted category is the one with the highest score. This type of score function is known as a linear predictor function and has the following general form: score ⁡ ( X i , k ) = β k ⋅ X i , {\displaystyle \operatorname {score} (\mathbf {X} _{i},k)={\boldsymbol {\beta }}_{k}\cdot \mathbf {X} _{i},} where Xi is the feature vector for instance i, βk is the vector of weights corresponding to category k, and score(Xi, k) is the score associated with assigning instance i to category k. In discrete choice theory, where instances represent people and categories represent choices, the score is considered the utility associated with person i choosing category k. Algorithms with this basic setup are known as linear classifiers. What distinguishes them is the procedure for determining (training) the optimal weights/coefficients and the way that the score is interpreted. Examples of such algorithms include Logistic regression – Statistical model for a binary dependent variable Multinomial logistic regression – Regression for more than two discrete outcomes Probit regression – Statistical regression where the dependent variable can take only two valuesPages displaying short descriptions of redirect targets The perceptron algorithm Support vector machine – Set of methods for supervised statistical learning Linear discriminant analysis – Method used in statistics, pattern recognition, and other fields == Algorithms == Since no single form of classification is appropriate for all data sets, a large toolkit of classification algorithms has been developed. The most commonly used include: Artificial neural networks – Computational model used in machine learningPages displaying short descriptions of redirect targets Boosting (machine learning) – Ensemble learning method Random forest – Tree-based ensemble machine learning methods Genetic programming – Evolving computer programs with techniques analogous to natural genetic processes Gene expression programming – Evolutionary algorithm Multi expression programming Linear genetic programming Kernel estimation – Concept in statisticsPages displaying short descriptions of redirect targets k-nearest neighbor – Non-parametric classification methodPages displaying short descriptions of redirect targets Learning vector quantization Linear classifier – Statistical classification in machine learning Fisher's linear discriminant – Method used in statistics, pattern recognition, and other fieldsPages displaying short descriptions of redirect targets Logistic r

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  ID3 algorithm

  In decision tree learning, ID3 (Iterative Dichotomiser 3) is a greedy algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm. The 3 in the name is meant to signify that this was Quinlan's third attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split on multi-valued attributes. == Algorithm == The ID3 algorithm begins with the original set S {\displaystyle S} as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S {\displaystyle S} and calculates the entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} or the information gain I G ( S ) {\displaystyle IG(S)} of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S {\displaystyle S} is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm continues to recurse on each subset, considering only attributes never selected before. Recursion on a subset may stop in one of these cases: every element in the subset belongs to the same class; in which case the node is turned into a leaf node and labelled with the class of the examples. there are no more attributes to be selected, but the examples still do not belong to the same class. In this case, the node is made a leaf node and labelled with the most common class of the examples in the subset. there are no examples in the subset, which happens when no example in the parent set was found to match a specific value of the selected attribute. An example could be the absence of a person among the population with age over 100 years. Then a leaf node is created and labelled with the most common class of the examples in the parent node's set. Throughout the algorithm, the decision tree is constructed with each non-terminal node (internal node) representing the selected attribute on which the data was split, and terminal nodes (leaf nodes) representing the class label of the final subset of this branch. === Summary === Calculate the entropy of every attribute a {\displaystyle a} of the data set S {\displaystyle S} . Partition ("split") the set S {\displaystyle S} into subsets using the attribute for which the resulting entropy after splitting is minimized; or, equivalently, information gain is maximum. Make a decision tree node containing that attribute. Recurse on subsets using the remaining attributes. === Properties === ID3 does not guarantee an optimal solution. It can converge upon local optima. It uses a greedy strategy by selecting the locally best attribute to split the dataset on each iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking longer. ID3 can overfit the training data. To avoid overfitting, smaller decision trees should be preferred over larger ones. This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time-consuming. === Usage === The ID3 algorithm is used by training on a data set S {\displaystyle S} to produce a decision tree which is stored in memory. At runtime, this decision tree is used to classify new test cases (feature vectors) by traversing the decision tree using the features of the datum to arrive at a leaf node. == The ID3 metrics == === Entropy === Entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} is a measure of the amount of uncertainty in the (data) set S {\displaystyle S} (i.e. entropy characterizes the (data) set S {\displaystyle S} ). H ( S ) = ∑ x ∈ X − p ( x ) log 2 ⁡ p ( x ) {\displaystyle \mathrm {H} {(S)}=\sum _{x\in X}{-p(x)\log _{2}p(x)}} Where, S {\displaystyle S} – The current dataset for which entropy is being calculated This changes at each step of the ID3 algorithm, either to a subset of the previous set in the case of splitting on an attribute or to a "sibling" partition of the parent in case the recursion terminated previously. X {\displaystyle X} – The set of classes in S {\displaystyle S} p ( x ) {\displaystyle p(x)} – The proportion of the number of elements in class x {\displaystyle x} to the number of elements in set S {\displaystyle S} When H ( S ) = 0 {\displaystyle \mathrm {H} {(S)}=0} , the set S {\displaystyle S} is perfectly classified (i.e. all elements in S {\displaystyle S} are of the same class). In ID3, entropy is calculated for each remaining attribute. The attribute with the smallest entropy is used to split the set S {\displaystyle S} on this iteration. Entropy in information theory measures how much information is expected to be gained upon measuring a random variable; as such, it can also be used to quantify the amount to which the distribution of the quantity's values is unknown. A constant quantity has zero entropy, as its distribution is perfectly known. In contrast, a uniformly distributed random variable (discretely or continuously uniform) maximizes entropy. Therefore, the greater the entropy at a node, the less information is known about the classification of data at this stage of the tree; and therefore, the greater the potential to improve the classification here. As such, ID3 is a greedy heuristic performing a best-first search for locally optimal entropy values. Its accuracy can be improved by preprocessing the data. === Information gain === Information gain I G ( A ) {\displaystyle IG(A)} is the measure of the difference in entropy from before to after the set S {\displaystyle S} is split on an attribute A {\displaystyle A} . In other words, how much uncertainty in S {\displaystyle S} was reduced after splitting set S {\displaystyle S} on attribute A {\displaystyle A} . I G ( S , A ) = H ( S ) − ∑ t ∈ T p ( t ) H ( t ) = H ( S ) − H ( S | A ) . {\displaystyle IG(S,A)=\mathrm {H} {(S)}-\sum _{t\in T}p(t)\mathrm {H} {(t)}=\mathrm {H} {(S)}-\mathrm {H} {(S|A)}.} Where, H ( S ) {\displaystyle \mathrm {H} (S)} – Entropy of set S {\displaystyle S} T {\displaystyle T} – The subsets created from splitting set S {\displaystyle S} by attribute A {\displaystyle A} such that S = ⋃ t ∈ T t {\displaystyle S=\bigcup _{t\in T}t} p ( t ) {\displaystyle p(t)} – The proportion of the number of elements in t {\displaystyle t} to the number of elements in set S {\displaystyle S} H ( t ) {\displaystyle \mathrm {H} (t)} – Entropy of subset t {\displaystyle t} In ID3, information gain can be calculated (instead of entropy) for each remaining attribute. The attribute with the largest information gain is used to split the set S {\displaystyle S} on this iteration.

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  Gaussian process emulator

  In statistics, Gaussian process emulator is one name for a general type of statistical model that has been used in contexts where the problem is to make maximum use of the outputs of a complicated (often non-random) computer-based simulation model. Each run of the simulation model is computationally expensive and each run is based on many different controlling inputs. The variation of the outputs of the simulation model is expected to vary reasonably smoothly with the inputs, but in an unknown way. The overall analysis involves two models: the simulation model, or "simulator", and the statistical model, or "emulator", which notionally emulates the unknown outputs from the simulator. The Gaussian process emulator model treats the problem from the viewpoint of Bayesian statistics. In this approach, even though the output of the simulation model is fixed for any given set of inputs, the actual outputs are unknown unless the computer model is run and hence can be made the subject of a Bayesian analysis. The main element of the Gaussian process emulator model is that it models the outputs as a Gaussian process on a space that is defined by the model inputs. The model includes a description of the correlation or covariance of the outputs, which enables the model to encompass the idea that differences in the output will be small if there are only small differences in the inputs.

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  Timeline of artificial intelligence risks in global finance

  The following article is a broad timeline of the course of events related to artificial intelligence risks in global finance. The AI boom has led to concerns including the existential risk from artificial intelligence, as the uptake on applications of artificial intelligence increases. By late 2025, global finance and artificial intelligence were "deeply intertwined". A June 2025 Menlo Ventures report raised concerns about the sustainability of future revenue and long-term profitability of AI, given the relatively low rate of consumer monetization. == 2017 == 30 NovemberThe New York Times said that new AI reports by McKinsey & Company, the National Bureau of Economic Research, and an AI Index created by university researchers, indicated an early AI boom. The Index built on a project—"The One Hundred Year Study on Artificial Intelligence" launched in 2014. == 2018 == 2018 was a year of incremental AI growth in finance. == 2022 == The release of ChatGPT by OpenAI became the catalyst for an artificial intelligence boom that continues to remake the global economy. According to a European Central Bank report, public interest in AI increased rapidly as evidenced with rising Google searches, AI jobs, models, patents, and innovations since late 2022. At that time Europe led the US in the size of its AI workforce. == 2023 == The regulatory body, the International Monetary Fund (IMF), published their report, "Generative Artificial Intelligence in Finance: Risk Considerations", drawing attention to oversight gaps and the need for regulations. The report explores the risks posed by using generative artificial intelligence (GenAI) systems in the financial sector including "broader risks to financial stability." == 2024 == January 12 In January 2024 Bloomberg's published its list of the "Magnificent Seven" Big Tech companies on the stock market based on their strength, size and market capitalization:Apple, Microsoft, Alphabet (Google), Amazon, Meta Platforms (Facebook), Nvidia, and Tesla. 21 June During the AI boom, Nvidia became the world's most valuable company, surpassing Microsoft, as its value increased to over US$4 trillion. In 2023 and 2024, the "Magnificent Seven" stocks were the primary drivers behind the increase in equity indexes, according to Reuters. == 2025 == === January === 23 January President Donald Trump's AI policy was announced calling for United States global leadership in artificial intelligence. The Economist noted that this politic shift in which the United States seeks "global dominance" in AI includes trimming regulations and assisting in expansion of infrastructure and increase in number of AI workers. Governments of Gulf nations were also investing trillions of dollars in AI. 27 January Against the backdrop of a tech war between China and the United States over AI dominance, within days of the launch of China's free DeepSeek App, it was the most downloaded app in the United States, rising to the first place in the Apple app store. President Trump responded immediately, saying this "sudden rise" should be a "wake-up" call to the United States, and called on US companies to be more competitive. === June === 26 June In their June 2025 report, Menlo Ventures estimated that only about 3% of consumers paid for artificial intelligence-related services, representing about $USD12 billion in annual spending. This is relatively low in contrast to the massive capital expenditure by AI infrastructure companies, which raises concerns about revenue sustainability and long-term profitability. === July === 23 July The Trump administration launched the US AI Action Plan, positioning the United States in a high-stakes technological race with China for global dominance in artificial intelligence, emphasizing that neither nation can afford to fall behind due to the exponential nature of AI advancement. The plan, a new government website and policy speech called for accelerated AI adoption across federal agencies, and a number of initiatives to make is easier for AI infrastructure expansion, and other measures to ensure American leadership in AI standards. Some leading experts warned that the administration failed to provide sufficient regulations and safeguards for AI safety. Concerns were raised about the negative impacts of cuts to research funding and tightened visa policies for scientists, potentially undermining public trust and America's ability to compete internationally. === September === 7 September The Economist cautioned that AI revenues are relatively modest compared to the high cost and investments in the creation of new data centers. Even Sam Altman, OpenAI CEO and one of the leading figures of the AI boom,, raised concerns about investors' outsized hopes for financial returns. At the same time, history has shown that new technologies, like railways and electricity, endured and spread after the initial hype faded. 12 September Economists warn that U.S. households' direct and indirect investments—mutual funds or retirement plans—in the stock market reached an unprecedented historically high level, now representing 45% of all financial assets, or about $USD51.2 trillion. Compared to the Dot-com bubble this represents a sharp increase in exposure. This makes U.S. households vulnerable to market downturns which in turn would result in decreasing consumer spending. U.S. household net worth rose to a record $176.3 trillion in the second quarter, an increase of $7.3 trillion since early 2025 and about $46 trillion higher than before the pandemic. Federal Reserve data attribute the surge primarily to gains in stock markets and housing values. However, the rise in wealth on paper coincided with increased household borrowing and growing government debt. 18 September Questions were being raised about how quickly the data centers, chips, servers, and GPUs assets of major AI companies will depreciate in value. Comparisons have been made to the Railway Mania in the aftermath of the stock market bubble where a valuable physical infrastructure remained standing, and the telecoms crash after the dot-com bubble which left fiber networks. 28 September There were warnings that record-high American stock ownership during the AI-fueled market boom is a red flag for systemic risk, as the current concentration in equities exceeds levels seen before the dot-com bubble burst in 2000, and could amplify the impact of any future stock market correction. === October === 3 October In 2025 alone, venture capitalists invested almost $USD200 billion in the artificial intelligence sector. 29 October Nvidia was the first company in the world to be valued at US$5 trillion, largely due to AI demand and strategic partnerships with leading technology and AI firms. Nvidia's increase in value was "meteoric". === November === 2 November Forbes reported that, since April, the 'Magnificent Seven' tech giants together contributed over 40% of the S&P 500's return, highlighting their outsized influence and the growing impact of AI on market valuations. CNN warned that while there is a current benefit to investors, with such a high concentration in the S&P 500, they are highly exposed to the fate of the Mag Seven. 2 November Globally there are 11,000 datacentres—huge campuses for AI infrastructure, including thousands of chips, GPUS, and servers. This represents a 500% increase over the last two decades. It is anticipated that $3USDtn more will be spent on increasing that number over the next two or three years. 5 November Concerns about the potential for a market bubble were raised as six of the AI-related Big Tech "Magnificent Seven"—that contribute to the AI boom—reported losing ground in the stock market. Global markets and artificial intelligence have become "deeply intertwined", according to a Reuters report. As of November 2025, more than 50% of the 20 largest S&P firms were deeply exposed to AI. In contrast, in 2000, the 20 S&P 500 firms represented 39% of its total value only 11 of these companies were exposed to the internet. If AI fails to deliver strong returns on their investments, these top S&P firms would be significantly impacted, according to the Economist. Analysts suggest that the AI market in 2025 may not behave like a traditional one, as investors are simultaneously aware of the risks and driven by the potential for outsized rewards. Leading AI labs may believe that the first company to achieve artificial general intelligence (AGI), when an AI system surpasses all human cognitive abilities and becomes capable of self-improvement—could dominate the future of technology and finance. While some have estimated that the potential value of such a breakthrough could be as high as $1.46 quadrillion, this figure is speculative and widely debated. 5 November Bloomberg described Nvidia's H100 Hopper-Blackwell AI chips as the "King of AI chips". Nvidia dominates the AI chip market with over 78% of the market share because of both speed and cost. According to B

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  ARKA descriptors in QSAR

  In computational chemistry and cheminformatics, ARKA descriptors in QSAR are a class of molecular descriptors used in quantitative structure–activity relationship (QSAR) modeling (or related approaches such as QSPR and QSTR), a computational method for predicting the biological activity or toxicity of chemical compounds based on their molecular structure. Molecular descriptors are numerical values that summarize information about a molecule's structure, topology, geometry, or physicochemical properties in a form suitable for machine learning or statistical modeling. ARKA (Arithmetic Residuals in K-Groups Analysis) descriptors differ from traditional descriptors by encoding atomic-level information through recursive autoregression techniques, which aim to capture subtle structural patterns and improve predictive accuracy. They are designed to be both interpretable and well-suited to modeling nonlinear relationships in QSAR studies. == Comparisons == While QSAR is essentially a similarity-based approach, the occurrence of activity/property cliffs may greatly reduce the predictive accuracy of the developed models. The novel Arithmetic Residuals in K-groups Analysis (ARKA) approach is a supervised dimensionality reduction technique developed by the DTC Laboratory, Jadavpur University that can easily identify activity cliffs in a data set. Activity cliffs are similar in their structures but differ considerably in their activity. The basic idea of the ARKA descriptors is to group the conventional QSAR descriptors based on a predefined criterion and then assign weightage to each descriptor in each group. ARKA descriptors have also been used to develop classification-based and regression-based QSAR models with acceptable quality statistics. The ARKA descriptors have been used for the identification of activity cliffs in QSAR studies and/or model development by multiple researchers. A tutorial presentation on the ARKA descriptors is available. Recently a multi-class ARKA framework has been proposed for improved q-RASAR model generation.

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  Random forest

  Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude of decision trees during training. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the output is the average of the predictions of the trees. Random forests correct for decision trees' habit of overfitting to their training set. The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is a way to implement the "stochastic discrimination" approach to classification proposed by Eugene Kleinberg. An extension of the algorithm was developed by Leo Breiman and Adele Cutler, who registered "Random Forests" as a trademark in 2006 (as of 2019, owned by Minitab, Inc.). The extension combines Breiman's "bagging" idea and random selection of features, introduced first by Ho and later independently by Amit and Geman in order to construct a collection of decision trees with controlled variance. == History == The general method of random decision forests was first proposed by Salzberg and Heath in 1993, with a method that used a randomized decision tree algorithm to create multiple trees and then combine them using majority voting. This idea was developed further by Ho in 1995. Ho established that forests of trees splitting with oblique hyperplanes can gain accuracy as they grow without suffering from overtraining, as long as the forests are randomly restricted to be sensitive to only selected feature dimensions. A subsequent work along the same lines concluded that other splitting methods behave similarly, as long as they are randomly forced to be insensitive to some feature dimensions. This observation that a more complex classifier (a larger forest) gets more accurate nearly monotonically is in sharp contrast to the common belief that the complexity of a classifier can only grow to a certain level of accuracy before being hurt by overfitting. The explanation of the forest method's resistance to overtraining can be found in Kleinberg's theory of stochastic discrimination. The early development of Breiman's notion of random forests was influenced by the work of Amit and Geman who introduced the idea of searching over a random subset of the available decisions when splitting a node, in the context of growing a single tree. The idea of random subspace selection from Ho was also influential in the design of random forests. This method grows a forest of trees, and introduces variation among the trees by projecting the training data into a randomly chosen subspace before fitting each tree or each node. Finally, the idea of randomized node optimization, where the decision at each node is selected by a randomized procedure, rather than a deterministic optimization was first introduced by Thomas G. Dietterich. The proper introduction of random forests was made in a paper by Leo Breiman, that has become one of the world's most cited papers. This paper describes a method of building a forest of uncorrelated trees using a CART like procedure, combined with randomized node optimization and bagging. In addition, this paper combines several ingredients, some previously known and some novel, which form the basis of the modern practice of random forests, in particular: Using out-of-bag error as an estimate of the generalization error. Measuring variable importance through permutation. The report also offers the first theoretical result for random forests in the form of a bound on the generalization error which depends on the strength of the trees in the forest and their correlation. == Algorithm == === Preliminaries: decision tree learning === Decision trees are a popular method for various machine learning tasks. Tree learning is almost "an off-the-shelf procedure for data mining", say Hastie et al., "because it is invariant under scaling and various other transformations of feature values, is robust to inclusion of irrelevant features, and produces inspectable models. However, they are seldom accurate". In particular, trees that are grown very deep tend to learn highly irregular patterns: they overfit their training sets, i.e. have low bias, but very high variance. Random forests are a way of averaging multiple deep decision trees, trained on different parts of the same training set, with the goal of reducing the variance. This comes at the expense of a small increase in the bias and some loss of interpretability, but generally greatly boosts the performance in the final model. === Bagging === The training algorithm for random forests applies the general technique of bootstrap aggregating, or bagging, to tree learners. Given a training set X = x1, ..., xn with responses Y = y1, ..., yn, bagging repeatedly (B times) selects a random sample with replacement of the training set and fits trees to these samples: After training, predictions for unseen samples x' can be made by averaging the predictions from all the individual regression trees on x': f ^ = 1 B ∑ b = 1 B f b ( x ′ ) {\displaystyle {\hat {f}}={\frac {1}{B}}\sum _{b=1}^{B}f_{b}(x')} or by taking the plurality vote in the case of classification trees. This bootstrapping procedure leads to better model performance because it decreases the variance of the model, without increasing the bias. This means that while the predictions of a single tree are highly sensitive to noise in its training set, the average of many trees is not, as long as the trees are not correlated. Simply training many trees on a single training set would give strongly correlated trees (or even the same tree many times, if the training algorithm is deterministic); bootstrap sampling is a way of de-correlating the trees by showing them different training sets. Additionally, an estimate of the uncertainty of the prediction can be made as the standard deviation of the predictions from all the individual regression trees on x′: σ = ∑ b = 1 B ( f b ( x ′ ) − f ^ ) 2 B − 1 . {\displaystyle \sigma ={\sqrt {\frac {\sum _{b=1}^{B}(f_{b}(x')-{\hat {f}})^{2}}{B-1}}}.} The number B of samples (equivalently, of trees) is a free parameter. Typically, a few hundred to several thousand trees are used, depending on the size and nature of the training set. B can be optimized using cross-validation, or by observing the out-of-bag error: the mean prediction error on each training sample xi, using only the trees that did not have xi in their bootstrap sample. The training and test error tend to level off after some number of trees have been fit. === From bagging to random forests === The above procedure describes the original bagging algorithm for trees. Random forests also include another type of bagging scheme: they use a modified tree learning algorithm that selects, at each candidate split in the learning process, a random subset of the features. This process is sometimes called "feature bagging". The reason for doing this is the correlation of the trees in an ordinary bootstrap sample: if one or a few features are very strong predictors for the response variable (target output), these features will be selected in many of the B trees, causing them to become correlated. An analysis of how bagging and random subspace projection contribute to accuracy gains under different conditions is given by Ho. Typically, for a classification problem with p {\displaystyle p} features, p {\displaystyle {\sqrt {p}}} (rounded down) features are used in each split. For regression problems the inventors recommend p / 3 {\displaystyle p/3} (rounded down) with a minimum node size of 5 as the default. In practice, the best values for these parameters should be tuned on a case-to-case basis for every problem. === ExtraTrees === Adding one further step of randomization yields extremely randomized trees, or ExtraTrees. As with ordinary random forests, they are an ensemble of individual trees, but there are two main differences: (1) each tree is trained using the whole learning sample (rather than a bootstrap sample), and (2) the top-down splitting is randomized: for each feature under consideration, a number of random cut-points are selected, instead of computing the locally optimal cut-point (based on, e.g., information gain or the Gini impurity). The values are chosen from a uniform distribution within the feature's empirical range (in the tree's training set). Then, of all the randomly chosen splits, the split that yields the highest score is chosen to split the node. Similar to ordinary random forests, the number of randomly selected features to be considered at each node can be specified. Default values for this parameter are p {\displaystyle {\sqrt {p}}} for classification and p {\displaystyle p} for regression, where p {\displaystyle p} is the number of features in the model. === Random forests for high-dimensional data === The basic random forest procedure may

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  ID3 algorithm

  In decision tree learning, ID3 (Iterative Dichotomiser 3) is a greedy algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm. The 3 in the name is meant to signify that this was Quinlan's third attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split on multi-valued attributes. == Algorithm == The ID3 algorithm begins with the original set S {\displaystyle S} as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S {\displaystyle S} and calculates the entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} or the information gain I G ( S ) {\displaystyle IG(S)} of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S {\displaystyle S} is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm continues to recurse on each subset, considering only attributes never selected before. Recursion on a subset may stop in one of these cases: every element in the subset belongs to the same class; in which case the node is turned into a leaf node and labelled with the class of the examples. there are no more attributes to be selected, but the examples still do not belong to the same class. In this case, the node is made a leaf node and labelled with the most common class of the examples in the subset. there are no examples in the subset, which happens when no example in the parent set was found to match a specific value of the selected attribute. An example could be the absence of a person among the population with age over 100 years. Then a leaf node is created and labelled with the most common class of the examples in the parent node's set. Throughout the algorithm, the decision tree is constructed with each non-terminal node (internal node) representing the selected attribute on which the data was split, and terminal nodes (leaf nodes) representing the class label of the final subset of this branch. === Summary === Calculate the entropy of every attribute a {\displaystyle a} of the data set S {\displaystyle S} . Partition ("split") the set S {\displaystyle S} into subsets using the attribute for which the resulting entropy after splitting is minimized; or, equivalently, information gain is maximum. Make a decision tree node containing that attribute. Recurse on subsets using the remaining attributes. === Properties === ID3 does not guarantee an optimal solution. It can converge upon local optima. It uses a greedy strategy by selecting the locally best attribute to split the dataset on each iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking longer. ID3 can overfit the training data. To avoid overfitting, smaller decision trees should be preferred over larger ones. This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time-consuming. === Usage === The ID3 algorithm is used by training on a data set S {\displaystyle S} to produce a decision tree which is stored in memory. At runtime, this decision tree is used to classify new test cases (feature vectors) by traversing the decision tree using the features of the datum to arrive at a leaf node. == The ID3 metrics == === Entropy === Entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} is a measure of the amount of uncertainty in the (data) set S {\displaystyle S} (i.e. entropy characterizes the (data) set S {\displaystyle S} ). H ( S ) = ∑ x ∈ X − p ( x ) log 2 ⁡ p ( x ) {\displaystyle \mathrm {H} {(S)}=\sum _{x\in X}{-p(x)\log _{2}p(x)}} Where, S {\displaystyle S} – The current dataset for which entropy is being calculated This changes at each step of the ID3 algorithm, either to a subset of the previous set in the case of splitting on an attribute or to a "sibling" partition of the parent in case the recursion terminated previously. X {\displaystyle X} – The set of classes in S {\displaystyle S} p ( x ) {\displaystyle p(x)} – The proportion of the number of elements in class x {\displaystyle x} to the number of elements in set S {\displaystyle S} When H ( S ) = 0 {\displaystyle \mathrm {H} {(S)}=0} , the set S {\displaystyle S} is perfectly classified (i.e. all elements in S {\displaystyle S} are of the same class). In ID3, entropy is calculated for each remaining attribute. The attribute with the smallest entropy is used to split the set S {\displaystyle S} on this iteration. Entropy in information theory measures how much information is expected to be gained upon measuring a random variable; as such, it can also be used to quantify the amount to which the distribution of the quantity's values is unknown. A constant quantity has zero entropy, as its distribution is perfectly known. In contrast, a uniformly distributed random variable (discretely or continuously uniform) maximizes entropy. Therefore, the greater the entropy at a node, the less information is known about the classification of data at this stage of the tree; and therefore, the greater the potential to improve the classification here. As such, ID3 is a greedy heuristic performing a best-first search for locally optimal entropy values. Its accuracy can be improved by preprocessing the data. === Information gain === Information gain I G ( A ) {\displaystyle IG(A)} is the measure of the difference in entropy from before to after the set S {\displaystyle S} is split on an attribute A {\displaystyle A} . In other words, how much uncertainty in S {\displaystyle S} was reduced after splitting set S {\displaystyle S} on attribute A {\displaystyle A} . I G ( S , A ) = H ( S ) − ∑ t ∈ T p ( t ) H ( t ) = H ( S ) − H ( S | A ) . {\displaystyle IG(S,A)=\mathrm {H} {(S)}-\sum _{t\in T}p(t)\mathrm {H} {(t)}=\mathrm {H} {(S)}-\mathrm {H} {(S|A)}.} Where, H ( S ) {\displaystyle \mathrm {H} (S)} – Entropy of set S {\displaystyle S} T {\displaystyle T} – The subsets created from splitting set S {\displaystyle S} by attribute A {\displaystyle A} such that S = ⋃ t ∈ T t {\displaystyle S=\bigcup _{t\in T}t} p ( t ) {\displaystyle p(t)} – The proportion of the number of elements in t {\displaystyle t} to the number of elements in set S {\displaystyle S} H ( t ) {\displaystyle \mathrm {H} (t)} – Entropy of subset t {\displaystyle t} In ID3, information gain can be calculated (instead of entropy) for each remaining attribute. The attribute with the largest information gain is used to split the set S {\displaystyle S} on this iteration.

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  Biorobotics

  Biorobotics is an interdisciplinary science that combines the fields of biomedical engineering, cybernetics, and robotics to develop new technologies that integrate biology with mechanical systems to develop more efficient communication, alter genetic information, and create machines that imitate biological systems. == Cybernetics == Cybernetics focuses on the communication and system of living organisms and machines that can be applied and combined with multiple fields of study such as biology, mathematics, computer science, engineering, and much more. This discipline falls under the branch of biorobotics because of its combined field of study between biological bodies and mechanical systems. Studying these two systems allows for advanced analysis on the functions and processes of each system as well as the interactions between them. === History === Cybernetic theory is a concept that has existed for centuries, dating back to the era of Plato where he applied the term to refer to the "governance of people". The term cybernetique is seen in the mid-1800s used by physicist André-Marie Ampère. The term cybernetics was popularized in the late 1940s to refer to a discipline that touched on, but was separate, from established disciplines, such as electrical engineering, mathematics, and biology. === Science === Cybernetics is often misunderstood because of the breadth of disciplines it covers. In the early 20th century, it was coined as an interdisciplinary field of study that combines biology, science, network theory, and engineering. Today, it covers all scientific fields with system related processes. The goal of cybernetics is to analyze systems and processes of any system or systems in an attempt to make them more efficient and effective. === Applications === Cybernetics is used as an umbrella term so applications extend to all systems related scientific fields such as biology, mathematics, computer science, engineering, management, psychology, sociology, art, and more. Cybernetics is used amongst several fields to discover principles of systems, adaptation of organisms, information analysis and much more. == Genetic engineering == Genetic engineering is a field that uses advances in technology to modify biological organisms. Through different methods, scientists are able to alter the genetic material of microorganisms, plants and animals to provide them with desirable traits. For example, making plants grow bigger, better, and faster. Genetic engineering is included in biorobotics because it uses new technologies to alter biology and change an organism's DNA for their and society's benefit. === History === Although humans have modified genetic material of animals and plants through artificial selection for millennia (such as the genetic mutations that developed teosinte into corn and wolves into dogs), genetic engineering refers to the deliberate alteration or insertion of specific genes to an organism's DNA. The first successful case of genetic engineering occurred in 1973 when Herbert Boyer and Stanley Cohen were able to transfer a gene with antibiotic resistance to a bacterium. === Science === There are three main techniques used in genetic engineering: The plasmid method, the vector method and the biolistic method. ==== Plasmid method ==== This technique is used mainly for microorganisms such as bacteria. Through this method, DNA molecules called plasmids are extracted from bacteria and placed in a lab where restriction enzymes break them down. As the enzymes do this, some develop a rough edge that resembles that of a staircase which is considered 'sticky' and capable of reconnecting. These 'sticky' molecules are inserted into another bacteria where they will connect to the DNA rings with the altered genetic material. ==== Vector method ==== The vector method is considered a more precise technique than the plasmid method as it involves the transfer of a specific gene instead of a whole sequence. In the vector method, a specific gene from a DNA strand is isolated through restriction enzymes in a laboratory and is inserted into a vector. Once the vector accepts the genetic code, it is inserted into the host cell where the DNA will be transferred. ==== Biolistic method ==== The biolistic method is typically used to alter the genetic material of plants. This method embeds the desired DNA with a metallic particle such as gold or tungsten in a high speed gun. The particle is then bombarded into the plant. Due to the high velocities and the vacuum generated during bombardment, the particle is able to penetrate the cell wall and inserts the new DNA into the cell. === Applications === Genetic engineering has many uses in the fields of medicine, research and agriculture. In the medical field, genetically modified bacteria are used to produce drugs such as insulin, human growth hormones and vaccines. In research, scientists genetically modify organisms to observe physical and behavioral changes to understand the function of specific genes. In agriculture, genetic engineering is extremely important as it is used by farmers to grow crops that are resistant to herbicides and to insects such as BTCorn. == Bionics == Bionics is a medical engineering field and a branch of biorobotics consisting of electrical and mechanical systems that imitate biological systems, such as prosthetics and hearing aids. It's a portmanteau that combines biology and electronics. === History === The history of bionics goes as far back in time as ancient Egypt. A prosthetic toe made out of wood and leather was found on the foot of a mummy. The time period of the mummy corpse was estimated to be from around the fifteenth century B.C. Bionics can also be witnessed in ancient Greece and Rome. Prosthetic legs and arms were made for amputee soldiers. In the early 16th century, a French military surgeon by the name of Ambroise Pare became a pioneer in the field of bionics. He was known for making various types of upper and lower prosthetics. One of his most famous prosthetics, Le Petit Lorrain, was a mechanical hand operated by catches and springs. During the early 19th century, Alessandro Volta further progressed bionics. He set the foundation for the creation of hearing aids with his experiments. He found that electrical stimulation could restore hearing by inserting an electrical implant to the saccular nerve of a patient's ear. In 1945, the National Academy of Sciences created the Artificial Limb Program, which focused on improving prosthetics since there were a large number of World War II amputee soldiers. Since this creation, prosthetic materials, computer design methods, and surgical procedures have improved, creating modern-day bionics. === Science === ==== Prosthetics ==== The important components that make up modern-day prosthetics are the pylon, the socket, and the suspension system. The pylon is the internal frame of the prosthetic that is made up of metal rods or carbon-fiber composites. The socket is the part of the prosthetic that connects the prosthetic to the person's missing limb. The socket consists of a soft liner that makes the fit comfortable, but also snug enough to stay on the limb. The suspension system is important in keeping the prosthetic on the limb. The suspension system is usually a harness system made up of straps, belts or sleeves that are used to keep the limb attached. The operation of a prosthetic could be designed in various ways. The prosthetic could be body-powered, externally-powered, or myoelectrically powered. Body-powered prosthetics consist of cables attached to a strap or harness, which is placed on the person's functional shoulder, allowing the person to manipulate and control the prosthetic as he or she deems fit. Externally-powered prosthetics consist of motors to power the prosthetic and buttons and switches to control the prosthetic. Myoelectrically powered prosthetics are new, advanced forms of prosthetics where electrodes are placed on the muscles above the limb. The electrodes will detect the muscle contractions and send electrical signals to the prosthetic to move the prosthetic. The downside to this type of prosthetic is that if the sensors are not placed correctly on the limb then the electrical impulses will fail to move the prosthetic. TrueLimb is a specific brand of prosthetics that uses myoelectrical sensors which enable a person to have control of their bionic limb. ==== Hearing aids ==== Four major components make up the hearing aid: the microphone, the amplifier, the receiver, and the battery. The microphone takes in outside sound, turns that sound to electrical signals, and sends those signals to the amplifier. The amplifier increases the sound and sends that sound to the receiver. The receiver changes the electrical signal back into sound and sends the sound into the ear. Hair cells in the ear will sense the vibrations from the sound, convert the vibrations into nerve signals, and send it to the brain so

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  Plate notation

  In Bayesian inference, plate notation is a method of representing variables that repeat in a graphical model. Instead of drawing each repeated variable individually, a plate or rectangle is used to group variables into a subgraph that repeat together, and a number is drawn on the plate to represent the number of repetitions of the subgraph in the plate. The assumptions are that the subgraph is duplicated that many times, the variables in the subgraph are indexed by the repetition number, and any links that cross a plate boundary are replicated once for each subgraph repetition. == Example == In this example, we consider Latent Dirichlet allocation, a Bayesian network that models how documents in a corpus are topically related. There are two variables not in any plate; α is the parameter of the uniform Dirichlet prior on the per-document topic distributions, and β is the parameter of the uniform Dirichlet prior on the per-topic word distribution. The outermost plate represents all the variables related to a specific document, including θ i {\displaystyle \theta _{i}} , the topic distribution for document i. The M in the corner of the plate indicates that the variables inside are repeated M times, once for each document. The inner plate represents the variables associated with each of the N i {\displaystyle N_{i}} words in document i: z i j {\displaystyle z_{ij}} is the topic distribution for the jth word in document i, and w i j {\displaystyle w_{ij}} is the actual word used. The N in the corner represents the repetition of the variables in the inner plate N j {\displaystyle N_{j}} times, once for each word in document i. The circle representing the individual words is shaded, indicating that each w i j {\displaystyle w_{ij}} is observable, and the other circles are empty, indicating that the other variables are latent variables. The directed edges between variables indicate dependencies between the variables: for example, each w i j {\displaystyle w_{ij}} depends on z i j {\displaystyle z_{ij}} and β. == Extensions == A number of extensions have been created by various authors to express more information than simply the conditional relationships. However, few of these have become standard. Perhaps the most commonly used extension is to use rectangles in place of circles to indicate non-random variables—either parameters to be computed, hyperparameters given a fixed value (or computed through empirical Bayes), or variables whose values are computed deterministically from a random variable. The diagram on the right shows a few more non-standard conventions used in some articles in Wikipedia (e.g. variational Bayes): Variables that are actually random vectors are indicated by putting the vector size in brackets in the middle of the node. Variables that are actually random matrices are similarly indicated by putting the matrix size in brackets in the middle of the node, with commas separating row size from column size. Categorical variables are indicated by placing their size (without a bracket) in the middle of the node. Categorical variables that act as "switches", and which pick one or more other random variables to condition on from a large set of such variables (e.g. mixture components), are indicated with a special type of arrow containing a squiggly line and ending in a T junction. Boldface is consistently used for vector or matrix nodes (but not categorical nodes). == Software implementation == Plate notation has been implemented in various TeX/LaTeX drawing packages, but also as part of graphical user interfaces to Bayesian statistics programs such as BUGS and BayesiaLab and PyMC.

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  Transkribus

  Transkribus is a platform for the text recognition, image analysis and structure recognition of historical documents. The platform was created in the context of the two EU projects "tranScriptorium" (2013–2015) and "READ" (Recognition and Enrichment of Archival Documents – 2016–2019). It was developed by the University of Innsbruck. Since July 1, 2019 the platform has been directed and further developed by the READ-COOP, a non-profit cooperative. The platform integrates tools developed by research groups throughout Europe, including the Pattern Recognition and Human Language Technology (PRHLT) group of the Technical University of Valencia and the Computational Intelligence Technology Lab (CITlab) group of University of Rostock. Comparable programs that offer similar functions are eScriptorium and OCR4All.

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  Causal Markov condition

  The Causal Markov (CM) condition states that, conditional on the set of all its direct causes, a node is independent of all variables which are not effects or direct causes of that node. In the event that the structure of a Bayesian network accurately depicts causality, the two conditions are equivalent. This is related to the Markov condition, an assumption made in Bayesian probability theory, that every node in a Bayesian network is conditionally independent of its nondescendants, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it. In a DAG, this local Markov condition is equivalent to the global Markov condition, which states that d-separations in the graph also correspond to conditional independence relations. This also means that a node is conditionally independent of the entire network, given its Markov blanket. A network may accurately embody the Markov condition without depicting causality, in which case it should not be assumed to embody the causal Markov condition. == Motivation == Statisticians are enormously interested in the ways in which certain events and variables are connected. The precise notion of what constitutes a cause and effect is necessary to understand the connections between them. The central idea behind the philosophical study of probabilistic causation is that causes raise the probabilities of their effects, all else being equal. A deterministic interpretation of causation means that if A causes B, then A must always be followed by B. In this sense, smoking does not cause cancer because some smokers never develop cancer. On the other hand, a probabilistic interpretation simply means that causes raise the probability of their effects. In this sense, changes in meteorological readings associated with a storm do cause that storm, since they raise its probability. (However, simply looking at a barometer does not change the probability of the storm, for a more detailed analysis, see:). == Examples == In a simple view, releasing one's hand from a hammer causes the hammer to fall. However, doing so in outer space does not produce the same outcome, calling into question if releasing one's fingers from a hammer always causes it to fall. A causal graph could be created to acknowledge that both the presence of gravity and the release of the hammer contribute to its falling. However, it would be very surprising if the surface underneath the hammer affected its falling. This essentially states the Causal Markov Condition, that given the existence of gravity the release of the hammer, it will fall regardless of what is beneath it. == Implications == === Dependence and Causation === It follows from the definition that if X and Y are in V and are probabilistically dependent, then either X causes Y, Y causes X, or X and Y are both effects of some common cause Z in V. This definition was seminally introduced by Hans Reichenbach as the Common Cause Principle (CCP). === Screening === It once again follows from the definition that the parents of X screen X from other "indirect causes" of X (parents of Parents(X)) and other effects of Parents(X) which are not also effects of X.

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  PenTile matrix family

  PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also

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  Preference regression

  Preference regression is a statistical technique used by marketers to determine consumers’ preferred core benefits. It usually supplements product positioning techniques like multi dimensional scaling or factor analysis and is used to create ideal vectors on perceptual maps. == Application == Starting with raw data from surveys, researchers apply positioning techniques to determine important dimensions and plot the position of competing products on these dimensions. Next they regress the survey data against the dimensions. The independent variables are the data collected in the survey. The dependent variable is the preference datum. Like all regression methods, the computer fits weights to best predict data. The resultant regression line is referred to as an ideal vector because the slope of the vector is the ratio of the preferences for the two dimensions. If all the data is used in the regression, the program will derive a single equation and hence a single ideal vector. This tends to be a blunt instrument so researchers refine the process with cluster analysis. This creates clusters that reflect market segments. Separate preference regressions are then done on the data within each segment. This provides an ideal vector for each segment. == Alternative methods == Self-stated importance method is an alternative method in which direct survey data is used to determine the weightings rather than statistical imputations. A third method is conjoint analysis in which an additive method is used.

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  Promoter based genetic algorithm

  The promoter based genetic algorithm (PBGA) is a genetic algorithm for neuroevolution developed by F. Bellas and R.J. Duro in the Integrated Group for Engineering Research (GII) at the University of Coruña, in Spain. It evolves variable size feedforward artificial neural networks (ANN) that are encoded into sequences of genes for constructing a basic ANN unit. Each of these blocks is preceded by a gene promoter acting as an on/off switch that determines if that particular unit will be expressed or not. == PBGA basics == The basic unit in the PBGA is a neuron with all of its inbound connections as represented in the following figure: The genotype of a basic unit is a set of real valued weights followed by the parameters of the neuron and proceeded by an integer valued field that determines the promoter gene value and, consequently, the expression of the unit. By concatenating units of this type we can construct the whole network. With this encoding it is imposed that the information that is not expressed is still carried by the genotype in evolution but it is shielded from direct selective pressure, maintaining this way the diversity in the population, which has been a design premise for this algorithm. Therefore, a clear difference is established between the search space and the solution space, permitting information learned and encoded into the genotypic representation to be preserved by disabling promoter genes. == Results == The PBGA was originally presented within the field of autonomous robotics, in particular in the real time learning of environment models of the robot. It has been used inside the Multilevel Darwinist Brain (MDB) cognitive mechanism developed in the GII for real robots on-line learning. In another paper it is shown how the application of the PBGA together with an external memory that stores the successful obtained world models, is an optimal strategy for adaptation in dynamic environments. Recently, the PBGA has provided results that outperform other neuroevolutionary algorithms in non-stationary problems, where the fitness function varies in time.

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