AI Coding Book

AI Coding Book — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  BabyCenter

  BabyCenter is an online media company based in San Francisco, New York City, Chicago, and Los Angeles that provides information on conception, pregnancy, birth, and early childhood development for parents and expecting parents. BabyCenter operates 8 country and region specific properties including websites, apps, emails, print publications, and an online community where parents can connect on a variety of topics. The visitors of website and the users of the app can sign up for free weekly email newsletters that guide them through pregnancy and their child's development. In addition to publishing detailed, medically reviewed information about pregnancy and parenting, BabyCenter, under its Mission Motherhood initiative, ran numerous social programs and has participated in public health initiatives in partnership with hospitals, healthcare agencies, nonprofits, NGOs, and government agencies to provide pregnancy and parenting advice. It also annually publishes the most popular baby names. BabyCenter LLC is part of the Everyday Health Group, a division of Ziff Davis. == History == BabyCenter was founded in October 1997 by Stanford University MBA graduates Matt Glickman and Mark Selcow, who recognized a need for information about pregnancy and parenting on the internet. BabyCenter was initially funded through $13.5 million in startup capital funding from venture capital firms, including Bessemer Venture Partners, Intel, and Trinity Ventures. The funds were used to open the BabyCenter Store in October 1998. In the early years of its operation, BabyCenter offered multiple resources and services for parents, including a website that provided medically reviewed information and guidance to new and expectant parents on such topics as fertility, labor, and childcare; a weekly email for pregnant women tailored to their week of pregnancy (based on their pregnancy due date); and community groups and chat rooms for pregnant couples and parents to discuss pregnancy and child-rearing strategies. The site grew quickly, and by early 1999 had 175 employees and an annual revenue of $35 million. In April of that year, the two founders sold BabyCenter to another website, eToys.com, for $190 million in stock. Twenty-three months later, in 2001, shortly before declaring bankruptcy, eToys sold the site to Johnson & Johnson for $10 million. During the eToys ownership, BabyCenter launched its first international E-commerce site in the UK during the spring of 2000. Starting in 2005, BabyCenter launched an expansion plan, extending its global network to Australia, Canada and other countries, staffing each outpost with local editors. In 2007, BabyCenter debuted a Mandarin-language site in China, initiated operations in India, launched a Spanish language website, and introduced its first mobile site. BabyCenter released My Pregnancy Today, its first mobile app, to Apple's App Store in August 2010 and to the Android market in April 2011. The app provided daily information, nutrition tips, advice relevant to the user's week of pregnancy, and 3-D animated videos showcasing a baby's development in utero. The My Pregnancy app was joined by a My Baby Today app in October 2011. In 2015, BabyCenter released Mom Feed, its first mobile app for parents of toddlers and older children (ages 1 to 8). Mom Feed offered personalized, stage-based information as well as content from the BabyCenter Community and Blog in a real-time stream. In 2016, BabyCenter launched its web-based Baby Names Finder. In 2018, Mom Feed was discontinued and BabyCenter replaced that experience with a separate Child Health content area on its website. Also in 2018, BabyCenter launched its mobile baby name generator, the Baby Names app, which, like the web-based Baby Names Finder, leverages data from hundreds of thousands of parents that culminates in its annual most popular Baby Names Report. In 2019, Johnson & Johnson sold Baby Center to Everyday Health Group, a division of New York-based parent company of Ziff Davis, Inc. Neither side disclosed terms of the deal. == Popular research == BabyCenter's most popular baby names is released annually and often cited by the media. In March 2024, BabyCenter did a review of the app Temu and said that the website has found products that have been recalled, could be counterfeit or circumvent U.S. safety standards and features that are important in preventing issues like choking. In 2025, BabyCenter released a report about the cost of raising a newborn baby in the first year. == Content and products == === Websites === BabyCenter has 8 country and region-specific websites around the world, including sites for the United States, Canada, Australia, Brazil, India, Germany, the United Kingdom, and Latin America. Users can find parenting and pregnancy advice in seven languages: English, Spanish, Portuguese, Arabic, French, German, and Hindi BabyCenter content for each country- or region-specific site is written by an editorial team based in that country or region. Medical and health content for each site is reviewed by a medical advisory board based there and adheres to that country or region's medical standards. For example, the U.S. site works with and follows the recommendations of such U.S. medical authorities as the American Academy of Pediatrics, the American Congress of Obstetrics & Gynecology and the Society for Maternal-Fetal Medicine. BabyCenter regularly conducts research and provides thought leadership on pregnancy and parenting topics, popularly cited by major media outlets including The Wall Street Journal, Forbes, The Washington Post, BuzzFeed, Insider, MarketWatch, Axios. === Community, blogs and social === From its earliest days, BabyCenter has had a community area that allows people to join a group of parents with children born in the same month, known as a Birth Club. BabyCenter launched a blog called Momformation in 2007. Eventually, the name was changed to BabyCenter Blog. In April 2021, the BabyCenter Community was identified in a research article within the journal PLOS Computational Biology as facilitating "unobstructed communication" between parents, which avoids the "strong echo chamber phenomena" that can foster and perpetuate vaccine misinformation. === My Pregnancy and Baby Today App === The app is available in six languages, although not all features are supported for every market. Initially the apps only featured pregnancy articles that could be found on the BabyCenter website, but over the years the feature set has expanded to include a growing list of app-specific tools such as weekly fetal development information, a kick tracker, a birth plan worksheet, a contraction timer, a baby growth tracker, a photo journal for pregnant women to record their pregnancy bellies, and a photo journal for documenting a baby's first year. === Mission Motherhood™ === BabyCenter was a cofounder of the Mobile Alliance for Maternal Action (MAMA), a public-private partnership between USAID, Johnson & Johnson, the UN Foundation, and BabyCenter from 2011 to-to 2015. The MAMA program sparked the creation of MomConnect, an initiative of the South African Department of Health for which BabyCenter developed SMS messages with health information about pregnancy and a child's first year of life. BabyCenter helped develop similar messages for mMitra, a voice messaging program in India. A research article in the Maternal and Child Health Journal stated the mMitra program offered strong evidence "that tailored mobile phone voice messages can improve key infant care knowledge and practices that lead to improved infant health outcomes in low-resource settings. BabyCenter's Mission Motherhood Messages were available to qualifying organizations on the BabyCenter website. BabyCenter contributed websites for Free Basics. These websites featured age and stage-based pregnancy and baby articles targeted to low-income, lower-education women who would not otherwise have access to health information. Content developed for this program was also used to support a UNICEF SMS program during the 2016 Zika outbreak. == Awards and recognition == In 1998, BabyCenter won a Webby Award for Best Home Site. Since then, it has been nominated for a Webby Award 19 times and won either a Webby or a People's Choice Webby Award 12 times – including a People's Voice win in 2021 for Lifestyle websites and mobile sites. In 2002, it won Service Journalism award from Online Journalism Awards (OJA). In 2015, BabyCenter won five Digital Health Awards for content about autism in children. In 2016, BabyCenter won seven Digital Health Awards: four for videos about the aches and pains of pregnancy, baby sleep, and the walking milestone in child development; two for articles about baby sleep training and sleep apnea in babies; and one for the BabyCenter mobile app My Pregnancy & Baby Today. In 2021, Forbes Health chose My Pregnancy & Baby Today as the best pregnancy app of 2021, and Women's Health identified it

  Read more →
• 

  BookCorpus

  BookCorpus (also sometimes referred to as the Toronto Book Corpus) is a dataset consisting of the text of around 7,000 self-published books scraped from the indie ebook distribution website Smashwords. It was the main corpus used to train the initial GPT model by OpenAI, and has been used as training data for other early large language models including Google's BERT. The dataset consists of around 985 million words, and the books that comprise it span a range of genres, including romance, science fiction, and fantasy. The corpus was introduced in a 2015 paper by researchers from the University of Toronto and MIT titled "Aligning Books and Movies: Towards Story-like Visual Explanations by Watching Movies and Reading Books". The authors described it as consisting of "free books written by yet unpublished authors," yet this is factually incorrect. These books were published by self-published ("indie") authors who priced them at free; the books were downloaded without the consent or permission of Smashwords or Smashwords authors and in violation of the Smashwords Terms of Service. The dataset was initially hosted on a University of Toronto webpage. An official version of the original dataset is no longer publicly available, though at least one substitute, BookCorpusOpen, has been created. Though not documented in the original 2015 paper, the site from which the corpus's books were scraped is now known to be Smashwords.

  Read more →
• 

  Multiclass classification

  In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (e.g., decision trees, k-NN, neural networks and multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms (e.g., classical binary support vector machine) and require decomposition strategies such as one-vs-all, one-vs-one, or ECOC to solve multiclass problems. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance (e.g., predicting that an image contains both an apple and an orange, in the previous example). == Better-than-random multiclass models == From the confusion matrix of a multiclass model, we can determine whether a model does better than chance. Let K ≥ 3 {\displaystyle K\geq 3} be the number of classes, O {\displaystyle {\mathcal {O}}} a set of observations, y ^ : O → { 1 , . . . , K } {\displaystyle {\hat {y}}:{\mathcal {O}}\to \{1,...,K\}} a model of the target variable y : O → { 1 , . . . , K } {\displaystyle y:{\mathcal {O}}\to \{1,...,K\}} and n i , j {\displaystyle n_{i,j}} be the number of observations in the set { y = i } ∩ { y ^ = j } {\displaystyle \{y=i\}\cap \{{\hat {y}}=j\}} . We note n i . = ∑ j n i , j {\displaystyle n_{i.}=\sum _{j}n_{i,j}} , n . j = ∑ i n i , j {\displaystyle n_{.j}=\sum _{i}n_{i,j}} , n = ∑ j n . j = ∑ i n i . {\displaystyle n=\sum _{j}n_{.j}=\sum _{i}n_{i.}} , λ i = n i . n {\displaystyle \lambda _{i}={\frac {n_{i.}}{n}}} and μ j = n . j n {\displaystyle \mu _{j}={\frac {n_{.j}}{n}}} . It is assumed that the confusion matrix ( n i , j ) i , j {\displaystyle (n_{i,j})_{i,j}} contains at least one non-zero entry in each row, that is λ i > 0 {\displaystyle \lambda _{i}>0} for any i {\displaystyle i} . Finally we call "normalized confusion matrix" the matrix of conditional probabilities ( P ( y ^ = j ∣ y = i ) ) i , j = ( n i , j n i . ) i , j {\displaystyle (\mathbb {P} ({\hat {y}}=j\mid y=i))_{i,j}=\left({\frac {n_{i,j}}{n_{i.}}}\right)_{i,j}} . === Intuitive explanation === The lift is a way of measuring the deviation from independence of two events A {\displaystyle A} and B {\displaystyle B} : L i f t ( A , B ) = P ( A ∩ B ) P ( A ) P ( B ) = P ( A ∣ B ) P ( A ) = P ( B ∣ A ) P ( B ) {\displaystyle \mathrm {Lift} (A,B)={\frac {\mathbb {P} (A\cap B)}{\mathbb {P} (A)\mathbb {P} (B)}}={\frac {\mathbb {P} (A\mid B)}{\mathbb {P} (A)}}={\frac {\mathbb {P} (B\mid A)}{\mathbb {P} (B)}}} We have L i f t ( A , B ) > 1 {\displaystyle \mathrm {Lift} (A,B)>1} if and only if events A {\displaystyle A} and B {\displaystyle B} occur simultaneously with a greater probability than if they were independent. In other words, if one of the two events occurs, the probability of observing the other event increases. A first condition to satisfy is to have L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} . And the quality of a model (better or worse than chance) does not change if we over- or undersample the dataset, that is if we multiply each row R i {\displaystyle R_{i}} of the confusion matrix by a constant c i {\displaystyle c_{i}} . Thus the second condition is that the necessary and sufficient conditions for doing better than chance need only depend on the normalized confusion matrix. The condition on lifts can be reformulated with One versus Rest binary models : for any i {\displaystyle i} , we define the binary target variable y i {\displaystyle y_{i}} which is the indicator of event { y = i } {\displaystyle \{y=i\}} , and the binary model y ^ i {\displaystyle {\hat {y}}_{i}} of y i {\displaystyle y_{i}} which is the indicator of event { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} . Each of the y ^ i {\displaystyle {\hat {y}}_{i}} models is a "One versus Rest" model. L i f t ( y = i , y ^ = i ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)} only depends on the events { y = i } {\displaystyle \{y=i\}} and { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} , so merging or not merging the other classes doesn't change its value. We therefore have L i f t ( y = i , y ^ = i ) = L i f t ( y i = 1 , y ^ i = 1 ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)=\mathrm {Lift} (y_{i}=1,{\hat {y}}_{i}=1)} and the first condition is that all binary One versus Rest models are better than chance. ==== Example ==== If K = 2 {\displaystyle K=2} and 2 is the class of interest , the normalized confusion matrix is ( s p e c i f i c i t y 1 − s p e c i f i c i t y 1 − s e n s i t i v i t y s e n s i t i v i t y ) {\displaystyle {\begin{pmatrix}\mathrm {specificity} &1-\mathrm {specificity} \\1-\mathrm {sensitivity} &\mathrm {sensitivity} \end{pmatrix}}} and we have L i f t ( y = 1 , y ^ = 1 ) − 1 = P ( y = y ^ = 1 ) λ 1 μ 1 − 1 = n 1 , 1 n n 1. n .1 − 1 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)-1={\frac {\mathbb {P} (y={\hat {y}}=1)}{\lambda _{1}\mu _{1}}}-1={\frac {n_{1,1}n}{n_{1.}n_{.1}}}-1} = n 1 , 1 ( n 1 , 1 + n 1 , 2 + n 2 , 1 + n 2 , 2 ) − ( n 1 , 1 + n 1 , 2 ) ( n 1 , 1 + n 2 , 1 ) n 1. n .1 = n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 n 1. n .1 {\displaystyle ={\frac {n_{1,1}(n_{1,1}+n_{1,2}+n_{2,1}+n_{2,2})-(n_{1,1}+n_{1,2})(n_{1,1}+n_{2,1})}{n_{1.}n_{.1}}}={\frac {n_{1,1}n_{2,2}-n_{1,2}n_{2,1}}{n_{1.}n_{.1}}}} . Thus L i f t ( y = 1 , y ^ = 1 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Similarly, by swapping the roles of 1 and 2, we find that L i f t ( y = 2 , y ^ = 2 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=2,{\hat {y}}=2)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Dividing by n 1. n 2. {\displaystyle n_{1.}n_{2.}} we find that the necessary and sufficient condition on the normalized confusion matrix is s e n s i t i v i t y s p e c i f i c i t y − ( 1 − s e n s i t i v i t y ) ( 1 − s p e c i f i c i t y ) ≥ 0 ⟺ s e n s i t i v i t y + s p e c i f i c i t y − 1 ≥ 0 ⟺ J ≥ 0 {\displaystyle \mathrm {sensitivity} \ \mathrm {specificity} -(1-\mathrm {sensitivity} )(1-\mathrm {specificity} )\geq 0\iff \mathrm {sensitivity} +\mathrm {specificity} -1\geq 0\iff J\geq 0} . This brings us back to the classical binary condition: Youden's J must be positive (or zero for random models). === Random models === A random model is a model that is independent of the target variable. This property is easily reformulated with the confusion matrix. This proposition shows that the model y ^ {\displaystyle {\hat {y}}} of y {\displaystyle y} is uninformative if and only if there are two families of numbers ( α i ) i {\displaystyle (\alpha _{i})_{i}} and ( β j ) j {\displaystyle (\beta _{j})_{j}} such that P ( { y = i } ∩ { y ^ = j } ) = α i β j {\displaystyle \mathbb {P} (\{y=i\}\cap \{{\hat {y}}=j\})=\alpha _{i}\beta _{j}} for any i {\displaystyle i} and j {\displaystyle j} . === Multiclass likelihood ratios and diagnostic odds ratios === We define generalized likelihood ratios calculated from the normalized confusion matrix: for any i {\displaystyle i} and j ≠ i {\displaystyle j\not =i} , let L R i , j = P ( y ^ = j ∣ y = j ) P ( y ^ = j ∣ y = i ) {\displaystyle \mathrm {LR} _{i,j}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)}}} . When K = 2 {\displaystyle K=2} , if 2 is the class of interest,, we find the classical likelihood ratios L R 1 , 2 = L R + {\displaystyle \mathrm {LR} _{1,2}=\mathrm {LR} _{+}} and L R 2 , 1 = 1 L R − {\displaystyle \mathrm {LR} _{2,1}={\frac {1}{\mathrm {LR} _{-}}}} . Multiclass diagnostic odds ratios can also be defined using the formula D O R i , j = D O R j , i = L R i , j L R j , i = n i , i n j , j n i , j n j , i = P ( y ^ = j ∣ y = j ) / P ( y ^ = i ∣ y = j ) P ( y ^ = j ∣ y = i ) / P ( y ^ = i ∣ y = i ) {\displaystyle \mathrm {DOR} _{i,j}=\mathrm {DOR} _{j,i}=\mathrm {LR} _{i,j}\mathrm {LR} _{j,i}={\frac {n_{i,i}n_{j,j}}{n_{i,j}n_{j,i}}}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)/\mathbb {P} ({\hat {y}}=i\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)/\mathbb {P} ({\hat {y}}=i\mid y=i)}}} We saw above that a better-than-chance model (or a random model) must verify L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} and λ i {\displaystyle \lambda _{i}} . According to the previous corollary, likelihood ratios are thus greater

  Read more →
• 

  Generalized multidimensional scaling

  Generalized multidimensional scaling (GMDS) is an extension of metric multidimensional scaling, in which the target space is non-Euclidean. When the dissimilarities are distances on a surface and the target space is another surface, GMDS allows finding the minimum-distortion embedding of one surface into another. GMDS is an emerging research direction. Currently, main applications are recognition of deformable objects (e.g. for three-dimensional face recognition) and texture mapping.

  Read more →
• 

  Keka HR

  Keka HR is a software company that provides cloud-based human resource management and payroll automation software. Keka HR specializes in providing business services in the field of HR technology, payroll automation, recruiting, leave, attendance and performance management. The company was founded by Vijay Yalamanchili on July 21, 2014. The company is headquartered in Hyderabad, with operations in Singapore and the United States. == History == Keka HR was established in 2014 in Hyderabad, Telangana, India. In 2015, the company entered the Indian HR market and received the HYSEA Startup Award. By 2019, Keka HR had surpassed $1 million in annual recurring revenue (ARR). During the COVID-19 pandemic in 2020, the company reported a sevenfold increase in sales. By 2021, the company had raised $1.6 million through Recur Club. In 2022, Keka HR secured $57 million in Series A funding from West Bridge Capital. The company's headquarters are located in Gachibowli, Hyderabad, with offices in Singapore and Seattle, Washington.

  Read more →
• 

  Fitness approximation

  Fitness approximation aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation. Fitness approximation in evolutionary optimization can be seen as a sub-area of data-driven evolutionary optimization. == Approximate models in function optimization == === Motivation === In many real-world optimization problems including engineering problems, the number of fitness function evaluations needed to obtain a good solution dominates the optimization cost. In order to obtain efficient optimization algorithms, it is crucial to use prior information gained during the optimization process. Conceptually, a natural approach to utilizing the known prior information is building a model of the fitness function to assist in the selection of candidate solutions for evaluation. A variety of techniques for constructing such a model, often also referred to as surrogates, metamodels or approximation models – for computationally expensive optimization problems have been considered. === Approaches === Common approaches to constructing approximate models based on learning and interpolation from known fitness values of a small population include: Low-degree polynomials and regression models Fourier surrogate modeling Artificial neural networks including Multilayer perceptrons Radial basis function network Support vector machines Due to the limited number of training samples and high dimensionality encountered in engineering design optimization, constructing a globally valid approximate model remains difficult. As a result, evolutionary algorithms using such approximate fitness functions may converge to local optima. Therefore, it can be beneficial to selectively use the original fitness function together with the approximate model.

  Read more →
• 

  Mean squared prediction error

  In statistics the mean squared prediction error (MSPE), also known as mean squared error of the predictions, of a smoothing, curve fitting, or regression procedure is the expected value of the squared prediction errors (PE), the square difference between the fitted values implied by the predictive function g ^ {\displaystyle {\widehat {g}}} and the values of the (unobservable) true value g. It is an inverse measure of the explanatory power of g ^ , {\displaystyle {\widehat {g}},} and can be used in the process of cross-validation of an estimated model. Knowledge of g would be required in order to calculate the MSPE exactly; in practice, MSPE is estimated. == Formulation == If the smoothing or fitting procedure has projection matrix (i.e., hat matrix) L, which maps the observed values vector y {\displaystyle y} to predicted values vector y ^ = L y , {\displaystyle {\hat {y}}=Ly,} then PE and MSPE are formulated as: P E i = g ( x i ) − g ^ ( x i ) , {\displaystyle \operatorname {PE_{i}} =g(x_{i})-{\widehat {g}}(x_{i}),} MSPE = E ⁡ [ PE i 2 ] = ∑ i = 1 n PE i 2 ⁡ / n . {\displaystyle \operatorname {MSPE} =\operatorname {E} \left[\operatorname {PE} _{i}^{2}\right]=\sum _{i=1}^{n}\operatorname {PE} _{i}^{2}/n.} The MSPE can be decomposed into two terms: the squared bias (mean error) of the fitted values and the variance of the fitted values: MSPE = ME 2 + VAR , {\displaystyle \operatorname {MSPE} =\operatorname {ME} ^{2}+\operatorname {VAR} ,} ME = E ⁡ [ g ^ ( x i ) − g ( x i ) ] {\displaystyle \operatorname {ME} =\operatorname {E} \left[{\widehat {g}}(x_{i})-g(x_{i})\right]} VAR = E ⁡ [ ( g ^ ( x i ) − E ⁡ [ g ( x i ) ] ) 2 ] . {\displaystyle \operatorname {VAR} =\operatorname {E} \left[\left({\widehat {g}}(x_{i})-\operatorname {E} \left[{g}(x_{i})\right]\right)^{2}\right].} The quantity SSPE=nMSPE is called sum squared prediction error. The root mean squared prediction error is the square root of MSPE: RMSPE=√MSPE. == Computation of MSPE over out-of-sample data == The mean squared prediction error can be computed exactly in two contexts. First, with a data sample of length n, the data analyst may run the regression over only q of the data points (with q < n), holding back the other n – q data points with the specific purpose of using them to compute the estimated model’s MSPE out of sample (i.e., not using data that were used in the model estimation process). Since the regression process is tailored to the q in-sample points, normally the in-sample MSPE will be smaller than the out-of-sample one computed over the n – q held-back points. If the increase in the MSPE out of sample compared to in sample is relatively slight, that results in the model being viewed favorably. And if two models are to be compared, the one with the lower MSPE over the n – q out-of-sample data points is viewed more favorably, regardless of the models’ relative in-sample performances. The out-of-sample MSPE in this context is exact for the out-of-sample data points that it was computed over, but is merely an estimate of the model’s MSPE for the mostly unobserved population from which the data were drawn. Second, as time goes on more data may become available to the data analyst, and then the MSPE can be computed over these new data. == Estimation of MSPE over the population == When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows. For the model y i = g ( x i ) + σ ε i {\displaystyle y_{i}=g(x_{i})+\sigma \varepsilon _{i}} where ε i ∼ N ( 0 , 1 ) {\displaystyle \varepsilon _{i}\sim {\mathcal {N}}(0,1)} , one may write n ⋅ MSPE ⁡ ( L ) = g T ( I − L ) T ( I − L ) g + σ 2 tr ⁡ [ L T L ] . {\displaystyle n\cdot \operatorname {MSPE} (L)=g^{\text{T}}(I-L)^{\text{T}}(I-L)g+\sigma ^{2}\operatorname {tr} \left[L^{\text{T}}L\right].} Using in-sample data values, the first term on the right side is equivalent to ∑ i = 1 n ( E ⁡ [ g ( x i ) − g ^ ( x i ) ] ) 2 = E ⁡ [ ∑ i = 1 n ( y i − g ^ ( x i ) ) 2 ] − σ 2 tr ⁡ [ ( I − L ) T ( I − L ) ] . {\displaystyle \sum _{i=1}^{n}\left(\operatorname {E} \left[g(x_{i})-{\widehat {g}}(x_{i})\right]\right)^{2}=\operatorname {E} \left[\sum _{i=1}^{n}\left(y_{i}-{\widehat {g}}(x_{i})\right)^{2}\right]-\sigma ^{2}\operatorname {tr} \left[\left(I-L\right)^{T}\left(I-L\right)\right].} Thus, n ⋅ MSPE ⁡ ( L ) = E ⁡ [ ∑ i = 1 n ( y i − g ^ ( x i ) ) 2 ] − σ 2 ( n − tr ⁡ [ L ] ) . {\displaystyle n\cdot \operatorname {MSPE} (L)=\operatorname {E} \left[\sum _{i=1}^{n}\left(y_{i}-{\widehat {g}}(x_{i})\right)^{2}\right]-\sigma ^{2}\left(n-\operatorname {tr} \left[L\right]\right).} If σ 2 {\displaystyle \sigma ^{2}} is known or well-estimated by σ ^ 2 {\displaystyle {\widehat {\sigma }}^{2}} , it becomes possible to estimate MSPE by n ⋅ M S P E ^ ⁡ ( L ) = ∑ i = 1 n ( y i − g ^ ( x i ) ) 2 − σ ^ 2 ( n − tr ⁡ [ L ] ) . {\displaystyle n\cdot \operatorname {\widehat {MSPE}} (L)=\sum _{i=1}^{n}\left(y_{i}-{\widehat {g}}(x_{i})\right)^{2}-{\widehat {\sigma }}^{2}\left(n-\operatorname {tr} \left[L\right]\right).} Colin Mallows advocated this method in the construction of his model selection statistic Cp, which is a normalized version of the estimated MSPE: C p = ∑ i = 1 n ( y i − g ^ ( x i ) ) 2 σ ^ 2 − n + 2 p . {\displaystyle C_{p}={\frac {\sum _{i=1}^{n}\left(y_{i}-{\widehat {g}}(x_{i})\right)^{2}}{{\widehat {\sigma }}^{2}}}-n+2p.} where p the number of estimated parameters p and σ ^ 2 {\displaystyle {\widehat {\sigma }}^{2}} is computed from the version of the model that includes all possible regressors. That concludes this proof.

  Read more →
• 

  Constructing skill trees

  Constructing skill trees (CST) is a hierarchical reinforcement learning algorithm which can build skill trees from a set of sample solution trajectories obtained from demonstration. CST uses an incremental MAP (maximum a posteriori) change point detection algorithm to segment each demonstration trajectory into skills and integrate the results into a skill tree. CST was introduced by George Konidaris, Scott Kuindersma, Andrew Barto and Roderic Grupen in 2010. == Algorithm == CST consists of mainly three parts;change point detection, alignment and merging. The main focus of CST is online change-point detection. The change-point detection algorithm is used to segment data into skills and uses the sum of discounted reward R t {\displaystyle R_{t}} as the target regression variable. Each skill is assigned an appropriate abstraction. A particle filter is used to control the computational complexity of CST. The change point detection algorithm is implemented as follows. The data for times t ∈ T {\displaystyle t\in T} and models Q with prior p ( q ∈ Q ) {\displaystyle p(q\in Q)} are given. The algorithm is assumed to be able to fit a segment from time j + 1 {\displaystyle j+1} to t using model q with the fit probability P ( j , t , q ) {\displaystyle P(j,t,q)_{}^{}} . A linear regression model with Gaussian noise is used to compute P ( j , t , q ) {\displaystyle P(j,t,q)} . The Gaussian noise prior has mean zero, and variance which follows I n v e r s e G a m m a ( v 2 , u 2 ) {\displaystyle \mathrm {InverseGamma} \left({\frac {v}{2}},{\frac {u}{2}}\right)} . The prior for each weight follows N o r m a l ( 0 , σ 2 δ ) {\displaystyle \mathrm {Normal} (0,\sigma ^{2}\delta )} . The fit probability P ( j , t , q ) {\displaystyle P(j,t,q)} is computed by the following equation. P ( j , t , q ) = π − n 2 δ m | ( A + D ) − 1 | 1 2 u v 2 ( y + u ) u + v 2 Γ ( n + v 2 ) Γ ( v 2 ) {\displaystyle P(j,t,q)={\frac {\pi ^{-{\frac {n}{2}}}}{\delta ^{m}}}\left|(A+D)^{-1}\right|^{\frac {1}{2}}{\frac {u^{\frac {v}{2}}}{(y+u)^{\frac {u+v}{2}}}}{\frac {\Gamma ({\frac {n+v}{2}})}{\Gamma ({\frac {v}{2}})}}} Then, CST compute the probability of the changepoint at time j with model q, P t ( j , q ) {\displaystyle P_{t}(j,q)} and P j MAP {\displaystyle P_{j}^{\text{MAP}}} using a Viterbi algorithm. P t ( j , q ) = ( 1 − G ( t − j − 1 ) ) P ( j , t , q ) p ( q ) P j MAP {\displaystyle P_{t}(j,q)=(1-G(t-j-1))P(j,t,q)p(q)P_{j}^{\text{MAP}}} P j MAP = max i , q P j ( i , q ) g ( j − i ) 1 − G ( j − i − 1 ) , ∀ j < t {\displaystyle P_{j}^{\text{MAP}}=\max _{i,q}{\frac {P_{j}(i,q)g(j-i)}{1-G(j-i-1)}},\forall j Read more →

• 

  Circle Hough Transform

  The circle Hough Transform (CHT) is a basic feature extraction technique used in digital image processing for detecting circles in imperfect images. The circle candidates are produced by “voting” in the Hough parameter space and then selecting local maxima in an accumulator matrix. It is a specialization of the Hough transform. == Theory == In a two-dimensional space, a circle can be described by: ( x − a ) 2 + ( y − b ) 2 = r 2 ( 1 ) {\displaystyle \left(x-a\right)^{2}+\left(y-b\right)^{2}=r^{2}\ \ \ \ \ (1)} where (a,b) is the center of the circle, and r is the radius. If a 2D point (x,y) is fixed, then the parameters can be found according to (1). The parameter space would be three dimensional, (a, b, r). And all the parameters that satisfy (x, y) would lie on the surface of an inverted right-angled cone whose apex is at (x, y, 0). In the 3D space, the circle parameters can be identified by the intersection of many conic surfaces that are defined by points on the 2D circle. This process can be divided into two stages. The first stage is fixing radius then find the optimal center of circles in a 2D parameter space. The second stage is to find the optimal radius in a one dimensional parameter space. === Find parameters with known radius R === If the radius is fixed, then the parameter space would be reduced to 2D (the position of the circle center). For each point (x, y) on the original circle, it can define a circle centered at (x, y) with radius R according to (1). The intersection point of all such circles in the parameter space would be corresponding to the center point of the original circle. Consider 4 points on a circle in the original image (left). The circle Hough transform is shown in the right. Note that the radius is assumed to be known. For each (x,y) of the four points (white points) in the original image, it can define a circle in the Hough parameter space centered at (x, y) with radius r. An accumulator matrix is used for tracking the intersection point. In the parameter space, the voting number of those points that have a newly defined circle passing through them would be increased by one for every circle. Then the local maxima point (the red point in the center in the right figure) can be found. The position (a, b) of the maxima would be the center of the original circle. === Multiple circles with known radius R === Multiple circles with same radius can be found with the same technique. Note that, in the accumulator matrix (right fig), there would be at least 3 local maxima points. === Accumulator matrix and voting === In practice, an accumulator matrix is introduced to find the intersection point in the parameter space. First, we need to divide the parameter space into “buckets” using a grid and produce an accumulator matrix according to the grid. The element in the accumulator matrix denotes the number of “circles” in the parameter space that are passing through the corresponding grid cell in the parameter space. The number is also called “voting number”. Initially, every element in the matrix is zeros. Then for each “edge” point in the original space, we can formulate a circle in the parameter space and increase the voting number of the grid cell which the circle passes through. This process is called “voting”. After voting, we can find local maxima in the accumulator matrix. The positions of the local maxima are corresponding to the circle centers in the original space. === Find circle parameter with unknown radius === Since the parameter space is 3D, the accumulator matrix would be 3D, too. We can iterate through possible radii; for each radius, we use the previous technique. Finally, find the local maxima in the 3D accumulator matrix. Accumulator array should be A[x,y,r] in the 3D space. Voting should be for each pixels, radius and theta A[x,y,r] += 1 The algorithm : For each A[a,b,r] = 0; Process the filtering algorithm on image Gaussian Blurring, convert the image to grayscale ( grayScaling), make Canny operator, The Canny operator gives the edges on image. Vote on all possible circles in accumulator. The local maximum voted circles of Accumulator A gives the circle Hough space. The maximum voted circle of Accumulator gives the circle. The Incrementing for Best Candidate : For each A[a,b,r] = 0; // fill with zeroes initially, instantiate 3D matrix For each cell(x,y) For each theta t = 0 to 360 // the possible theta 0 to 360 b = y – r sin(t PI / 180); //polar coordinate for center (convert to radians) a = x – r cos(t PI / 180); //polar coordinate for center (convert to radians) A[a,b,r] +=1; //voting end end == Examples == === Find circles in a shoe-print === The original picture (right) is first turned into a binary image (left) using a threshold and Gaussian filter. Then edges (mid) are found from it using canny edge detection. After this, all the edge points are used by the Circle Hough Transform to find underlying circle structure. == Limitations == Since the parameter space of the CHT is three dimensional, it may require lots of storage and computation. Choosing a bigger grid size can ameliorate this problem. However, choosing an appropriate grid size is difficult. Since too coarse a grid can lead to large values of the vote being obtained falsely because many quite different structures correspond to a single bucket. Too fine a grid can lead to structures not being found because votes resulting from tokens that are not exactly aligned end up in different buckets, and no bucket has a large vote. Also, the CHT is not very robust to noise. == Extensions == === Adaptive Hough Transform === J. Illingworth and J. Kittler introduced this method for implementing Hough Transform efficiently. The AHT uses a small accumulator array and the idea of a flexible iterative "coarse to fine" accumulation and search strategy to identify significant peaks in the Hough parameter spaces. This method is substantially superior to the standard Hough Transform implementation in both storage and computational requirements. == Application == === People Counting === Since the head would be similar to a circle in an image, CHT can be used for detecting heads in a picture, so as to count the number of persons in the image. === Brain Aneurysm Detection === Modified Hough Circle Transform (MHCT) is used on the image extracted from Digital Subtraction Angiogram (DSA) to detect and classify aneurysms type. == Implementation code == Circle Detection via Standard Hough Transform, by Amin Sarafraz, Mathworks (File Exchange) Hough Circle Transform, OpenCV-Python Tutorials (archived version on archive.org)

  Read more →
• 

  Extremal Ensemble Learning

  Extremal Ensemble Learning (EEL) is a machine learning algorithmic paradigm for graph partitioning. EEL creates an ensemble of partitions and then uses information contained in the ensemble to find new and improved partitions. The ensemble evolves and learns how to form improved partitions through extremal updating procedure. The final solution is found by achieving consensus among its member partitions about what the optimal partition is. == Reduced-Network Extremal Ensemble Learning (RenEEL) == A particular implementation of the EEL paradigm is the Reduced-Network Extremal Ensemble Learning (RenEEL) scheme for partitioning a graph. RenEEL uses consensus across many partitions in an ensemble to create a reduced network that can be efficiently analyzed to find more accurate partitions. These better quality partitions are subsequently used to update the ensemble. An algorithm that utilizes the RenEEL scheme is currently the best algorithm for finding the graph partition with maximum modularity, which is an NP-hard problem.

  Read more →
• 

  Dynamic Bayesian network

  A dynamic Bayesian network (DBN) is a Bayesian network (BN) which relates variables to each other over adjacent time steps. == History == A dynamic Bayesian network (DBN) is often called a "two-timeslice" BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by Paul Dagum in the early 1990s at Stanford University's Section on Medical Informatics. Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden Markov models into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains. Today, DBNs are common in robotics, and have shown potential for a wide range of data mining applications. For example, they have been used in speech recognition, digital forensics, protein sequencing, and bioinformatics. DBN is a generalization of hidden Markov models and Kalman filters. DBNs are conceptually related to probabilistic Boolean networks and can, similarly, be used to model dynamical systems at steady-state.

  Read more →
• 

  Recursive neural network

  A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order. These networks were first introduced to learn distributed representations of structure (such as logical terms), but have been successful in multiple applications, for instance in learning sequence and tree structures in natural language processing (mainly continuous representations of phrases and sentences based on word embeddings). == Architectures == === Basic === In the simplest architecture, nodes are combined into parents using a weight matrix (which is shared across the whole network) and a non-linearity such as the tanh {\displaystyle \tanh } hyperbolic function. If c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} are n {\displaystyle n} -dimensional vector representations of nodes, their parent will also be an n {\displaystyle n} -dimensional vector, defined as: p 1 , 2 = tanh ⁡ ( W [ c 1 ; c 2 ] ) {\displaystyle p_{1,2}=\tanh(W[c_{1};c_{2}])} where W {\displaystyle W} is a learned n × 2 n {\displaystyle n\times 2n} weight matrix. This architecture, with a few improvements, has been used for successfully parsing natural scenes, syntactic parsing of natural language sentences, and recursive autoencoding and generative modeling of 3D shape structures in the form of cuboid abstractions. === Recursive cascade correlation (RecCC) === RecCC is a constructive neural network approach to deal with tree domains with pioneering applications to chemistry and extension to directed acyclic graphs. === Unsupervised RNN === A framework for unsupervised RNN has been introduced in 2004. === Tensor === Recursive neural tensor networks use a single tensor-based composition function for all nodes in the tree. == Training == === Stochastic gradient descent === Typically, stochastic gradient descent (SGD) is used to train the network. The gradient is computed using backpropagation through structure (BPTS), a variant of backpropagation through time used for recurrent neural networks. == Properties == The universal approximation capability of RNNs over trees has been proved in literature. == Related models == === Recurrent neural networks === Recurrent neural networks are recursive artificial neural networks with a certain structure: that of a linear chain. Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step. === Tree Echo State Networks === An efficient approach to implement recursive neural networks is given by the Tree Echo State Network within the reservoir computing paradigm. === Extension to graphs === Extensions to graphs include graph neural network (GNN), Neural Network for Graphs (NN4G), and more recently convolutional neural networks for graphs.

  Read more →
• 

  Path tracing

  Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects and participating media to generate realistic (physically plausible) images. It is based on earlier, more limited, ray tracing algorithms. Path tracing is used to create photorealistic images for artistic purposes, and for applications such as architectural rendering and product design. It is also used to render frames for animated films, and visual effects for film and television. Because it can be very accurate and unbiased, it is commonly used to generate reference images when testing the quality of other rendering algorithms. The technique uses the Monte Carlo method to compute estimates of global illumination and simulate the ways different materials reflect (or scatter), transmit, absorb, and emit light. It can incorporate simple modeling of the effects of aperture and lens (depth of field, and bokeh) and shutter speed (motion blur), or more realistic simulation of the optical components in a camera. The algorithm works by describing illumination in a scene using the rendering equation, or light transport equation, and finding an approximate solution using Monte Carlo integration. An inefficient (but accurate) version of the algorithm can be very simple, and involves tracing a ray from the camera, allowing this ray to bounce in random directions as it hits different objects in the scene, and computing the amount of light transmitted along the path to the camera whenever the path encounters a light source. This process is repeated many times for each pixel (each repetition, with generated path and transmitted light, is called a sample), and the results are averaged. One main difference between this algorithm and standard ray tracing is that a single unbranching path is traced each time, while "Whitted-style" or "Cook-style" ray tracing recursively samples branching paths (e.g. when light is both reflected and refracted by a glass object). More practical versions incorporate improvements such as quasi-Monte Carlo methods (techniques that distribute samples more evenly), importance sampling (take more samples of paths that are likely to transport more light), and next event estimation (allow a very limited form of branching, and sample additional paths that connect to the lights more directly). Because path tracing uses random samples there is noise in the final image, which decreases as more samples are taken. Images commonly require many thousands of samples per pixel (spp) to reduce noise to an acceptable level, and denoising techniques (e.g. based on neural networks) are often used. Denoising is usually necessary when path tracing is used for real-time rendering in video games, because relatively few samples can be taken. Many alternative algorithms for path tracing have been developed, although they do not always outperform more straightforward implementations. These include bidirectional path tracing (which traces paths forwards from the light source as well as backwards from the camera), Metropolis light transport, and ways of combining path tracing with photon mapping. Video games often use biased versions of path tracing to improve performance (e.g. limiting the number of bounces in each path). A family of techniques called ReSTIR has been developed that can help real-time path tracing by sharing data between nearby pixels and consecutive frames. == History == Like all ray tracing methods, path tracing is based on ray casting, which Arthur Appel used for computer graphics rendering in the late 1960s. In 1980, John Turner Whitted published a recursive ray tracing algorithm that allows rendering images of scenes containing mirrored surfaces and refractive transparent objects. In 1984, Cook et al. described a form of ray tracing called distributed ray tracing, which uses Monte Carlo integration to render effects such as depth of field, motion blur, reflection from rough surfaces, and area lights. The same year, the radiosity method (not a ray tracing method) was published, which was the first physically based method for rendering diffuse global illumination. In 1986, Jim Kajiya published a paper exploring how to use distributed ray tracing to render physically-based global illumination, and this paper also introduced and named the method called "path tracing". Path tracing and other distributed ray tracing techniques were further refined in the late 1980s and early 1990s by researchers such as James Arvo and Peter Shirley, and by Greg Ward in the open source Radiance software. Despite being theoretically able to render any lighting, the original form of path tracing can sometimes be very inefficient (or noisy) for rendering light that is reflected or refracted before illuminating a visible surface, including diffuse global illumination where light enters an area through narrow gaps, because it traces paths only from the camera. To address this, variations of path tracing that trace paths from both the camera and from light sources, called bidirectional path tracing, were published in 1993 by Eric Lafortune and Yves Willems, and in 1997 by Eric Veach and Leonidas Guibas. In 1997 Veach and Guibas also published an alternative method called Metropolis light transport, which combines bidirectional path tracing with the Metropolis method. Veach's lengthy Ph.D. dissertation described both techniques, along with the theoretical background of path tracing; later, the book Physically Based Rendering (which won an Academy Award for Technical Achievement in 2014) helped to make information about path tracing more widely available. Path tracing requires tracing a large number of paths of light in order to produce an image with a visually acceptable amount of noise. This made path tracing very slow on computers available in the 1980s and 1990s, and noise remained a problem when trying to reproduce the style of earlier computer graphics animated films. Most animated films produced until around 2010, by studios such as Pixar, used rasterization-based rendering, with ray tracing used selectively for reflections (and later for precomputed or cached global illumination). However the speed of computers rapidly increased during the 1990s. Blue Sky Studios pioneered using Monte Carlo ray tracing for global illumination in animation, including in the 1998 short film "Bunny", but they did not disclose the precise techniques used. Path tracing gradually become more practical for film production in the early 2000s. The Arnold renderer, developed by Marcos Fajardo, was used by Sony Pictures Imageworks to produce the feature-length film Monster House, released in 2006. Pixar rewrote their RenderMan software to use path tracing, and released their first feature-length path-traced film Finding Dory in 2016. Although path tracing still had a large computational cost, animation studios discovered that less human labor was required when using it, for example because global illumination no longer needed to be faked by manually placing lights. The amount of noise present in path traced images still caused difficulties, particularly when rendering motion blur (which was used extensively by earlier animated films) but denoising techniques were developed to address this. New techniques were also needed for rendering hair and fur, and to handle the extremely large scenes sometimes required by films. Renderers such as Arnold, and Disney's Hyperion, originally only used CPUs for rendering, but as GPUs became more capable (and APIs such as CUDA, OpenCL, and OptiX were released) researchers and developers began adapting algorithms and implementations to use GPUs. GPUs can dramatically reduce rendering time: for example using a high-end GPU to accelerate portions of the rendering code can make it over 30 times faster than using only a high-end CPU. == Description == Kajiya's 1986 paper defined a recursive integral equation called the rendering equation, which describes a simplified form of light transport. Using Monte Carlo integration for the integral on the right side of the equation leads fairly directly to the path tracing algorithm: I ( x , x ′ ) = g ( x , x ′ ) [ ϵ ( x , x ′ ) + ∫ S ρ ( x , x ′ , x ″ ) I ( x ′ , x ″ ) d x ″ ] {\displaystyle I(x,x')=g(x,x')\left[\epsilon (x,x')+\int _{S}\rho (x,x',x'')I(x',x'')dx''\right]} This expresses I(x,x'), the light arriving at point x from point x', as the product of a geometry term, g(x,x'), which is 0 if there is something blocking the light between the two points and 1 otherwise, and the amount of light leaving point x' and traveling towards x. The light leaving point x' is the sum of the light emitted by the surface at x', and the integral of the light arriving at x' from all other points in the scene (the integration domain S) and being reflected towards x. The factor ρ(x,x',x''), which calculates how much light is reflected, must take into account the angles at which the light is arriving and leaving, and

  Read more →
• 

  Learning classifier system

  Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component (e.g. typically a genetic algorithm in evolutionary computation) with a learning component (performing either supervised learning, reinforcement learning, or unsupervised learning). Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions (e.g. behavior modeling, classification, data mining, regression, function approximation, or game strategy). This approach allows complex solution spaces to be broken up into smaller, simpler parts for the reinforcement learning that is inside artificial intelligence research. The founding concepts behind learning classifier systems came from attempts to model complex adaptive systems, using rule-based agents to form an artificial cognitive system (i.e. artificial intelligence). == Methodology == The architecture and components of a given learning classifier system can be quite variable. It is useful to think of an LCS as a machine consisting of several interacting components. Components may be added or removed, or existing components modified/exchanged to suit the demands of a given problem domain (like algorithmic building blocks) or to make the algorithm flexible enough to function in many different problem domains. As a result, the LCS paradigm can be flexibly applied to many problem domains that call for machine learning. The major divisions among LCS implementations are as follows: (1) Michigan-style architecture vs. Pittsburgh-style architecture, (2) reinforcement learning vs. supervised learning, (3) incremental learning vs. batch learning, (4) online learning vs. offline learning, (5) strength-based fitness vs. accuracy-based fitness, and (6) complete action mapping vs best action mapping. These divisions are not necessarily mutually exclusive. For example, XCS, the best known and best studied LCS algorithm, is Michigan-style, was designed for reinforcement learning but can also perform supervised learning, applies incremental learning that can be either online or offline, applies accuracy-based fitness, and seeks to generate a complete action mapping. === Elements of a generic LCS algorithm === Keeping in mind that LCS is a paradigm for genetic-based machine learning rather than a specific method, the following outlines key elements of a generic, modern (i.e. post-XCS) LCS algorithm. For simplicity let us focus on Michigan-style architecture with supervised learning. See the illustrations on the right laying out the sequential steps involved in this type of generic LCS. ==== Environment ==== The environment is the source of data upon which an LCS learns. It can be an offline, finite training dataset (characteristic of a data mining, classification, or regression problem), or an online sequential stream of live training instances. Each training instance is assumed to include some number of features (also referred to as attributes, or independent variables), and a single endpoint of interest (also referred to as the class, action, phenotype, prediction, or dependent variable). Part of LCS learning can involve feature selection, therefore not all of the features in the training data need to be informative. The set of feature values of an instance is commonly referred to as the state. For simplicity let's assume an example problem domain with Boolean/binary features and a Boolean/binary class. For Michigan-style systems, one instance from the environment is trained on each learning cycle (i.e. incremental learning). Pittsburgh-style systems perform batch learning, where rule sets are evaluated in each iteration over much or all of the training data. ==== Rule/classifier/population ==== A rule is a context dependent relationship between state values and some prediction. Rules typically take the form of an {IF:THEN} expression, (e.g. {IF 'condition' THEN 'action'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign'}). A critical concept in LCS and rule-based machine learning alike, is that an individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Think of a rule as a "local-model" of the solution space. Rules can be represented in many different ways to handle different data types (e.g. binary, discrete-valued, ordinal, continuous-valued). Given binary data LCS traditionally applies a ternary rule representation (i.e. rules can include either a 0, 1, or '#' for each feature in the data). The 'don't care' symbol (i.e. '#') serves as a wild card within a rule's condition allowing rules, and the system as a whole to generalize relationships between features and the target endpoint to be predicted. Consider the following rule (#1###0 ~ 1) (i.e. condition ~ action). This rule can be interpreted as: IF the second feature = 1 AND the sixth feature = 0 THEN the class prediction = 1. We would say that the second and sixth features were specified in this rule, while the others were generalized. This rule, and the corresponding prediction are only applicable to an instance when the condition of the rule is satisfied by the instance. This is more commonly referred to as matching. In Michigan-style LCS, each rule has its own fitness, as well as a number of other rule-parameters associated with it that can describe the number of copies of that rule that exist (i.e. the numerosity), the age of the rule, its accuracy, or the accuracy of its reward predictions, and other descriptive or experiential statistics. A rule along with its parameters is often referred to as a classifier. In Michigan-style systems, classifiers are contained within a population [P] that has a user defined maximum number of classifiers. Unlike most stochastic search algorithms (e.g. evolutionary algorithms), LCS populations start out empty (i.e. there is no need to randomly initialize a rule population). Classifiers will instead be initially introduced to the population with a covering mechanism. In any LCS, the trained model is a set of rules/classifiers, rather than any single rule/classifier. In Michigan-style LCS, the entire trained (and optionally, compacted) classifier population forms the prediction model. ==== Matching ==== One of the most critical and often time-consuming elements of an LCS is the matching process. The first step in an LCS learning cycle takes a single training instance from the environment and passes it to [P] where matching takes place. In step two, every rule in [P] is now compared to the training instance to see which rules match (i.e. are contextually relevant to the current instance). In step three, any matching rules are moved to a match set [M]. A rule matches a training instance if all feature values specified in the rule condition are equivalent to the corresponding feature value in the training instance. For example, assuming the training instance is (001001 ~ 0), these rules would match: (###0## ~ 0), (00###1 ~ 0), (#01001 ~ 1), but these rules would not (1##### ~ 0), (000##1 ~ 0), (#0#1#0 ~ 1). Notice that in matching, the endpoint/action specified by the rule is not taken into consideration. As a result, the match set may contain classifiers that propose conflicting actions. In the fourth step, since we are performing supervised learning, [M] is divided into a correct set [C] and an incorrect set [I]. A matching rule goes into the correct set if it proposes the correct action (based on the known action of the training instance), otherwise it goes into [I]. In reinforcement learning LCS, an action set [A] would be formed here instead, since the correct action is not known. ==== Covering ==== At this point in the learning cycle, if no classifiers made it into either [M] or [C] (as would be the case when the population starts off empty), the covering mechanism is applied (fifth step). Covering is a form of online smart population initialization. Covering randomly generates a rule that matches the current training instance (and in the case of supervised learning, that rule is also generated with the correct action. Assuming the training instance is (001001 ~ 0), covering might generate any of the following rules: (#0#0## ~ 0), (001001 ~ 0), (#010## ~ 0). Covering not only ensures that each learning cycle there is at least one correct, matching rule in [C], but that any rule initialized into the population will match at least one training instance. This prevents LCS from exploring the search space of rules that do not match any training instances. ==== Parameter updates/credit assignment/learning ==== In the sixth step, the rule parameters of any rule in [M] are updated to reflect the new experience gained from the current training instance. Depending on the LCS algorithm, a number of updates can take place at this step. For supervised learning, we can simply update the accuracy/error of a

  Read more →
• 

  VIGRA

  VIGRA is the abbreviation for "Vision with Generic Algorithms". It is a free open-source computer vision library which focuses on customizable algorithms and data structures. VIGRA component can be easily adapted to specific needs of target application without compromising execution speed, by using template techniques similar to those in the C++ Standard Template Library. == Features == VIGRA is cross-platform, with working builds on Microsoft Windows, Mac OS X, Linux, and OpenBSD. Since version 1.7.1, VIGRA provides Python bindings based on numpy framework. == History == VIGRA was originally designed and implemented by scientists at University of Hamburg faculty of computer science; its core maintainers are now working at Heidelberg Collaboratory for Image Processing (HCI) University of Heidelberg. In the meantime, many developers have contributed to the project. == Application == CellCognition and ilastik uses VIGRA computer vision library. OpenOffice.org uses VIGRA as part of its headless software rendering backend; LibreOffice does so until version 5.2.

  Read more →