Argument Interchange Format

The Argument Interchange Format (AIF) is an international effort to develop a representational mechanism for exchanging argument resources between research groups, tools, and domains using a semantically rich language. AIF traces its history back to a 2005 colloquium in Budapest. The result of the work in Budapest was first published as a draft description in 2006. Building on this foundation, further work then used the AIF to build foundations for the Argument Web. AIF-RDF is the extended ontology represented in the Resource Description Framework Schema (RDFS) semantic language. The Argument Interchange Format introduces a small set of ontological concepts that aim to capture a common understanding of argument -- one that works in multiple domains (both domains of argumentation and also domains of academic research), so that data can be shared and re-used across different projects in different areas. These ontological concepts are: Information (I-nodes) Applications of Rules of Inference (RA-nodes) Applications of Rules of Conflict (CA-nodes) Applications of Rules of Preference (PA-nodes) extended by: Schematic Forms (F-nodes) that are instantiated by RA, CA and PA nodes The AIF has reifications in a variety of development environments and implementation languages including MySQL database schema RDF Prolog JSON as well as translations to visual languages such as DOT and SVG. AIF data can be accessed online at AIFdb.

Multi-model database

In the field of database design, a multi-model database is a database management system designed to support multiple data models against a single, integrated backend. In contrast, most database management systems are organized around a single data model that determines how data can be organized, stored, and manipulated. Document, graph, relational, and key–value models are examples of data models that may be supported by a multi-model database. == Background == The relational data model became popular after its publication by Edgar F. Codd in 1970. Due to increasing requirements for horizontal scalability and fault tolerance, NoSQL databases became prominent after 2009. NoSQL databases use a variety of data models, with document, graph, and key–value models being popular. A multi-model database is a database that can store, index and query data in more than one model. For some time, databases have primarily supported only one model, such as: relational database, document-oriented database, graph database or triplestore. A database that combines many of these is multi-model. This should not be confused with multimodal database systems such as Pixeltable or ApertureDB, which focus on unified management of different media types (images, video, audio, text) rather than different data models. For some time, it was all but forgotten (or considered irrelevant) that there were any other database models besides relational. The relational model and notion of third normal form were the default standard for all data storage. However, prior to the dominance of relational data modeling, from about 1980 to 2005, the hierarchical database model was commonly used. Since 2000 or 2010, many NoSQL models that are non-relational, including documents, triples, key–value stores and graphs are popular. Arguably, geospatial data, temporal data, and text data are also separate models, though indexed, queryable text data is generally termed a "search engine" rather than a database. The first time the word "multi-model" has been associated to the databases was on May 30, 2012 in Cologne, Germany, during the Luca Garulli's key note "NoSQL Adoption – What’s the Next Step?". Luca Garulli envisioned the evolution of the 1st generation NoSQL products into new products with more features able to be used by multiple use cases. The idea of multi-model databases can be traced back to Object–Relational Data Management Systems (ORDBMS) in the early 1990s and in a more broader scope even to federated and integrated DBMSs in the early 1980s. An ORDBMS system manages different types of data such as relational, object, text and spatial by plugging domain specific data types, functions and index implementations into the DBMS kernels. A multi-model database is most directly a response to the "polyglot persistence" approach of knitting together multiple database products, each handing a different model, to achieve a multi-model capability as described by Martin Fowler. This strategy has two major disadvantages: it leads to a significant increase in operational complexity, and there is no support for maintaining data consistency across the separate data stores, so multi-model databases have begun to fill in this gap. Multi-model databases are intended to offer the data modeling advantages of polyglot persistence, without its disadvantages. Operational complexity, in particular, is reduced through the use of a single data store. == Benchmarking multi-model databases == As more and more platforms are proposed to deal with multi-model data, there are a few works on benchmarking multi-model databases. For instance, Pluciennik, Oliveira, and UniBench reviewed existing multi-model databases and made an evaluation effort towards comparing multi-model databases and other SQL and NoSQL databases respectively. They pointed out that the advantages of multi-model databases over single-model databases are as follows : == Architecture == The main difference between the available multi-model databases is related to their architectures. Multi-model databases can support different models either within the engine or via different layers on top of the engine. Some products may provide an engine which supports documents and graphs while others provide layers on top of a key-key store. With a layered architecture, each data model is provided via its own component. == User-defined data models == In addition to offering multiple data models in a single data store, some databases allow developers to easily define custom data models. This capability is enabled by ACID transactions with high performance and scalability. In order for a custom data model to support concurrent updates, the database must be able to synchronize updates across multiple keys. ACID transactions, if they are sufficiently performant, allow such synchronization. JSON documents, graphs, and relational tables can all be implemented in a manner that inherits the horizontal scalability and fault-tolerance of the underlying data store. == Theoretical Foundation for Multi-Model Databases == The traditional theory of relations is not enough to accurately describe multi-model database systems. Recent research is focused on developing a new theoretical foundation for these systems. Category theory can provide a unified, rigorous language for modeling, integrating, and transforming different data models. By representing multi-model data as sets and their relationships as functions or relations within the Set category, we can create a formal framework to describe, manipulate, and understand various data models and how they interact.

Receptron

The receptron (short for "reservoir perceptron") is a neuromorphic data processing model — specifically neuromorphic computing — that generalizes the traditional perceptron, by incorporating non-linear interactions between inputs. Unlike classical perceptron, which rely on linearly independent weights, the receptron leverages complexity in physical substrates, such as the electric conduction properties of nanostructured materials or optical speckle fields, to perform classification tasks. The receptron bridges unconventional computing and neural network principles, enabling solutions that do not require the training approaches typical of artificial neural networks based on the perceptron model. == Algorithm == The receptron is an algorithm for supervised learning of binary classifiers, so a classification algorithm that makes its predictions based on a predictor function, combining a set of weights with the feature vector. The mathematical model is based on the sum of inputs with non-linear interactions: S = ∑ k = 1 n x j w ~ j ( x → ) | S ∈ R {\displaystyle S=\sum _{k=1}^{n}x_{j}{\widetilde {w}}_{j}({\vec {x}})|S\in R} (1) where j ∈ [ 1 , n ] {\displaystyle j\in [1,n]} and w ~ j {\displaystyle {\widetilde {w}}_{j}} are non-linear weight functions depending on the inputs, x → {\displaystyle {\vec {x}}} . Nonlinearity will typically make the system extremely complex, and allowing for the solution of problems not solvable through the simpler rules of a linear system, such as the perceptron or McCulloch Pitts neurons, which is based on the sum of linearly independent weights: S = ∑ k = 1 n x j w j p {\displaystyle S=\sum _{k=1}^{n}x_{j}w_{j}^{p}} (2) where w j {\displaystyle w_{j}} are constant real values. A consequence of this simplicity is the limitation to linearly separable functions, which necessitates multi-layer architectures and training algorithms like backpropagation As in the perceptron case, the summation in Eq. 1 origins the activation of the receptron output through the thresholding process, Y ( x 1 , . . . , x n ) = { 1 if S > th 0 if S ≤ th {\displaystyle Y(x_{1},...,x_{n})={\begin{cases}1&{\text{if }}S>{\text{th}}\\0&{\text{if }}S\leq {\text{th}}\end{cases}}} (3) where th is a constant threshold parameter. Equation 3 can be written by using the Heaviside step function. The weight functions w ~ ( x → ) {\displaystyle {\widetilde {w}}({\vec {x}})} can be written with a finite number of parameters w j 1 . . . j n {\displaystyle w_{j_{1}...j_{n}}} , simplifying the model representation. One can Taylor-expand w ~ ( x → ) {\displaystyle {\widetilde {w}}({\vec {x}})} and use the idempotency of Boolean variables ( x j ) q = x j ∀ q ≥ 1 {\displaystyle (x_{j})^{q}=x_{j}\forall q\geq 1} such that S ′ = b + ∑ k = 1 n x j w ~ j ( x → ) {\displaystyle S'=b+\sum _{k=1}^{n}x_{j}{\widetilde {w}}_{j}({\vec {x}})} can be written as S ′ ( x → ) = b + ∑ j w j x j + ∑ j < k w j k x j x k + ∑ j < k < l w j k l x j x k x l + . . . {\displaystyle S'({\vec {x}})=b+\sum _{j}w_{j}x_{j}+\sum _{j

Targeted maximum likelihood estimation

Targeted Maximum Likelihood Estimation (TMLE) (also more accurately referred to as Targeted Minimum Loss-Based Estimation) is a general statistical estimation framework for causal inference and semiparametric models. TMLE combines ideas from maximum likelihood estimation, semiparametric efficiency theory, and machine learning. It was introduced by Mark J. van der Laan and colleagues in the mid-2000s as a method that yields asymptotically efficient plug-in estimators while allowing the use of flexible, data-adaptive algorithms such as ensemble machine learning for nuisance parameter estimation. TMLE is used in epidemiology, biostatistics, and the social sciences to estimate causal effects in observational and experimental studies. Applications of TMLE include Longitudinal TMLE (LTMLE) for time-varying treatments and confounders. Variations in how the targeting step in TMLE is carried out have resulted in various versions of TMLE such as Collaborative TMLE (CTMLE) and Adaptive TMLE for improved finite-sample performance and automated variable selection. == History == The TMLE framework was first described by van der Laan and Rubin (2006) as a general approach for the construction of efficient plug-in estimators of smooth features of the data density. It was demonstrated in the context of causal inference and missing data problems. It was developed to address limitations of traditional doubly robust methods, such as Augmented Inverse Probability Weighting (AIPW), by respecting the plug-in principle in the sense that it respects that the target parameter is a function of the data density that is an element of the statistical model. TMLE estimates the data density or relevant parts of it with machine learning and targets these machine learning fits before it is plugged in the target parameter mapping. In this manner, a TMLE always respects global knowledge and satisfies known bounds such as that the target parameter is a probability . Since its introduction, TMLE has been developed in a series of theoretical and applied papers, culminating in book-length treatments of the method and its applications to survival analysis, adaptive designs, and longitudinal data. == Methodology == At its core, TMLE is a two-step estimation procedure: Initial estimation: Machine learning methods (such as the Super Learner ensemble) are used to obtain flexible estimates of nuisance parameters, such as outcome regressions and propensity scores. Targeting step: The initial estimate is updated by solving a score equation (the efficient influence function) so that the final estimator is consistent, asymptotically normal, and efficient under mild regularity conditions. The targeted machine learning fit is then mapped into the corresponding estimator of the target parameter by simply plugging it in the target parameter mapping. This approach balances the bias–variance trade-off by combining data-adaptive estimation with semiparametric efficiency theory. TMLE is doubly robust, meaning it remains consistent if either the outcome model or the treatment model is consistently estimated. === Formula === Here we explain the TMLE of the average treatment effect of a binary treatment on an outcome adjusting for baseline covariates. Consider i.i.d. observations O i = ( W i , A i , Y i ) {\displaystyle O_{i}=(W_{i},A_{i},Y_{i})} from a distribution P 0 {\displaystyle P_{0}} , where W {\displaystyle W} are baseline covariates, A {\displaystyle A} is a binary treatment, and Y {\displaystyle Y} is an outcome. Let Q ¯ ( a , w ) = E [ Y ∣ A = a , W = w ] {\displaystyle {\bar {Q}}(a,w)=\mathbb {E} [Y\mid A=a,W=w]} represent the outcome model and g ( a ∣ w ) = P ( A = a ∣ W = w ) {\displaystyle g(a\mid w)=P(A=a\mid W=w)} represent the propensity score. The average treatment effect (ATE) is given by ψ 0 = E { Q ¯ ( 1 , W ) − Q ¯ ( 0 , W ) } . {\displaystyle \psi _{0}=\mathbb {E} \{{\bar {Q}}(1,W)-{\bar {Q}}(0,W)\}.} A basic TMLE for the ATE proceeds as follows: Step 1: Estimate initial models. Obtain estimates Q ¯ ^ ( a , w ) {\displaystyle {\hat {\bar {Q}}}(a,w)} and g ^ ( a ∣ w ) {\displaystyle {\hat {g}}(a\mid w)} , often using flexible methods such as Super Learner. Step 2: Compute the clever covariate. Define: H ( A , W ) = A g ^ ( 1 ∣ W ) − 1 − A g ^ ( 0 ∣ W ) . {\displaystyle H(A,W)={\frac {A}{{\hat {g}}(1\mid W)}}-{\frac {1-A}{{\hat {g}}(0\mid W)}}.} Step 3: Estimate the fluctuation parameter. Fit a logistic regression of Y {\displaystyle Y} on H ( A , W ) {\displaystyle H(A,W)} with logit ⁡ ( Q ¯ ^ ( A , W ) ) {\displaystyle \operatorname {logit} ({\hat {\bar {Q}}}(A,W))} as offset. This yields ε ^ {\displaystyle {\hat {\varepsilon }}} , the MLE that solves the score equation: 1 n ∑ i = 1 n H ( A i , W i ) { Y i − Q ¯ ^ ε ( A i , W i ) } = 0. {\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}H(A_{i},W_{i}){\big \{}Y_{i}-{\hat {\bar {Q}}}^{\varepsilon }(A_{i},W_{i}){\big \}}=0.} Step 4: Update the initial estimate. Apply the "blip" to obtain the targeted estimate: Q ¯ ^ ∗ ( A , W ) = expit ⁡ ( logit ⁡ ( Q ¯ ^ ( A , W ) ) + ε ^ H ( A , W ) ) . {\displaystyle {\hat {\bar {Q}}}^{}(A,W)=\operatorname {expit} {\Big (}\operatorname {logit} {\big (}{\hat {\bar {Q}}}(A,W){\big )}+{\hat {\varepsilon }}\,H(A,W){\Big )}.} Step 5: Compute the TMLE. The ATE estimate is: ψ ^ TMLE = 1 n ∑ i = 1 n [ Q ¯ ^ ∗ ( 1 , W i ) − Q ¯ ^ ∗ ( 0 , W i ) ] . {\displaystyle {\hat {\psi }}_{\text{TMLE}}={\frac {1}{n}}\sum _{i=1}^{n}{\big [}{\hat {\bar {Q}}}^{}(1,W_{i})-{\hat {\bar {Q}}}^{}(0,W_{i}){\big ]}.} Inference. The efficient influence function (EIF) for the ATE is: D ∗ ( O ) = H ( A , W ) { Y − Q ¯ ∗ ( A , W ) } + Q ¯ ∗ ( 1 , W ) − Q ¯ ∗ ( 0 , W ) − ψ . {\displaystyle D^{}(O)=H(A,W)\{Y-{\bar {Q}}^{}(A,W)\}+{\bar {Q}}^{}(1,W)-{\bar {Q}}^{}(0,W)-\psi .} The variance is estimated by σ ^ 2 = n − 1 ∑ i = 1 n ( D ∗ ( O i ) ) 2 {\displaystyle {\hat {\sigma }}^{2}=n^{-1}\sum _{i=1}^{n}{\big (}D^{}(O_{i}){\big )}^{2}} , yielding Wald-type confidence intervals ψ ^ TMLE ± z 1 − α / 2 σ ^ / n {\displaystyle {\hat {\psi }}_{\text{TMLE}}\pm z_{1-\alpha /2}\,{\hat {\sigma }}/{\sqrt {n}}} . Remark. For continuous outcomes, a linear fluctuation Q ¯ ^ ∗ = Q ¯ ^ + ε ^ H {\displaystyle {\hat {\bar {Q}}}^{}={\hat {\bar {Q}}}+{\hat {\varepsilon }}\,H} may be used instead. For bounded continuous outcomes, the logistic fluctuation (after rescaling Y {\displaystyle Y} to [ 0 , 1 ] {\displaystyle [0,1]} ) is often preferred for improved finite-sample performance. == Applications == TMLE has been applied in: Epidemiology: Estimating causal effects of exposures and interventions in observational cohort studies. Clinical trials and real-world evidence: The Targeted Learning roadmap provides a structured framework for generating and validating real-world evidence (RWE), bridging randomized trials and observational data using TMLE and related estimation techniques. This approach enables transparency, sensitivity analysis, and stronger causal inference for regulatory and clinical trial contexts. High-dimensional settings: Integration with ensemble methods for causal effect estimation. TMLE has been successfully applied in pharmacoepidemiology where a large number of covariates are automatically selected to adjust for confounding. In a study of post–myocardial infarction statin use and 1-year mortality, TMLE demonstrated robust performance relative to inverse probability weighting in scenarios with hundreds of potential confounders. == Derivatives and extensions == Longitudinal TMLE (LTMLE): A methodological extension of TMLE for longitudinal data with time-varying treatments, confounders, and censoring. It allows the estimation of dynamic treatment regimes and intervention-specific causal effects over time. This framework was originally introduced by van der Laan & Gruber (2012). Collaborative TMLE (CTMLE): Enhances finite-sample performance and variable selection by collaboratively fitting the treatment mechanism in conjunction with the target parameter. == Software == Several R packages implement TMLE and related methods: tmle: Functions for binary, categorical, and continuous outcomes. ltmle: Implementation for longitudinal data with time-varying treatments and outcomes. ctmle: Algorithms for collaborative TMLE and adaptive variable selection. SuperLearner: A theoretically grounded, cross-validated ensemble learning method that combines predictions from multiple algorithms to minimize predictive risk. Widely used in TMLE for estimating nuisance parameters. The original implementation is available as the R package SuperLearner. Recent machine learning platforms like H2O AutoML implement similar ensemble strategies, combining diverse learners in parallel and leveraging stacking and blending techniques, effectively functioning as a large-scale Super Learner.

Word2vec

Word2vec is a technique in natural language processing for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus. Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. Word2vec was developed by Tomáš Mikolov, Kai Chen, Greg Corrado, Ilya Sutskever and Jeff Dean at Google, and published in 2013. Word2vec represents a word as a high-dimension vector of numbers which capture relationships between words. In particular, words which appear in similar contexts are mapped to vectors which are nearby as measured by cosine similarity. This indicates the level of semantic similarity between the words, so for example the vectors for walk and ran are nearby, as are those for "but" and "however", and "Berlin" and "Germany". == Approach == Word2vec is a group of related models that are used to produce word embeddings. These models are shallow, two-layer neural networks that are trained to reconstruct linguistic contexts of words. Word2vec takes as its input a large corpus of text and produces a mapping of the set of words to a vector space, typically of several hundred dimensions, with each unique word in the corpus being assigned a vector in the space. Word2vec can use either of two model architectures to produce these distributed representations of words: continuous bag of words (CBOW) or continuously sliding skip-gram. In both architectures, word2vec considers both individual words and a sliding context window as it iterates over the corpus. The CBOW can be viewed as a 'fill in the blank' task, where the word embedding represents the way the word influences the relative probabilities of other words in the context window. Words which are semantically similar should influence these probabilities in similar ways, because semantically similar words should be used in similar contexts. The order of context words does not influence prediction (bag of words assumption). In the continuous skip-gram architecture, the model uses the current word to predict the surrounding window of context words. The skip-gram architecture weighs nearby context words more heavily than more distant context words. According to the authors' note, CBOW is faster while skip-gram does a better job for infrequent words. After the model is trained, the learned word embeddings are positioned in the vector space such that words that share common contexts in the corpus — that is, words that are semantically and syntactically similar — are located close to one another in the space. More dissimilar words are located farther from one another in the space. == Mathematical details == This section is based on expositions. A corpus is a sequence of words. Both CBOW and skip-gram are methods to learn one vector per word appearing in the corpus. Let V {\displaystyle V} ("vocabulary") be the set of all words appearing in the corpus C {\displaystyle C} . Our goal is to learn one vector v w ∈ R d {\displaystyle v_{w}\in \mathbb {R} ^{d}} for each word w ∈ V {\displaystyle w\in V} . The idea of skip-gram is that the vector of a word should be close to the vector of each of its neighbors. The idea of CBOW is that the vector-sum of a word's neighbors should be close to the vector of the word. === Continuous bag-of-words (CBOW) === The idea of CBOW is to represent each word with a vector, such that it is possible to predict a word using the sum of the vectors of its neighbors. Specifically, for each word w i {\displaystyle w_{i}} in the corpus, the one-hot encoding of the word is used as the input to the neural network. The output of the neural network is a probability distribution over the dictionary, representing a prediction of individual words in the neighborhood of w i {\displaystyle w_{i}} . The objective of training is to maximize ∑ i ln ⁡ Pr ( w i ∣ w i + j : j ∈ N ) {\displaystyle \sum _{i}\ln \Pr(w_{i}\mid w_{i+j}\colon j\in N)} where N {\displaystyle N} is a set of (non-zero) indices representing the relative locations of nearby words considered to be in w i {\displaystyle w_{i}} 's neighborhood. For example, if we want each word in the corpus to be predicted by every other word in a small span of 4 words. The set of relative indexes of neighbor words will be: N = { − 2 , − 1 , + 1 , + 2 } {\displaystyle N=\{-2,-1,+1,+2\}} , and the objective is to maximize ∑ i ln ⁡ Pr ( w i ∣ w i − 2 , w i − 1 , w i + 1 , w i + 2 ) {\displaystyle \sum _{i}\ln \Pr(w_{i}\mid w_{i-2},w_{i-1},w_{i+1},w_{i+2})} . In standard bag-of-words, a word's context is represented by a word-count (aka a word histogram) of its neighboring words. For example, the "sat" in "the cat sat on the mat" is represented as {"the": 2, "cat": 1, "on": 1}. Note that the last word "mat" is not used to represent "sat", because it is outside the neighborhood N = { − 2 , − 1 , + 1 , + 2 } {\displaystyle N=\{-2,-1,+1,+2\}} . In continuous bag-of-words, the histogram is multiplied by a matrix V {\displaystyle V} to obtain a continuous representation of the word's context. The matrix V {\displaystyle V} is also called a dictionary. Its columns are the word vectors. It has D {\displaystyle D} columns, where D {\displaystyle D} is the size of the dictionary. Let d {\displaystyle d} be the length of each word vector. We have V ∈ R d × D {\displaystyle V\in \mathbb {R} ^{d\times D}} . For example, multiplying the word histogram {"the": 2, "cat": 1, "on": 1} with V {\displaystyle V} , we obtain 2 v the + v cat + v on {\displaystyle 2v_{\text{the}}+v_{\text{cat}}+v_{\text{on}}} . This is then multiplied with another matrix V ′ {\displaystyle V'} of shape R D × d {\displaystyle \mathbb {R} ^{D\times d}} . Each row of it is a word vector v ′ {\displaystyle v'} . This results in a vector of length D {\displaystyle D} , one entry per dictionary entry. Then, apply the softmax to obtain a probability distribution over the dictionary. This system can be visualized as a neural network, similar in spirit to an autoencoder, of architecture linear-linear-softmax, as depicted in the diagram. The system is trained by gradient descent to minimize the cross-entropy loss. In full formula, the cross-entropy loss is: − ∑ i ln ⁡ e v w i ′ ⋅ ( ∑ j ∈ N v w j + i ) ∑ w ′ e v w ′ ′ ⋅ ( ∑ j ∈ N v w j + i ) {\displaystyle -\sum _{i}\ln {\frac {e^{v_{w_{i}}'\cdot (\sum _{j\in N}v_{w_{j+i}})}}{\sum _{w'}e^{v_{w'}'\cdot (\sum _{j\in N}v_{w_{j+i}})}}}} where the outer summation ∑ i {\displaystyle \sum _{i}} is over the words in a corpus, the quantity ∑ j ∈ N v w j + i {\displaystyle \sum _{j\in N}v_{w_{j+i}}} is the sum of a word's neighbors' vectors, etc. Once such a system is trained, we have two trained matrices V , V ′ {\displaystyle V,V'} . Either the column vectors of V {\displaystyle V} or the row vectors of V ′ {\displaystyle V'} can serve as the dictionary. For example, the word "sat" can be represented as either the "sat"-th column of V {\displaystyle V} or the "sat"-th row of V ′ {\displaystyle V'} . It is also possible to simply define V ′ = V ⊤ {\displaystyle V'=V^{\top }} , in which case there would no longer be a choice. === Skip-gram === The idea of skip-gram is to represent each word with a vector, such that it is possible to predict the vectors of its neighbors using the vector of a word. The architecture is still linear-linear-softmax, the same as CBOW, but the input and the output are switched. Specifically, for each word w i {\displaystyle w_{i}} in the corpus, the one-hot encoding of the word is used as the input to the neural network. The output of the neural network is a probability distribution over the dictionary, representing a prediction of individual words in the neighborhood of w i {\displaystyle w_{i}} . The objective of training is to maximize ∑ i ∑ j ∈ N ln ⁡ Pr ( w j + i ∣ w i ) {\displaystyle \sum _{i}\sum _{j\in N}\ln \Pr(w_{j+i}\mid w_{i})} . In full formula, the loss function is − ∑ i ∑ j ∈ N ln ⁡ e v w j + i ′ ⋅ v w i ∑ w ′ e v w ′ ′ ⋅ v w i {\displaystyle -\sum _{i}\sum _{j\in N}\ln {\frac {e^{v_{w_{j+i}}'\cdot v_{w_{i}}}}{\sum _{w'}e^{v_{w'}'\cdot v_{w_{i}}}}}} Same as CBOW, once such a system is trained, we have two trained matrices V , V ′ {\displaystyle V,V'} . Either the column vectors of V {\displaystyle V} or the row vectors of V ′ {\displaystyle V'} can serve as the dictionary. It is also possible to simply define V ′ = V ⊤ {\displaystyle V'=V^{\top }} , in which case there would no longer be a choice. Essentially, skip-gram and CBOW are exactly the same in architecture. They only differ in the objective function during training. == History == During the 1980s, there were some early attempts at using neural networks to represent words and concepts as vectors. In 2010, Tomáš Mikolov (then at Brno University of Technology) with co-authors applied a simple recurrent neural network with a single hidden

AppyStore

AppyStore is a comprehensive learning videos and games app for kids up to the age of 8 years. The platform developed by Mauj Mobile, a mobile value-added services (VAS) provider curates content to help in child development by leveraging technology. Mauj is funded by Sequoia Capital, Westbridge Capital and Intel Capital. == Background == AppyStore was launched in 2014 as a platform providing content for kids between the ages of 1.5 and 6 years. AppyStore subsequently extended its services for kids up to 8 years of age. The company operates on a subscription-based model and claims to have 5,000 learning games and videos segregated in 18 learning areas developed to help children gain optimal skills and qualities. According to an article published in Business Standard, the application is claimed to be one of the top 5 apps that help to enhance the logical and imaginative capabilities of children. AppyStore was awarded the Best app for kids by Google Play in December 2017. == Service == The company provides content via a website and an Android app. The website and android app provide learning games, rhymes, phonics, reading, stories, science, numbers, maths, logic videos comprising puzzles, worksheets, videos and fun activities and the premium subscription also includes physical worksheets which are home delivered. This content is educational and has been handpicked by teachers and experts with an understanding of the major areas of child development milestones for children up to 8 years of age. The mobile application also allows parents to track the progress of their child on the basis of the number of videos viewed.

Multi-model database

Receptron

Targeted maximum likelihood estimation

Word2vec

AppyStore

Receptron

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