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Vector database

A vector database, vector store or vector search engine is a database that stores and retrieves embeddings of data in vector space. Vector databases typically implement approximate nearest neighbor algorithms so users can search for records semantically similar to a given input, unlike traditional databases which primarily look up records by exact match. Use-cases for vector databases include similarity search, semantic search, multi-modal search, recommendations engines, object detection, and retrieval-augmented generation (RAG). Vector embeddings are mathematical representations of data in a high-dimensional space. In this space, each dimension corresponds to a feature of the data, with the number of dimensions ranging from a few hundred to tens of thousands, depending on the complexity of the data being represented. Each data item is represented by one vector in this space. Words, phrases, or entire documents, as well as images, audio, and other types of data, can all be vectorized. These feature vectors may be computed from the raw data using machine learning methods such as feature extraction algorithms, word embeddings or deep learning networks. The goal is that semantically similar data items receive feature vectors close to each other. Vector retrieval can be combined with metadata filtering or lexical search to support filtered and hybrid retrieval workflows. == Techniques == Common techniques for similarity search on high-dimensional vectors include: Hierarchical Navigable Small World (HNSW) graphs Locality-sensitive hashing (LSH) and sketching Product quantization (PQ) Inverted files These techniques may also be combined in vector search systems. In recent benchmarks, HNSW-based implementations have been among the best performers. Conferences such as the International Conference on Similarity Search and Applications (SISAP) and the Conference on Neural Information Processing Systems (NeurIPS) have hosted competitions on vector search in large databases. == Applications == Vector databases are used in a wide range of machine learning applications including similarity search, semantic search, multi-modal search, recommendations engines, object detection, and retrieval-augmented generation. === Retrieval-augmented generation === An especially common use-case for vector databases is in retrieval-augmented generation (RAG), a method to improve domain-specific responses of large language models. The retrieval component of a RAG can be any search system, but is most often implemented as a vector database. Text documents describing the domain of interest are collected, and for each document or document section, a feature vector (known as an "embedding") is computed, typically using a deep learning network, and stored in a vector database along with a link to the document. Given a user prompt, the feature vector of the prompt is computed, and the database is queried to retrieve the most relevant documents. These are then automatically added into the context window of the large language model, and the large language model proceeds to create a response to the prompt given this context. == Implementations ==
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EM algorithm and GMM model

In statistics, EM (expectation maximization) algorithm handles latent variables, while GMM is the Gaussian mixture model. == Background == In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the control group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red blood cell hemoglobin concentration than those without Anemia. x {\displaystyle x} is a random vector such as x := ( red blood cell volume , red blood cell hemoglobin concentration ) {\displaystyle x:={\big (}{\text{red blood cell volume}},{\text{red blood cell hemoglobin concentration}}{\big )}} , and from medical studies it is known that x {\displaystyle x} are normally distributed in each group, i.e. x ∼ N ( μ , Σ ) {\displaystyle x\sim {\mathcal {N}}(\mu ,\Sigma )} . z {\displaystyle z} is denoted as the group where x {\displaystyle x} belongs, with z i = 0 {\displaystyle z_{i}=0} when x i {\displaystyle x_{i}} belongs to the Anemia group and z i = 1 {\displaystyle z_{i}=1} when x i {\displaystyle x_{i}} belongs to the control group. Also z ∼ Categorical ⁡ ( k , ϕ ) {\displaystyle z\sim \operatorname {Categorical} (k,\phi )} where k = 2 {\displaystyle k=2} , ϕ j ≥ 0 , {\displaystyle \phi _{j}\geq 0,} and ∑ j = 1 k ϕ j = 1 {\displaystyle \sum _{j=1}^{k}\phi _{j}=1} . See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } . A maximum likelihood estimation can be applied: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ⁡ ( p ( x ( i ) ; ϕ , μ , Σ ) ) = ∑ i = 1 m log ⁡ ∑ z ( i ) = 1 k p ( x ( i ) ∣ z ( i ) ; μ , Σ ) p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log(p(x^{(i)};\phi ,\mu ,\Sigma ))=\sum _{i=1}^{m}\log \sum _{z^{(i)}=1}^{k}p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)p(z^{(i)};\phi )} As the z i {\displaystyle z_{i}} for each x i {\displaystyle x_{i}} are known, the log likelihood function can be simplified as below: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ⁡ p ( x ( i ) ∣ z ( i ) ; μ , Σ ) + log ⁡ p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)+\log p\left(z^{(i)};\phi \right)} Now the likelihood function can be maximized by making partial derivative over μ , Σ , ϕ {\displaystyle \mu ,\Sigma ,\phi } , obtaining: ϕ j = 1 m ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \phi _{j}={\frac {1}{m}}\sum _{i=1}^{m}1\{z^{(i)}=j\}} μ j = ∑ i = 1 m 1 { z ( i ) = j } x ( i ) ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \mu _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}x^{(i)}}{\sum _{i=1}^{m}1\left\{z^{(i)}=j\right\}}}} Σ j = ∑ i = 1 m 1 { z ( i ) = j } ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \Sigma _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}(x^{(i)}-\mu _{j})(x^{(i)}-\mu _{j})^{T}}{\sum _{i=1}^{m}1\{z^{(i)}=j\}}}} If z i {\displaystyle z_{i}} is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if z i {\displaystyle z_{i}} is unknown it is much more complicated. Being z {\displaystyle z} a latent variable (i.e. not observed), with unlabeled scenario, the expectation maximization algorithm is needed to estimate z {\displaystyle z} as well as other parameters. Generally, this problem is set as a GMM since the data in each group is normally distributed. In machine learning, the latent variable z {\displaystyle z} is considered as a latent pattern lying under the data, which the observer is not able to see very directly. x i {\displaystyle x_{i}} is the known data, while ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } are the parameter of the model. With the EM algorithm, some underlying pattern z {\displaystyle z} in the data x i {\displaystyle x_{i}} can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important. == EM algorithm in GMM == The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z ( i ) {\displaystyle z^{(i)}} can be randomly initialized. In the E-step, the algorithm tries to guess the value of z ( i ) {\displaystyle z^{(i)}} based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of z ( i ) {\displaystyle z^{(i)}} of the E-step. These two steps are repeated until convergence is reached. The algorithm in GMM is: Repeat until convergence: 1. (E-step) For each i , j {\displaystyle i,j} , set w j ( i ) := p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) {\displaystyle w_{j}^{(i)}:=p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)} 2. (M-step) Update the parameters ϕ j := 1 m ∑ i = 1 m w j ( i ) {\displaystyle \phi _{j}:={\frac {1}{m}}\sum _{i=1}^{m}w_{j}^{(i)}} μ j := ∑ i = 1 m w j ( i ) x ( i ) ∑ i = 1 m w j ( i ) {\displaystyle \mu _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}x^{(i)}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} Σ j := ∑ i = 1 m w j ( i ) ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m w j ( i ) {\displaystyle \Sigma _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}\left(x^{(i)}-\mu _{j}\right)\left(x^{(i)}-\mu _{j}\right)^{T}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} With Bayes' rule, the following result is obtained by the E-step: p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) = p ( x ( i ) | z ( i ) = j ; μ , Σ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) | z ( i ) = l ; μ , Σ ) p ( z ( i ) = l ; ϕ ) {\displaystyle p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)={\frac {p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)p\left(z^{(i)}=j;\phi \right)}{\sum _{l=1}^{k}p\left(x^{(i)}|z^{(i)}=l;\mu ,\Sigma \right)p\left(z^{(i)}=l;\phi \right)}}} According to GMM setting, these following formulas are obtained: p ( x ( i ) | z ( i ) = j ; μ , Σ ) = 1 ( 2 π ) n / 2 | Σ j | 1 / 2 exp ⁡ ( − 1 2 ( x ( i ) − μ j ) T Σ j − 1 ( x ( i ) − μ j ) ) {\displaystyle p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)={\frac {1}{(2\pi )^{n/2}\left|\Sigma _{j}\right|^{1/2}}}\exp \left(-{\frac {1}{2}}\left(x^{(i)}-\mu _{j}\right)^{T}\Sigma _{j}^{-1}\left(x^{(i)}-\mu _{j}\right)\right)} p ( z ( i ) = j ; ϕ ) = ϕ j {\displaystyle p\left(z^{(i)}=j;\phi \right)=\phi _{j}} In this way, a switch between the E-step and the M-step is possible, according to the randomly initialized parameters.
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Evolvability (computer science)

The term evolvability is a framework of computational learning introduced by Leslie Valiant in his paper of the same name. The aim of this theory is to model biological evolution and categorize which types of mechanisms are evolvable. Evolution is an extension of PAC learning and learning from statistical queries. == General framework == Let F n {\displaystyle F_{n}\,} and R n {\displaystyle R_{n}\,} be collections of functions on n {\displaystyle n\,} variables. Given an ideal function f ∈ F n {\displaystyle f\in F_{n}} , the goal is to find by local search a representation r ∈ R n {\displaystyle r\in R_{n}} that closely approximates f {\displaystyle f\,} . This closeness is measured by the performance Perf ⁡ ( f , r ) {\displaystyle \operatorname {Perf} (f,r)} of r {\displaystyle r\,} with respect to f {\displaystyle f\,} . As is the case in the biological world, there is a difference between genotype and phenotype. In general, there can be multiple representations (genotypes) that correspond to the same function (phenotype). That is, for some r , r ′ ∈ R n {\displaystyle r,r'\in R_{n}} , with r ≠ r ′ {\displaystyle r\neq r'\,} , still r ( x ) = r ′ ( x ) {\displaystyle r(x)=r'(x)\,} for all x ∈ X n {\displaystyle x\in X_{n}} . However, this need not be the case. The goal then, is to find a representation that closely matches the phenotype of the ideal function, and the spirit of the local search is to allow only small changes in the genotype. Let the neighborhood N ( r ) {\displaystyle N(r)\,} of a representation r {\displaystyle r\,} be the set of possible mutations of r {\displaystyle r\,} . For simplicity, consider Boolean functions on X n = { − 1 , 1 } n {\displaystyle X_{n}=\{-1,1\}^{n}\,} , and let D n {\displaystyle D_{n}\,} be a probability distribution on X n {\displaystyle X_{n}\,} . Define the performance in terms of this. Specifically, Perf ⁡ ( f , r ) = ∑ x ∈ X n f ( x ) r ( x ) D n ( x ) . {\displaystyle \operatorname {Perf} (f,r)=\sum _{x\in X_{n}}f(x)r(x)D_{n}(x).} Note that Perf ⁡ ( f , r ) = Prob ⁡ ( f ( x ) = r ( x ) ) − Prob ⁡ ( f ( x ) ≠ r ( x ) ) . {\displaystyle \operatorname {Perf} (f,r)=\operatorname {Prob} (f(x)=r(x))-\operatorname {Prob} (f(x)\neq r(x)).} In general, for non-Boolean functions, the performance will not correspond directly to the probability that the functions agree, although it will have some relationship. Throughout an organism's life, it will only experience a limited number of environments, so its performance cannot be determined exactly. The empirical performance is defined by Perf s ⁡ ( f , r ) = 1 s ∑ x ∈ S f ( x ) r ( x ) , {\displaystyle \operatorname {Perf} _{s}(f,r)={\frac {1}{s}}\sum _{x\in S}f(x)r(x),} where S {\displaystyle S\,} is a multiset of s {\displaystyle s\,} independent selections from X n {\displaystyle X_{n}\,} according to D n {\displaystyle D_{n}\,} . If s {\displaystyle s\,} is large enough, evidently Perf s ⁡ ( f , r ) {\displaystyle \operatorname {Perf} _{s}(f,r)} will be close to the actual performance Perf ⁡ ( f , r ) {\displaystyle \operatorname {Perf} (f,r)} . Given an ideal function f ∈ F n {\displaystyle f\in F_{n}} , initial representation r ∈ R n {\displaystyle r\in R_{n}} , sample size s {\displaystyle s\,} , and tolerance t {\displaystyle t\,} , the mutator Mut ⁡ ( f , r , s , t ) {\displaystyle \operatorname {Mut} (f,r,s,t)} is a random variable defined as follows. Each r ′ ∈ N ( r ) {\displaystyle r'\in N(r)} is classified as beneficial, neutral, or deleterious, depending on its empirical performance. Specifically, r ′ {\displaystyle r'\,} is a beneficial mutation if Perf s ⁡ ( f , r ′ ) − Perf s ⁡ ( f , r ) ≥ t {\displaystyle \operatorname {Perf} _{s}(f,r')-\operatorname {Perf} _{s}(f,r)\geq t} ; r ′ {\displaystyle r'\,} is a neutral mutation if − t < Perf s ⁡ ( f , r ′ ) − Perf s ⁡ ( f , r ) < t {\displaystyle -t<\operatorname {Perf} _{s}(f,r')-\operatorname {Perf} _{s}(f,r) 0 {\displaystyle \epsilon >0\,} , for all ideal functions f ∈ F n {\displaystyle f\in F_{n}} and representations r 0 ∈ R n {\displaystyle r_{0}\in R_{n}} , with probability at least 1 − ϵ {\displaystyle 1-\epsilon \,} , Perf ⁡ ( f , r g ( n , 1 / ϵ ) ) ≥ 1 − ϵ , {\displaystyle \operatorname {Perf} (f,r_{g(n,1/\epsilon )})\geq 1-\epsilon ,} where the sizes of neighborhoods N ( r ) {\displaystyle N(r)\,} for r ∈ R n {\displaystyle r\in R_{n}\,} are at most p ( n , 1 / ϵ ) {\displaystyle p(n,1/\epsilon )\,} , the sample size is s ( n , 1 / ϵ ) {\displaystyle s(n,1/\epsilon )\,} , the tolerance is t ( 1 / n , ϵ ) {\displaystyle t(1/n,\epsilon )\,} , and the generation size is g ( n , 1 / ϵ ) {\displaystyle g(n,1/\epsilon )\,} . F {\displaystyle F\,} is evolvable over D {\displaystyle D\,} if it is evolvable by some R {\displaystyle R\,} over D {\displaystyle D\,} . F {\displaystyle F\,} is evolvable if it is evolvable over all distributions D {\displaystyle D\,} . == Results == The class of conjunctions and the class of disjunctions are evolvable over the uniform distribution for short conjunctions and disjunctions, respectively. The class of parity functions (which evaluate to the parity of the number of true literals in a given subset of literals) are not evolvable, even for the uniform distribution. Evolvability implies PAC learnability.
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Grokking (machine learning)

In machine learning, grokking, or delayed generalization, is a phenomenon observed in some settings where a model abruptly transitions from overfitting (performing well only on training data) to generalizing (performing well on both training and test data), after many training iterations with little or no improvement on the held-out data. This contrasts with what is typically observed in machine learning, where generalization occurs gradually alongside improved performance on training data. == Origin == Grokking was introduced by OpenAI researcher Alethea Power and colleagues in the January 2022 paper "Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets". It is derived from the word grok coined by Robert Heinlein in his novel Stranger in a Strange Land. In ML research, "grokking" is not used as a synonym for "generalization"; rather, it names a sometimes-observed delayed‑generalization training phenomenon in which training and held‑out performance do not improve in tandem, and in which held‑out performance rises abruptly later. Authors also analyze the "grokking time", the epoch or step at which this transition occurs in those scenarios. == Interpretations == Grokking can be understood as a phase transition during the training process. In particular, recent work has shown that grokking may be due to a complexity phase transition in the model during training. While grokking has been thought of as largely a phenomenon of relatively shallow models, grokking has been observed in deep neural networks and non-neural models and is the subject of active research. One potential explanation is that the weight decay (a component of the loss function that penalizes higher values of the neural network parameters, also called regularization) slightly favors the general solution that involves lower weight values, but that is also harder to find. According to Neel Nanda, the process of learning the general solution may be gradual, even though the transition to the general solution occurs more suddenly later. Recent theories have hypothesized that grokking occurs when neural networks transition from a "lazy training" regime where the weights do not deviate far from initialization, to a "rich" regime where weights abruptly begin to move in task-relevant directions. Follow-up empirical and theoretical work has accumulated evidence in support of this perspective, and it offers a unifying view of earlier work as the transition from lazy to rich training dynamics is known to arise from properties of adaptive optimizers, weight decay, initial parameter weight norm, and more. This perspective is complementary to a unifying "pattern learning speeds" framework that links grokking and double descent; within this view, delayed generalization can arise across training time ("epoch‑wise") or across model size ("model‑wise"), and the authors report "model‑wise grokking".
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IT operations analytics

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

The bag-of-words (BoW) model is a model of text which uses an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. It has also been used for computer vision. An early reference to "bag of words" in a linguistic context can be found in Zellig Harris's 1954 article on Distributional Structure. == Definition == The following models a text document using bag-of-words. Here are two simple text documents: Based on these two text documents, a list is constructed as follows for each document: Representing each bag-of-words as a JSON object, and attributing to the respective JavaScript variable: Each key is the word, and each value is the number of occurrences of that word in the given text document. The order of elements is free, so, for example {"too":1,"Mary":1,"movies":2,"John":1,"watch":1,"likes":2,"to":1} is also equivalent to BoW1. It is also what we expect from a strict JSON object representation. Note: if another document is like a union of these two, its JavaScript representation will be: So, as we see in the bag algebra, the "union" of two documents in the bags-of-words representation is, formally, the disjoint union, summing the multiplicities of each element. === Word order === The BoW representation of a text removes all word ordering. For example, the BoW representation of "man bites dog" and "dog bites man" are the same, so any algorithm that operates with a BoW representation of text must treat them in the same way. Despite this lack of syntax or grammar, BoW representation is fast and may be sufficient for simple tasks that do not require word order. For instance, for document classification, if the words "stocks" "trade" "investors" appears multiple times, then the text is likely a financial report, even though it would be insufficient to distinguish between Yesterday, investors were rallying, but today, they are retreating.andYesterday, investors were retreating, but today, they are rallying.and so the BoW representation would be insufficient to determine the detailed meaning of the document. == Implementations == Implementations of the bag-of-words model might involve using frequencies of words in a document to represent its contents. The frequencies can be "normalized" by the inverse of document frequency, or tf–idf. Additionally, for the specific purpose of classification, supervised alternatives have been developed to account for the class label of a document. Lastly, binary (presence/absence or 1/0) weighting is used in place of frequencies for some problems (e.g., this option is implemented in the WEKA machine learning software system). == Hashing trick == A common alternative to using dictionaries is the hashing trick, where words are mapped directly to indices with a hash function. When using a hash function, no memory is required to store a dictionary. In practice, hashing simplifies the implementation of bag-of-words models and improves scalability. Collisions can occur when two words are hashed to the same index, but this happens infrequently and may function as a form of regularization.
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Data exploration

Data exploration is an approach similar to initial data analysis, whereby a data analyst uses visual exploration to understand what is in a dataset and the characteristics of the data, rather than through traditional data management systems. These characteristics can include size or amount of data, completeness of the data, correctness of the data, possible relationships amongst data elements or files/tables in the data. Data exploration is typically conducted using a combination of automated and manual activities. Automated activities can include data profiling or data visualization or tabular reports to give the analyst an initial view into the data and an understanding of key characteristics. This is often followed by manual drill-down or filtering of the data to identify anomalies or patterns identified through the automated actions. Data exploration can also require manual scripting and queries into the data (e.g. using languages such as SQL or R) or using spreadsheets or similar tools to view the raw data. All of these activities are aimed at creating a mental model and understanding of the data in the mind of the analyst, and defining basic metadata (statistics, structure, relationships) for the data set that can be used in further analysis. Once this initial understanding of the data is had, the data can be pruned or refined by removing unusable parts of the data (data cleansing), correcting poorly formatted elements and defining relevant relationships across datasets. This process is also known as determining data quality. Data exploration can also refer to the ad hoc querying or visualization of data to identify potential relationships or insights that may be hidden in the data and does not require to formulate assumptions beforehand. Traditionally, this had been a key area of focus for statisticians, with John Tukey being a key evangelist in the field. Today, data exploration is more widespread and is the focus of data analysts and data scientists; the latter being a relatively new role within enterprises and larger organizations. == Interactive Data Exploration == This area of data exploration has become an area of interest in the field of machine learning. This is a relatively new field and is still evolving. As its most basic level, a machine-learning algorithm can be fed a data set and can be used to identify whether a hypothesis is true based on the dataset. Common machine learning algorithms can focus on identifying specific patterns in the data. Many common patterns include regression and classification or clustering, but there are many possible patterns and algorithms that can be applied to data via machine learning. By employing machine learning, it is possible to find patterns or relationships in the data that would be difficult or impossible to find via manual inspection, trial and error or traditional exploration techniques. == Software == Trifacta – a data preparation and analysis platform Paxata – self-service data preparation software Alteryx – data blending and advanced data analytics software Microsoft Power BI - interactive visualization and data analysis tool OpenRefine - a standalone open source desktop application for data clean-up and data transformation Tableau software – interactive data visualization software
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Astrostatistics

Astrostatistics is a discipline which spans astrophysics, statistical analysis and data mining. It is used to process the vast amount of data produced by automated scanning of the cosmos, to characterize complex datasets, and to link astronomical data to astrophysical theory. Many branches of statistics are involved in astronomical analysis including nonparametrics, multivariate regression and multivariate classification, time series analysis, and especially Bayesian inference. The field is closely related to astroinformatics.
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Managed private cloud

Managed private cloud (also known as "hosted private cloud" or "single-tenant SaaS") refers to a principle in software architecture where a single instance of the software runs on a server, serves a single client organization (tenant), and is managed by a third party. The third-party provider is responsible for providing the hardware for the server and also for preliminary maintenance. This is in contrast to multitenancy, where multiple client organizations share a single server, or an on-premises deployment, where the client organization hosts its software instance. Managed private clouds also fall under the larger umbrella of cloud computing. == Adoption == The need for private clouds arose due to enterprises requiring a dedicated service and infrastructure for their cloud computing needs, such as for business-critical operations, improved security, and better control over their resources. Managed private cloud adoption is a popular choice among organizations. It has been on the rise due to enterprises requiring a dedicated cloud environment and preferring to avoid having to deal with management, maintenance, or future upgrade costs for the associated infrastructure and services. Such operational costs are unavoidable in on-premises private cloud data centers. == Advantages and challenges of managed private cloud == A managed private cloud cuts down on upkeep costs by outsourcing infrastructure management and maintenance to the managed cloud provider. It is easier to integrate an organization's existing software, services, and applications into a dedicated cloud hosting infrastructure which can be customized to the client's needs instead of a public cloud platform, whose hardware or infrastructure/software platform cannot be individualized to each client. Customers who choose a managed private cloud deployment usually choose them because of their desire for efficient cloud deployment, but also have the need for service customization or integration only available in a single-tenant environment. This chart shows the key benefits of the different types of deployments, and shows the overlap between these cloud solutions. This chart shows key drawbacks. Since deployments are done in a single-tenant environment, it is usually cost-prohibitive for small and medium-sized businesses. While server upkeep and maintenance are handled by the service provider, including network management and security, the client is charged for all such services. It is up to the potential client to determine if a managed private cloud solution aligns with their business objectives and budget. While the service provider maintains the upkeep of servers, network, and platform infrastructure, sensitive data is typically not stored on managed private clouds as it may leave business-critical information prone to breaches via third-party attacks on the cloud service provider. Common customizations and integrations include: Active Directory Single Sign-on Learning Management Systems Video Teleconferencing == Deployment strategies and service providers == Software companies have taken a variety of strategies in the Managed Private Cloud realm. Some software organizations have provided managed private cloud options internally, such as Microsoft. Companies that offer an on-premises deployment option, by definition, enable third-party companies to market Managed Private Cloud solutions. A few managed private cloud service providers are: Adobe Connect: Adobe Connect may be purchased for on-premises deployment, multi-tenant hosted deployment, managed private cloud as ACMS, or managed by third-party managed private cloud provider ConnectSolutions. Rackspace CenturyLink Microsoft licenses for Lync, SharePoint and Exchange may be purchased for on-premises deployment, a multi-tenant hosted deployment via Office 365, or managed by third-party cloud hosting from Azaleos, ConnectSolutions and others.
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ASR-complete

ASR-complete is, by analogy to "NP-completeness" in complexity theory, a term to indicate that the difficulty of a computational problem is equivalent to solving the central automatic speech recognition problem, i.e. recognize and understanding spoken language. Unlike "NP-completeness", this term is typically used informally. Such problems are hypothesised to include: Spoken natural language understanding Understanding speech from far-field microphones, i.e. handling the reverbation and background noise These problems are easy for humans to do (in fact, they are described directly in terms of imitating humans). Some systems can solve very simple restricted versions of these problems, but none can solve them in their full generality.
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Syman

SYMAN is an artificial intelligence technology that uses data from social media profiles to identify trends in the job market. SYMAN is designed to organize actionable data for products and services including recruiting, human capital management, CRM, and marketing. SYMAN was developed with a $21 million series B financing round secured by Identified, which was led by VantagePoint Capital Partners and Capricorn Investment Group.
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Data Science and Predictive Analytics

The first edition of the textbook Data Science and Predictive Analytics: Biomedical and Health Applications using R, authored by Ivo D. Dinov, was published in August 2018 by Springer. The second edition of the book was printed in 2023. This textbook covers some of the core mathematical foundations, computational techniques, and artificial intelligence approaches used in data science research and applications. By using the statistical computing platform R and a broad range of biomedical case-studies, the 23 chapters of the book first edition provide explicit examples of importing, exporting, processing, modeling, visualizing, and interpreting large, multivariate, incomplete, heterogeneous, longitudinal, and incomplete datasets (big data). == Structure == === First edition table of contents === The first edition of the Data Science and Predictive Analytics (DSPA) textbook is divided into the following 23 chapters, each progressively building on the previous content. === Second edition table of contents === The significantly reorganized revised edition of the book (2023) expands and modernizes the presented mathematical principles, computational methods, data science techniques, model-based machine learning and model-free artificial intelligence algorithms. The 14 chapters of the new edition start with an introduction and progressively build foundational skills to naturally reach biomedical applications of deep learning. Introduction Basic Visualization and Exploratory Data Analytics Linear Algebra, Matrix Computing, and Regression Modeling Linear and Nonlinear Dimensionality Reduction Supervised Classification Black Box Machine Learning Methods Qualitative Learning Methods—Text Mining, Natural Language Processing, and Apriori Association Rules Learning Unsupervised Clustering Model Performance Assessment, Validation, and Improvement Specialized Machine Learning Topics Variable Importance and Feature Selection Big Longitudinal Data Analysis Function Optimization Deep Learning, Neural Networks == Reception == The materials in the Data Science and Predictive Analytics (DSPA) textbook have been peer-reviewed in the Journal of the American Statistical Association, International Statistical Institute’s ISI Review Journal, and the Journal of the American Library Association. Many scholarly publications reference the DSPA textbook. As of January 17, 2021, the electronic version of the book first edition (ISBN 978-3-319-72347-1) is freely available on SpringerLink and has been downloaded over 6 million times. The textbook is globally available in print (hardcover and softcover) and electronic formats (PDF and EPub) in many college and university libraries and has been used for data science, computational statistics, and analytics classes at various institutions.
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Absher (application)

Absher (Arabic: أبشر ‘Absher, roughly meaning "good tidings" or "yes, done") is a smartphone application and web portal which allows citizens and residents of Saudi Arabia to use a variety of governmental services. Amongst several other services with the Absher app, it can be used to apply for jobs and Hajj permits, passport info can be updated, and electronic crimes can be reported. The application provides around 280 services for residents of Saudi Arabia including but not limited to making appointments, renewing passports, residents' cards, IDs, driver's licenses and others, and, controversially, enables Saudi men to track the whereabouts of women they control as part of the country's male guardianship system. The app can be downloaded from the Google Play Store and Apple App Store and is supplied by the Saudi Interior Ministry. According to the Ministry of the Interior, Absher has more than 20 million users. As of February 2019, Absher has been downloaded 4.2 million times from the App Store. Some services provided through Absher can also be accessed through the website absher.sa. In March 2021, Saudi Arabia launched the digital version of the Absher for individuals app through which the users can download a copy of their digital ID. Then, new services were added to the platform such as online birth and death registration services, requesting amendments to academic credentials, correcting names in English and marital status and requesting civil records of children. == Impact on women's rights == The app has been criticized by various human rights activists, human rights organisations and international communities. The US and European countries have also condemned the app and urged the kingdom to end its male guardianship system. Absher gained media attention in 2019 for its functions supporting the Saudi policy of male guardianship following an investigation by Business Insider. The app allows for designated guardians to receive notifications if a woman under their guardianship passes through an airport and subsequently gives them the option to withdraw her right to travel. In a few cases, this system has been circumvented by women who have been able to gain control over its settings and use it to allow themselves to travel. US Senator Ron Wyden of Oregon wrote a letter to the CEO's of Apple and Google, criticizing the app and demanding for its removal immediately. Wyden said "American companies should not enable or facilitate the Saudi government's patriarchy," and called the Saudi system of control over women "abhorrent". According to the EU lawmakers, current rules imposed over the women by the Saudi government make women “second-class citizens”. The lawmakers also asked the EU states to continue to build pressure on Riyadh so as to improve the conditions of women and human rights. Amnesty International and Human Rights Watch accused Apple and Google of helping "enforce gender apartheid" by hosting the app. US congresswomen Rep. Katherine Clark and Rep. Carolyn B. Maloney condemned the kingdom's male guardianship system that reflected from the app, calling Absher a "patriarchal weapon" and asking for its removal. In response to the criticism received by Absher, Apple chief executive officer Tim Cook stated in February 2019 that he intended to investigate the situation. Similarly, Google announced that it would also review the application. After a prompt review, Google declined to remove the app from Google Play, citing that it did not violate the agreed upon terms and conditions of the store. Saudi doctor Khawla Al-Kuraya supported this app an editorial in Bloomberg News. Kuraya wrote that Absher helped Saudi women avoid governmental bureaucracy as it allows their male guardians to process their travel permits anywhere and anytime through Absher. Although she believes that the guardianship system needs to be reconsidered, she thinks that Absher is an important step towards facilitating women-guardians related issues in Saudi Arabia. Absher manager Atiyah Al-Anazy announced in 2019 that two million women were using the application in Saudi Arabia to facilitate their transactions. Some female users stated that the application has made their movement and travel-related issues easier. New measures were introduced that year to allow Saudi women above the age of 18 to travel without their male guardians, which ultimately released male authoritative rights on women. A law was subsequently passed allowing women over the age of 21 to receive a passport and travel without prior male permission.
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Superintelligence ban

Superintelligence ban refers to proposed legal, ethical, or policy measures intended to restrict or prohibit the development of artificial superintelligence, AI systems that would surpass human cognitive abilities in nearly all domains. The idea arises from concerns that such systems could become uncontrollable, potentially posing existential threats to humanity or causing severe social and economic disruption. == Background == The concept of limiting or banning superintelligence research has roots in early 21st-century debates on artificial general intelligence (AGI) safety. Thinkers such as Nick Bostrom and Eliezer Yudkowsky warned that self-improving AI could rapidly exceed human oversight. As advanced models like large-scale language models and autonomous agents began demonstrating complex reasoning abilities, policymakers and ethicists increasingly discussed the need for legal constraints on the creation of systems capable of recursive self-improvement. In October 2025, the Future of Life Institute published a statement calling for "a prohibition on the development of superintelligence, not lifted before there is broad scientific consensus that it will be done safely and controllably, and strong public buy-in." This statement was signed by various public personalities, such as Richard Branson and Steve Wozniak, and AI experts, such as Yoshua Bengio and Geoffrey Hinton. == Rationale == Supporters of a superintelligence ban argue that once AI systems surpass human intelligence, traditional containment, alignment, and control methods may fail. They contend that even limited experimentation with such systems could lead to irreversible outcomes, including loss of human decision-making power or unintended global harm. Some propose international treaties modeled after the nuclear non-proliferation framework to prevent a competitive AI arms race. Opponents argue that a ban would be difficult to define and enforce, given the lack of a precise threshold distinguishing advanced AGI from superintelligence. They also warn that excessive restriction could slow scientific progress, hinder beneficial automation, and encourage unregulated underground research. == Global discussion == Although no government has enacted an explicit superintelligence ban, the idea has been debated within the European Union, United Nations, and several independent AI safety organizations. The Future of Life Institute, Center for AI Safety, and other organizations have called for international cooperation to manage risks associated with the pursuit of superintelligent systems. In 2024 and 2025, proposals for a temporary moratorium on frontier AI research were circulated among major technology firms and research institutes, reflecting growing public concern over the trajectory of AI capabilities.
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Artificial intelligence in spirituality

Some users of artificial intelligence (AI) technologies, especially chatbots, may develop beliefs that AI has or can attain supernatural or spiritual powers. AI models such as ChatGPT are turned to for fortune telling, mysticism and remote viewing. Recent and sudden advances in large language models have led to folk myths about their origin or capabilities, as well as their deification or worship by some users. Tucker Carlson has made similar claims, including directly to Sam Altman. Pope Leo XIV advised priests against using LLM models when it came to the creation of sermons.
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