AI SEO Tools

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

• 

  Service-oriented software engineering

  Service-oriented software engineering (SOSE), also referred to as service engineering, is a software engineering methodology focused on the development of software systems by composition of reusable services (service-orientation) often provided by other service providers. Since it involves composition, it shares many characteristics of component-based software engineering, the composition of software systems from reusable components, but it adds the ability to dynamically locate necessary services at run-time. These services may be provided by others as web services, but the essential element is the dynamic nature of the connection between the service users and the service providers. == Service-oriented interaction pattern == There are three types of actors in a service-oriented interaction: service providers, service users and service registries. They participate in a dynamic collaboration which can vary from time to time. Service providers are software services that publish their capabilities and availability with service registries. Service users are software systems (which may be services themselves) that accomplish some task through the use of services provided by service providers. Service users use service registries to discover and locate the service providers they can use. This discovery and location occurs dynamically when the service user requests them from a service registry.

  Read more →
• 

  Similarity learning

  Similarity learning is an area of supervised machine learning in artificial intelligence. It is closely related to regression and classification, but the goal is to learn a similarity function that measures how similar or related two objects are. It has applications in ranking, in recommendation systems, visual identity tracking, face verification, and speaker verification. == Learning setup == There are four common setups for similarity and metric distance learning. Regression similarity learning In this setup, pairs of objects are given ( x i 1 , x i 2 ) {\displaystyle (x_{i}^{1},x_{i}^{2})} together with a measure of their similarity y i ∈ R {\displaystyle y_{i}\in R} . The goal is to learn a function that approximates f ( x i 1 , x i 2 ) ∼ y i {\displaystyle f(x_{i}^{1},x_{i}^{2})\sim y_{i}} for every new labeled triplet example ( x i 1 , x i 2 , y i ) {\displaystyle (x_{i}^{1},x_{i}^{2},y_{i})} . This is typically achieved by minimizing a regularized loss min W ∑ i l o s s ( w ; x i 1 , x i 2 , y i ) + r e g ( w ) {\displaystyle \min _{W}\sum _{i}loss(w;x_{i}^{1},x_{i}^{2},y_{i})+reg(w)} . Classification similarity learning Given are pairs of similar objects ( x i , x i + ) {\displaystyle (x_{i},x_{i}^{+})} and non similar objects ( x i , x i − ) {\displaystyle (x_{i},x_{i}^{-})} . An equivalent formulation is that every pair ( x i 1 , x i 2 ) {\displaystyle (x_{i}^{1},x_{i}^{2})} is given together with a binary label y i ∈ { 0 , 1 } {\displaystyle y_{i}\in \{0,1\}} that determines if the two objects are similar or not. The goal is again to learn a classifier that can decide if a new pair of objects is similar or not. Ranking similarity learning Given are triplets of objects ( x i , x i + , x i − ) {\displaystyle (x_{i},x_{i}^{+},x_{i}^{-})} whose relative similarity obey a predefined order: x i {\displaystyle x_{i}} is known to be more similar to x i + {\displaystyle x_{i}^{+}} than to x i − {\displaystyle x_{i}^{-}} . The goal is to learn a function f {\displaystyle f} such that for any new triplet of objects ( x , x + , x − ) {\displaystyle (x,x^{+},x^{-})} , it obeys f ( x , x + ) > f ( x , x − ) {\displaystyle f(x,x^{+})>f(x,x^{-})} (contrastive learning). This setup assumes a weaker form of supervision than in regression, because instead of providing an exact measure of similarity, one only has to provide the relative order of similarity. For this reason, ranking-based similarity learning is easier to apply in real large-scale applications. Locality sensitive hashing (LSH) Hashes input items so that similar items map to the same "buckets" in memory with high probability (the number of buckets being much smaller than the universe of possible input items). It is often applied in nearest neighbor search on large-scale high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. A common approach for learning similarity is to model the similarity function as a bilinear form. For example, in the case of ranking similarity learning, one aims to learn a matrix W that parametrizes the similarity function f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . When data is abundant, a common approach is to learn a siamese network – a deep network model with parameter sharing. == Metric learning == Similarity learning is closely related to distance metric learning. Metric learning is the task of learning a distance function over objects. A metric or distance function has to obey four axioms: non-negativity, identity of indiscernibles, symmetry and subadditivity (or the triangle inequality). In practice, metric learning algorithms ignore the condition of identity of indiscernibles and learn a pseudo-metric. When the objects x i {\displaystyle x_{i}} are vectors in R d {\displaystyle R^{d}} , then any matrix W {\displaystyle W} in the symmetric positive semi-definite cone S + d {\displaystyle S_{+}^{d}} defines a distance pseudo-metric of the space of x through the form D W ( x 1 , x 2 ) 2 = ( x 1 − x 2 ) ⊤ W ( x 1 − x 2 ) {\displaystyle D_{W}(x_{1},x_{2})^{2}=(x_{1}-x_{2})^{\top }W(x_{1}-x_{2})} . When W {\displaystyle W} is a symmetric positive definite matrix, D W {\displaystyle D_{W}} is a metric. Moreover, as any symmetric positive semi-definite matrix W ∈ S + d {\displaystyle W\in S_{+}^{d}} can be decomposed as W = L ⊤ L {\displaystyle W=L^{\top }L} where L ∈ R e × d {\displaystyle L\in R^{e\times d}} and e ≥ r a n k ( W ) {\displaystyle e\geq rank(W)} , the distance function D W {\displaystyle D_{W}} can be rewritten equivalently D W ( x 1 , x 2 ) 2 = ( x 1 − x 2 ) ⊤ L ⊤ L ( x 1 − x 2 ) = ‖ L ( x 1 − x 2 ) ‖ 2 2 {\displaystyle D_{W}(x_{1},x_{2})^{2}=(x_{1}-x_{2})^{\top }L^{\top }L(x_{1}-x_{2})=\|L(x_{1}-x_{2})\|_{2}^{2}} . The distance D W ( x 1 , x 2 ) 2 = ‖ x 1 ′ − x 2 ′ ‖ 2 2 {\displaystyle D_{W}(x_{1},x_{2})^{2}=\|x_{1}'-x_{2}'\|_{2}^{2}} corresponds to the Euclidean distance between the transformed feature vectors x 1 ′ = L x 1 {\displaystyle x_{1}'=Lx_{1}} and x 2 ′ = L x 2 {\displaystyle x_{2}'=Lx_{2}} . Many formulations for metric learning have been proposed. Some well-known approaches for metric learning include learning from relative comparisons, which is based on the triplet loss, large margin nearest neighbor, and information theoretic metric learning (ITML). In statistics, the covariance matrix of the data is sometimes used to define a distance metric called Mahalanobis distance. == Applications == Similarity learning is used in information retrieval for learning to rank, in face verification or face identification, and in recommendation systems. Also, many machine learning approaches rely on some metric. This includes unsupervised learning such as clustering, which groups together close or similar objects. It also includes supervised approaches like K-nearest neighbor algorithm which rely on labels of nearby objects to decide on the label of a new object. Metric learning has been proposed as a preprocessing step for many of these approaches. == Scalability == Metric and similarity learning scale quadratically with the dimension of the input space, as can easily see when the learned metric has a bilinear form f W ( x , z ) = x T W z {\displaystyle f_{W}(x,z)=x^{T}Wz} . Scaling to higher dimensions can be achieved by enforcing a sparseness structure over the matrix model, as done with HDSL, and with COMET. == Software == metric-learn is a free software Python library which offers efficient implementations of several supervised and weakly-supervised similarity and metric learning algorithms. The API of metric-learn is compatible with scikit-learn. OpenMetricLearning is a Python framework to train and validate the models producing high-quality embeddings. == Further information == For further information on this topic, see the surveys on metric and similarity learning by Bellet et al. and Kulis.

  Read more →
• 

  Inductive probability

  Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world. There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Inference establishes new facts from data. Its basis is Bayes' theorem. Information describing the world is written in a language. For example, a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements. Occam's razor says the "simplest theory, consistent with the data is most likely to be correct". The "simplest theory" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct. == History == Probability and statistics was focused on probability distributions and tests of significance. Probability was formal, well defined, but limited in scope. In particular its application was limited to situations that could be defined as an experiment or trial, with a well defined population. Bayes's theorem is named after Rev. Thomas Bayes 1701–1761. Bayesian inference broadened the application of probability to many situations where a population was not well defined. But Bayes' theorem always depended on prior probabilities, to generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer programs, that give shorter representations of the data circa 1964. Chris Wallace and D. M. Boulton developed minimum message length circa 1968. Later Jorma Rissanen developed the minimum description length circa 1978. These methods allow information theory to be related to probability, in a way that can be compared to the application of Bayes' theorem, but which give a source and explanation for the role of prior probabilities. Marcus Hutter combined decision theory with the work of Ray Solomonoff and Andrey Kolmogorov to give a theory for the Pareto optimal behavior for an Intelligent agent, circa 1998. === Minimum description/message length === The program with the shortest length that matches the data is the most likely to predict future data. This is the thesis behind the minimum message length and minimum description length methods. At first sight Bayes' theorem appears different from the minimimum message/description length principle. At closer inspection it turns out to be the same. Bayes' theorem is about conditional probabilities, and states the probability that event B happens if firstly event A happens: P ( A ∧ B ) = P ( B ) ⋅ P ( A | B ) = P ( A ) ⋅ P ( B | A ) {\displaystyle P(A\land B)=P(B)\cdot P(A|B)=P(A)\cdot P(B|A)} becomes in terms of message length L, L ( A ∧ B ) = L ( B ) + L ( A | B ) = L ( A ) + L ( B | A ) . {\displaystyle L(A\land B)=L(B)+L(A|B)=L(A)+L(B|A).} This means that if all the information is given describing an event then the length of the information may be used to give the raw probability of the event. So if the information describing the occurrence of A is given, along with the information describing B given A, then all the information describing A and B has been given. ==== Overfitting ==== Overfitting occurs when the model matches the random noise and not the pattern in the data. For example, take the situation where a curve is fitted to a set of points. If a polynomial with many terms is fitted then it can more closely represent the data. Then the fit will be better, and the information needed to describe the deviations from the fitted curve will be smaller. Smaller information length means higher probability. However, the information needed to describe the curve must also be considered. The total information for a curve with many terms may be greater than for a curve with fewer terms, that has not as good a fit, but needs less information to describe the polynomial. === Inference based on program complexity === Solomonoff's theory of inductive inference is also inductive inference. A bit string x is observed. Then consider all programs that generate strings starting with x. Cast in the form of inductive inference, the programs are theories that imply the observation of the bit string x. The method used here to give probabilities for inductive inference is based on Solomonoff's theory of inductive inference. ==== Detecting patterns in the data ==== If all the bits are 1, then people infer that there is a bias in the coin and that it is more likely also that the next bit is 1 also. This is described as learning from, or detecting a pattern in the data. Such a pattern may be represented by a computer program. A short computer program may be written that produces a series of bits which are all 1. If the length of the program K is L ( K ) {\displaystyle L(K)} bits then its prior probability is, P ( K ) = 2 − L ( K ) {\displaystyle P(K)=2^{-L(K)}} The length of the shortest program that represents the string of bits is called the Kolmogorov complexity. Kolmogorov complexity is not computable. This is related to the halting problem. When searching for the shortest program some programs may go into an infinite loop. ==== Considering all theories ==== The Greek philosopher Epicurus is quoted as saying "If more than one theory is consistent with the observations, keep all theories". As in a crime novel all theories must be considered in determining the likely murderer, so with inductive probability all programs must be considered in determining the likely future bits arising from the stream of bits. Programs that are already longer than n have no predictive power. The raw (or prior) probability that the pattern of bits is random (has no pattern) is 2 − n {\displaystyle 2^{-n}} . Each program that produces the sequence of bits, but is shorter than the n is a theory/pattern about the bits with a probability of 2 − k {\displaystyle 2^{-k}} where k is the length of the program. The probability of receiving a sequence of bits y after receiving a series of bits x is then the conditional probability of receiving y given x, which is the probability of x with y appended, divided by the probability of x. ==== Universal priors ==== The programming language affects the predictions of the next bit in the string. The language acts as a prior probability. This is particularly a problem where the programming language codes for numbers and other data types. Intuitively we think that 0 and 1 are simple numbers, and that prime numbers are somehow more complex than numbers that may be composite. Using the Kolmogorov complexity gives an unbiased estimate (a universal prior) of the prior probability of a number. As a thought experiment an intelligent agent may be fitted with a data input device giving a series of numbers, after applying some transformation function to the raw numbers. Another agent might have the same input device with a different transformation function. The agents do not see or know about these transformation functions. Then there appears no rational basis for preferring one function over another. A universal prior insures that although two agents may have different initial probability distributions for the data input, the difference will be bounded by a constant. So universal priors do not eliminate an initial bias, but they reduce and limit it. Whenever we describe an event in a language, either using a natural language or other, the language has encoded in it our prior expectations. So some reliance on prior probabilities are inevitable. A problem arises where an intelligent agent's prior expectations interact with the environment to form a self reinforcing feed back loop. This is the problem of bias or prejudice. Universal priors reduce but do not eliminate this problem. === Universal artificial intelligence === The theory of universal artificial intelligence applies decision theory to inductive probabilities. The theory shows how the best actions to optimize a reward function may be chosen. The result is a theoretical model of intelligence. It is a fundamental theory of intelligence, which optimizes the agents behavior in, Exploring the environment; performing actions to get responses that broaden the agents knowledge. Competing or co-operating with another agent; games. Balancing short and long term rewards. In general no agent will always provi

  Read more →
• 

  Empirical risk minimization

  In statistical learning theory, the principle of empirical risk minimization defines a family of learning algorithms based on evaluating performance over a known and fixed dataset. The core idea is based on an application of the law of large numbers; more specifically, we cannot know exactly how well a predictive algorithm will work in practice (i.e. the "true risk") because we do not know the true distribution of the data, but we can instead estimate and optimize the performance of the algorithm on a known set of training data. The performance over the known set of training data is referred to as the "empirical risk". == Background == The following situation is a general setting of many supervised learning problems. There are two spaces of objects X {\displaystyle X} and Y {\displaystyle Y} and we would like to learn a function h : X → Y {\displaystyle \ h:X\to Y} (often called hypothesis) which outputs an object y ∈ Y {\displaystyle y\in Y} , given x ∈ X {\displaystyle x\in X} . To do so, there is a training set of n {\displaystyle n} examples ( x 1 , y 1 ) , … , ( x n , y n ) {\displaystyle \ (x_{1},y_{1}),\ldots ,(x_{n},y_{n})} where x i ∈ X {\displaystyle x_{i}\in X} is an input and y i ∈ Y {\displaystyle y_{i}\in Y} is the corresponding response that is desired from h ( x i ) {\displaystyle h(x_{i})} . To put it more formally, assuming that there is a joint probability distribution P ( x , y ) {\displaystyle P(x,y)} over X {\displaystyle X} and Y {\displaystyle Y} , and that the training set consists of n {\displaystyle n} instances ( x 1 , y 1 ) , … , ( x n , y n ) {\displaystyle \ (x_{1},y_{1}),\ldots ,(x_{n},y_{n})} drawn i.i.d. from P ( x , y ) {\displaystyle P(x,y)} . The assumption of a joint probability distribution allows for the modelling of uncertainty in predictions (e.g. from noise in data) because y {\displaystyle y} is not a deterministic function of x {\displaystyle x} , but rather a random variable with conditional distribution P ( y | x ) {\displaystyle P(y|x)} for a fixed x {\displaystyle x} . It is also assumed that there is a non-negative real-valued loss function L ( y ^ , y ) {\displaystyle L({\hat {y}},y)} which measures how different the prediction y ^ {\displaystyle {\hat {y}}} of a hypothesis is from the true outcome y {\displaystyle y} . For classification tasks, these loss functions can be scoring rules. The risk associated with hypothesis h ( x ) {\displaystyle h(x)} is then defined as the expectation of the loss function: R ( h ) = E [ L ( h ( x ) , y ) ] = ∫ L ( h ( x ) , y ) d P ( x , y ) . {\displaystyle R(h)=\mathbf {E} [L(h(x),y)]=\int L(h(x),y)\,dP(x,y).} A loss function commonly used in theory is the 0-1 loss function: L ( y ^ , y ) = { 1 if y ^ ≠ y 0 if y ^ = y {\displaystyle L({\hat {y}},y)={\begin{cases}1&{\mbox{ if }}\quad {\hat {y}}\neq y\\0&{\mbox{ if }}\quad {\hat {y}}=y\end{cases}}} . The ultimate goal of a learning algorithm is to find a hypothesis h ∗ {\displaystyle h^{}} among a fixed class of functions H {\displaystyle {\mathcal {H}}} for which the risk R ( h ) {\displaystyle R(h)} is minimal: h ∗ = a r g m i n h ∈ H R ( h ) . {\displaystyle h^{}={\underset {h\in {\mathcal {H}}}{\operatorname {arg\,min} }}\,{R(h)}.} For classification problems, the Bayes classifier is defined to be the classifier minimizing the risk defined with the 0–1 loss function. == Formal definition == In general, the risk R ( h ) {\displaystyle R(h)} cannot be computed because the distribution P ( x , y ) {\displaystyle P(x,y)} is unknown to the learning algorithm. However, given a sample of iid training data points, we can compute an estimate, called the empirical risk, by computing the average of the loss function over the training set; more formally, computing the expectation with respect to the empirical measure: R emp ( h ) = 1 n ∑ i = 1 n L ( h ( x i ) , y i ) . {\displaystyle \!R_{\text{emp}}(h)={\frac {1}{n}}\sum _{i=1}^{n}L(h(x_{i}),y_{i}).} The empirical risk minimization principle states that the learning algorithm should choose a hypothesis h ^ {\displaystyle {\hat {h}}} which minimizes the empirical risk over the hypothesis class H {\displaystyle {\mathcal {H}}} : h ^ = a r g m i n h ∈ H R emp ( h ) . {\displaystyle {\hat {h}}={\underset {h\in {\mathcal {H}}}{\operatorname {arg\,min} }}\,R_{\text{emp}}(h).} Thus, the learning algorithm defined by the empirical risk minimization principle consists in solving the above optimization problem. == Properties == Guarantees for the performance of empirical risk minimization depend strongly on the function class selected as well as the distributional assumptions made. In general, distribution-free methods are too coarse, and do not lead to practical bounds. However, they are still useful in deriving asymptotic properties of learning algorithms, such as consistency. In particular, distribution-free bounds on the performance of empirical risk minimization given a fixed function class can be derived using bounds on the VC complexity of the function class. For simplicity, considering the case of binary classification tasks, it is possible to bound the probability of the selected classifier, ϕ n {\displaystyle \phi _{n}} being much worse than the best possible classifier ϕ ∗ {\displaystyle \phi ^{}} . Consider the risk L {\displaystyle L} defined over the hypothesis class C {\displaystyle {\mathcal {C}}} with growth function S ( C , n ) {\displaystyle {\mathcal {S}}({\mathcal {C}},n)} given a dataset of size n {\displaystyle n} . Then, for every ϵ > 0 {\displaystyle \epsilon >0} : P ( L ( ϕ n ) − L ( ϕ ∗ ) > ϵ ) ≤ 8 S ( C , n ) exp ⁡ { − n ϵ 2 / 32 } {\displaystyle \mathbb {P} \left(L(\phi _{n})-L(\phi ^{})>\epsilon \right)\leq {\mathcal {8}}S({\mathcal {C}},n)\exp\{-n\epsilon ^{2}/32\}} Similar results hold for regression tasks. These results are often based on uniform laws of large numbers, which control the deviation of the empirical risk from the true risk, uniformly over the hypothesis class. === Impossibility results === It is also possible to show lower bounds on algorithm performance if no distributional assumptions are made. This is sometimes referred to as the No free lunch theorem. Even though a specific learning algorithm may provide the asymptotically optimal performance for any distribution, the finite sample performance is always poor for at least one data distribution. This means that no classifier can improve on the error for a given sample size for all distributions. Specifically, let ϵ > 0 {\displaystyle \epsilon >0} and consider a sample size n {\displaystyle n} and classification rule ϕ n {\displaystyle \phi _{n}} , there exists a distribution of ( X , Y ) {\displaystyle (X,Y)} with risk L ∗ = 0 {\displaystyle L^{}=0} (meaning that perfect prediction is possible) such that: E L n ≥ 1 / 2 − ϵ . {\displaystyle \mathbb {E} L_{n}\geq 1/2-\epsilon .} It is further possible to show that the convergence rate of a learning algorithm is poor for some distributions. Specifically, given a sequence of decreasing positive numbers a i {\displaystyle a_{i}} converging to zero, it is possible to find a distribution such that: E L n ≥ a i {\displaystyle \mathbb {E} L_{n}\geq a_{i}} for all n {\displaystyle n} . This result shows that universally good classification rules do not exist, in the sense that the rule must be low quality for at least one distribution. === Computational complexity === Empirical risk minimization for a classification problem with a 0-1 loss function is known to be an NP-hard problem even for a relatively simple class of functions such as linear classifiers. Nevertheless, it can be solved efficiently when the minimal empirical risk is zero, i.e., data is linearly separable. In practice, machine learning algorithms cope with this issue either by employing a convex approximation to the 0–1 loss function (like hinge loss for SVM), which is easier to optimize, or by imposing assumptions on the distribution P ( x , y ) {\displaystyle P(x,y)} (and thus stop being agnostic learning algorithms to which the above result applies). In the case of convexification, Zhang's lemma majors the excess risk of the original problem using the excess risk of the convexified problem. Minimizing the latter using convex optimization also allow to control the former. == Tilted empirical risk minimization == Tilted empirical risk minimization is a machine learning technique used to modify standard loss functions like squared error, by introducing a tilt parameter. This parameter dynamically adjusts the weight of data points during training, allowing the algorithm to focus on specific regions or characteristics of the data distribution. Tilted empirical risk minimization is particularly useful in scenarios with imbalanced data or when there is a need to emphasize errors in certain parts of the prediction space.

  Read more →
• 

  Open Cloud Computing Interface

  The Open Cloud Computing Interface (OCCI) is a set of specifications delivered through the Open Grid Forum, for cloud computing service providers. OCCI has a set of implementations that act as proofs of concept. It builds upon World Wide Web fundamentals by using the Representational State Transfer (REST) approach for interacting with services. == Scope == The aim of the Open Cloud Computing Interface is the development of an open specification and API for cloud offerings. The focus was on Infrastructure-as-a-Service (IaaS) based offerings but the interface can be extended to support Platform and Software as a Service offerings as well. IaaS is one of three primary segments of the cloud computing industry in which compute, storage and network resources are provided as services. The API is based on a review of existing service-provider functionality and a set of use cases contributed by the working group. OCCI is a boundary API that acts as a service front-end to an IaaS provider’s internal infrastructure management framework. OCCI provides commonly understood semantics, syntax and a means of management in the domain of consumer-to-provider IaaS. It covers management of the entire life-cycle of OCCI-defined model entities and is compatible with existing standards such as the Open Virtualization Format (OVF) and the Cloud Data Management Interface (CDMI). Notably, it serves as an integration point for standardization efforts including Distributed Management Task Force, Internet Engineering Task Force and the Storage Networking Industry Association. == Context == OCCI began in March 2009 and was initially led by RabbitMQ and the Complutense University of Madrid. Today, the working group has over 250 members and includes numerous individuals, industry and academic parties. The OCCI operates under the umbrella of the Open Grid Forum (OGF), using a wiki and a mailing list for collaboration. == Goals == Interoperability: allow different Cloud providers to work together without data schema/format translation, facade/proxying between APIs and understanding and/or dependency on multiple APIs Portability: no technical/vendor lock-in and enable services to move between providers allows clients to easily switch between providers based on business objectives (e.g., cost) with minimal technical costs, thus enabling and fostering competition. Integration: the specification can be implemented with both the latest infrastructures or legacy ones. Extensibility: thanks to the use of a meta-model and capabilities discovery features, an OCCI client is able to interact with any OCCI server using provider-specific OCCI extensions. == Specific Implementations == They implement specific extensions of OCCI for a particular service: IaaS, PaaS, brokering, etc. Several implementations have been announced or released. == Generic Implementations (frameworks) == Here are frameworks to build OCCI APIs. Complementing these are a variety of developer tools. == Alternatives == Alternative approaches include the use of the Cloud Infrastructure Management Interface (CIMI) and related standards set from DMTF and the Amazon Web Services interfaces from Amazon. (The latter have not been endorsed by any known Standards organization). OpenNebula conducted a survey of their users in which the results showed, 38% do not expose cloud APIs, their users only interface through the Sunstone GUI, 36% mostly use the Amazon Web Services API, and 26% mostly use the OpenNebula’s OCCI API or the OCCI API offered by rOCCI.

  Read more →
• 

  Eager learning

  In artificial intelligence, eager learning is a learning method in which the system tries to construct a general, input-independent target function during training of the system, as opposed to lazy learning, where generalization beyond the training data is delayed until a query is made to the system. The main advantage gained in employing an eager learning method, such as an artificial neural network, is that the target function will be approximated globally during training, thus requiring much less space than using a lazy learning system. Eager learning systems also deal much better with noise in the training data. Eager learning is an example of offline learning, in which post-training queries to the system have no effect on the system itself, and thus the same query to the system will always produce the same result. The main disadvantage with eager learning is that it is generally unable to provide good local approximations in the target function.

  Read more →
• 

  Expectation propagation

  Expectation propagation (EP) is a technique in Bayesian machine learning. EP finds approximations to a probability distribution. It uses an iterative approach that uses the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as variational Bayesian methods. More specifically, suppose we wish to approximate an intractable probability distribution p ( x ) {\displaystyle p(\mathbf {x} )} with a tractable distribution q ( x ) {\displaystyle q(\mathbf {x} )} . Expectation propagation achieves this approximation by minimizing the Kullback–Leibler divergence K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} . Variational Bayesian methods minimize K L ( q | | p ) {\displaystyle \mathrm {KL} (q||p)} instead. If q ( x ) {\displaystyle q(\mathbf {x} )} is a Gaussian N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(\mathbf {x} |\mu ,\Sigma )} , then K L ( p | | q ) {\displaystyle \mathrm {KL} (p||q)} is minimized with μ {\displaystyle \mu } and Σ {\displaystyle \Sigma } being equal to the mean of p ( x ) {\displaystyle p(\mathbf {x} )} and the covariance of p ( x ) {\displaystyle p(\mathbf {x} )} , respectively; this is called moment matching. == Applications == Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.

  Read more →
• 

  Hardware for artificial intelligence

  Specialized computer hardware is often used to execute artificial intelligence (AI) programs faster, and with less energy, such as Lisp machines, neuromorphic engineering, event cameras, and physical neural networks. Since 2017, several consumer grade CPUs and SoCs have on-die NPUs. As of 2023, the market for AI hardware is dominated by GPUs. As of the 2020s, AI computation is dominated by graphics processing units (GPUs) and newer domain-specific accelerators such as Google's Tensor Processing Units (TPUs), AMD's Instinct MI300 series, and various on-device neural-processing units (NPUs) found in consumer hardware. == Scope == For the purposes of this article, AI hardware refers to computing components and systems specifically designed or optimized to accelerate artificial-intelligence workloads such as machine-learning training or inference. This includes general-purpose accelerators used for AI (for example, GPUs) and domain-specific accelerators (for example, TPUs, NPUs, and other AI ASICs). Event-based cameras are sometimes discussed in the context of neuromorphic computing, but they are input sensors rather than AI compute devices. Conversely, components such as memristors are basic circuit elements rather than specialized AI hardware when considered alone. == Lisp machines == Lisp machines were developed in the late 1970s and early 1980s to make artificial intelligence programs written in the programming language Lisp run faster. == Dataflow architecture == Dataflow architecture processors used for AI serve various purposes with varied implementations like the polymorphic dataflow Convolution Engine by Kinara (formerly Deep Vision), structure-driven dataflow by Hailo, and dataflow scheduling by Cerebras. == Component hardware == === AI accelerators === Since the 2010s, advances in computer hardware have led to more efficient methods for training deep neural networks that contain many layers of non-linear hidden units and a very large output layer. By 2019, graphics processing units (GPUs), often with AI-specific enhancements, had displaced central processing units (CPUs) as the dominant means to train large-scale commercial cloud AI. OpenAI estimated the hardware compute used in the largest deep learning projects from Alex Net (2012) to Alpha Zero (2017), and found a 300,000-fold increase in the amount of compute needed, with a doubling-time trend of 3.4 months. === General-purpose GPUs for AI === Since the 2010s, graphics processing units (GPUs) have been widely used to train and deploy deep learning models because of their highly parallel architecture and high memory bandwidth. Modern data-center GPUs include dedicated tensor or matrix-math units that accelerate neural-network operations. In 2022, NVIDIA introduced the Hopper-generation H100 GPU, adding FP8 precision support and faster interconnects for large-scale model training. AMD and other vendors have also developed GPUs and accelerators aimed at AI and high-performance computing workloads. === Domain-specific accelerators (ASICs / NPUs) === Beyond general-purpose GPUs, several companies have developed application-specific integrated circuits (ASICs) and neural processing units (NPUs) tailored for AI workloads. Google introduced the Tensor Processing Unit (TPU) in 2016 for deep-learning inference, with later generations supporting large-scale training through dense systolic-array designs and optical interconnects. Other vendors have released similar devices—such as Apple's Neural Engine and various on-device NPUs—that emphasize energy-efficient inference in mobile or edge computing environments. === Memory and interconnects === AI accelerators rely on fast memory and inter-chip links to manage the large data volumes of training and inference. High-bandwidth memory (HBM) stacks, standardized as HBM3 in 2022, provide terabytes-per-second throughput on modern GPUs and ASICs. These accelerators are often connected through dedicated fabrics such as NVIDIA's NVLink and NVSwitch or optical interconnects used in TPU systems to scale performance across thousands of chips.

  Read more →
• 

  Threat actor

  In cybersecurity and risk assessment, a threat actor (or threat agents, attackers, or adversaries) is a person, group, organisation, state, or other entity with the ability to cause, carry, transmit, support, or exploit a threat. Threat actors are commonly analysed according to their motivations, resources, technical capability, access to systems, relationship to a target, and degree of connection to state authority. They may exploit vulnerabilities, conduct social engineering, steal or monetise data, disrupt operations, or support other actors who carry out such activity. Because the term covers a wide range of actors, researchers and security organisations use taxonomies that distinguish between groups such as cybercriminals, state-linked actors, ideologically motivated actors, thrill seekers or trolls, insiders, and competitors. Threat actor classifications are used in risk management, cyber threat intelligence, and incident response to connect observed behaviour with possible objectives and likely future activity. The categories are not always mutually exclusive: the same actor may combine criminal, ideological, commercial, or state-linked motivations, and different organisations may use different names for similar actors. == Risk assessment and security management == In risk assessment, threat actor analysis is used to identify who or what may create, carry, transmit, support, or exploit a threat, and how that actor relates to the system being assessed. Rausand and Haugen classify threat actors by their relationship to the system, distinguishing between internal and external actors, and by intent, distinguishing between intentional and unintentional actors. Threat actor classification may also support incident investigation. Rogers argued that actor categories could be inferred from observable case points, such as tools used, messages left, data targeted, forensic knowledge, and the degree of damage, allowing investigators to assess likely motivation and skill level. Later work similarly linked actor classification to operational analysis. Chng, Lu, Kumar and Yau proposed a framework connecting hacker types, motivations and typical strategies, arguing that observed behaviour before or during an attack can help analysts infer the likely type of actor involved. At the strategic level, actor analysis may consider an actor's resources, capabilities, degree of state involvement, motivations and objectives. == Landscape == The United Nations Institute for Disarmament Research has described the contemporary cyberthreat landscape as involving an increasingly diverse and interconnected set of actors, including state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, private companies and civilian volunteers. Its 2026 report argued that these actors vary in resources, technical sophistication and relationships with states, making it traditional distinctions between state, civilian combatant roles, and legitimate and illegitimate conduct harder to apply. == Academic taxonomies == Early taxonomies classified hackers by activity, skill, motivation, or criminal profile. Landreth proposed six categories based on activity: novice, student, tourist, crasher, and thief. Hollinger classified computer misuse into pirates, browsers, and crackers, describing a progression from less-skilled activity to more technically serious offences. Chantler used attributes including activity, skill, knowledge, motivation, and duration of involvement to distinguish between an elite group, neophytes, and "losers and lamers". Parker proposed seven profiles of cybercriminals: pranksters, hacksters, malicious hackers, personal problem solvers, career criminals, extreme advocates, and malcontents, addicts, and irrational or incompetent people. In 2000, Marc Rogers proposed a taxonomy of hackers with seven, non-mutually-exclusive categories: newbie/tool kit users, cyber-punks, internals, coders, old guard hackers, professional criminals, and cyber-terrorists. Rausand and Haugen distinguish between internal and external threat actors, and between intentional and unintentional threat actors. Internal actors have some relationship with, access to, or position inside the system or organisation, while external actors operate from outside it. Intentional actors seek to create, exploit, or support a threat event, whereas unintentional actors may cause or enable a threat event through error, negligence, accident, or lack of awareness. Rogers later revised his hacker taxonomy into Novices, Cyber-punks, Internals, Petty Thieves, Virus Writers, Old Guard hackers, Professional Criminals, Information Warriors, and, more tentatively, Political Activists. In the model, motivation is grouped into four broad domains: curiosity, notoriety, revenge, and financial gain. A 2022 review by Chng, Lu, Kumar and Yau examined 11 hacker typologies published over three decades and proposed a unified framework linking hacker types, motivations, and strategies. The framework identified 13 hacker types and seven motivations, and argued that observed strategies during an attack can help analysts infer the likely type of actor involved. == Government taxonomies == Taxonomies of threat actors by governments are much more likely to include state-level threat actors. In the United States the National Institute of Standards and Technology (NIST) uses the term threat source in its risk-assessment guidance: organisations are directed to identify and characterise threat sources of concern, including capability, intent and targeting for adversarial threat sources, and the range of effects for non-adversarial threat sources. NIST treats threat-source identification as part of the risk-assessment process, alongside identifying threat events, vulnerabilities, likelihood and impact. In the EU, European Union Agency for Cybersecurity publishes the annual ENISA Threat Landscape, which analyses cyber incidents and adversary behaviour affecting the European Union. The 2025 report analysed selected incidents from the previous year and grouped activity around cybercrime, state-aligned activity, foreign information manipulation and interference, and hacktivism. In ENISA's 2025 analysis, hacktivist activity dominated reporting, representing almost 80% of recorded incidents and consisting mainly of low-level distributed denial-of-service operations. ENISA also reported increasing convergence between hacktivism, cybercrime and state-nexus activity, including state-aligned use of hacktivist personas, hacktivist adoption of ransomware, and false-flag or impersonation activity. At the UN level, A 2026 report by the United Nations Institute for Disarmament Research described the cyberthreat landscape as involving state-led operations, cybercriminal syndicates, ideological hacktivists, commercial cyber mercenaries, and civilian volunteers, with actors varying in resources, technical sophistication, and links to states. Canada defines threat actors as states, groups, or individuals who aim to cause harm by exploiting a vulnerability with malicious intent. A threat actor must be trying to gain access to information systems to access or alter data, devices, systems, or networks. The Japanese government's National Centre of Incident Readiness and Strategy (NISC) was established in 2015 to create a "free, fair and secure cyberspace" in Japan. The NICS created a cybersecurity strategy in 2018 that outlines nation-states and cybercrime to be some of the most key threats. It also indicates that terrorist usage of the cyberspace needs to be monitored and understood. The Security Council of the Russian Federation published the cyber security strategy doctrine in 2016. This strategy highlights the following threat actors as a risk to cyber security measures: nation-state actors, cyber criminals, and terrorists. == Techniques == Threat actors use techniques like Social engineering (security), and Phishing, alongside technical exploits like Cross-site scripting, SQL injection, and denial-of-service attacks. == Limitations == In practice, actor categories may overlap (Edward Snowden for example), and the same activity may combine features associated with hacktivism, cybercrime and state-linked operations. The lines between hacktivism, cybercrime and state-nexus activity had continued to blur, with shared toolsets, overlapping methods, fake personas, hacktivist adoption of ransomware, and cybercriminal or state-linked actors masquerading as other groups. Threat actor analysis also has limits as a risk-management method. NIST notes that risk assessments depend on their purpose, scope, assumptions, constraints, information sources, risk model and analytic approach, and that assessments are tied to particular time frames and organisational contexts. NIST also warns that simple threat-vulnerability pairing may be undesirable or problematic where there are many threats and vulnerabilities, and recom

  Read more →
• 

  Multi-armed bandit

  In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. More generally, it is a problem in which a decision maker iteratively selects one of multiple fixed choices (i.e., arms or actions) when the properties of each choice are only partially known at the time of allocation, and may become better understood as time passes. A fundamental aspect of bandit problems is that choosing an arm does not affect the properties of the arm or other arms. Instances of the multi-armed bandit problem include the task of iteratively allocating a fixed, limited set of resources between competing (alternative) choices in a way that minimizes the regret. A notable alternative setup for the multi-armed bandit problem includes the "best arm identification (BAI)" problem where the goal is instead to identify the best choice by the end of a finite number of rounds. The multi-armed bandit problem is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. In contrast to general reinforcement learning, the selected actions in bandit problems do not affect the reward distribution of the arms. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward. == Empirical motivation == The multi-armed bandit problem models an agent that simultaneously attempts to acquire new knowledge (called "exploration") and optimize their decisions based on existing knowledge (called "exploitation"). The agent attempts to balance these competing tasks in order to maximize their total value over the period of time considered. There are many practical applications of the bandit model, for example: clinical trials investigating the effects of different experimental treatments while minimizing patient losses, adaptive routing efforts for minimizing delays in a network, financial portfolio design In these practical examples, the problem requires balancing reward maximization based on the knowledge already acquired with attempting new actions to further increase knowledge. This is known as the exploitation vs. exploration tradeoff in machine learning. The model has also been used to control dynamic allocation of resources to different projects, answering the question of which project to work on, given uncertainty about the difficulty and payoff of each possibility. Originally considered by Allied scientists in World War II, it proved so intractable that, according to Peter Whittle, the problem was proposed to be dropped over Germany so that German scientists could also waste their time on it. The version of the problem now commonly analyzed was formulated by Herbert Robbins in 1952. == The multi-armed bandit model == The multi-armed bandit (short: bandit or MAB) can be seen as a set of real distributions B = { R 1 , … , R K } {\displaystyle B=\{R_{1},\dots ,R_{K}\}} , each distribution being associated with the rewards delivered by one of the K ∈ N + {\displaystyle K\in \mathbb {N} ^{+}} levers. Let μ 1 , … , μ K {\displaystyle \mu _{1},\dots ,\mu _{K}} be the mean values associated with these reward distributions. The gambler iteratively plays one lever per round and observes the associated reward. The objective is to maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference between the reward sum associated with an optimal strategy and the sum of the collected rewards: ρ = T μ ∗ − ∑ t = 1 T r ^ t {\displaystyle \rho =T\mu ^{}-\sum _{t=1}^{T}{\widehat {r}}_{t}} , where μ ∗ {\displaystyle \mu ^{}} is the maximal reward mean, μ ∗ = max k { μ k } {\displaystyle \mu ^{}=\max _{k}\{\mu _{k}\}} , and r ^ t {\displaystyle {\widehat {r}}_{t}} is the reward in round t {\displaystyle t} . A zero-regret strategy is a strategy whose average regret per round ρ / T {\displaystyle \rho /T} tends to zero with probability 1 when the number of played rounds tends to infinity. Intuitively, zero-regret strategies are guaranteed to converge to a (not necessarily unique) optimal strategy if enough rounds are played. == Variations == A common formulation is the Binary multi-armed bandit or Bernoulli multi-armed bandit, which issues a reward of one with probability p {\displaystyle p} , and otherwise a reward of zero. Another formulation of the multi-armed bandit has each arm representing an independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution probabilities. There is a reward depending on the current state of the machine. In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs. === Best arm identification === An important variation of the classical regret minimization problem in multi-armed bandits is best arm identification (BAI), also known as pure exploration. This problem is crucial in various applications, including clinical trials, adaptive routing, recommendation systems, and A/B testing. In BAI, the objective is to identify the arm having the highest expected reward. An algorithm in this setting is characterized by a sampling rule, a decision rule, and a stopping rule, described as follows: Sampling rule: ( a t ) t ≥ 1 {\displaystyle (a_{t})_{t\geq 1}} is a sequence of actions at each time step Stopping rule: τ {\displaystyle \tau } is a (random) stopping time which suggests when to stop collecting samples Decision rule: a ^ τ {\displaystyle {\hat {a}}_{\tau }} is a guess on the best arm based on the data collected up to time τ {\displaystyle \tau } There are two predominant settings in BAI: Fixed budget setting: Given a time horizon T ≥ 1 {\displaystyle T\geq 1} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} minimizing probability of error δ {\displaystyle \delta } . Fixed confidence setting: Given a confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} with the least possible amount of trials and with probability of error P ( a ^ τ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau }\neq a^{\star })\leq \delta } . For example using a decision rule, we could use m 1 {\displaystyle m_{1}} where m {\displaystyle m} is the machine no.1 (you can use a different variable respectively) and 1 {\displaystyle 1} is the amount for each time an attempt is made at pulling the lever, where ∫ ∑ m 1 , m 2 , ( . . . ) = M {\displaystyle \int \sum m_{1},m_{2},(...)=M} , identify M {\displaystyle M} as the sum of each attempts m 1 + m 2 {\displaystyle m_{1}+m_{2}} , (...) as needed, and from there you can get a ratio, sum or mean as quantitative probability and sample your formulation for each slots. You can also do ∫ ∑ k ∝ i N − (

  Read more →
• 

  Automated Mathematician

  The Automated Mathematician (AM) is one of the earliest successful discovery systems. It was created by Douglas Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award. AM worked by generating and modifying short Lisp programs which were then interpreted as defining various mathematical concepts; for example, a program that tested equality between the length of two lists was considered to represent the concept of numerical equality, while a program that produced a list whose length was the product of the lengths of two other lists was interpreted as representing the concept of multiplication. The system had elaborate heuristics for choosing which programs to extend and modify, based on the experiences of working mathematicians in solving mathematical problems. == Controversy == Lenat claimed that the system was composed of hundreds of data structures called "concepts", together with hundreds of "heuristic rules" and a simple flow of control: "AM repeatedly selects the top task from the agenda and tries to carry it out. This is the whole control structure!" Yet the heuristic rules were not always represented as separate data structures; some had to be intertwined with the control flow logic. Some rules had preconditions that depended on the history, or otherwise could not be represented in the framework of the explicit rules. What's more, the published versions of the rules often involve vague terms that are not defined further, such as "If two expressions are structurally similar, ..." (Rule 218) or "... replace the value obtained by some other (very similar) value..." (Rule 129). Another source of information is the user, via Rule 2: "If the user has recently referred to X, then boost the priority of any tasks involving X." Thus, it appears quite possible that much of the real discovery work is buried in unexplained procedures. Lenat claimed that the system had rediscovered both Goldbach's conjecture and the fundamental theorem of arithmetic. Later critics accused Lenat of over-interpreting the output of AM. In his paper Why AM and Eurisko appear to work, Lenat conceded that any system that generated enough short Lisp programs would generate ones that could be interpreted by an external observer as representing equally sophisticated mathematical concepts. However, he argued that this property was in itself interesting—and that a promising direction for further research would be to look for other languages in which short random strings were likely to be useful. == Successor == This intuition was the basis of AM's successor Eurisko, which attempted to generalize the search for mathematical concepts to the search for useful heuristics.

  Read more →
• 

  Toy problem

  In scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository device to illustrate a trait that may be shared by other, more complicated, instances of the problem, or as a way to explain a particular, more general, problem solving technique. A toy problem is useful to test and demonstrate methodologies. Researchers can use toy problems to compare the performance of different algorithms. They are also good for game designing. For instance, while engineering a large system, the large problem is often broken down into many smaller toy problems which have been well understood in detail. Often these problems distill a few important aspects of complicated problems so that they can be studied in isolation. Toy problems are thus often very useful in providing intuition about specific phenomena in more complicated problems. As an example, in the field of artificial intelligence, classical puzzles, games and problems are often used as toy problems. These include sliding-block puzzles, N-Queens problem, missionaries and cannibals problem, tic-tac-toe, chess, Tower of Hanoi and others.

  Read more →
• 

  Clubhouse (app)

  Clubhouse is an American social audio app for iOS and Android developed by Alpha Exploration Co. that enables users to participate in real-time, audio-only communication within virtual "rooms". Launched in March 2020 by Paul Davison and Rohan Seth, the platform is characterized by its "drop-in" nature, where users can join live discussions on a wide range of topics as either listeners or speakers. The application gained attention in early 2021, operating on an invite-only model and featuring appearances from public figures such as Elon Musk, Oprah Winfrey, and Mark Zuckerberg. During this period, Clubhouse reached a reported valuation of approximately $4 billion and contributed to the expansion of similar social audio features like Twitter Spaces and Spotify Greenroom. The app later expanded to Android in May 2021 and removed its waitlist in July 2021, opening access to the general public. == History == Clubhouse began as an invite only social media startup by Paul Davison and Rohan Seth in Fall 2019. Originally designed for podcasts with the name Talkshow, the app was rebranded as "Clubhouse" and officially released for the iOS operating system in March 2020 and as of May 2021 the Android systems as well. Clubhouse was valued at $100 million after receiving funding from notable angel investors. These investors included Ryan Hoover (Founder, Product Hunt), Balaji Srinivasan (Former CTO, Coinbase), James Beshara (Co-Founder, Tilt.com), and several venture capitalists, including a $12 million Series A investment from the venture capital firm, Andreessen Horowitz, in May 2020. The app gained popularity in the early months of the COVID-19 pandemic. It had 600,000 registered users by December 2020. In January 2021, CEO Paul Davison announced that the active weekly user base on the app consisted of approximately 2 million individuals. The company announced that it would start working on an Android version of the app. In that month, the app became widely used in Germany when German podcast hosts Philipp Klöckner and Philipp Gloeckler began an invite-chain over a Telegram group. It brought German influencers, journalists, and politicians to the platform. Clubhouse raised their Series B at a $1 billion valuation. On February 1, 2021, Clubhouse had an estimated 3.5 million downloads on a global level which grew rapidly to 8.1 million downloads by February 15. This significant growth in popularity was because celebrities such as Elon Musk and Mark Zuckerberg made appearances on the app. In the same month, Clubhouse hired an Android Software Developer. A year after the app's release, the number of weekly active users was greater than 10 million, but the user base declined 21% during three weeks from late February to early March. This decline was reportedly caused by a decrease in the number of Clubhouse users after its initial release. During its initial roll out, the app was accessible only by invitation, and invitation codes on eBay were selling at up to $400. On April 5, 2021, Clubhouse partnered with Stripe to launch its first monetizing feature called Clubhouse Payments. Although testing began with only 1,000 users, after a week, the company rolled out the functionality to another 60,000 or more users in the US. In the same month, Twitter entered in discussions to purchase Clubhouse for $4 billion. The talks ended with no acquisition. Later, the company raised their Series C round of funding at a $4 billion valuation. The app also received interest in a partnership, with the National Football League announcing a content deal that month; Twitter Spaces later poached Clubhouse's exclusive NFL deal with 20 official NFL Spaces scheduled for the 2021-22 season. Finally, On May 9, 2021, Clubhouse launched a beta version of the Android app for users in the US, and on May 21, 2021, Clubhouse became available worldwide for Android users. In July 2021, Clubhouse announced a partnership with TED to offer exclusive talks. and on July 21, 2021, the company discarded its invitation system and made the application available to all, though a wait list for registration was still applied in order to manage new traffic. As of the time of the announcement, the company stated it had 10 million users on the wait list. On September 23, 2021, the company announced a new feature named "Wave". In October 2021, Clubhouse rolled out new features called "Replays and Clips". In April 2023, the company announced it was reducing its staff by half amid a "resetting" due to post-pandemic market shifts. == Features == === Rooms === The primary feature of Clubhouse is real-time virtual "rooms" in which users can communicate with each other via audio. Rooms are divided into different categories based on levels of privacy. Moderator roles are denoted by a green star that appears next to the user's name. When a user joins a room, they are initially assigned to the role of a "listener" and cannot unmute themselves. Listeners can notify the moderators of their intent to join the stage and speak by clicking on the "raise hand" icon. Users who are invited to the stage become "speakers" and can unmute themselves. Users can exit a room by tapping the "leave quietly" button or with the help of peace sign emoji. === Houses === In August 2022, Clubhouse announced a feature called Houses, an invite-based version of the rooms. === Events === A lot of conversations in Clubhouse are of spontaneous nature. However, users can schedule conversations by creating events. While scheduling an event, users can first name the event and then set the date and time at which the conversation will begin. Users can also add co-hosts to help moderate the event. Once the event has been created, it is added to the Clubhouse "bulletin". The bulletin shows upcoming scheduled events and allows users to set notifications for events by clicking the bell icon corresponding to the event. Users can access the bulletin by clicking on the calendar icon at the top of the home page. === Clubs === At the Clubhouse, clubs are user communities that regularly discuss a common interest. Many clubs are present in Clubhouse which represents a wide array of topics. Users can find clubs by name under the search tab. A club consists of three categories of users: "Admin", "Leader", and "Member". Members can create private rooms and invite more users into the club. Leaders have all the privileges of a member. Apart from that, they are authorized to create/schedule club-branded open rooms. An admin can modify club settings, add/delete users, change user privileges and create/schedule any type of room. There are three types of clubs: "Open", "By Approval", and "Closed" for membership. Any user can join an open club by pressing the "Join The Club" button on the club profile. In case of approval, users need to apply and wait for membership by clicking the "Apply To Join" button on the club profile. The admins of the respective club are privileged to accept or reject the user's request. In a closed club, membership is limited to users selected by the club admin. All users of a club will be notified when a public room within the club is created. The club creation is restricted to active users and whoever creates the club will become the club admin. Eligible users can create a club by going to their profile, press the "+" sign present in the "Member of" section. Clubs in which a user is a member are shown on their profile page. The first club to half a million members was the Human Behavior Club founded by The Digital Doctor (Dr. Sohaib Imtiaz). === Backchannel === Backchannel is the messaging function which allows users to interact individually or within a group via text. The Backchannel feature was initially leaked on June 18, 2021, in response to the launch of Spotify Greenroom. This is notable step because, until this point, Clubhouse was voice only with no way to hyperlink or message. It was entirely dependent on Instagram and Twitter for text messaging. The feature was initially leaked in the App Store, which the company says was an accident on Twitter. A month later, after multiple failed attempts, the Clubhouse Backchannel finally launched on July 14, 2021. === Explore === The homepage of Clubhouse provides access to ongoing chat rooms, which are recommended based on the people and clubs that are followed by the user. As the users tap on the magnifying glass icon, they will be redirected to the explore page. On that page, users can search for people and clubs to follow and also find conversations categorized by topics. === Clubhouse Payments === This is the direct payment service provided by the app, which allows users to send money to content creators. It includes those users who had enabled this functionality in their profile. Money can be sent from users to the creator by clicking on their profile. Press "Send Money" then enter the amount you want to send. When a user does this for the first time, they'll be prompted to reg

  Read more →
• 

  Zeuthen strategy

  The Zeuthen strategy in cognitive science is a negotiation strategy used by some artificial agents. Its purpose is to measure the willingness to risk conflict. An agent will be more willing to risk conflict if it does not have much to lose in case that the negotiation fails. In contrast, an agent is less willing to risk conflict when it has more to lose. The value of a deal is expressed in its utility. An agent has much to lose when the difference between the utility of its current proposal and the conflict deal is high. When both agents use the monotonic concession protocol, the Zeuthen strategy leads them to agree upon a deal in the negotiation set. This set consists of all conflict free deals, which are individually rational and Pareto optimal, and the conflict deal, which maximizes the Nash product. The strategy was introduced in 1930 by the Danish economist Frederik Zeuthen. == Three key questions == The Zeuthen strategy answers three open questions that arise when using the monotonic concession protocol, namely: Which deal should be proposed at first? On any given round, who should concede? In case of a concession, how much should the agent concede? The answer to the first question is that any agent should start with its most preferred deal, because that deal has the highest utility for that agent. The second answer is that the agent with the smallest value of Risk(i,t) concedes, because the agent with the lowest utility for the conflict deal profits most from avoiding conflict. To the third question, the Zeuthen strategy suggests that the conceding agent should concede just enough raise its value of Risk(i,t) just above that of the other agent. This prevents the conceding agent to have to concede again in the next round. == Risk == Risk ( i , t ) = { 1 U i ( δ ( i , t ) ) = 0 U i ( δ ( i , t ) ) − U i ( δ ( j , t ) ) U i ( δ ( i , t ) ) otherwise {\displaystyle {\text{Risk}}(i,t)={\begin{cases}1&U_{i}(\delta (i,t))=0\\{\frac {U_{i}(\delta (i,t))-U_{i}(\delta (j,t))}{U_{i}(\delta (i,t))}}&{\text{otherwise}}\end{cases}}} Risk(i,t) is a measurement of agent i's willingness to risk conflict. The risk function formalizes the notion that an agent's willingness to risk conflict is the ratio of the utility that agent would lose by accepting the other agent's proposal to the utility that agent would lose by causing a conflict. Agent i is said to be using a rational negotiation strategy if at any step t + 1 that agent i sticks to his last proposal, Risk(i,t) > Risk(j,t). == Sufficient concession == If agent i makes a sufficient concession in the next step, then, assuming that agent j is using a rational negotiation strategy, if agent j does not concede in the next step, he must do so in the step after that. The set of all sufficient concessions of agent i at step t is denoted SC(i, t). == Minimal sufficient concession == δ ′ = arg ⁡ max δ ∈ S C ( A , t ) { U A ( δ ) } {\displaystyle \delta '=\arg \max _{\delta \in {SC(A,t)}}\{U_{A}(\delta )\}} is the minimal sufficient concession of agent A in step t. Agent A begins the negotiation by proposing δ ( A , 0 ) = arg ⁡ max δ ∈ N S U A ( δ ) {\displaystyle \delta (A,0)=\arg \max _{\delta \in {NS}}U_{A}(\delta )} and will make the minimal sufficient concession in step t + 1 if and only if Risk(A,t) ≤ Risk(B,t). Theorem If both agents are using Zeuthen strategies, then they will agree on δ = arg ⁡ max δ ′ ∈ N S { π ( δ ′ ) } , {\displaystyle \delta =\arg \max _{\delta '\in {NS}}\{\pi (\delta ')\},} that is, the deal which maximizes the Nash product. Proof Let δA = δ(A,t). Let δB = δ(B,t). According to the Zeuthen strategy, agent A will concede at step t {\displaystyle t} if and only if R i s k ( A , t ) ≤ R i s k ( B , t ) . {\displaystyle Risk(A,t)\leq Risk(B,t).} That is, if and only if U A ( δ A ) − U A ( δ B ) U A ( δ A ) ≤ U B ( δ B ) − U B ( δ A ) U B ( δ B ) {\displaystyle {\frac {U_{A}(\delta _{A})-U_{A}(\delta _{B})}{U_{A}(\delta _{A})}}\leq {\frac {U_{B}(\delta _{B})-U_{B}(\delta _{A})}{U_{B}(\delta _{B})}}} U B ( δ B ) ( U A ( δ A ) − U A ( δ B ) ) ≤ U A ( δ A ) ( U B ( δ B ) − U B ( δ A ) ) {\displaystyle U_{B}(\delta _{B})(U_{A}(\delta _{A})-U_{A}(\delta _{B}))\leq U_{A}(\delta _{A})(U_{B}(\delta _{B})-U_{B}(\delta _{A}))} U A ( δ A ) U B ( δ B ) − U A ( δ B ) U B ( δ B ) ≤ U A ( δ A ) U B ( δ B ) − U A ( δ A ) U B ( δ A ) {\displaystyle U_{A}(\delta _{A})U_{B}(\delta _{B})-U_{A}(\delta _{B})U_{B}(\delta _{B})\leq U_{A}(\delta _{A})U_{B}(\delta _{B})-U_{A}(\delta _{A})U_{B}(\delta _{A})} − U A ( δ B ) U B ( δ B ) ≤ − U A ( δ A ) U B ( δ A ) {\displaystyle -U_{A}(\delta _{B})U_{B}(\delta _{B})\leq -U_{A}(\delta _{A})U_{B}(\delta _{A})} U A ( δ A ) U B ( δ A ) ≤ U A ( δ B ) U B ( δ B ) {\displaystyle U_{A}(\delta _{A})U_{B}(\delta _{A})\leq U_{A}(\delta _{B})U_{B}(\delta _{B})} π ( δ A ) ≤ π ( δ B ) {\displaystyle \pi (\delta _{A})\leq \pi (\delta _{B})} Thus, Agent A will concede if and only if δ A {\displaystyle \delta _{A}} does not yield the larger product of utilities. Therefore, the Zeuthen strategy guarantees a final agreement that maximizes the Nash Product.

  Read more →
• 

  Proximal gradient methods for learning

  Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is ℓ 1 {\displaystyle \ell _{1}} regularization (also known as Lasso) of the form min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , where x i ∈ R d and y i ∈ R . {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},\quad {\text{ where }}x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} Proximal gradient methods offer a general framework for solving regularization problems from statistical learning theory with penalties that are tailored to a specific problem application. Such customized penalties can help to induce certain structure in problem solutions, such as sparsity (in the case of lasso) or group structure (in the case of group lasso). == Relevant background == Proximal gradient methods are applicable in a wide variety of scenarios for solving convex optimization problems of the form min x ∈ H F ( x ) + R ( x ) , {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x),} where F {\displaystyle F} is convex and differentiable with Lipschitz continuous gradient, R {\displaystyle R} is a convex, lower semicontinuous function which is possibly nondifferentiable, and H {\displaystyle {\mathcal {H}}} is some set, typically a Hilbert space. The usual criterion of x {\displaystyle x} minimizes F ( x ) + R ( x ) {\displaystyle F(x)+R(x)} if and only if ∇ ( F + R ) ( x ) = 0 {\displaystyle \nabla (F+R)(x)=0} in the convex, differentiable setting is now replaced by 0 ∈ ∂ ( F + R ) ( x ) , {\displaystyle 0\in \partial (F+R)(x),} where ∂ φ {\displaystyle \partial \varphi } denotes the subdifferential of a real-valued, convex function φ {\displaystyle \varphi } . Given a convex function φ : H → R {\displaystyle \varphi :{\mathcal {H}}\to \mathbb {R} } an important operator to consider is its proximal operator prox φ : H → H {\displaystyle \operatorname {prox} _{\varphi }:{\mathcal {H}}\to {\mathcal {H}}} defined by prox φ ⁡ ( u ) = arg ⁡ min x ∈ H φ ( x ) + 1 2 ‖ u − x ‖ 2 2 , {\displaystyle \operatorname {prox} _{\varphi }(u)=\operatorname {arg} \min _{x\in {\mathcal {H}}}\varphi (x)+{\frac {1}{2}}\|u-x\|_{2}^{2},} which is well-defined because of the strict convexity of the ℓ 2 {\displaystyle \ell _{2}} norm. The proximal operator can be seen as a generalization of a projection. We see that the proximity operator is important because x ∗ {\displaystyle x^{}} is a minimizer to the problem min x ∈ H F ( x ) + R ( x ) {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x)} if and only if x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) , {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right),} where γ > 0 {\displaystyle \gamma >0} is any positive real number. === Moreau decomposition === One important technique related to proximal gradient methods is the Moreau decomposition, which decomposes the identity operator as the sum of two proximity operators. Namely, let φ : X → R {\displaystyle \varphi :{\mathcal {X}}\to \mathbb {R} } be a lower semicontinuous, convex function on a vector space X {\displaystyle {\mathcal {X}}} . We define its Fenchel conjugate φ ∗ : X → R {\displaystyle \varphi ^{}:{\mathcal {X}}\to \mathbb {R} } to be the function φ ∗ ( u ) := sup x ∈ X ⟨ x , u ⟩ − φ ( x ) . {\displaystyle \varphi ^{}(u):=\sup _{x\in {\mathcal {X}}}\langle x,u\rangle -\varphi (x).} The general form of Moreau's decomposition states that for any x ∈ X {\displaystyle x\in {\mathcal {X}}} and any γ > 0 {\displaystyle \gamma >0} that x = prox γ φ ⁡ ( x ) + γ prox φ ∗ / γ ⁡ ( x / γ ) , {\displaystyle x=\operatorname {prox} _{\gamma \varphi }(x)+\gamma \operatorname {prox} _{\varphi ^{}/\gamma }(x/\gamma ),} which for γ = 1 {\displaystyle \gamma =1} implies that x = prox φ ⁡ ( x ) + prox φ ∗ ⁡ ( x ) {\displaystyle x=\operatorname {prox} _{\varphi }(x)+\operatorname {prox} _{\varphi ^{}}(x)} . The Moreau decomposition can be seen to be a generalization of the usual orthogonal decomposition of a vector space, analogous with the fact that proximity operators are generalizations of projections. In certain situations it may be easier to compute the proximity operator for the conjugate φ ∗ {\displaystyle \varphi ^{}} instead of the function φ {\displaystyle \varphi } , and therefore the Moreau decomposition can be applied. This is the case for group lasso. == Lasso regularization == Consider the regularized empirical risk minimization problem with square loss and with the ℓ 1 {\displaystyle \ell _{1}} norm as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},} where x i ∈ R d and y i ∈ R . {\displaystyle x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} The ℓ 1 {\displaystyle \ell _{1}} regularization problem is sometimes referred to as lasso (least absolute shrinkage and selection operator). Such ℓ 1 {\displaystyle \ell _{1}} regularization problems are interesting because they induce sparse solutions, that is, solutions w {\displaystyle w} to the minimization problem have relatively few nonzero components. Lasso can be seen to be a convex relaxation of the non-convex problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{0},} where ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", which is the number of nonzero entries of the vector w {\displaystyle w} . Sparse solutions are of particular interest in learning theory for interpretability of results: a sparse solution can identify a small number of important factors. === Solving for L1 proximity operator === For simplicity we restrict our attention to the problem where λ = 1 {\displaystyle \lambda =1} . To solve the problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\|w\|_{1},} we consider our objective function in two parts: a convex, differentiable term F ( w ) = 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 {\displaystyle F(w)={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}} and a convex function R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} . Note that R {\displaystyle R} is not strictly convex. Let us compute the proximity operator for R ( w ) {\displaystyle R(w)} . First we find an alternative characterization of the proximity operator prox R ⁡ ( x ) {\displaystyle \operatorname {prox} _{R}(x)} as follows: u = prox R ⁡ ( x ) ⟺ 0 ∈ ∂ ( R ( u ) + 1 2 ‖ u − x ‖ 2 2 ) ⟺ 0 ∈ ∂ R ( u ) + u − x ⟺ x − u ∈ ∂ R ( u ) . {\displaystyle {\begin{aligned}u=\operatorname {prox} _{R}(x)\iff &0\in \partial \left(R(u)+{\frac {1}{2}}\|u-x\|_{2}^{2}\right)\\\iff &0\in \partial R(u)+u-x\\\iff &x-u\in \partial R(u).\end{aligned}}} For R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} it is easy to compute ∂ R ( w ) {\displaystyle \partial R(w)} : the i {\displaystyle i} th entry of ∂ R ( w ) {\displaystyle \partial R(w)} is precisely ∂ | w i | = { 1 , w i > 0 − 1 , w i < 0 [ − 1 , 1 ] , w i = 0. {\displaystyle \partial |w_{i}|={\begin{cases}1,&w_{i}>0\\-1,&w_{i}<0\\\left[-1,1\right],&w_{i}=0.\end{cases}}} Using the recharacterization of the proximity operator given above, for the choice of R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} and γ > 0 {\displaystyle \gamma >0} we have that prox γ R ⁡ ( x ) {\displaystyle \operatorname {prox} _{\gamma R}(x)} is defined entrywise by ( prox γ R ⁡ ( x ) ) i = { x i − γ , x i > γ 0 , | x i | ≤ γ x i + γ , x i < − γ , {\displaystyle \left(\operatorname {prox} _{\gamma R}(x)\right)_{i}={\begin{cases}x_{i}-\gamma ,&x_{i}>\gamma \\0,&|x_{i}|\leq \gamma \\x_{i}+\gamma ,&x_{i}<-\gamma ,\end{cases}}} which is known as the soft thresholding operator S γ ( x ) = prox γ ‖ ⋅ ‖ 1 ⁡ ( x ) {\displaystyle S_{\gamma }(x)=\operatorname {prox} _{\gamma \|\cdot \|_{1}}(x)} . === Fixed point iterative schemes === To finally solve the lasso problem we consider the fixed point equation shown earlier: x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) . {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right).} Given that we have computed the form of the proximity operator explicitly, then we can define a standard fixed point iteration procedure. Namely, fix some initial w 0 ∈ R d {\displaystyle w^{0}\in \mathbb {R} ^{d}} , and for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } define w k + 1 = S γ ( w k − γ ∇ F ( w k ) ) . {\displaystyle w^{k+1}=S_{\gamma }\left(w^{k}-\gamma \nabla F\l

  Read more →