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Algorithm selection

Algorithm selection (sometimes also called per-instance algorithm selection or offline algorithm selection) is a meta-algorithmic technique to choose an algorithm from a portfolio on an instance-by-instance basis. It is motivated by the observation that on many practical problems, different algorithms have different performance characteristics. That is, while one algorithm performs well in some scenarios, it performs poorly in others and vice versa for another algorithm. If we can identify when to use which algorithm, we can optimize for each scenario and improve overall performance. This is what algorithm selection aims to do. The only prerequisite for applying algorithm selection techniques is that there exists (or that there can be constructed) a set of complementary algorithms. == Definition == Given a portfolio P {\displaystyle {\mathcal {P}}} of algorithms A ∈ P {\displaystyle {\mathcal {A}}\in {\mathcal {P}}} , a set of instances i ∈ I {\displaystyle i\in {\mathcal {I}}} and a cost metric m : P × I → R {\displaystyle m:{\mathcal {P}}\times {\mathcal {I}}\to \mathbb {R} } , the algorithm selection problem consists of finding a mapping s : I → P {\displaystyle s:{\mathcal {I}}\to {\mathcal {P}}} from instances I {\displaystyle {\mathcal {I}}} to algorithms P {\displaystyle {\mathcal {P}}} such that the cost ∑ i ∈ I m ( s ( i ) , i ) {\displaystyle \sum _{i\in {\mathcal {I}}}m(s(i),i)} across all instances is optimized. == Examples == === Boolean satisfiability problem (and other hard combinatorial problems) === A well-known application of algorithm selection is the Boolean satisfiability problem. Here, the portfolio of algorithms is a set of (complementary) SAT solvers, the instances are Boolean formulas, the cost metric is for example average runtime or number of unsolved instances. So, the goal is to select a well-performing SAT solver for each individual instance. In the same way, algorithm selection can be applied to many other N P {\displaystyle {\mathcal {NP}}} -hard problems (such as mixed integer programming, CSP, AI planning, TSP, MAXSAT, QBF and answer set programming). Competition-winning systems in SAT are SATzilla, 3S and CSHC === Machine learning === In machine learning, algorithm selection is better known as meta-learning. The portfolio of algorithms consists of machine learning algorithms (e.g., Random Forest, SVM, DNN), the instances are data sets and the cost metric is for example the error rate. So, the goal is to predict which machine learning algorithm will have a small error on each data set. == Instance features == The algorithm selection problem is mainly solved with machine learning techniques. By representing the problem instances by numerical features f {\displaystyle f} , algorithm selection can be seen as a multi-class classification problem by learning a mapping f i ↦ A {\displaystyle f_{i}\mapsto {\mathcal {A}}} for a given instance i {\displaystyle i} . Instance features are numerical representations of instances. For example, we can count the number of variables, clauses, average clause length for Boolean formulas, or number of samples, features, class balance for ML data sets to get an impression about their characteristics. === Static vs. probing features === We distinguish between two kinds of features: Static features are in most cases some counts and statistics (e.g., clauses-to-variables ratio in SAT). These features ranges from very cheap features (e.g. number of variables) to very complex features (e.g., statistics about variable-clause graphs). Probing features (sometimes also called landmarking features) are computed by running some analysis of algorithm behavior on an instance (e.g., accuracy of a cheap decision tree algorithm on an ML data set, or running for a short time a stochastic local search solver on a Boolean formula). These feature often cost more than simple static features. === Feature costs === Depending on the used performance metric m {\displaystyle m} , feature computation can be associated with costs. For example, if we use running time as performance metric, we include the time to compute our instance features into the performance of an algorithm selection system. SAT solving is a concrete example, where such feature costs cannot be neglected, since instance features for CNF formulas can be either very cheap (e.g., to get the number of variables can be done in constant time for CNFs in the DIMACs format) or very expensive (e.g., graph features which can cost tens or hundreds of seconds). It is important to take the overhead of feature computation into account in practice in such scenarios; otherwise a misleading impression of the performance of the algorithm selection approach is created. For example, if the decision which algorithm to choose can be made with perfect accuracy, but the features are the running time of the portfolio algorithms, there is no benefit to the portfolio approach. This would not be obvious if feature costs were omitted. == Approaches == === Regression approach === One of the first successful algorithm selection approaches predicted the performance of each algorithm m ^ A : I → R {\displaystyle {\hat {m}}_{\mathcal {A}}:{\mathcal {I}}\to \mathbb {R} } and selected the algorithm with the best predicted performance a r g min A ∈ P m ^ A ( i ) {\displaystyle arg\min _{{\mathcal {A}}\in {\mathcal {P}}}{\hat {m}}_{\mathcal {A}}(i)} for an instance i {\displaystyle i} . === Clustering approach === A common assumption is that the given set of instances I {\displaystyle {\mathcal {I}}} can be clustered into homogeneous subsets and for each of these subsets, there is one well-performing algorithm for all instances in there. So, the training consists of identifying the homogeneous clusters via an unsupervised clustering approach and associating an algorithm with each cluster. A new instance is assigned to a cluster and the associated algorithm selected. A more modern approach is cost-sensitive hierarchical clustering using supervised learning to identify the homogeneous instance subsets. === Pairwise cost-sensitive classification approach === A common approach for multi-class classification is to learn pairwise models between every pair of classes (here algorithms) and choose the class that was predicted most often by the pairwise models. We can weight the instances of the pairwise prediction problem by the performance difference between the two algorithms. This is motivated by the fact that we care most about getting predictions with large differences correct, but the penalty for an incorrect prediction is small if there is almost no performance difference. Therefore, each instance i {\displaystyle i} for training a classification model A 1 {\displaystyle {\mathcal {A}}_{1}} vs A 2 {\displaystyle {\mathcal {A}}_{2}} is associated with a cost | m ( A 1 , i ) − m ( A 2 , i ) | {\displaystyle |m({\mathcal {A}}_{1},i)-m({\mathcal {A}}_{2},i)|} . == Requirements == The algorithm selection problem can be effectively applied under the following assumptions: The portfolio P {\displaystyle {\mathcal {P}}} of algorithms is complementary with respect to the instance set I {\displaystyle {\mathcal {I}}} , i.e., there is no single algorithm A ∈ P {\displaystyle {\mathcal {A}}\in {\mathcal {P}}} that dominates the performance of all other algorithms over I {\displaystyle {\mathcal {I}}} (see figures to the right for examples on complementary analysis). In some application, the computation of instance features is associated with a cost. For example, if the cost metric is running time, we have also to consider the time to compute the instance features. In such cases, the cost to compute features should not be larger than the performance gain through algorithm selection. == Application domains == Algorithm selection is not limited to single domains but can be applied to any kind of algorithm if the above requirements are satisfied. Application domains include: hard combinatorial problems: SAT, Mixed Integer Programming, CSP, AI Planning, TSP, MAXSAT, QBF and Answer Set Programming combinatorial auctions in machine learning, the problem is known as meta-learning software design black-box optimization multi-agent systems numerical optimization linear algebra, differential equations evolutionary algorithms vehicle routing problem power systems For an extensive list of literature about algorithm selection, we refer to a literature overview. == Variants of algorithm selection == === Online selection === Online algorithm selection refers to switching between different algorithms during the solving process. This is useful as a hyper-heuristic. In contrast, offline algorithm selection selects an algorithm for a given instance only once and before the solving process. === Computation of schedules === An extension of algorithm selection is the per-instance algorithm scheduling problem, in which we do not select only one solver, but we select a time budget for each algorithm
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Charge based boundary element fast multipole method

The charge-based formulation of the boundary element method (BEM) is a dimensionality reduction numerical technique that is used to model quasistatic electromagnetic phenomena in highly complex conducting media (targeting, e.g., the human brain) with a very large (up to approximately 1 billion) number of unknowns. The charge-based BEM solves an integral equation of the potential theory written in terms of the induced surface charge density. This formulation is naturally combined with fast multipole method (FMM) acceleration, and the entire method is known as charge-based BEM-FMM. The combination of BEM and FMM is a common technique in different areas of computational electromagnetics and, in the context of bioelectromagnetism, it provides improvements over the finite element method. == Historical development == Along with more common electric potential-based BEM, the quasistatic charge-based BEM, derived in terms of the single-layer (charge) density, for a single-compartment medium has been known in the potential theory since the beginning of the 20th century. For multi-compartment conducting media, the surface charge density formulation first appeared in discretized form (for faceted interfaces) in the 1964 paper by Gelernter and Swihart. A subsequent continuous form, including time-dependent and dielectric effects, appeared in the 1967 paper by Barnard, Duck, and Lynn. The charge-based BEM has also been formulated for conducting, dielectric, and magnetic media, and used in different applications. In 2009, Greengard et al. successfully applied the charge-based BEM with fast multipole acceleration to molecular electrostatics of dielectrics. A similar approach to realistic modeling of the human brain with multiple conducting compartments was first described by Makarov et al. in 2018. Along with this, the BEM-based multilevel fast multipole method has been widely used in radar and antenna studies at microwave frequencies as well as in acoustics. == Physical background - surface charges in biological media == The charge-based BEM is based on the concept of an impressed (or primary) electric field E i {\displaystyle \mathbf {E} ^{i}} and a secondary electric field E s {\displaystyle \mathbf {E} ^{s}} . The impressed field is usually known a priori or is trivial to find. For the human brain, the impressed electric field can be classified as one of the following: A conservative field E i {\displaystyle \mathbf {E} ^{i}} derived from an impressed density of EEG or MEG current sources in a homogeneous infinite medium with the conductivity σ {\displaystyle \sigma } at the source location; An instantaneous solenoidal field E i {\displaystyle \mathbf {E} ^{i}} of an induction coil obtained from Faraday's law of induction in a homogeneous infinite medium (air), when transcranial magnetic stimulation (TMS) problems are concerned; A surface field E i {\displaystyle \mathbf {E} ^{i}} derived from an impressed surface current density J i = σ E i {\displaystyle \mathbf {J} ^{i}=\sigma \mathbf {E} ^{i}} of current electrodes injecting electric current at a boundary of a compartment with conductivity σ {\displaystyle \sigma } when transcranial direct-current stimulation (tDCS) or deep brain stimulation (DBS) are concerned; A conservative field E i {\displaystyle \mathbf {E} ^{i}} of charges deposited on voltage electrodes for tDCS or DBS. This specific problem requires a coupled treatment since these charges will depend on the environment; In application to multiscale modeling, a field E i {\displaystyle \mathbf {E} ^{i}} obtained from any other macroscopic numerical solution in a small (mesoscale or microscale) spatial domain within the brain. For example, a constant field can be used. When the impressed field is "turned on", free charges located within a conducting volume D immediately begin to redistribute and accumulate at the boundaries (interfaces) of regions of different conductivity in D. A surface charge density ρ ( r ) {\displaystyle \rho (\mathbf {r} )} appears on the conductivity interfaces. This charge density induces a secondary conservative electric field E s {\displaystyle \mathbf {E} ^{s}} following Coulomb's law. One example is a human under a direct current powerline with the known field E i {\displaystyle \mathbf {E} ^{i}} directed down. The superior surface of the human's conducting body will be charged negatively while its inferior portion is charged positively. These surface charges create a secondary electric field that effectively cancels or blocks the primary field everywhere in the body so that no current will flow within the body under DC steady state conditions. Another example is a human head with electrodes attached. At any conductivity interface with a normal vector n {\displaystyle \mathbf {n} } pointing from an "inside" (-) compartment of conductivity σ − {\displaystyle \sigma ^{-}} to an "outside" (+) compartment of conductivity σ + {\displaystyle \sigma ^{+}} , Kirchhoff's current law requires continuity of the normal component of the electric current density. This leads to the interfacial boundary condition in the form for every facet at a triangulated interface. As long as σ ± {\displaystyle \sigma ^{\pm }} are different from each other, the two normal components of the electric field, E ± ⋅ n {\displaystyle \mathbf {E} ^{\pm }\cdot \mathbf {n} } , must also be different. Such a jump across the interface is only possible when a sheet of surface charge exists at that interface. Thus, if an electric current or voltage is applied, the surface charge density follows. The goal of the numerical analysis is to find the unknown surface charge distribution and thus the total electric field E = E i + E s {\displaystyle \mathbf {E} =\mathbf {E} ^{i}+\mathbf {E} ^{s}} (and the total electric potential if required) anywhere in space. == System of equations for surface charges == Below, a derivation is given based on Gauss's law and Coulomb's law. All conductivity interfaces, denoted by S, are discretized into planar triangular facets t m {\displaystyle t_{m}} with centers r m {\displaystyle \mathbf {r} _{m}} . Assume that an m-th facet with the normal vector n m {\displaystyle \mathbf {n} _{m}} and area A m {\displaystyle A_{m}} carries a uniform surface charge density ρ m {\displaystyle \rho _{m}} . If a volumetric tetrahedral mesh were present, the charged facets would belong to tetrahedra with different conductivity values. We first compute the electric field E m + {\displaystyle \mathbf {E} _{m}^{+}} at the point r m + δ n m {\displaystyle \mathbf {r} _{m}+\delta \mathbf {n} _{m}} , for δ → 0 + {\displaystyle \delta \rightarrow 0^{+}} i.e., just outside facet 𝑚 at its center. This field contains three contributions: The continuous impressed electric field E i {\displaystyle \mathbf {E} ^{i}} itself; An electric field of the m-th charged facet itself. Very close to the facet, it can be approximated as the electric field of an infinite sheet of uniform surface charge ρ m {\displaystyle \rho _{m}} . By Gauss's law, it is given by + ρ m / 2 ε 0 ⋅ n m {\displaystyle +\rho _{m}/2\varepsilon _{0}\cdot \mathbf {n} _{m}} where ε 0 {\displaystyle \varepsilon _{0}} is a background electrical permittivity; An electric field generated by all other facets t n {\displaystyle t_{n}} , which we approximate as point charges of charge A n ρ n {\displaystyle A_{n}\rho _{n}} at each center r n {\displaystyle \mathbf {r} _{n}} . A similar treatment holds for the electric field E m − {\displaystyle \mathbf {E} _{m}^{-}} just inside facet 𝑚, but the electric field of the flat sheet of charge changes its sign. Using Coulomb's law to calculate the contribution of facets different from t m {\displaystyle t_{m}} , we find From this equation, we see that the normal component of the electric field indeed undergoes a jump through the charged interface. This is equivalent to a jump relation of the potential theory. As a second step, the two expressions for E m ± {\displaystyle \mathbf {E} _{m}^{\pm }} are substituted into the interfacial boundary condition σ − E m − ⋅ n m = σ + E m + ⋅ n m {\displaystyle \sigma ^{-}\mathbf {E} _{m}^{-}\cdot \mathbf {n} _{m}=\sigma ^{+}\mathbf {E} _{m}^{+}\cdot \mathbf {n} _{m}} , applied to every facet 𝑚. This operation leads to a system of linear equations for unknown charge densities ρ m {\displaystyle \rho _{m}} which solves the problem: where K m = σ − − σ + σ − + σ + {\displaystyle K_{m}={\frac {\sigma ^{-}-\sigma ^{+}}{\sigma ^{-}+\sigma ^{+}}}} is the electric conductivity contrast at the m-th facet. The normalization constant ε 0 {\displaystyle \varepsilon _{0}} will cancel out after the solution is substituted in the expression for E s {\displaystyle \mathbf {E} ^{s}} and becomes redundant. == Application of fast multipole method == For modern characterizations of brain topologies with ever-increasing levels of complexity, the above system of equations for ρ m {\displaystyle \rho _{m}} is very large; it is t
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Frequent pattern discovery

Frequent pattern discovery (or FP discovery, FP mining, or Frequent itemset mining) is part of knowledge discovery in databases, Massive Online Analysis, and data mining; it describes the task of finding the most frequent and relevant patterns in large datasets. The concept was first introduced for mining transaction databases. Frequent patterns are defined as subsets (itemsets, subsequences, or substructures) that appear in a data set with frequency no less than a user-specified or auto-determined threshold. == Techniques == Techniques for FP mining include: market basket analysis cross-marketing catalog design clustering classification recommendation systems For the most part, FP discovery can be done using association rule learning with particular algorithms Eclat, FP-growth and the Apriori algorithm. Other strategies include: Frequent subtree mining Structure mining Sequential pattern mining and respective specific techniques. Implementations exist for various machine learning systems or modules like MLlib for Apache Spark.
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BrownBoost

BrownBoost is a boosting algorithm that may be robust to noisy datasets. BrownBoost is an adaptive version of the boost by majority algorithm. As is the case for all boosting algorithms, BrownBoost is used in conjunction with other machine learning methods. BrownBoost was introduced by Yoav Freund in 2001. == Motivation == AdaBoost performs well on a variety of datasets; however, it can be shown that AdaBoost does not perform well on noisy data sets. This is a result of AdaBoost's focus on examples that are repeatedly misclassified. In contrast, BrownBoost effectively "gives up" on examples that are repeatedly misclassified. The core assumption of BrownBoost is that noisy examples will be repeatedly mislabeled by the weak hypotheses and non-noisy examples will be correctly labeled frequently enough to not be "given up on." Thus only noisy examples will be "given up on," whereas non-noisy examples will contribute to the final classifier. In turn, if the final classifier is learned from the non-noisy examples, the generalization error of the final classifier may be much better than if learned from noisy and non-noisy examples. The user of the algorithm can set the amount of error to be tolerated in the training set. Thus, if the training set is noisy (say 10% of all examples are assumed to be mislabeled), the booster can be told to accept a 10% error rate. Since the noisy examples may be ignored, only the true examples will contribute to the learning process. == Algorithm description == BrownBoost uses a non-convex potential loss function, thus it does not fit into the AdaBoost framework. The non-convex optimization provides a method to avoid overfitting noisy data sets. However, in contrast to boosting algorithms that analytically minimize a convex loss function (e.g. AdaBoost and LogitBoost), BrownBoost solves a system of two equations and two unknowns using standard numerical methods. The only parameter of BrownBoost ( c {\displaystyle c} in the algorithm) is the "time" the algorithm runs. The theory of BrownBoost states that each hypothesis takes a variable amount of time ( t {\displaystyle t} in the algorithm) which is directly related to the weight given to the hypothesis α {\displaystyle \alpha } . The time parameter in BrownBoost is analogous to the number of iterations T {\displaystyle T} in AdaBoost. A larger value of c {\displaystyle c} means that BrownBoost will treat the data as if it were less noisy and therefore will give up on fewer examples. Conversely, a smaller value of c {\displaystyle c} means that BrownBoost will treat the data as more noisy and give up on more examples. During each iteration of the algorithm, a hypothesis is selected with some advantage over random guessing. The weight of this hypothesis α {\displaystyle \alpha } and the "amount of time passed" t {\displaystyle t} during the iteration are simultaneously solved in a system of two non-linear equations ( 1. uncorrelated hypothesis w.r.t example weights and 2. hold the potential constant) with two unknowns (weight of hypothesis α {\displaystyle \alpha } and time passed t {\displaystyle t} ). This can be solved by bisection (as implemented in the JBoost software package) or Newton's method (as described in the original paper by Freund). Once these equations are solved, the margins of each example ( r i ( x j ) {\displaystyle r_{i}(x_{j})} in the algorithm) and the amount of time remaining s {\displaystyle s} are updated appropriately. This process is repeated until there is no time remaining. The initial potential is defined to be 1 m ∑ j = 1 m 1 − erf ( c ) = 1 − erf ( c ) {\displaystyle {\frac {1}{m}}\sum _{j=1}^{m}1-{\mbox{erf}}({\sqrt {c}})=1-{\mbox{erf}}({\sqrt {c}})} . Since a constraint of each iteration is that the potential be held constant, the final potential is 1 m ∑ j = 1 m 1 − erf ( r i ( x j ) / c ) = 1 − erf ( c ) {\displaystyle {\frac {1}{m}}\sum _{j=1}^{m}1-{\mbox{erf}}(r_{i}(x_{j})/{\sqrt {c}})=1-{\mbox{erf}}({\sqrt {c}})} . Thus the final error is likely to be near 1 − erf ( c ) {\displaystyle 1-{\mbox{erf}}({\sqrt {c}})} . However, the final potential function is not the 0–1 loss error function. For the final error to be exactly 1 − erf ( c ) {\displaystyle 1-{\mbox{erf}}({\sqrt {c}})} , the variance of the loss function must decrease linearly w.r.t. time to form the 0–1 loss function at the end of boosting iterations. This is not yet discussed in the literature and is not in the definition of the algorithm below. The final classifier is a linear combination of weak hypotheses and is evaluated in the same manner as most other boosting algorithms. == BrownBoost learning algorithm definition == Input: m {\displaystyle m} training examples ( x 1 , y 1 ) , … , ( x m , y m ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{m},y_{m})} where x j ∈ X , y j ∈ Y = { − 1 , + 1 } {\displaystyle x_{j}\in X,\,y_{j}\in Y=\{-1,+1\}} The parameter c {\displaystyle c} Initialise: s = c {\displaystyle s=c} . (The value of s {\displaystyle s} is the amount of time remaining in the game) r i ( x j ) = 0 {\displaystyle r_{i}(x_{j})=0} ∀ j {\displaystyle \forall j} . The value of r i ( x j ) {\displaystyle r_{i}(x_{j})} is the margin at iteration i {\displaystyle i} for example x j {\displaystyle x_{j}} . While s > 0 {\displaystyle s>0} : Set the weights of each example: W i ( x j ) = e − ( r i ( x j ) + s ) 2 c {\displaystyle W_{i}(x_{j})=e^{-{\frac {(r_{i}(x_{j})+s)^{2}}{c}}}} , where r i ( x j ) {\displaystyle r_{i}(x_{j})} is the margin of example x j {\displaystyle x_{j}} Find a classifier h i : X → { − 1 , + 1 } {\displaystyle h_{i}:X\to \{-1,+1\}} such that ∑ j W i ( x j ) h i ( x j ) y j > 0 {\displaystyle \sum _{j}W_{i}(x_{j})h_{i}(x_{j})y_{j}>0} Find values α , t {\displaystyle \alpha ,t} that satisfy the equation: ∑ j h i ( x j ) y j e − ( r i ( x j ) + α h i ( x j ) y j + s − t ) 2 c = 0 {\displaystyle \sum _{j}h_{i}(x_{j})y_{j}e^{-{\frac {(r_{i}(x_{j})+\alpha h_{i}(x_{j})y_{j}+s-t)^{2}}{c}}}=0} . (Note this is similar to the condition E W i + 1 [ h i ( x j ) y j ] = 0 {\displaystyle E_{W_{i+1}}[h_{i}(x_{j})y_{j}]=0} set forth by Schapire and Singer. In this setting, we are numerically finding the W i + 1 = exp ⁡ ( ⋯ ⋯ ) {\displaystyle W_{i+1}=\exp \left({\frac {\cdots }{\cdots }}\right)} such that E W i + 1 [ h i ( x j ) y j ] = 0 {\displaystyle E_{W_{i+1}}[h_{i}(x_{j})y_{j}]=0} .) This update is subject to the constraint ∑ ( Φ ( r i ( x j ) + α h ( x j ) y j + s − t ) − Φ ( r i ( x j ) + s ) ) = 0 {\displaystyle \sum \left(\Phi \left(r_{i}(x_{j})+\alpha h(x_{j})y_{j}+s-t\right)-\Phi \left(r_{i}(x_{j})+s\right)\right)=0} , where Φ ( z ) = 1 − erf ( z / c ) {\displaystyle \Phi (z)=1-{\mbox{erf}}(z/{\sqrt {c}})} is the potential loss for a point with margin r i ( x j ) {\displaystyle r_{i}(x_{j})} Update the margins for each example: r i + 1 ( x j ) = r i ( x j ) + α h ( x j ) y j {\displaystyle r_{i+1}(x_{j})=r_{i}(x_{j})+\alpha h(x_{j})y_{j}} Update the time remaining: s = s − t {\displaystyle s=s-t} Output: H ( x ) = sign ( ∑ i α i h i ( x ) ) {\displaystyle H(x)={\textrm {sign}}\left(\sum _{i}\alpha _{i}h_{i}(x)\right)} == Empirical results == In preliminary experimental results with noisy datasets, BrownBoost outperformed AdaBoost's generalization error; however, LogitBoost performed as well as BrownBoost. An implementation of BrownBoost can be found in the open source software JBoost.
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Tribute (website)

Tribute is an American video-sharing website headquartered in Brooklyn. Created in 2014 by Andrew Horn and Rory Petty, the platform lets customers create video montages (called "tributes") for occasions including weddings, birthdays, anniversaries, get well soon, and memorials. Tribute.co allows users to record video messages, request submissions from friends and family, insert photos, add music, and send the resulting video tribute montage to a recipient. == Overview == Tribute's collaborative technology starts with inviting people to contribute via email, SMS or social media. Participants receive a prompt to record a short video via their phone, computer or tablet. The site's video editing software allows users to drag and drop the clips in their desired order without prior video editing experience. == History == When Andrew Horn turned twenty-seven, his girlfriend, Miki Agrawal surprised him with a video montage containing clips of his family and closest friends explaining why they loved him. This resulted in Andrew's idea to create Tribute–a "living eulogy" video-compilation service that he co-founded with software engineer Rory Petty. Founded in 2014, Tribute's activity accelerated in 2020 due to the COVID-19 pandemic, and it had sent over 5 million videos as of December 2021. While social distance restrictions were in effect, the site provided a way for people to connect while in-person celebrations were put on hold. For each video sold, Tribute makes one available to hospitals for free and has partnered with Cleveland Clinic Cancer Center in Ohio, Lurie Children's Hospital in Illinois and CarePoint Health in New Jersey.
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Taguchi loss function

The Taguchi loss function is graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting the value of products produced by a company. Praised by Dr. W. Edwards Deming (the business guru of the 1980s American quality movement), it made clear the concept that quality does not suddenly plummet when, for instance, a machinist exceeds a rigid blueprint tolerance. Instead 'loss' in value progressively increases as variation increases from the intended condition. This was considered a breakthrough in describing quality, and helped fuel the continuous improvement movement. The concept of Taguchi's quality loss function was in contrast with the American concept of quality, popularly known as goal post philosophy, the concept given by American quality guru Phil Crosby. Goal post philosophy emphasizes that if a product feature doesn't meet the designed specifications it is termed as a product of poor quality (rejected), irrespective of amount of deviation from the target value (mean value of tolerance zone). This concept has similarity with the concept of scoring a 'goal' in the game of football or hockey, because a goal is counted 'one' irrespective of the location of strike of the ball in the 'goal post', whether it is in the center or towards the corner. This means that if the product dimension goes out of the tolerance limit the quality of the product drops suddenly. Through his concept of the quality loss function, Taguchi explained that from the customer's point of view this drop of quality is not sudden. The customer experiences a loss of quality the moment product specification deviates from the 'target value'. This 'loss' is depicted by a quality loss function and it follows a parabolic curve mathematically given by L = k(y–m)2, where m is the theoretical 'target value' or 'mean value' and y is the actual size of the product, k is a constant and L is the loss. This means that if the difference between 'actual size' and 'target value' i.e. (y–m) is large, loss would be more, irrespective of tolerance specifications. In Taguchi's view tolerance specifications are given by engineers and not by customers; what the customer experiences is 'loss'. This equation is true for a single product; if 'loss' is to be calculated for multiple products the loss function is given by L = k[S2 + ( y ¯ {\displaystyle {\bar {y}}} – m)2], where S2 is the 'variance of product size' and y ¯ {\displaystyle {\bar {y}}} is the average product size. == Overview == The Taguchi loss function is important for a number of reasons—primarily, to help engineers better understand the importance of designing for variation.
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Evolutionary attractor

An evolutionary attractor is a point in an evolutionary space where a selection process will always drive trait values towards that point from the region around it. Because of the importance of evolution through natural selection, often such an evolutionary space will be defined by genetic or phenotypic traits, or possibly both. In this case the selection process will be a form of natural selection. The existence of an evolutionary attractor in a biological evolutionary space does not always imply that it can be reached from all points in that evolutionary space, nor does it identify what will happen when the evolutionary attractor is reached. While an evolutionary attractor may represent a point in evolutionary space that is resistant to further selection, such as an evolutionarily stable strategy, other possibilities are available. Because identification of an evolutionary attractor on its own does not describe everything about the evolutionary space in which it lies, this has led to interest in the evolutionary dynamics surrounding evolutionary attractors and in evolutionary spaces in general. (Theoretical biologists and mathematicians working in the area may prefer the terms adaptive dynamics or evolutionary invasion analysis to evolutionary dynamics.) These fields use differential equations which allows a more complete understanding of the dynamics in evolutionary spaces including the existence or otherwise of evolutionary attractors. Advances in the study of molecular evolution have also led to the identification of evolutionary attractors at a molecular level. Because biological evolutionary processes have been studied using evolutionary game theory, a technique inspired by game theory originally derived to address economic problems, not only can evolutionary attractors be found in biology but economists studying evolutionary economic models have also identified evolutionary attractors. Evolution in biology has also inspired evolutionary computation in computer science. Many algorithms in this field use a form of selection inspired by natural selection to generate results through evolutionary algorithms. This is therefore another area in which evolutionary attractors have been identified. == Evolutionary attractors in biology == It is not probably not surprising that biology is the field where most examples of evolutionary attractors have been identified, given the importance of evolution through natural selection. === Evolutionary attractors in adaptive landscapes === An evolutionary attractor is a point in genetic and/or phenotypic trait space, that evolution will always drive trait values towards via a selection process. The concept of an evolutionary attractor arose in population genetics following the origin of the adaptive landscape originally proposed by Sewall Wright in 1932. The height of a point in an adaptive landscape is a measure of evolutionary fitness. If a point in an adaptive landscape is a peak, then selection will always drive traits towards it and it will be an evolutionary attractor. While population genetics deals with discrete genetic traits, quantitative genetics extended such concepts to deal with continuous genetic traits, where the concept of evolutionary attractor is also valid. === Evolutionary attractors in evolutionary game models === Evolutionary game theory introduced into evolutionary biology concepts originally used in economics, with the advantage that evolution could be studied in relation to strategic choices made in animal conflicts. This is of particular interest because of the concept of the evolutionarily stable strategy or ESS, a strategy that once established is resistant to invasion by other strategies. ESSs will not always be evolutionary attractors, but if they are they will persist over evolutionary time. === Dynamics around evolutionary attractors in biology === Evolutionary attractors in biology do not exist in isolation. By definition they must exist in an evolutionary trait space where selection drives all traits towards them from a region immediately around them. That is, they must be convergence stable. Eshel (1983) modified the definition of an ESS by considering individually advantageous reduction from a majority deviation: he created the term continuous stability. A continuously stable ESS can be shown to be convergence stable, therefore it will act as an evolutionary attractor. But the nature of evolutionary trait spaces in biology means that it is not possible to guarantee that the region of convergence to the evolutionary attractor covers the whole of the trait space, nor that there is only one evolutionary attractor in a particular trait space. These issues have led to the emergence of the related fields of evolutionary dynamics, adaptive dynamics and evolutionary invasion analysis, all of which use differential equations to understand the dynamics in evolutionary trait spaces. Hence, if one or more evolutionary attractor exists in an evolutionary trait space, they provide techniques to understand the dynamics in that trait space around the evolutionary attractor. === Evolutionary attractors in an ecological context === Evolution in biology does not take place in single species in isolation. Ecological interaction of species leads to coevolution. Important examples of this are host-parasite or host-pathogen interaction, which can make both the dynamics around evolutionary attractors more complex, and the occurrence and number of evolutionary attractors more diverse. Evolutionary attractors have been identified in the analysis of evolutionary epidemiology of plant pathogens. In the above study working on plant populations the authors were able to identify evolutionary attractors using methods from adaptive dynamics. A model applied to the analysis of a maize (Zea mays L.) virus identified convergence stable equilibria through simulation modelling. A related model identified evolutionary attractors in the interaction of plants with fungal pathogens. === Evolutionary attractors in molecular genetics === As mentioned above much of the consideration of evolutionary attractors in biology has been through investigation of selection at a genetic or phenotypic level or both, in a single species or in coevolving species. Advances in the study of molecular genetics now allow the study of evolutionary attractors to be taken to a molecular genetic level. Wilson et. al (2019) studied the evolution of gene regulatory networks and identified the emergence of evolutionary attractors. == Evolutionary attractors in economics == Evolutionary game theory as applied in biology was inspired by game theory originally devised for applications in economics. Game theory remains an active field of research outside of biology, and thus it is not surprising that researchers in evolutionary economics use evolutionary game theory. Evolutionary attractors have been demonstrated by economists studying the evolutionary dynamics of market entry with market dynamics based on the replicator dynamics of biological evolutionary games. == Evolutionary attractors in computing == Evolutionary computation is a branch of computer science inspired by biological evolution. Many algorithms in evolutionary computation use a form of selection. Thus evolutionary attractors have been identified in computer science as well as in biology and economics. Evolutionary algorithms have generated evolutionary attractors, probably because of the similarity between adaptive hill-climbing in evolutionary heuristics and the adaptive landscape originated to explain evolution through natural selection.
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List of datasets for machine-learning research

These datasets are used in machine learning (ML) research and have been cited in peer-reviewed academic journals. Datasets are an integral part of the field of machine learning. Major advances in this field can result from advances in learning algorithms (such as deep learning), computer hardware, and, less intuitively, the availability of high-quality training datasets. High-quality labeled training datasets for supervised and semi-supervised machine-learning algorithms are usually difficult and expensive to produce because of the large amount of time needed to label the data. Although they do not need to be labeled, high-quality unlabeled datasets for unsupervised learning can also be difficult and costly to produce. Many organizations, including governments, publish and share their datasets, often using common metadata formats (such as Croissant). The datasets are classified, based on the licenses, into two groups: open data and non-open data. The datasets from various governmental-bodies are presented in List of open government data sites. The datasets are ported on open data portals. They are made available for searching, depositing and accessing through interfaces like Open API. The datasets are made available as various sorted types and subtypes. == List of sorting used for datasets == The data portal is classified based on its type of license. The open source license based data portals are known as open data portals which are used by many government organizations and academic institutions. == List of open data portals == == List of portals suitable for multiple types of applications == The data portal sometimes lists a wide variety of subtypes of datasets pertaining to many machine learning applications. == List of portals suitable for a specific subtype of applications == The data portals which are suitable for a specific subtype of machine learning application are listed in the subsequent sections. == Image data == == Text data == These datasets consist primarily of text for tasks such as natural language processing, sentiment analysis, translation, and cluster analysis. === Reviews === === News articles === === Messages === === Twitter and tweets === === Dialogues === === Legal === === Other text === == Sound data == These datasets consist of sounds and sound features used for tasks such as speech recognition and speech synthesis. === Speech === === Music === === Other sounds === == Signal data == Datasets containing electric signal information requiring some sort of signal processing for further analysis. === Electrical === === Motion-tracking === === Other signals === == Chemical data == Datasets from physical systems. === Chemical Reactions with transition states (TS) === === OpenReACT-CHON-EFH === OpenReACT-CHON-EFH (Open Reaction Dataset of Atomic ConfiguraTions comprising C, H, O and N with Energies, Forces and Hessians) is a 2025 open-access benchmark for machine-learning interatomic potentials. RTP set – 35,087 stationary-point geometries (reactant, transition state and product) drawn from 11,961 elementary reactions, each labeled with density-functional energies, atomic forces and full Hessian matrices at the ωB97X-D/6-31G(d) level. IRC set – 34,248 structures along 600 minimum-energy reaction paths, used to test extrapolation beyond trained stationary points. NMS set – 62,527 off-equilibrium geometries generated by normal-mode sampling to probe model robustness under thermal perturbations. The collection underpins the study Does Hessian Data Improve the Performance of Machine Learning Potentials? and was used to train and benchmark the machine-learning interatomic potentials reported therein. The dataset itself is distributed under a CC licence via Figshare. == Physical data == Datasets from physical systems. === High-energy physics === === Systems === === Astronomy === === Earth science === === Other physical === == Biological data == Datasets from biological systems. === Human === === Animal === === Fungi === === Plant === === Microbe === === Drug discovery === == Anomaly data == == Question answering data == This section includes datasets that deals with structured data. == Dialog or instruction prompted data == This section includes datasets that contains multi-turn text with at least two actors, a "user" and an "agent". The user makes requests for the agent, which performs the request. == Cybersecurity == == Climate and sustainability == == Code data == == Multivariate data == === Financial === === Weather === === Census === === Transit === === Internet === === Games === === Other multivariate === == Curated repositories of datasets == As datasets come in myriad formats and can sometimes be difficult to use, there has been considerable work put into curating and standardizing the format of datasets to make them easier to use for machine learning research. OpenML: Web platform with Python, R, Java, and other APIs for downloading hundreds of machine learning datasets, evaluating algorithms on datasets, and benchmarking algorithm performance against dozens of other algorithms. PMLB: A large, curated repository of benchmark datasets for evaluating supervised machine learning algorithms. Provides classification and regression datasets in a standardized format that are accessible through a Python API. Metatext NLP: https://metatext.io/datasets web repository maintained by community, containing nearly 1000 benchmark datasets, and counting. Provides many tasks from classification to QA, and various languages from English, Portuguese to Arabic. Appen: Off The Shelf and Open Source Datasets hosted and maintained by the company. These biological, image, physical, question answering, signal, sound, text, and video resources number over 250 and can be applied to over 25 different use cases.
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Cognitive robotics

Cognitive robotics or cognitive technology is a subfield of robotics concerned with endowing a robot with intelligent behavior by providing it with a processing architecture that will allow it to learn and reason about how to behave in response to complex goals in a complex world. Cognitive robotics may be considered the engineering branch of embodied cognitive science and embodied embedded cognition, consisting of robotic process automation, artificial intelligence, machine learning, deep learning, optical character recognition, image processing, process mining, analytics, software development and system integration. == Core issues == While traditional cognitive modeling approaches have assumed symbolic coding schemes as a means for depicting the world, translating the world into these kinds of symbolic representations has proven to be problematic if not untenable. Perception and action and the notion of symbolic representation are therefore core issues to be addressed in cognitive robotics. == Starting point == Cognitive robotics views human or animal cognition as a starting point for the development of robotic information processing, as opposed to more traditional artificial intelligence techniques. Target robotic cognitive capabilities include perception processing, attention allocation, anticipation, planning, complex motor coordination, reasoning about other agents and perhaps even about their own mental states. Robotic cognition embodies the behavior of intelligent agents in the physical world (or a virtual world, in the case of simulated cognitive robotics). Ultimately, the robot must be able to act in the real world. == Learning techniques == === Motor Babble === A preliminary robot learning technique called motor babbling involves correlating pseudo-random complex motor movements by the robot with resulting visual and/or auditory feedback such that the robot may begin to expect a pattern of sensory feedback given a pattern of motor output. Desired sensory feedback may then be used to inform a motor control signal. This is thought to be analogous to how a baby learns to reach for objects or learns to produce speech sounds. For simpler robot systems, where, for instance, inverse kinematics may feasibly be used to transform anticipated feedback (desired motor result) into motor output, this step may be skipped. === Imitation === Once a robot can coordinate its motors to produce a desired result, the technique of learning by imitation may be used. The robot monitors the performance of another agent and then the robot tries to imitate that agent. It is often a challenge to transform imitation information from a complex scene into a desired motor result for the robot. Note that imitation is a high-level form of cognitive behavior and imitation is not necessarily required in a basic model of embodied animal cognition. === Knowledge acquisition === A more complex learning approach is "autonomous knowledge acquisition": the robot is left to explore the environment on its own. A system of goals and beliefs is typically assumed. A somewhat more directed mode of exploration can be achieved by "curiosity" algorithms, such as Intelligent Adaptive Curiosity or Category-Based Intrinsic Motivation. These algorithms generally involve breaking sensory input into a finite number of categories and assigning some sort of prediction system (such as an artificial neural network) to each. The prediction system keeps track of the error in its predictions over time. Reduction in prediction error is considered learning. The robot then preferentially explores categories in which it is learning (or reducing prediction error) the fastest. == Other architectures == Some researchers in cognitive robotics have tried using architectures such as (ACT-R and Soar (cognitive architecture)) as a basis of their cognitive robotics programs. These highly modular symbol-processing architectures have been used to simulate operator performance and human performance when modeling simplistic and symbolized laboratory data. The idea is to extend these architectures to handle real-world sensory input as that input continuously unfolds through time. What is needed is a way to somehow translate the world into a set of symbols and their relationships. == Questions == Some of the fundamental questions to be answered in cognitive robotics are: How much human programming should or can be involved to support the learning processes? How can one quantify progress? Some of the adopted ways are reward and punishment. But what kind of reward and what kind of punishment? In humans, when teaching a child, for example, the reward would be candy or some encouragement, and the punishment can take many forms. But what is an effective way with robots?
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Multidimensional analysis

In statistics, econometrics and related fields, multidimensional analysis (MDA) is a data analysis process that groups data into two categories: data dimensions and measurements. For example, a data set consisting of the number of wins for a single football team at each of several years is a single-dimensional (in this case, longitudinal) data set. A data set consisting of the number of wins for several football teams in a single year is also a single-dimensional (in this case, cross-sectional) data set. A data set consisting of the number of wins for several football teams over several years is a two-dimensional data set. == Higher dimensions == In many disciplines, two-dimensional data sets are also called panel data. While, strictly speaking, two- and higher-dimensional data sets are "multi-dimensional", the term "multidimensional" tends to be applied only to data sets with three or more dimensions. For example, some forecast data sets provide forecasts for multiple target periods, conducted by multiple forecasters, and made at multiple horizons. The three dimensions provide more information than can be gleaned from two-dimensional panel data sets. == Software == Computer software for MDA include Online analytical processing (OLAP) for data in relational databases, pivot tables for data in spreadsheets, and Array DBMSs for general multi-dimensional data (such as raster data) in science, engineering, and business.
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Homogeneity blockmodeling

In mathematics applied to analysis of social structures, homogeneity blockmodeling is an approach in blockmodeling, which is best suited for a preliminary or main approach to valued networks, when a prior knowledge about these networks is not available. This is because homogeneity blockmodeling emphasizes the similarity of link (tie) strengths within the blocks over the pattern of links. In this approach, tie (link) values (or statistical data computed on them) are assumed to be equal (homogenous) within blocks. This approach to the generalized blockmodeling of valued networks was first proposed by Aleš Žiberna in 2007 with the basic idea, "that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values". The newly–formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Similar approach to the homogeneity blockmodeling, dealing with direct approach for structural equivalence, was previously suggested by Stephen P. Borgatti and Martin G. Everett (1992).
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Multi expression programming

Multi Expression Programming (MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is a Genetic Programming variant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have been tested). In the simplest variant, MEP chromosomes are linear strings of instructions. This representation was inspired by Three-address code. MEP strength consists in the ability to encode multiple solutions, of a problem, in the same chromosome. In this way, one can explore larger zones of the search space. For most of the problems this advantage comes with no running-time penalty compared with genetic programming variants encoding a single solution in a chromosome. == Representation == MEP chromosomes are arrays of instructions represented in Three-address code format. Each instruction contains a variable, a constant, or a function. If the instruction is a function, then the arguments (given as instruction's addresses) are also present. === Example of MEP program === Here is a simple MEP chromosome (labels on the left side are not a part of the chromosome): 1: a 2: b 3: + 1, 2 4: c 5: d 6: + 4, 5 7: 3, 5 == Fitness computation == When the chromosome is evaluated it is unclear which instruction will provide the output of the program. In many cases, a set of programs is obtained, some of them being completely unrelated (they do not have common instructions). For the above chromosome, here is the list of possible programs obtained during decoding: E1 = a, E2 = b, E4 = c, E5 = d, E3 = a + b. E6 = c + d. E7 = (a + b) d. Each instruction is evaluated as a possible output of the program. The fitness (or error) is computed in a standard manner. For instance, in the case of symbolic regression, the fitness is the sum of differences (in absolute value) between the expected output (called target) and the actual output. == Fitness assignment process == Which expression will represent the chromosome? Which one will give the fitness of the chromosome? In MEP, the best of them (which has the lowest error) will represent the chromosome. This is different from other GP techniques: In Linear genetic programming the last instruction will give the output. In Cartesian Genetic Programming the gene providing the output is evolved like all other genes. Note that, for many problems, this evaluation has the same complexity as in the case of encoding a single solution in each chromosome. Thus, there is no penalty in running time compared to other techniques. == Software == === MEPX === MEPX is a cross-platform (Windows, macOS, and Linux Ubuntu) free software for the automatic generation of computer programs. It can be used for data analysis, particularly for solving symbolic regression, statistical classification and time-series problems. === libmep === Libmep is a free and open source library implementing Multi Expression Programming technique. It is written in C++. === hmep === hmep is a new open source library implementing Multi Expression Programming technique in Haskell programming language.
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Lesk algorithm

The Lesk algorithm is a classical algorithm for word sense disambiguation introduced by Michael E. Lesk in 1986. It operates on the premise that words within a given context are likely to share a common meaning. This algorithm compares the dictionary definitions of an ambiguous word with the words in its surrounding context to determine the most appropriate sense. Variations, such as the Simplified Lesk algorithm, have demonstrated improved precision and efficiency. However, the Lesk algorithm has faced criticism for its sensitivity to definition wording and its reliance on brief glosses. Researchers have sought to enhance its accuracy by incorporating additional resources like thesauruses and syntactic models. == Overview == The Lesk algorithm is based on the assumption that words in a given "neighborhood" (section of text) will tend to share a common topic. A simplified version of the Lesk algorithm is to compare the dictionary definition of an ambiguous word with the terms contained in its neighborhood. Versions have been adapted to use WordNet. An implementation might look like this: for every sense of the word being disambiguated one should count the number of words that are in both the neighborhood of that word and in the dictionary definition of that sense the sense that is to be chosen is the sense that has the largest number of this count. A frequently used example illustrating this algorithm is for the context "pine cone". The following dictionary definitions are used: PINE 1. kinds of evergreen tree with needle-shaped leaves 2. waste away through sorrow or illness CONE 1. solid body which narrows to a point 2. something of this shape whether solid or hollow 3. fruit of certain evergreen trees As can be seen, the best intersection is Pine #1 ⋂ Cone #3 = 2. == Simplified Lesk algorithm == In Simplified Lesk algorithm, the correct meaning of each word in a given context is determined individually by locating the sense that overlaps the most between its dictionary definition and the given context. Rather than simultaneously determining the meanings of all words in a given context, this approach tackles each word individually, independent of the meaning of the other words occurring in the same context. "A comparative evaluation performed by Vasilescu et al. (2004) has shown that the simplified Lesk algorithm can significantly outperform the original definition of the algorithm, both in terms of precision and efficiency. By evaluating the disambiguation algorithms on the Senseval-2 English all words data, they measure a 58% precision using the simplified Lesk algorithm compared to the only 42% under the original algorithm. Note: Vasilescu et al. implementation considers a back-off strategy for words not covered by the algorithm, consisting of the most frequent sense defined in WordNet. This means that words for which all their possible meanings lead to zero overlap with current context or with other word definitions are by default assigned sense number one in WordNet." Simplified LESK Algorithm with smart default word sense (Vasilescu et al., 2004) The COMPUTEOVERLAP function returns the number of words in common between two sets, ignoring function words or other words on a stop list. The original Lesk algorithm defines the context in a more complex way. == Criticisms == Unfortunately, Lesk’s approach is very sensitive to the exact wording of definitions, so the absence of a certain word can radically change the results. Further, the algorithm determines overlaps only among the glosses of the senses being considered. This is a significant limitation in that dictionary glosses tend to be fairly short and do not provide sufficient vocabulary to relate fine-grained sense distinctions. A lot of work has appeared offering different modifications of this algorithm. These works use other resources for analysis (thesauruses, synonyms dictionaries or morphological and syntactic models): for instance, it may use such information as synonyms, different derivatives, or words from definitions of words from definitions. == Lesk variants == Original Lesk (Lesk, 1986) Adapted/Extended Lesk (Banerjee and Pederson, 2002/2003): In the adaptive lesk algorithm, a word vector is created corresponds to every content word in the wordnet gloss. Concatenating glosses of related concepts in WordNet can be used to augment this vector. The vector contains the co-occurrence counts of words co-occurring with w in a large corpus. Adding all the word vectors for all the content words in its gloss creates the Gloss vector g for a concept. Relatedness is determined by comparing the gloss vector using the Cosine similarity measure. There are a lot of studies concerning Lesk and its extensions: Wilks and Stevenson, 1998, 1999; Mahesh et al., 1997; Cowie et al., 1992; Yarowsky, 1992; Pook and Catlett, 1988; Kilgarriff and Rosensweig, 2000; Kwong, 2001; Nastase and Szpakowicz, 2001; Gelbukh and Sidorov, 2004.
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State–action–reward–state–action

State–action–reward–state–action (SARSA) is an algorithm for learning a Markov decision process policy, used in the reinforcement learning area of machine learning. It was proposed by Rummery and Niranjan in a technical note with the name "Modified Connectionist Q-Learning" (MCQ-L). The alternative name SARSA, proposed by Rich Sutton, was only mentioned as a footnote. This name reflects the fact that the main function for updating the Q-value depends on the current state of the agent "S1", the action the agent chooses "A1", the reward "R2" the agent gets for choosing this action, the state "S2" that the agent enters after taking that action, and finally the next action "A2" the agent chooses in its new state. The acronym for the quintuple (St, At, Rt+1, St+1, At+1) is SARSA. Some authors use a slightly different convention and write the quintuple (St, At, Rt, St+1, At+1), depending on which time step the reward is formally assigned. The rest of the article uses the former convention. == Algorithm == Q new ( S t , A t ) ← ( 1 − α ) Q ( S t , A t ) + α [ R t + 1 + γ Q ( S t + 1 , A t + 1 ) ] {\displaystyle Q^{\textrm {new}}(S_{t},A_{t})\leftarrow (1-\alpha )Q(S_{t},A_{t})+\alpha \,[R_{t+1}+\gamma \,Q(S_{t+1},A_{t+1})]} A SARSA agent interacts with the environment and updates the policy based on actions taken, hence this is known as an on-policy learning algorithm. The Q value for a state-action is updated by an error, adjusted by the learning rate α. Q values represent the possible reward received in the next time step for taking action a in state s, plus the discounted future reward received from the next state-action observation. Watkin's Q-learning updates an estimate of the optimal state-action value function Q ∗ {\displaystyle Q^{}} based on the maximum reward of available actions. While SARSA learns the Q values associated with taking the policy it follows itself, Watkin's Q-learning learns the Q values associated with taking the optimal policy while following an exploration/exploitation policy. Some optimizations of Watkin's Q-learning may be applied to SARSA. == Hyperparameters == === Learning rate (alpha) === The learning rate determines to what extent newly acquired information overrides old information. A factor of 0 will make the agent not learn anything, while a factor of 1 would make the agent consider only the most recent information. === Discount factor (gamma) === The discount factor determines the importance of future rewards. A discount factor of 0 makes the agent "opportunistic", or "myopic", e.g., by only considering current rewards, while a factor approaching 1 will make it strive for a long-term high reward. If the discount factor meets or exceeds 1, the Q {\displaystyle Q} values may diverge. === Initial conditions (Q(S0, A0)) === Since SARSA is an iterative algorithm, it implicitly assumes an initial condition before the first update occurs. A high (infinite) initial value, also known as "optimistic initial conditions", can encourage exploration: no matter what action takes place, the update rule causes it to have higher values than the other alternative, thus increasing their choice probability. In 2013 it was suggested that the first reward r {\displaystyle r} could be used to reset the initial conditions. According to this idea, the first time an action is taken the reward is used to set the value of Q {\displaystyle Q} . This allows immediate learning in case of fixed deterministic rewards. This resetting-of-initial-conditions (RIC) approach seems to be consistent with human behavior in repeated binary choice experiments.
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Extremal Ensemble Learning

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