Quantification (machine learning)

In machine learning, quantification (variously called learning to quantify, or supervised prevalence estimation, or class prior estimation) is the task of using supervised learning in order to train models (quantifiers) that estimate the relative frequencies (also known as prevalence values) of the classes of interest in a sample of unlabelled data items. For instance, in a sample of 100,000 unlabelled tweets known to express opinions about a certain political candidate, a quantifier may be used to estimate the percentage of these tweets which belong to class `Positive' (i.e., which manifest a positive stance towards this candidate), and to do the same for classes `Neutral' and `Negative'. Quantification may also be viewed as the task of training predictors that estimate a (discrete) probability distribution, i.e., that generate a predicted distribution that approximates the unknown true distribution of the items across the classes of interest. Quantification is different from classification, since the goal of classification is to predict the class labels of individual data items, while the goal of quantification it to predict the class prevalence values of sets of data items. Quantification is also different from regression, since in regression the training data items have real-valued labels, while in quantification the training data items have class labels. It has been shown in multiple research works that performing quantification by classifying all unlabelled instances and then counting the instances that have been attributed to each class (the 'classify and count' method) usually leads to suboptimal quantification accuracy. This suboptimality may be seen as a direct consequence of 'Vapnik's principle', which states: If you possess a restricted amount of information for solving some problem, try to solve the problem directly and never solve a more general problem as an intermediate step. It is possible that the available information is sufficient for a direct solution but is insufficient for solving a more general intermediate problem. In our case, the problem to be solved directly is quantification, while the more general intermediate problem is classification. As a result of the suboptimality of the 'classify and count' method, quantification has evolved as a task in its own right, different (in goals, methods, techniques, and evaluation measures) from classification. == Quantification tasks == === Quantification tasks according to the set of classes === The main variants of quantification, according to the characteristics of the set of classes used, are: Binary quantification, corresponding to the case in which there are only n = 2 {\displaystyle n=2} classes and each data item belongs to exactly one of them; Single-label multiclass quantification, corresponding to the case in which there are n > 2 {\displaystyle n>2} classes and each data item belongs to exactly one of them; Multi-label multiclass quantification, corresponding to the case in which there are n ≥ 2 {\displaystyle n\geq 2} classes and each data item can belong to zero, one, or several classes at the same time; Ordinal quantification, corresponding to the single-label multiclass case in which a total order is defined on the set of classes. Regression quantification, a task which stands to 'standard' quantification as regression stands to classification. Strictly speaking, this task is not a quantification task as defined above (since the individual items do not have class labels but are labelled by real values), but has enough commonalities with other quantification tasks to be considered one of them. Most known quantification methods address the binary case or the single-label multiclass case, and only few of them address the multi-label, ordinal, and regression cases. Binary-only methods include the Mixture Model (MM) method, the HDy method, SVM(KLD), and SVM(Q). Methods that can deal with both the binary case and the single-label multiclass case include probabilistic classify and count (PCC), adjusted classify and count (ACC), probabilistic adjusted classify and count (PACC), the Saerens-Latinne-Decaestecker EM-based method (SLD), and KDEy. Methods for multi-label quantification include regression-based quantification (RQ) and label powerset-based quantification (LPQ). Methods for the ordinal case include ordinal versions of the above-mentioned ACC, PACC, and SLD methods, and ordinal versions of the above-mentioned HDy method. Methods for the regression case include Regress and splice and Adjusted regress and sum. === Quantification tasks according to the type of data === Several subtasks of quantification may be identified according to the type of data involved. Example such tasks are: Quantification of networked data. This task consists of performing quantification when the datapoints are members of a relation, i.e., are interlinked. As such, this task is a strict relative of collective classification. Quantification over time. This task consists of performing quantification on sets that become available in a temporal sequence, i.e., as a data stream, and finds application in contexts in which class prevalence values must be monitored over time. == Evaluation measures for quantification == Several evaluation measures can be used for evaluating the error of a quantification method. Since quantification consists of generating a predicted probability distribution that estimates a true probability distribution, these evaluation measures are ones that compare two probability distributions. Most evaluation measures for quantification belong to the class of divergences. Evaluation measures for binary quantification, single-label multiclass quantification, and multi-label quantification, are Absolute Error Squared Error Relative Absolute Error Kullback–Leibler divergence Pearson Divergence Evaluation measures for ordinal quantification are Normalized Match Distance (a particular case of the Earth Mover's Distance) Root Normalized Order-Aware Distance == Applications == Quantification is of special interest in fields such as the social sciences, epidemiology, market research, allocating resources, and ecological modelling, since these fields are inherently concerned with aggregate data. However, quantification is also useful as a building block for solving other downstream tasks, such as improving the accuracy of classifiers on out-of-distribution data, measuring classifier bias and ranker bias, and estimating the accuracy of classifiers on out-of-distribution data. == Resources == LQ 2021: the 1st International Workshop on Learning to Quantify LQ 2022: the 2nd International Workshop on Learning to Quantify LQ 2023: the 3rd International Workshop on Learning to Quantify LQ 2024: the 4th International Workshop on Learning to Quantify LQ 2025: the 5th International Workshop on Learning to Quantify LeQua 2022: the 1st Data Challenge on Learning to Quantify LeQua 2024: the 2nd Data Challenge on Learning to Quantify QuaPy: An open-source Python-based software library for quantification QuantificationLib: A Python library for quantification and prevalence estimation

Representation collapse

Representation collapse is a phenomenon in machine learning and representation learning where a model maps different inputs to the same or very similar embeddings, which means it loses important information about how the data is spread out. It is frequently encountered in self-supervised learning, especially within contrastive and non-contrastive frameworks, when training objectives or model architectures do not maintain variance across representations. Collapse results in degenerate solutions characterized by uninformative learned features, significantly impairing downstream task performance. Various techniques have been proposed to mitigate representation collapse, including the use of negative samples, architectural asymmetry, stop-gradient operations, variance regularization, and redundancy reduction objectives, as seen in methods such as SimCLR, BYOL, and VICReg. Comprehending and averting representation collapse is regarded as a fundamental challenge in the advancement of stable and efficient self-supervised learning systems.

Proper generalized decomposition

The proper generalized decomposition (PGD) is an iterative numerical method for solving boundary value problems (BVPs), that is, partial differential equations constrained by a set of boundary conditions, such as the Poisson's equation or the Laplace's equation. The PGD algorithm computes an approximation of the solution of the BVP by successive enrichment. This means that, in each iteration, a new component (or mode) is computed and added to the approximation. In principle, the more modes obtained, the closer the approximation is to its theoretical solution. Unlike POD principal components, PGD modes are not necessarily orthogonal to each other. By selecting only the most relevant PGD modes, a reduced order model of the solution is obtained. Because of this, PGD is considered a dimensionality reduction algorithm. == Description == The proper generalized decomposition is a method characterized by a variational formulation of the problem, a discretization of the domain in the style of the finite element method, the assumption that the solution can be approximated as a separate representation and a numerical greedy algorithm to find the solution. === Variational formulation === In the Proper Generalized Decomposition method, the variational formulation involves translating the problem into a format where the solution can be approximated by minimizing (or sometimes maximizing) a functional. A functional is a scalar quantity that depends on a function, which in this case, represents our problem. The most commonly implemented variational formulation in PGD is the Bubnov-Galerkin method. This method is chosen for its ability to provide an approximate solution to complex problems, such as those described by partial differential equations (PDEs). In the Bubnov-Galerkin approach, the idea is to project the problem onto a space spanned by a finite number of basis functions. These basis functions are chosen to approximate the solution space of the problem. In the Bubnov-Galerkin method, we seek an approximate solution that satisfies the integral form of the PDEs over the domain of the problem. This is different from directly solving the differential equations. By doing so, the method transforms the problem into finding the coefficients that best fit this integral equation in the chosen function space. While the Bubnov-Galerkin method is prevalent, other variational formulations are also used in PGD, depending on the specific requirements and characteristics of the problem, such as: Petrov-Galerkin Method: This method is similar to the Bubnov-Galerkin approach but differs in the choice of test functions. In the Petrov-Galerkin method, the test functions (used to project the residual of the differential equation) are different from the trial functions (used to approximate the solution). This can lead to improved stability and accuracy for certain types of problems. Collocation Method: In collocation methods, the differential equation is satisfied at a finite number of points in the domain, known as collocation points. This approach can be simpler and more direct than the integral-based methods like Galerkin's, but it may also be less stable for some problems. Least Squares Method: This approach involves minimizing the square of the residual of the differential equation over the domain. It is particularly useful when dealing with problems where traditional methods struggle with stability or convergence. Mixed Finite Element Method: In mixed methods, additional variables (such as fluxes or gradients) are introduced and approximated along with the primary variable of interest. This can lead to more accurate and stable solutions for certain problems, especially those involving incompressibility or conservation laws. Discontinuous Galerkin Method: This is a variant of the Galerkin method where the solution is allowed to be discontinuous across element boundaries. This method is particularly useful for problems with sharp gradients or discontinuities. === Domain discretization === The discretization of the domain is a well defined set of procedures that cover (a) the creation of finite element meshes, (b) the definition of basis function on reference elements (also called shape functions) and (c) the mapping of reference elements onto the elements of the mesh. === Separate representation === PGD assumes that the solution u of a (multidimensional) problem can be approximated as a separate representation of the form u ≈ u N ( x 1 , x 2 , … , x d ) = ∑ i = 1 N X 1 i ( x 1 ) ⋅ X 2 i ( x 2 ) ⋯ X d i ( x d ) , {\displaystyle \mathbf {u} \approx \mathbf {u} ^{N}(x_{1},x_{2},\ldots ,x_{d})=\sum _{i=1}^{N}\mathbf {X_{1}} _{i}(x_{1})\cdot \mathbf {X_{2}} _{i}(x_{2})\cdots \mathbf {X_{d}} _{i}(x_{d}),} where the number of addends N and the functional products X1(x1), X2(x2), ..., Xd(xd), each depending on a variable (or variables), are unknown beforehand. === Greedy algorithm === The solution is sought by applying a greedy algorithm, usually the fixed point algorithm, to the weak formulation of the problem. For each iteration i of the algorithm, a mode of the solution is computed. Each mode consists of a set of numerical values of the functional products X1(x1), ..., Xd(xd), which enrich the approximation of the solution. Due to the greedy nature of the algorithm, the term 'enrich' is used rather than 'improve', since some modes may actually worsen the approach. The number of computed modes required to obtain an approximation of the solution below a certain error threshold depends on the stopping criterion of the iterative algorithm. == Features == PGD is suitable for solving high-dimensional problems, since it overcomes the limitations of classical approaches. In particular, PGD avoids the curse of dimensionality, as solving decoupled problems is computationally much less expensive than solving multidimensional problems. Therefore, PGD enables to re-adapt parametric problems into a multidimensional framework by setting the parameters of the problem as extra coordinates: u ≈ u N ( x 1 , … , x d ; k 1 , … , k p ) = ∑ i = 1 N X 1 i ( x 1 ) ⋯ X d i ( x d ) ⋅ K 1 i ( k 1 ) ⋯ K p i ( k p ) , {\displaystyle \mathbf {u} \approx \mathbf {u} ^{N}(x_{1},\ldots ,x_{d};k_{1},\ldots ,k_{p})=\sum _{i=1}^{N}\mathbf {X_{1}} _{i}(x_{1})\cdots \mathbf {X_{d}} _{i}(x_{d})\cdot \mathbf {K_{1}} _{i}(k_{1})\cdots \mathbf {K_{p}} _{i}(k_{p}),} where a series of functional products K1(k1), K2(k2), ..., Kp(kp), each depending on a parameter (or parameters), has been incorporated to the equation. In this case, the obtained approximation of the solution is called computational vademecum: a general meta-model containing all the particular solutions for every possible value of the involved parameters. == Sparse Subspace Learning == The Sparse Subspace Learning (SSL) method leverages the use of hierarchical collocation to approximate the numerical solution of parametric models. With respect to traditional projection-based reduced order modeling, the use of a collocation enables non-intrusive approach based on sparse adaptive sampling of the parametric space. This allows to recover the lowdimensional structure of the parametric solution subspace while also learning the functional dependency from the parameters in explicit form. A sparse low-rank approximate tensor representation of the parametric solution can be built through an incremental strategy that only needs to have access to the output of a deterministic solver. Non-intrusiveness makes this approach straightforwardly applicable to challenging problems characterized by nonlinearity or non affine weak forms.

Constructing skill trees

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

Random indexing

Random indexing is a dimensionality reduction method and computational framework for distributional semantics, based on the insight that very-high-dimensional vector space model implementations are impractical, that models need not grow in dimensionality when new items (e.g. new terminology) are encountered, and that a high-dimensional model can be projected into a space of lower dimensionality without compromising L2 distance metrics if the resulting dimensions are chosen appropriately. This is the original point of the random projection approach to dimension reduction first formulated as the Johnson–Lindenstrauss lemma, and locality-sensitive hashing has some of the same starting points. Random indexing, as used in representation of language, originates from the work of Pentti Kanerva on sparse distributed memory, and can be described as an incremental formulation of a random projection. It can be also verified that random indexing is a random projection technique for the construction of Euclidean spaces—i.e. L2 normed vector spaces. In Euclidean spaces, random projections are elucidated using the Johnson–Lindenstrauss lemma. The TopSig technique extends the random indexing model to produce bit vectors for comparison with the Hamming distance similarity function. It is used for improving the performance of information retrieval and document clustering. In a similar line of research, Random Manhattan Integer Indexing (RMII) is proposed for improving the performance of the methods that employ the Manhattan distance between text units. Many random indexing methods primarily generate similarity from co-occurrence of items in a corpus. Reflexive Random Indexing (RRI) generates similarity from co-occurrence and from shared occurrence with other items.

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.

GeWorkbench

geWorkbench (genomics Workbench) is an open-source software platform for integrated genomic data analysis. It is a desktop application written in the programming language Java. geWorkbench uses a component architecture. As of 2016, there are more than 70 plug-ins available, providing for the visualization and analysis of gene expression, sequence, and structure data. geWorkbench is the Bioinformatics platform of MAGNet, the National Center for the Multi-scale Analysis of Genomic and Cellular Networks, one of the 8 National Centers for Biomedical Computing funded through the NIH Roadmap (NIH Common Fund). Many systems and structure biology tools developed by MAGNet investigators are available as geWorkbench plugins. == Features == Computational analysis tools such as t-test, hierarchical clustering, self-organizing maps, regulatory network reconstruction, BLAST searches, pattern-motif discovery, protein structure prediction, structure-based protein annotation, etc. Visualization of gene expression (heatmaps, volcano plot), molecular interaction networks (through Cytoscape), protein sequence and protein structure data (e.g., MarkUs). Integration of gene and pathway annotation information from curated sources as well as through Gene Ontology enrichment analysis. Component integration through platform management of inputs and outputs. Among data that can be shared between components are expression datasets, interaction networks, sample and marker (gene) sets and sequences. Dataset history tracking - complete record of data sets used and input settings. Integration with 3rd party tools such as GenePattern, Cytoscape, and Genomespace. Demonstrations of each feature described can be found at GeWorkbench-web Tutorials. == Versions == geWorkbench is open-source software that can be downloaded and installed locally. A zip file of the released version Java source is also available. Prepackaged installer versions also exist for Windows, Macintosh, and Linux.