Curriculum learning is a technique in machine learning in which a model is trained on examples of increasing difficulty, where the definition of "difficulty" may be provided externally or discovered as part of the training process. This is intended to attain good performance more quickly, or to converge to a better local optimum if the global optimum is not found. == Approach == Most generally, curriculum learning is the technique of successively increasing the difficulty of examples in the training set that is presented to a model over multiple training iterations. This can produce better results than exposing the model to the full training set immediately under some circumstances; most typically, when the model is able to learn general principles from easier examples, and then gradually incorporate more complex and nuanced information as harder examples are introduced, such as edge cases. This has been shown to work in many domains, most likely as a form of regularization. There are several major variations in how the technique is applied: A concept of "difficulty" must be defined. This may come from human annotation or an external heuristic; for example in language modeling, shorter sentences might be classified as easier than longer ones. Another approach is to use the performance of another model, with examples accurately predicted by that model being classified as easier (providing a connection to boosting). Difficulty can be increased steadily or in distinct epochs, and in a deterministic schedule or according to a probability distribution. This may also be moderated by a requirement for diversity at each stage, in cases where easier examples are likely to be disproportionately similar to each other. Applications must also decide the schedule for increasing the difficulty. Simple approaches may use a fixed schedule, such as training on easy examples for half of the available iterations and then all examples for the second half. Other approaches use self-paced learning to increase the difficulty in proportion to the performance of the model on the current set. Since curriculum learning only concerns the selection and ordering of training data, it can be combined with many other techniques in machine learning. The success of the method assumes that a model trained for an easier version of the problem can generalize to harder versions, so it can be seen as a form of transfer learning. Some authors also consider curriculum learning to include other forms of progressively increasing complexity, such as increasing the number of model parameters. It is frequently combined with reinforcement learning, such as learning a simplified version of a game first. Some domains have shown success with anti-curriculum learning: training on the most difficult examples first. One example is the ACCAN method for speech recognition, which trains on the examples with the lowest signal-to-noise ratio first. == History == The term "curriculum learning" was introduced by Yoshua Bengio et al in 2009, with reference to the psychological technique of shaping in animals and structured education for humans: beginning with the simplest concepts and then building on them. The authors also note that the application of this technique in machine learning has its roots in the early study of neural networks such as Jeffrey Elman's 1993 paper Learning and development in neural networks: the importance of starting small. Bengio et al showed good results for problems in image classification, such as identifying geometric shapes with progressively more complex forms, and language modeling, such as training with a gradually expanding vocabulary. They conclude that, for curriculum strategies, "their beneficial effect is most pronounced on the test set", suggesting good generalization. The technique has since been applied to many other domains: Natural language processing: Part-of-speech tagging Intent detection Sentiment analysis Machine translation Speech recognition Language model pre-training Image recognition: Facial recognition Object detection Reinforcement learning: Game-playing Graph learning Matrix factorization
BBC Own It
The BBC Own It app was a British information site designed to protect and support children using the Internet. The app was launched in 2017 and retired in 2022, though the website retired in 2024 and has since moved to BBC Teach. As part of the BBC's partnership with Internet Matters, the not-for-profit contributed to content on the BBC Own It website. == History == In 2016, The Royal Foundation of The Duke and Duchess of Cambridge established The Royal Foundation Taskforce on the Prevention of Cyberbullying. Work began in 2017 by the BBC to create an app about cyberbullying and online safety (later titled Own It) in response to a call for action from the Taskforce. In December 2017, the BBC launched Own It. In November 2018, work on the BBC Own It App was announced by Prince William. In September 2019, the BBC Own It App was launched into the AppStore and Google Play. In 2022, the BBC discontinued the app, although the website was still active, however in 2024, the website was discontinued, and now any links to the website now redirect to a BBC Teach page. == Awards == UXUK award for Best Education or Learning Experience (2019) Banff World Media Festival Rockies Award for Children & Youth Interactive Content (2020) CogX Award for Best Innovation In Natural Language Processing (2020)
Operational taxonomic unit
An operational taxonomic unit (OTU) is an operational definition used to classify groups of closely related individuals. The term was originally introduced in 1963 by Robert R. Sokal and Peter H. A. Sneath in the context of numerical taxonomy, where an "operational taxonomic unit" is simply the group of organisms currently being studied. In this sense, an OTU is a pragmatic definition to group individuals by similarity, equivalent to but not necessarily in line with classical Linnaean taxonomy or modern evolutionary taxonomy. Nowadays, however, the term is commonly used in a different context and refers to clusters of (uncultivated or unknown) organisms, grouped by DNA sequence similarity of a specific taxonomic marker gene (originally coined as mOTU; molecular OTU). In other words, OTUs are pragmatic proxies for "species" at different taxonomic levels, in the absence of traditional systems of biological classification as are available for macroscopic organisms. For several years, OTUs have been the most commonly used units of diversity, especially when analysing small subunit 16S (for prokaryotes) or 18S rRNA (for eukaryotes) marker gene sequence datasets. == Molecular OTU by clustering of marker gene sequences == In the approach represented by DNA barcoding, a particular locus is chosen to be used as the marker gene for classification. This locus should be universally present in the scope selected, variable enough to be different among close-related species, and be flanked by conservative sequences that allow for easy amplification and detection. There are databases containing sequences for such marker genes from many different species, allowing for comparison. (Sometimes only using one locus does not provide sufficient resolution, so multiple marker genes are used. This is the case for plants, where rbcL+matK is common.) Sequences obtained this way can be clustered according to their similarity to one another, and operational taxonomic units are defined based on the similarity threshold set by the researcher. The exact threshold depends on the taxa in question and the mutational rates of the selected locus in the taxon. 97–99% are commonly used, but "it is now recognized to be somewhat arbitrary as sequence variation within and among species varies across taxa". 100% similarity (fully identical) is also common, also known as single variants. It remains debatable how well this commonly used method recapitulates true microbial species phylogeny or ecology. Although OTUs can be calculated differently when using different algorithms or thresholds, research by Schmidt et al. (2014) demonstrated that 16S-derived microbial OTUs were generally ecologically consistent across habitats and several clustering approaches. The number of OTUs defined may be inflated due to errors in DNA sequencing. === OTU clustering approaches === There are three main approaches to clustering OTUs: De novo, for which the clustering is based on similarities between sequencing reads. Closed-reference, for which the clustering is performed against a reference database of sequences. Open-reference, where clustering is first performed against a reference database of sequences, then any remaining sequences that could not be mapped to the reference are clustered de novo. Using a reference provides taxonomic context for the OTUs found. Alternatively, taxonomic context can be found after the construction of clusters by comparing representative sequences from clusters against a reference database. There are also specialized classifiers for this purpose which are much faster than naive comparison using BLAST. === OTU clustering algorithms === Hierarchical clustering algorithms (HCA): uclust & cd-hit & ESPRIT Bayesian clustering: CROP == Molecular OTU by other methods == In addition to similarity-based grouping, marker gene sequences can be sorted into OTUs using molecular phylogeny, k-mer composition, or hybrid methods combining these methods with similarity. There are also Bayesian tree-less methods and machine learning approaches. Using phylogeny often involves manually assigning terminal clades or single nodes to an OTU, so this is usually only done for refinement. Genome skimming can be used to obtain high-copy DNA without the need to choose marker genes or to design PCR primers for the chosen genes. It can provide fairly good coverage of organelle DNA and repetitive elements such as ribosomal DNA, both of which can be used like marker genes in OTU analysis. Whole-genome sequencing is more expensive and involves the production and processing of more data. By considering the entire genome, many (sometimes over 100) marker genes can be used at the same time, producing highly resolved phylogenies that correctly identify problematic taxa. It is also possible to use entire genomes for OTU assignment. For example, genomes from different bacterial species almost always have an average nucleotide identity lower than 95%, a fact that can be used to define new OTUs (and likely new species).
Ordinal regression
In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant. It can be considered an intermediate problem between regression and classification. Examples of ordinal regression are ordered logit and ordered probit. Ordinal regression turns up often in the social sciences, for example in the modeling of human levels of preference (on a scale from, say, 1–5 for "very poor" through "excellent"), as well as in information retrieval. In machine learning, ordinal regression may also be called ranking learning. == Linear models for ordinal regression == Ordinal regression can be performed using a generalized linear model (GLM) that fits both a coefficient vector and a set of thresholds to a dataset. Suppose one has a set of observations, represented by length-p vectors x1 through xn, with associated responses y1 through yn, where each yi is an ordinal variable on a scale 1, ..., K. For simplicity, and without loss of generality, we assume y is a non-decreasing vector, that is, yi ≤ {\displaystyle \leq } yi+1. To this data, one fits a length-p coefficient vector w and a set of thresholds θ1, ..., θK−1 with the property that θ1 < θ2 < ... < θK−1. This set of thresholds divides the real number line into K disjoint segments, corresponding to the K response levels. The model can now be formulated as Pr ( y ≤ i ∣ x ) = σ ( θ i − w ⋅ x ) {\displaystyle \Pr(y\leq i\mid \mathbf {x} )=\sigma (\theta _{i}-\mathbf {w} \cdot \mathbf {x} )} or, the cumulative probability of the response y being at most i is given by a function σ (the inverse link function) applied to a linear function of x. Several choices exist for σ; the logistic function σ ( θ i − w ⋅ x ) = 1 1 + e − ( θ i − w ⋅ x ) {\displaystyle \sigma (\theta _{i}-\mathbf {w} \cdot \mathbf {x} )={\frac {1}{1+e^{-(\theta _{i}-\mathbf {w} \cdot \mathbf {x} )}}}} gives the ordered logit model, while using the CDF of the standard normal distribution gives the ordered probit model. A third option is to use an exponential function σ ( θ i − w ⋅ x ) = 1 − exp ( − exp ( θ i − w ⋅ x ) ) {\displaystyle \sigma (\theta _{i}-\mathbf {w} \cdot \mathbf {x} )=1-\exp(-\exp(\theta _{i}-\mathbf {w} \cdot \mathbf {x} ))} which gives the proportional hazards model. === Latent variable model === The probit version of the above model can be justified by assuming the existence of a real-valued latent variable (unobserved quantity) y, determined by y ∗ = w ⋅ x + ε {\displaystyle y^{}=\mathbf {w} \cdot \mathbf {x} +\varepsilon } where ε is normally distributed with zero mean and unit variance, conditioned on x. The response variable y results from an "incomplete measurement" of y, where one only determines the interval into which y falls: y = { 1 if y ∗ ≤ θ 1 , 2 if θ 1 < y ∗ ≤ θ 2 , 3 if θ 2 < y ∗ ≤ θ 3 ⋮ K if θ K − 1 < y ∗ . {\displaystyle y={\begin{cases}1&{\text{if}}~~y^{}\leq \theta _{1},\\2&{\text{if}}~~\theta _{1} Quadratic unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem with a wide range of applications from finance and economics to machine learning. QUBO is an NP hard problem, and for many classical problems from theoretical computer science, like maximum cut, graph coloring and the partition problem, embeddings into QUBO have been formulated. Embeddings for machine learning models include support-vector machines, clustering and probabilistic graphical models. Moreover, due to its close connection to Ising models, QUBO constitutes a central problem class for adiabatic quantum computation, where it is solved through a physical process called quantum annealing. == Definition == Let B = { 0 , 1 } {\displaystyle \mathbb {B} =\lbrace 0,1\rbrace } the set of binary digits (or bits), then B n {\displaystyle \mathbb {B} ^{n}} is the set of binary vectors of fixed length n ∈ N {\displaystyle n\in \mathbb {N} } . Given a symmetric or upper triangular matrix Q ∈ R n × n {\displaystyle {\boldsymbol {Q}}\in \mathbb {R} ^{n\times n}} , whose entries Q i j {\displaystyle Q_{ij}} define a weight for each pair of indices i , j ∈ { 1 , … , n } {\displaystyle i,j\in \lbrace 1,\dots ,n\rbrace } , we can define the function f Q : B n → R {\displaystyle f_{\boldsymbol {Q}}:\mathbb {B} ^{n}\rightarrow \mathbb {R} } that assigns a value to each binary vector x {\displaystyle {\boldsymbol {x}}} through f Q ( x ) = x ⊺ Q x = ∑ i = 1 n ∑ j = 1 n Q i j x i x j . {\displaystyle f_{\boldsymbol {Q}}({\boldsymbol {x}})={\boldsymbol {x}}^{\intercal }{\boldsymbol {Qx}}=\sum _{i=1}^{n}\sum _{j=1}^{n}Q_{ij}x_{i}x_{j}.} Alternatively, the linear and quadratic parts can be separated as f Q ′ , q ( x ) = x ⊺ Q ′ x + q ⊺ x , {\displaystyle f_{{\boldsymbol {Q}}',{\boldsymbol {q}}}({\boldsymbol {x}})={\boldsymbol {x}}^{\intercal }{\boldsymbol {Q}}'{\boldsymbol {x}}+{\boldsymbol {q}}^{\intercal }{\boldsymbol {x}},} where Q ′ ∈ R n × n {\displaystyle {\boldsymbol {Q}}'\in \mathbb {R} ^{n\times n}} and q ∈ R n {\displaystyle {\boldsymbol {q}}\in \mathbb {R} ^{n}} . This is equivalent to the previous definition through Q = Q ′ + diag [ q ] {\displaystyle {\boldsymbol {Q}}={\boldsymbol {Q}}'+\operatorname {diag} [{\boldsymbol {q}}]} using the diag operator, exploiting that x = x ⋅ x {\displaystyle x=x\cdot x} for all binary values x {\displaystyle x} . Intuitively, the weight Q i j {\displaystyle Q_{ij}} is added if both x i = 1 {\displaystyle x_{i}=1} and x j = 1 {\displaystyle x_{j}=1} . The QUBO problem consists of finding a binary vector x ∗ {\displaystyle {\boldsymbol {x}}^{}} that minimizes f Q {\displaystyle f_{\boldsymbol {Q}}} , i.e., ∀ x ∈ B n : f Q ( x ∗ ) ≤ f Q ( x ) {\displaystyle \forall {\boldsymbol {x}}\in \mathbb {B} ^{n}:~f_{\boldsymbol {Q}}({\boldsymbol {x}}^{})\leq f_{\boldsymbol {Q}}({\boldsymbol {x}})} . In general, x ∗ {\displaystyle {\boldsymbol {x}}^{}} is not unique, meaning there may be a set of minimizing vectors with equal value w.r.t. f Q {\displaystyle f_{\boldsymbol {Q}}} . The complexity of QUBO arises from the number of candidate binary vectors to be evaluated, as | B n | = 2 n {\displaystyle \left|\mathbb {B} ^{n}\right|=2^{n}} grows exponentially in n {\displaystyle n} . Sometimes, QUBO is defined as the problem of maximizing f Q {\displaystyle f_{\boldsymbol {Q}}} , which is equivalent to minimizing f − Q = − f Q {\displaystyle f_{-{\boldsymbol {Q}}}=-f_{\boldsymbol {Q}}} . == Properties == QUBO is scale invariant for positive factors α > 0 {\displaystyle \alpha >0} , which leave the optimum x ∗ {\displaystyle {\boldsymbol {x}}^{}} unchanged: f α Q ( x ) = x ⊺ ( α Q ) x = α ( x ⊺ Q x ) = α f Q ( x ) {\displaystyle f_{\alpha {\boldsymbol {Q}}}({\boldsymbol {x}})={\boldsymbol {x}}^{\intercal }(\alpha {\boldsymbol {Q}}){\boldsymbol {x}}=\alpha ({\boldsymbol {x}}^{\intercal }{\boldsymbol {Qx}})=\alpha f_{\boldsymbol {Q}}({\boldsymbol {x}})} . In its general form, QUBO is NP-hard and cannot be solved efficiently by any known polynomial-time algorithm. However, there are polynomially-solvable special cases, where Q {\displaystyle {\boldsymbol {Q}}} has certain properties, for example: If all coefficients are positive, the optimum is trivially x ∗ = ( 0 , … , 0 ) ⊺ {\displaystyle {\boldsymbol {x}}^{}=(0,\dots ,0)^{\intercal }} . Similarly, if all coefficients are negative, the optimum is x ∗ = ( 1 , … , 1 ) ⊺ {\displaystyle {\boldsymbol {x}}^{}=(1,\dots ,1)^{\intercal }} . If Q {\displaystyle {\boldsymbol {Q}}} is diagonal, the bits can be optimized independently, and the problem is solvable in O ( n ) {\displaystyle {\mathcal {O}}(n)} . The optimal variable assignments are simply x i ∗ = 1 {\displaystyle x_{i}^{}=1} if Q i i < 0 {\displaystyle Q_{ii}<0} , and x i ∗ = 0 {\displaystyle x_{i}^{}=0} otherwise. If all off-diagonal elements of Q {\displaystyle {\boldsymbol {Q}}} are non-positive, the corresponding QUBO problem is solvable in polynomial time. QUBO can be solved using integer linear programming solvers like CPLEX or Gurobi Optimizer. This is possible since QUBO can be reformulated as a linear constrained binary optimization problem. To achieve this, substitute the product x i x j {\displaystyle x_{i}x_{j}} by an additional binary variable z i j ∈ B {\displaystyle z_{ij}\in \mathbb {B} } and add the constraints x i ≥ z i j {\displaystyle x_{i}\geq z_{ij}} , x j ≥ z i j {\displaystyle x_{j}\geq z_{ij}} and x i + x j − 1 ≤ z i j {\displaystyle x_{i}+x_{j}-1\leq z_{ij}} . Note that z i j {\displaystyle z_{ij}} can also be relaxed to continuous variables within the bounds zero and one. == Applications == QUBO is a structurally simple, yet computationally hard optimization problem. It can be used to encode a wide range of optimization problems from various scientific areas. === Maximum Cut === Given a graph G = ( V , E ) {\displaystyle G=(V,E)} with vertex set V = { 1 , … , n } {\displaystyle V=\lbrace 1,\dots ,n\rbrace } and edges E ⊆ V × V {\displaystyle E\subseteq V\times V} , the maximum cut (max-cut) problem consists of finding two subsets S , T ⊆ V {\displaystyle S,T\subseteq V} with T = V ∖ S {\displaystyle T=V\setminus S} , such that the number of edges between S {\displaystyle S} and T {\displaystyle T} is maximized. The more general weighted max-cut problem assumes edge weights w i j ≥ 0 ∀ i , j ∈ V {\displaystyle w_{ij}\geq 0~\forall i,j\in V} , with ( i , j ) ∉ E ⇒ w i j = 0 {\displaystyle (i,j)\notin E\Rightarrow w_{ij}=0} , and asks for a partition S , T ⊆ V {\displaystyle S,T\subseteq V} that maximizes the sum of edge weights between S {\displaystyle S} and T {\displaystyle T} , i.e., max S ⊆ V ∑ i ∈ S , j ∉ S w i j . {\displaystyle \max _{S\subseteq V}\sum _{i\in S,j\notin S}w_{ij}.} By setting w i j = 1 {\displaystyle w_{ij}=1} for all ( i , j ) ∈ E {\displaystyle (i,j)\in E} this becomes equivalent to the original max-cut problem above, which is why we focus on this more general form in the following. For every vertex in i ∈ V {\displaystyle i\in V} we introduce a binary variable x i {\displaystyle x_{i}} with the interpretation x i = 0 {\displaystyle x_{i}=0} if i ∈ S {\displaystyle i\in S} and x i = 1 {\displaystyle x_{i}=1} if i ∈ T {\displaystyle i\in T} . As T = V ∖ S {\displaystyle T=V\setminus S} , every i {\displaystyle i} is in exactly one set, meaning there is a 1:1 correspondence between binary vectors x ∈ B n {\displaystyle {\boldsymbol {x}}\in \mathbb {B} ^{n}} and partitions of V {\displaystyle V} into two subsets. We observe that, for any i , j ∈ V {\displaystyle i,j\in V} , the expression x i ( 1 − x j ) + ( 1 − x i ) x j {\displaystyle x_{i}(1-x_{j})+(1-x_{i})x_{j}} evaluates to 1 if and only if i {\displaystyle i} and j {\displaystyle j} are in different subsets, equivalent to logical XOR. Let W ∈ R + n × n {\displaystyle {\boldsymbol {W}}\in \mathbb {R} _{+}^{n\times n}} with W i j = w i j ∀ i , j ∈ V {\displaystyle W_{ij}=w_{ij}~\forall i,j\in V} . By extending above expression to matrix-vector form we find that x ⊺ W ( 1 − x ) + ( 1 − x ) ⊺ W x = − 2 x ⊺ W x + ( W 1 + W ⊺ 1 ) ⊺ x {\displaystyle {\boldsymbol {x}}^{\intercal }{\boldsymbol {W}}({\boldsymbol {1}}-{\boldsymbol {x}})+({\boldsymbol {1}}-{\boldsymbol {x}})^{\intercal }{\boldsymbol {Wx}}=-2{\boldsymbol {x}}^{\intercal }{\boldsymbol {Wx}}+({\boldsymbol {W1}}+{\boldsymbol {W}}^{\intercal }{\boldsymbol {1}})^{\intercal }{\boldsymbol {x}}} is the sum of weights of all edges between S {\displaystyle S} and T {\displaystyle T} , where 1 = ( 1 , 1 , … , 1 ) ⊺ ∈ R n {\displaystyle {\boldsymbol {1}}=(1,1,\dots ,1)^{\intercal }\in \mathbb {R} ^{n}} . As this is a quadratic function over x {\displaystyle {\boldsymbol {x}}} , it is a QUBO problem whose parameter matrix we can read from above expression as Q = 2 W − diag [ W 1 + W ⊺ 1 ] , {\displaystyle {\boldsymbol {Q}}=2{\boldsymbol {W}}-\operatorname {diag} [{\boldsymbol {W1}}+{\boldsymbol {W}}^{\intercal }{\bol Transfer learning (TL) is a technique in machine learning (ML) in which knowledge learned from a task is re-used in order to boost performance on a related task. For example, for image classification, knowledge gained while learning to recognize cars could be applied when trying to recognize trucks. This topic is related to the psychological literature on transfer of learning, although practical ties between the two fields are limited. Reusing or transferring information from previously learned tasks to new tasks has the potential to significantly improve learning efficiency. Since transfer learning makes use of training with multiple objective functions it is related to cost-sensitive machine learning and multi-objective optimization. == History == In 1976, Bozinovski and Fulgosi published a paper addressing transfer learning in neural network training. The paper gives a mathematical and geometrical model of the topic. In 1981, a report considered the application of transfer learning to a dataset of images representing letters of computer terminals, experimentally demonstrating positive and negative transfer learning. In 1992, Lorien Pratt formulated the discriminability-based transfer (DBT) algorithm. By 1998, the field had advanced to include multi-task learning, along with more formal theoretical foundations. Influential publications on transfer learning include the book Learning to Learn in 1998, a 2009 survey and a 2019 survey. Ng said in his NIPS 2016 tutorial that TL would become the next driver of machine learning commercial success after supervised learning. In the 2020 paper, "Rethinking Pre-Training and self-training", Zoph et al. reported that pre-training can hurt accuracy, and advocate self-training instead. == Definition == The definition of transfer learning is given in terms of domains and tasks. A domain D {\displaystyle {\mathcal {D}}} consists of: a feature space X {\displaystyle {\mathcal {X}}} and a marginal probability distribution P ( X ) {\displaystyle P(X)} , where X = { x 1 , . . . , x n } ∈ X {\displaystyle X=\{x_{1},...,x_{n}\}\in {\mathcal {X}}} . Given a specific domain, D = { X , P ( X ) } {\displaystyle {\mathcal {D}}=\{{\mathcal {X}},P(X)\}} , a task consists of two components: a label space Y {\displaystyle {\mathcal {Y}}} and an objective predictive function f : X → Y {\displaystyle f:{\mathcal {X}}\rightarrow {\mathcal {Y}}} . The function f {\displaystyle f} is used to predict the corresponding label f ( x ) {\displaystyle f(x)} of a new instance x {\displaystyle x} . This task, denoted by T = { Y , f ( x ) } {\displaystyle {\mathcal {T}}=\{{\mathcal {Y}},f(x)\}} , is learned from the training data consisting of pairs { x i , y i } {\displaystyle \{x_{i},y_{i}\}} , where x i ∈ X {\displaystyle x_{i}\in {\mathcal {X}}} and y i ∈ Y {\displaystyle y_{i}\in {\mathcal {Y}}} . Given a source domain D S {\displaystyle {\mathcal {D}}_{S}} and learning task T S {\displaystyle {\mathcal {T}}_{S}} , a target domain D T {\displaystyle {\mathcal {D}}_{T}} and learning task T T {\displaystyle {\mathcal {T}}_{T}} , where D S ≠ D T {\displaystyle {\mathcal {D}}_{S}\neq {\mathcal {D}}_{T}} , or T S ≠ T T {\displaystyle {\mathcal {T}}_{S}\neq {\mathcal {T}}_{T}} , transfer learning aims to help improve the learning of the target predictive function f T ( ⋅ ) {\displaystyle f_{T}(\cdot )} in D T {\displaystyle {\mathcal {D}}_{T}} using the knowledge in D S {\displaystyle {\mathcal {D}}_{S}} and T S {\displaystyle {\mathcal {T}}_{S}} . == Applications == Algorithms for transfer learning are available in Markov logic networks and Bayesian networks. Transfer learning has been applied to cancer subtype discovery, building utilization, general game playing, text classification, digit recognition, medical imaging and spam filtering. In 2020, it was discovered that, due to their similar physical natures, transfer learning is possible between electromyographic (EMG) signals from the muscles and classifying the behaviors of electroencephalographic (EEG) brainwaves, from the gesture recognition domain to the mental state recognition domain. It was noted that this relationship worked in both directions, showing that electroencephalographic can likewise be used to classify EMG. The experiments noted that the accuracy of neural networks and convolutional neural networks were improved through transfer learning both prior to any learning (compared to standard random weight distribution) and at the end of the learning process (asymptote). That is, results are improved by exposure to another domain. Moreover, the end-user of a pre-trained model can change the structure of fully-connected layers to improve performance. The constellation model is a probabilistic, generative model for category-level object recognition in computer vision. Like other part-based models, the constellation model attempts to represent an object class by a set of N parts under mutual geometric constraints. Because it considers the geometric relationship between different parts, the constellation model differs significantly from appearance-only, or "bag-of-words" representation models, which explicitly disregard the location of image features. The problem of defining a generative model for object recognition is difficult. The task becomes significantly complicated by factors such as background clutter, occlusion, and variations in viewpoint, illumination, and scale. Ideally, we would like the particular representation we choose to be robust to as many of these factors as possible. In category-level recognition, the problem is even more challenging because of the fundamental problem of intra-class variation. Even if two objects belong to the same visual category, their appearances may be significantly different. However, for structured objects such as cars, bicycles, and people, separate instances of objects from the same category are subject to similar geometric constraints. For this reason, particular parts of an object such as the headlights or tires of a car still have consistent appearances and relative positions. The Constellation Model takes advantage of this fact by explicitly modeling the relative location, relative scale, and appearance of these parts for a particular object category. Model parameters are estimated using an unsupervised learning algorithm, meaning that the visual concept of an object class can be extracted from an unlabeled set of training images, even if that set contains "junk" images or instances of objects from multiple categories. It can also account for the absence of model parts due to appearance variability, occlusion, clutter, or detector error. == History == The idea for a "parts and structure" model was originally introduced by Fischler and Elschlager in 1973. This model has since been built upon and extended in many directions. The Constellation Model, as introduced by Dr. Perona and his colleagues, was a probabilistic adaptation of this approach. In the late '90s, Burl et al. revisited the Fischler and Elschlager model for the purpose of face recognition. In their work, Burl et al. used manual selection of constellation parts in training images to construct a statistical model for a set of detectors and the relative locations at which they should be applied. In 2000, Weber et al. made the significant step of training the model using a more unsupervised learning process, which precluded the necessity for tedious hand-labeling of parts. Their algorithm was particularly remarkable because it performed well even on cluttered and occluded image data. Fergus et al. then improved upon this model by making the learning step fully unsupervised, having both shape and appearance learned simultaneously, and accounting explicitly for the relative scale of parts. == The method of Weber and Welling et al. == In the first step, a standard interest point detection method, such as Harris corner detection, is used to generate interest points. Image features generated from the vicinity of these points are then clustered using k-means or another appropriate algorithm. In this process of vector quantization, one can think of the centroids of these clusters as being representative of the appearance of distinctive object parts. Appropriate feature detectors are then trained using these clusters, which can be used to obtain a set of candidate parts from images. As a result of this process, each image can now be represented as a set of parts. Each part has a type, corresponding to one of the aforementioned appearance clusters, as well as a location in the image space. === Basic generative model === Weber & Welling here introduce the concept of foreground and background. Foreground parts correspond to an instance of a target object class, whereas background parts correspond to background clutter or false detections. Let T be the number of different types of parts. The positions of all parts extracted from an image can then be represented in the following "matrix," X o = ( x 11 , x 12 , ⋯ , x 1 N 1 x 21 , x 22 , ⋯ , x 2 N 2 ⋮ x T 1 , x T 2 , ⋯ , x T N T ) {\displaystyle X^{o}={\begin{pmatrix}x_{11},x_{12},{\cdots },x_{1N_{1}}\\x_{21},x_{22},{\cdots },x_{2N_{2}}\\\vdots \\x_{T1},x_{T2},{\cdots },x_{TN_{T}}\end{pmatrix}}} where N i {\displaystyle N_{i}\,} represents the number of parts of type i ∈ { 1 , … , T } {\displaystyle i\in \{1,\dots ,T\}} observed in the image. The superscript o indicates that these positions are observable, as opposed to missing. The positions of unobserved object parts can be represented by the vector x m {\displaystyle x^{m}\,} . Suppose that the object will be composed of F {\displaystyle F\,} distinct foreground parts. For notational simplicity, we assume here that F = T {\displaystyle F=T\,} , though the model can be generalized to F > T {\displaystyle F>T\,} . A hypothesis h {\displaystyle h\,} is then defined as a set of indices, with h i = j {\displaystyle h_{i}=j\,} , indicating that point x i j {\displaystyle x_{ij}\,} is a foreground point in X o {\displaystyle X^{o}\,} . The generative probabilistic model is defined through the joint probability density p ( X o , x m , h ) {\displaystyle p(X^{o},x^{m},h)\,} . === Model details === The rest of this section summarizes the details of Weber & Welling's model for a single component model. The formulas for multiple component models are extensions of those described here. To parametrize the joint probability density, Weber & Welling introduce the auxiliary variables b {\displaystyle b\,} and n {\displaystyle n\,} , where b {\displaystyle b\,} is a binary vector encoding the presence/absence of parts in detection ( b i = 1 {\displaystyle b_{i}=1\,} if h i > 0 {\displaystyle h_{i}>0\,} , otherwise b i = 0 {\displaystyle b_{i}=0\,} ), and n {\displaystyle n\,} is a vector where n i {\displaystyle n_{i}\,} denotes the number of background candidates included in the i t h {\displaystyle i^{th}} row of X o {\displaystyle X^{o}\,} . Since b {\displaystyle b\,} and n {\displaystyle n\,} are completely determined by h {\displaystyle h\,} and the size of X o {\displaystyle X^{o}\,} , we have p ( X o , x m , h ) = p ( X o , x m , h , n , b ) {\displaystyle p(X^{o},x^{m},h)=p(X^{o},x^{m},h,n,b)\,} . By decomposition, p ( X o , x m , h , n , b ) = p ( X o , x m | h , n , b ) p ( h | n , b ) p ( n ) p ( b ) {\displaystyle p(X^{o},x^{m},h,n,b)=p(X^{o},x^{m}|h,n,b)p(h|n,b)p(n)p(b)\,} The probability density over the number of background detections can be modeled by a Poisson distribution, p ( n ) = ∏ i = 1 T 1 n i ! ( M i ) n i e − M i {\displaystyle p(n)=\prod _{i=1}^{T}{\frac {1}{n_{i}!}}(M_{i})^{n_{i}}e^{-M_{i}}} where M i {\displaystyle M_{i}\,} is the average number of background detections of type i {\displaystyle i\,} per image. Depending on the number of parts F {\displaystyle F\,} , the probability p ( b ) {\displaystyle p(b)\,} can be modeled either as an explicit table of length 2 F {\displaystyle 2^{F}\,} , or, if F {\displaystyle F\,} is large, as F {\displaystyle F\,} independent probabilities, each governing the presence of an individual part. The density p ( h | n , b ) {\displaystyle p(h|n,b)\,} is modeled by p ( h | n , b ) = { 1 ∏ f = 1 F N f b f , if h ∈ H ( b , n ) 0 , for other h {\displaystyle p(h|n,b)={\begin{cases}{\frac {1}{\textstyle \prod _{f=1}^{F}N_{f}^{b_{f}}}},&{\mbox{if }}h\in H(b,n)\\0,&{\mbox{for other }}h\end{cases}}} where H ( b , n ) {\displaystyle H(b,n)\,} denotes the set of all hypotheses consistent with b {\displaystyle b\,} and n {\displaystyle n\,} , and N f {\displaystyle N_{f}\,} denotes the total number of detections of parts of type f {\displaystyle f\,} . This expresses the fact that all consistent hypotheses, of which there are ∏ f = 1 F N f b f {\displaystyle \textstyle \prod _{f=1}^{F}N_{f}^{b_{f}}} , are equally likely in the absence of information on part locations. And finally, p ( X o , x m | h , n ) = p f g ( z ) p b g ( x b g ) {\displaystyle p(X^{o},x^{m}|h,n)=p_{fg}(z)p_{bg}(x_{bg})\,} where z = ( x o x m ) {\displaystyle z=(x^{o}x^{m})\,} are the coordinates of all foreground detections, observed and missing, and x b g {\displaystyle x_{bg}\,} represents the coordinates of the background detections. Note that foreground detections are assumed to be independent of the background. p f g ( z ) {\displaystyle p_{fg}(z)\,} is modeled as a joint Gaussian with mean μ {\displaystyle \mu \,} and covariance Σ {\displaystyle \Sigma \,} . === Classification === The ultimate objective of this model is to classify images into classes "object present" (class C 1 {\displaystyle C_{1}\,} ) and "object absent" (class C 0 {\displaystyle C_{0}\,} ) given tQuadratic unconstrained binary optimization
Transfer learning
Constellation model