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Section: Types > Non-exhaustive cross-validation > Repeated random sub-sampling validation. This method, also known as Monte Carlo cross-validation, creates multiple random splits of the dataset into training and validation data. For each such split, the model is fit to the training data, and predictive accuracy is ass... | Wikipedia - Cross-validation (statistics) - Types > Non-exhaustive cross-validation > Repeated random sub-sampling validation | 304 | 1,504 | null |
Section: Nested cross-validation > k*l-fold cross-validation. This is a truly nested variant which contains an outer loop of k sets and an inner loop of l sets. The total data set is split into k sets. One by one, a set is selected as the (outer) test set and the k - 1 other sets are combined into the corresponding out... | Wikipedia - Cross-validation (statistics) - Nested cross-validation > k*l-fold cross-validation | 268 | 1,206 | null |
Section: Nested cross-validation > k-fold cross-validation with validation and test set. This is a type of k*l-fold cross-validation when l = k - 1. A single k-fold cross-validation is used with both a validation and test set. The total data set is split into k sets. One by one, a set is selected as test set. Then, one... | Wikipedia - Cross-validation (statistics) - Nested cross-validation > k-fold cross-validation with validation and test set | 214 | 969 | null |
Section: Measures of fit. The goal of cross-validation is to estimate the expected level of fit of a model to a data set that is independent of the data that were used to train the model. It can be used to estimate any quantitative measure of fit that is appropriate for the data and model. For example, for binary class... | Wikipedia - Cross-validation (statistics) - Measures of fit | 164 | 830 | null |
Section: Using prior information. When users apply cross-validation to select a good configuration λ {\displaystyle \lambda } , then they might want to balance the cross-validated choice with their own estimate of the configuration. In this way, they can attempt to counter the volatility of cross-validation when the sa... | Wikipedia - Cross-validation (statistics) - Using prior information | 295 | 1,382 | null |
If λ i {\displaystyle \lambda _{i}} denotes the i t h {\displaystyle i^{th}} candidate configuration that might be selected, then the loss function that is to be minimized can be defined as L λ i = ( 1 − γ ) Relative Accuracy i + γ Relative Simplicity i . {\displaystyle L_{\lambda _{i}}=(1-\gamma ){\mbox{ Relative Accu... | Wikipedia - Cross-validation (statistics) - Using prior information | 287 | 887 | null |
The relative simplicity term measures the amount that λ i {\displaystyle \lambda _{i}} deviates from λ R {\displaystyle \lambda _{R}} relative to the maximum amount of deviation from λ R {\displaystyle \lambda _{R}} . Accordingly, relative simplicity can be specified as ( λ i − λ R ) 2 ( λ max − λ R ) 2 {\displaystyle ... | Wikipedia - Cross-validation (statistics) - Using prior information | 294 | 965 | null |
, C {\displaystyle c=1,2,...,C} by specifying the loss function as L λ i = Relative Accuracy i + ∑ c = 1 C γ c 1 − γ c Relative Simplicity i , c . {\displaystyle L_{\lambda _{i}}={\mbox{ Relative Accuracy}}_{i}+\sum _{c=1}^{C}{\frac {\gamma _{c}}{1-\gamma _{c}}}{\mbox{ Relative Simplicity}}_{i,c}.} Hoornweg (2018) show... | Wikipedia - Cross-validation (statistics) - Using prior information | 187 | 538 | null |
Section: Statistical properties. Suppose we choose a measure of fit F, and use cross-validation to produce an estimate F* of the expected fit EF of a model to an independent data set drawn from the same population as the training data. If we imagine sampling multiple independent training sets following the same distrib... | Wikipedia - Cross-validation (statistics) - Statistical properties | 167 | 857 | null |
Section: Computational issues. Most forms of cross-validation are straightforward to implement as long as an implementation of the prediction method being studied is available. In particular, the prediction method can be a "black box" – there is no need to have access to the internals of its implementation. If the pred... | Wikipedia - Cross-validation (statistics) - Computational issues | 198 | 1,045 | null |
Section: Limitations and misuse. Cross-validation only yields meaningful results if the validation set and training set are drawn from the same population and only if human biases are controlled. In many applications of predictive modeling, the structure of the system being studied evolves over time (i.e. it is "non-st... | Wikipedia - Cross-validation (statistics) - Limitations and misuse | 324 | 1,647 | null |
New evidence is that cross-validation by itself is not very predictive of external validity, whereas a form of experimental validation known as swap sampling that does control for human bias can be much more predictive of external validity. As defined by this large MAQC-II study across 30,000 models, swap sampling inco... | Wikipedia - Cross-validation (statistics) - Limitations and misuse | 335 | 1,736 | null |
Performing mean-centering, rescaling, dimensionality reduction, outlier removal or any other data-dependent preprocessing using the entire data set. While very common in practice, this has been shown to introduce biases into the cross-validation estimates. By allowing some of the training data to also be included in th... | Wikipedia - Cross-validation (statistics) - Limitations and misuse | 246 | 1,283 | null |
Section: Applications. Cross-validation can be used to compare the performances of different predictive modeling procedures. For example, suppose we are interested in optical character recognition, and we are considering using either a Support Vector Machine (SVM) or k-nearest neighbors (KNN) to predict the true charac... | Wikipedia - Cross-validation (statistics) - Applications | 306 | 1,575 | null |
Article: Curse of dimensionality. The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Be... | Wikipedia - Curse of dimensionality - Summary | 227 | 1,249 | null |
Section: Domains > Sampling. There is an exponential increase in volume associated with adding extra dimensions to a mathematical space. For example, 102 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube, i.e. a line) with no more than 10−2 = 0.01 distance betw... | Wikipedia - Curse of dimensionality - Domains > Sampling | 240 | 971 | null |
Section: Domains > Machine learning. In machine learning problems that involve learning a "state-of-nature" from a finite number of data samples in a high-dimensional feature space with each feature having a range of possible values, typically an enormous amount of training data is required to ensure that there are sev... | Wikipedia - Curse of dimensionality - Domains > Machine learning | 342 | 1,754 | null |
Nevertheless, in the context of a simple classifier (e.g., linear discriminant analysis in the multivariate Gaussian model under the assumption of a common known covariance matrix), Zollanvari, et al., showed both analytically and empirically that as long as the relative cumulative efficacy of an additional feature set... | Wikipedia - Curse of dimensionality - Domains > Machine learning | 254 | 1,223 | null |
Section: Domains > Data mining. In data mining, the curse of dimensionality refers to a data set with too many features. Consider the first table, which depicts 200 individuals and 2000 genes (features) with a 1 or 0 denoting whether or not they have a genetic mutation in that gene. A data mining application to this da... | Wikipedia - Curse of dimensionality - Domains > Data mining | 317 | 1,506 | null |
The growth is depicted in the permutation table (see right). As we can see from the permutation table above, one of the major problems data miners face regarding the curse of dimensionality is that the space of possible parameter values grows exponentially or factorially as the number of features in the data set grows.... | Wikipedia - Curse of dimensionality - Domains > Data mining | 342 | 1,765 | null |
Section: Domains > Distance function. When a measure such as a Euclidean distance is defined using many coordinates, there is little difference in the distances between different pairs of points. One way to illustrate the "vastness" of high-dimensional Euclidean space is to compare the proportion of an inscribed hypers... | Wikipedia - Curse of dimensionality - Domains > Distance function | 231 | 852 | null |
As the dimension d {\displaystyle d} of the space increases, the hypersphere becomes an insignificant volume relative to that of the hypercube. This can clearly be seen by comparing the proportions as the dimension d {\displaystyle d} goes to infinity: V h y p e r s p h e r e V h y p e r c u b e = π d / 2 d 2 d − 1 Γ (... | Wikipedia - Curse of dimensionality - Domains > Distance function | 331 | 1,072 | null |
In high dimensions, the volume of the d-dimensional unit hypercube (with coordinates of the vertices ± 1 {\displaystyle \pm 1} ) is concentrated near a sphere with the radius d / 3 {\displaystyle {\sqrt {d}}/{\sqrt {3}}} for large dimension d. Indeed, for each coordinate x i {\displaystyle x_{i}} the average value of x... | Wikipedia - Curse of dimensionality - Domains > Distance function | 198 | 509 | null |
Indeed, for each coordinate x i {\displaystyle x_{i}} the average value of x i 2 {\displaystyle x_{i}^{2}} in the cube is ⟨ x i 2 ⟩ = 1 2 ∫ − 1 1 x 2 d x = 1 3 {\displaystyle \left\langle x_{i}^{2}\right\rangle ={\frac {1}{2}}\int _{-1}^{1}x^{2}dx={\frac {1}{3}}} . The variance of x i 2 {\displaystyle x_{i}^{2}} for un... | Wikipedia - Curse of dimensionality - Domains > Distance function | 302 | 652 | null |
The variance of x i 2 {\displaystyle x_{i}^{2}} for uniform distribution in the cube is 1 2 ∫ − 1 1 x 4 d x − ⟨ x i 2 ⟩ 2 = 4 45 {\displaystyle {\frac {1}{2}}\int _{-1}^{1}x^{4}dx-\left\langle x_{i}^{2}\right\rangle ^{2}={\frac {4}{45}}} Therefore, the squared distance from the origin, r 2 = ∑ i x i 2 {\textstyle r^{2}... | Wikipedia - Curse of dimensionality - Domains > Distance function | 313 | 915 | null |
This also helps to understand the chi-squared distribution. Indeed, the (non-central) chi-squared distribution associated to a random point in the interval [-1, 1] is the same as the distribution of the length-squared of a random point in the d-cube. By the law of large numbers, this distribution concentrates itself in... | Wikipedia - Curse of dimensionality - Domains > Distance function | 348 | 1,264 | null |
For any fixed n, it turns out that the difference between the minimum and the maximum distance between a random reference point Q and a list of n random data points P1,...,Pn become indiscernible compared to the minimum distance: lim d → ∞ E ( dist max ( d ) − dist min ( d ) dist min ( d ) ) → 0 {\displaystyle \l... | Wikipedia - Curse of dimensionality - Domains > Distance function | 333 | 1,387 | null |
Machine learning can be understood as the problem of assigning instances to their respective generative process of origin, with class labels acting as symbolic representations of individual generative processes. The curse's derivation assumes all instances are independent, identical outcomes of a single high dimensiona... | Wikipedia - Curse of dimensionality - Domains > Distance function | 190 | 1,053 | null |
Section: Domains > Nearest neighbor search. The effect complicates nearest neighbor search in high dimensional space. It is not possible to quickly reject candidates by using the difference in one coordinate as a lower bound for a distance based on all the dimensions. However, it has recently been observed that the mer... | Wikipedia - Curse of dimensionality - Domains > Nearest neighbor search | 152 | 806 | null |
Section: Domains > Nearest neighbor search > k-nearest neighbor classification. Another effect of high dimensionality on distance functions concerns k-nearest neighbor (k-NN) graphs constructed from a data set using a distance function. As the dimension increases, the indegree distribution of the k-NN digraph becomes s... | Wikipedia - Curse of dimensionality - Domains > Nearest neighbor search > k-nearest neighbor classification | 154 | 715 | null |
Section: Domains > Anomaly detection. In a 2012 survey, Zimek et al. identified the following problems when searching for anomalies in high-dimensional data: Concentration of scores and distances: derived values such as distances become numerically similar Irrelevant attributes: in high dimensional data, a significant ... | Wikipedia - Curse of dimensionality - Domains > Anomaly detection | 183 | 1,033 | null |
Section: Domains > Blessing of dimensionality. Surprisingly and despite the expected "curse of dimensionality" difficulties, common-sense heuristics based on the most straightforward methods "can yield results which are almost surely optimal" for high-dimensional problems. The term "blessing of dimensionality" was intr... | Wikipedia - Curse of dimensionality - Domains > Blessing of dimensionality | 349 | 1,817 | null |
Section: Synthetic oversampling techniques for traditional machine learning. Synthetic Minority Over-sampling Technique (SMOTE) is a method used to address imbalanced datasets in machine learning. In such datasets, the number of samples in different classes varies significantly, leading to biased model performance. For... | Wikipedia - Data augmentation - Synthetic oversampling techniques for traditional machine learning | 178 | 1,020 | null |
Section: Data augmentation for image classification. When convolutional neural networks grew larger in mid-1990s, there was a lack of data to use, especially considering that some part of the overall dataset should be spared for later testing. It was proposed to perturb existing data with affine transformations to crea... | Wikipedia - Data augmentation - Data augmentation for image classification | 170 | 889 | null |
Section: Data augmentation for signal processing > Biological signals. Synthetic data augmentation is of paramount importance for machine learning classification, particularly for biological data, which tend to be high dimensional and scarce. The applications of robotic control and augmentation in disabled and able-bod... | Wikipedia - Data augmentation - Data augmentation for signal processing > Biological signals | 343 | 1,496 | null |
Lotte proposed a method of "Artificial Trial Generation Based on Analogy" where three data examples x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} provide examples and an artificial x s y n t h e t i c {\displaystyle x_{synthetic}} is formed which is to x 3 {\displaystyle x_{3}} what x 2 {\displaystyle x_{2}} is to ... | Wikipedia - Data augmentation - Data augmentation for signal processing > Biological signals | 315 | 1,280 | null |
studied the approaches of magnitude warping, wavelet decomposition, and synthetic surface EMG models (generative approaches) for hand gesture recognition, finding classification performance increases of up to +16% when augmented data was introduced during training. More recently, data augmentation studies have begun to... | Wikipedia - Data augmentation - Data augmentation for signal processing > Biological signals | 153 | 842 | null |
Article: Data exploration. Data exploration is an approach similar to initial data analysis, whereby a data analyst uses visual exploration to understand what is in a dataset and the characteristics of the data, rather than through traditional data management systems. These characteristics can include size or amount of... | Wikipedia - Data exploration - Summary | 338 | 1,801 | null |
Article: Data preprocessing. Data preprocessing can refer to manipulation, filtration or augmentation of data before it is analyzed, and is often an important step in the data mining process. Data collection methods are often loosely controlled, resulting in out-of-range values, impossible data combinations, and missin... | Wikipedia - Data preprocessing - Summary | 274 | 1,462 | null |
Section: Applications > Data mining. Data preprocessing allows for the removal of unwanted data with the use of data cleaning, this allows the user to have a dataset to contain more valuable information after the preprocessing stage for data manipulation later in the data mining process. Editing such dataset to either ... | Wikipedia - Data preprocessing - Applications > Data mining | 323 | 1,677 | null |
Section: Applications > Semantic data preprocessing. Semantic data mining is a subset of data mining that specifically seeks to incorporate domain knowledge, such as formal semantics, into the data mining process. Domain knowledge is the knowledge of the environment the data was processed in. Domain knowledge can have ... | Wikipedia - Data preprocessing - Applications > Semantic data preprocessing | 335 | 1,802 | null |
Applications include the medical field, language processing, banking, and even tutoring, among many more. There are various strengths to using a semantic data mining and ontological based approach. As previously mentioned, these tools can help during the per-processing phase by filtering out non-desirable data from the... | Wikipedia - Data preprocessing - Applications > Semantic data preprocessing | 313 | 1,680 | null |
In general, this illustrates the incredible strength of using semantic data mining and ontologies. They allow for quicker and more efficient data extraction on the user side, as the user has fewer variables to account for, since the semantically pre-processed data and ontology built for the data have already accounted ... | Wikipedia - Data preprocessing - Applications > Semantic data preprocessing | 345 | 1,819 | null |
Article: Astroinformatics. Astroinformatics is an interdisciplinary field of study involving the combination of astronomy, data science, machine learning, informatics, and information/communications technologies. The field is closely related to astrostatistics. Data-driven astronomy (DDA) refers to the use of data scie... | Wikipedia - Astroinformatics - Summary | 166 | 911 | null |
Section: Background. Astroinformatics is primarily focused on developing the tools, methods, and applications of computational science, data science, machine learning, and statistics for research and education in data-oriented astronomy. Early efforts in this direction included data discovery, metadata standards develo... | Wikipedia - Astroinformatics - Background | 350 | 1,971 | null |
Another aim is to help develop new methods and software for astronomers, as well as to help facilitate the process and analysis of the rapidly growing amount of data in the field of astronomy. Astroinformatics is described as the "fourth paradigm" of astronomical research. There are many research areas involved with as... | Wikipedia - Astroinformatics - Background | 324 | 1,717 | null |
Informatics has been recently defined as "the use of digital data, information, and related services for research and knowledge generation". However the usual, or commonly used definition is "informatics is the discipline of organizing, accessing, integrating, and mining data from multiple sources for discovery and dec... | Wikipedia - Astroinformatics - Background | 349 | 1,818 | null |
The team of Astrophysicists led by Kevin Schawinski in Oxford University were in charge of this project and Kevin and his colleague Chris Linlott figured out that it would take a period of 3–5 years for such a team to complete the work. There they came up with the idea of using Machine Learning and Data Science techniq... | Wikipedia - Astroinformatics - Background | 198 | 1,012 | null |
Section: Methodology. The data retrieved from the sky surveys are first brought for data preprocessing. In this, redundancies are removed and filtrated. Further, feature extraction is performed on this filtered data set, which is further taken for processes. Some of the renowned sky surveys are listed below: The Paloma... | Wikipedia - Astroinformatics - Methodology | 229 | 1,060 | null |
Section: Key Concepts. Data-driven models encompass a wide range of techniques and methodologies that aim to intelligently process and analyse large datasets. Examples include fuzzy logic, fuzzy and rough sets for handling uncertainty, neural networks for approximating functions, global optimization and evolutionary co... | Wikipedia - Data-driven model - Key Concepts | 295 | 1,694 | null |
Section: Definition. A decision list (DL) of length r is of the form: if f1 then output b1 else if f2 then output b2 ... else if fr then output br where fi is the ith formula and bi is the ith boolean for i ∈ { 1... r } {\displaystyle i\in \{1...r\}} . The last if-then-else is the default case, which means formula fr i... | Wikipedia - Decision list - Definition | 152 | 532 | null |
Article: Decision tree pruning. Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves... | Wikipedia - Decision tree pruning - Summary | 248 | 1,282 | null |
Section: Techniques. Pruning processes can be divided into two types (pre- and post-pruning). Pre-pruning procedures prevent a complete induction of the training set by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered... | Wikipedia - Decision tree pruning - Techniques | 249 | 1,131 | null |
Section: Pruning algorithms > Cost complexity pruning. Cost complexity pruning generates a series of trees T 0 … T m {\displaystyle T_{0}\dots T_{m}} where T 0 {\displaystyle T_{0}} is the initial tree and T m {\displaystyle T_{m}} is the root alone. At step i {\displaystyle i} , the tree is created by r... | Wikipedia - Decision tree pruning - Pruning algorithms > Cost complexity pruning | 347 | 1,079 | null |
The subtree t {\displaystyle t} that minimizes err ( prune ( T , t ) , S ) − err ( T , S ) | leaves ( T ) | − | leaves ( prune ( T , t ) ) | {\displaystyle {\frac {\operatorname {err} (\operatorname {prune} (T,t),S)-\operatorname {err} (T,S)}{\left\vert \operatorname {leaves} (T)\right\vert -\left\vert \ope... | Wikipedia - Decision tree pruning - Pruning algorithms > Cost complexity pruning | 242 | 740 | null |
Section: Use in imaging modalities > Optical imaging and microscopy. Diffuse optical tomography, optical coherence tomography and microscopy can be improved by deep neural networks beyond traditional methods. Furthermore, deep learning can also enhance photoacoustic imaging (see Deep learning in photoacoustic imaging),... | Wikipedia - Deep Tomographic Reconstruction - Use in imaging modalities > Optical imaging and microscopy | 150 | 753 | null |
Article: Developmental robotics. Developmental robotics (DevRob), sometimes called epigenetic robotics, is a scientific field which aims at studying the developmental mechanisms, architectures and constraints that allow lifelong and open-ended learning of new skills and new knowledge in embodied machines. As in human c... | Wikipedia - Developmental robotics - Summary | 244 | 1,405 | null |
Section: Background. Can a robot learn like a child? Can it learn a variety of new skills and new knowledge unspecified at design time and in a partially unknown and changing environment? How can it discover its body and its relationships with the physical and social environment? How can its cognitive capacities contin... | Wikipedia - Developmental robotics - Background | 341 | 1,982 | null |
the machine/robot has to be able to learn new tasks that are unknown by the engineer; It emphasizes open-ended development and lifelong learning, i.e. the capacity of an organism to acquire continuously novel skills. This should not be understood as a capacity for learning "anything" or even “everything”, but just that... | Wikipedia - Developmental robotics - Background | 292 | 1,716 | null |
Section: Research directions > Skill domains. Due to the general approach and methodology, developmental robotics projects typically focus on having robots develop the same types of skills as human infants. A first category that is important being investigated is the acquisition of sensorimotor skills. These include th... | Wikipedia - Developmental robotics - Research directions > Skill domains | 226 | 1,222 | null |
Section: Research directions > Mechanisms and constraints. The sensorimotor and social spaces in which humans and robot live are so large and complex that only a small part of potentially learnable skills can actually be explored and learnt within a life-time. Thus, mechanisms and constraints are necessary to guide dev... | Wikipedia - Developmental robotics - Research directions > Mechanisms and constraints | 327 | 1,845 | null |
Thus, social acceptance of developmental robots is also investigated; Statistical inference biases and cumulative knowledge/skill reuse: biases characterizing both representations/encodings and inference mechanisms can typically allow considerable improvement of the efficiency of learning and are thus studied. Related ... | Wikipedia - Developmental robotics - Research directions > Mechanisms and constraints | 245 | 1,376 | null |
Section: Open questions. As developmental robotics is a relatively new research field and at the same time very ambitious, many fundamental open challenges remain to be solved. First of all, existing techniques are far from allowing real-world high-dimensional robots to learn an open-ended repertoire of increasingly co... | Wikipedia - Developmental robotics - Open questions | 350 | 1,964 | null |
This is deeply linked with the problem of the emergence of symbols, sometimes referred to as the "symbol grounding problem" when it comes to language acquisition. Actually, the very existence and need for symbols in the brain are actively questioned, and alternative concepts, still allowing for compositionality and fun... | Wikipedia - Developmental robotics - Open questions | 288 | 1,571 | null |
Section: Main conferences. International Conference on Development and Learning: http://www.cogsci.ucsd.edu/~triesch/icdl/ Epigenetic Robotics: https://www.lucs.lu.se/epirob/ ICDL-EpiRob: http://www.icdl-epirob.org/ (the two above joined since 2011) Developmental Robotics: http://cs.brynmawr.edu/DevRob05/ The NSF/DARPA... | Wikipedia - Developmental robotics - Main conferences | 167 | 613 | null |
Article: Discovery system (artificial intelligence). A discovery system is an artificial intelligence system that attempts to discover new scientific concepts or laws. The aim of discovery systems is to automate scientific data analysis and the scientific discovery process. Ideally, an artificial intelligence system sh... | Wikipedia - Discovery system (artificial intelligence) - Summary | 322 | 1,751 | null |
Section: Modern discovery systems (2009–present). After a couple of decades with little interest in discovery systems, the interest in using AI to uncover natural laws and scientific explanations was renewed by the work of Michael Schmidt, then a PhD student in Computational Biology at Cornell University. Schmidt and h... | Wikipedia - Discovery system (artificial intelligence) - Modern discovery systems (2009–present) | 167 | 853 | null |
Article: Document classification. Document classification or document categorization is a problem in library science, information science and computer science. The task is to assign a document to one or more classes or categories. This may be done "manually" (or "intellectually") or algorithmically. The intellectual cl... | Wikipedia - Document classification - Summary | 205 | 1,156 | null |
Section: "Content-based" versus "request-based" classification. Content-based classification is classification in which the weight given to particular subjects in a document determines the class to which the document is assigned. It is, for example, a common rule for classification in libraries, that at least 20% of th... | Wikipedia - Document classification - "Content-based" versus "request-based" classification | 302 | 1,577 | null |
Section: Classification versus indexing. Sometimes a distinction is made between assigning documents to classes ("classification") versus assigning subjects to documents ("subject indexing") but as Frederick Wilfrid Lancaster has argued, this distinction is not fruitful. "These terminological distinctions,” he writes, ... | Wikipedia - Document classification - Classification versus indexing | 223 | 1,041 | null |
Section: Applications. Classification techniques have been applied to spam filtering, a process which tries to discern E-mail spam messages from legitimate emails email routing, sending an email sent to a general address to a specific address or mailbox depending on topic language identification, automatically determin... | Wikipedia - Document classification - Applications | 183 | 1,045 | null |
Article: Domain adaptation. Domain adaptation is a field associated with machine learning and transfer learning. It addresses the challenge of training a model on one data distribution (the source domain) and applying it to a related but different data distribution (the target domain). A common example is spam filterin... | Wikipedia - Domain adaptation - Summary | 180 | 1,027 | null |
Section: Classification of domain adaptation problems > Distribution shifts. Common distribution shifts are classified as follows: Covariate Shift occurs when the input distributions of the source and destination change, but the relationship between inputs and labels remains unchanged. The above-mentioned spam filterin... | Wikipedia - Domain adaptation - Classification of domain adaptation problems > Distribution shifts | 248 | 1,386 | null |
Section: Classification of domain adaptation problems > Data available during training. Domain adaptation problems typically assume that some data from the target domain is available during training. Problems can be classified according to the type of this available data: Unsupervised: Unlabeled data from the target do... | Wikipedia - Domain adaptation - Classification of domain adaptation problems > Data available during training | 266 | 1,344 | null |
Section: Formalization. Let X {\displaystyle X} be the input space (or description space) and let Y {\displaystyle Y} be the output space (or label space). The objective of a machine learning algorithm is to learn a mathematical model (a hypothesis) h : X → Y {\displaystyle h:X\to Y} able to attach a label from Y {\dis... | Wikipedia - Domain adaptation - Formalization | 312 | 1,001 | null |
The objective is then to learn h {\displaystyle h} (from S {\displaystyle S} ) such that it commits the least error possible for labelling new examples coming from the distribution D S {\displaystyle D_{S}} . The main difference between supervised learning and domain adaptation is that in the latter situation we study ... | Wikipedia - Domain adaptation - Formalization | 244 | 982 | null |
Article: Eager learning. In artificial intelligence, eager learning is a learning method in which the system tries to construct a general, input-independent target function during training of the system, as opposed to lazy learning, where generalization beyond the training data is delayed until a query is made to the s... | Wikipedia - Eager learning - Summary | 188 | 1,006 | null |
Section: Compound scaling. EfficientNet introduces compound scaling, which, instead of scaling one dimension of the network at a time, such as depth (number of layers), width (number of channels), or resolution (input image size), uses a compound coefficient ϕ {\displaystyle \phi } to scale all three dimensions simulta... | Wikipedia - EfficientNet - Compound scaling | 278 | 903 | null |
Specifically, given a baseline network, the depth, width, and resolution are scaled according to the following equations: depth multiplier: d = α ϕ width multiplier: w = β ϕ resolution multiplier: r = γ ϕ {\displaystyle {\begin{aligned}{\text{depth multiplier: }}d&=\alpha ^{\phi }\\{\text{width multiplier: }}w&=\beta ^... | Wikipedia - EfficientNet - Compound scaling | 312 | 888 | null |
The α ⋅ β 2 ⋅ γ 2 ≈ 2 {\displaystyle \alpha \cdot \beta ^{2}\cdot \gamma ^{2}\approx 2} condition is such that increasing ϕ {\displaystyle \phi } by a factor of ϕ 0 {\displaystyle \phi _{0}} would increase the total FLOPs of running the network on an image approximately 2 ϕ 0 {\displaystyle 2^{\phi _{0}}} times. The hy... | Wikipedia - EfficientNet - Compound scaling | 286 | 1,099 | null |
Article: ELMo. ELMo (embeddings from language model) is a word embedding method for representing a sequence of words as a corresponding sequence of vectors. It was created by researchers at the Allen Institute for Artificial Intelligence, and University of Washington and first released in February 2018. It is a bidirec... | Wikipedia - ELMo - Summary | 214 | 1,077 | null |
Section: Architecture. ELMo is a multilayered bidirectional LSTM on top of a token embedding layer. The output of all LSTMs concatenated together consists of the token embedding. The input text sequence is first mapped by an embedding layer into a sequence of vectors. Then two parts are run in parallel over it. The for... | Wikipedia - ELMo - Architecture | 290 | 1,311 | null |
Section: Architecture > Contextual word representation. The architecture of ELMo accomplishes a contextual understanding of tokens. For example, the first forward LSTM of ELMo would process each input token in the context of all previous tokens, and the first backward LSTM would process each token in the context of all... | Wikipedia - ELMo - Architecture > Contextual word representation | 274 | 1,302 | null |
Section: Historical context. ELMo is one link in a historical evolution of language modelling. Consider a simple problem of document classification, where we want to assign a label (e.g., "spam", "not spam", "politics", "sports") to a given piece of text. The simplest approach is the "bag of words" approach, where each... | Wikipedia - ELMo - Historical context | 315 | 1,406 | null |
Section: Background. In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the Control Group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red bl... | Wikipedia - EM algorithm and GMM model - Background | 309 | 1,057 | null |
z {\displaystyle z} is denoted as the group where x {\displaystyle x} belongs, with z i = 0 {\displaystyle z_{i}=0} when x i {\displaystyle x_{i}} belongs to Anemia Group and z i = 1 {\displaystyle z_{i}=1} when x i {\displaystyle x_{i}} belongs to Control Group. Also z ∼ Categorical ( k , ϕ ) {\displaystyle z\sim \o... | Wikipedia - EM algorithm and GMM model - Background | 225 | 625 | null |
A maximum likelihood estimation can be applied: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ( p ( x ( i ) ; ϕ , μ , Σ ) ) = ∑ i = 1 m log ∑ z ( i ) = 1 k p ( x ( i ) ∣ z ( i ) ; μ , Σ ) p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log(p(x^{(i)};\phi ,\mu ,\Sigma ))=\sum _{i=1}^{m}\log \sum _{z^{(i... | Wikipedia - EM algorithm and GMM model - Background | 348 | 719 | null |
\right)+\log p\left(z^{(i)};\phi \right)} Now the likelihood function can be maximized by making partial derivative over μ , Σ , ϕ {\displaystyle \mu ,\Sigma ,\phi } , obtaining: ϕ j = 1 m ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \phi _{j}={\frac {1}{m}}\sum _{i=1}^{m}1\{z^{(i)}=j\}} μ j = ∑ i = 1 m 1 { z ( i ) = j }... | Wikipedia - EM algorithm and GMM model - Background | 348 | 647 | null |
_{j})(x^{(i)}-\mu _{j})^{T}}{\sum _{i=1}^{m}1\{z^{(i)}=j\}}}} If z i {\displaystyle z_{i}} is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if z i {\displaystyle z_{i}} is unknown it is much more complicated. Being z {\displaystyle z} a latent variable (i.e. ... | Wikipedia - EM algorithm and GMM model - Background | 319 | 1,128 | null |
Section: EM algorithm in GMM. The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z ( i ) {\displaystyle z^{(i)}} can be randomly initialized. In the E-step, the algorithm tries to guess the value of z ( i ) {\displaystyle z^{(i)}} based on the parameters, while in t... | Wikipedia - EM algorithm and GMM model - EM algorithm in GMM | 256 | 754 | null |
(M-step) Update the parameters ϕ j := 1 m ∑ i = 1 m w j ( i ) {\displaystyle \phi _{j}:={\frac {1}{m}}\sum _{i=1}^{m}w_{j}^{(i)}} μ j := ∑ i = 1 m w j ( i ) x ( i ) ∑ i = 1 m w j ( i ) {\displaystyle \mu _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}x^{(i)}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} Σ j := ∑ i = 1 m w j ( i ) ( x ( i ) ... | Wikipedia - EM algorithm and GMM model - EM algorithm in GMM | 350 | 598 | null |
) = j | x ( i ) ; ϕ , μ , Σ ) = p ( x ( i ) | z ( i ) = j ; μ , Σ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) | z ( i ) = l ; μ , Σ ) p ( z ( i ) = l ; ϕ ) {\displaystyle p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)={\frac {p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)p\left(z^{(i)}=j;\phi \right)}{\sum _{l=1}^{... | Wikipedia - EM algorithm and GMM model - EM algorithm in GMM | 344 | 645 | null |
\right)={\frac {1}{(2\pi )^{n/2}\left|\Sigma _{j}\right|^{1/2}}}\exp \left(-{\frac {1}{2}}\left(x^{(i)}-\mu _{j}\right)^{T}\Sigma _{j}^{-1}\left(x^{(i)}-\mu _{j}\right)\right)} p ( z ( i ) = j ; ϕ ) = ϕ j {\displaystyle p\left(z^{(i)}=j;\phi \right)=\phi _{j}} In this way, a switch between the E-step and the M-step is ... | Wikipedia - EM algorithm and GMM model - EM algorithm in GMM | 197 | 396 | null |
Article: Embedding (machine learning). Embedding in machine learning refers to a representation learning technique that maps complex, high-dimensional data into a lower-dimensional vector space of numerical vectors. It also denotes the resulting representation, where meaningful patterns or relationships are preserved. ... | Wikipedia - Embedding (machine learning) - Summary | 295 | 1,268 | null |
Section: Description. Mathematical models have tremendous power to describe observations of real-world systems. They are routinely used to test hypothesis, explain mechanisms and predict future outcomes. However, real-world systems are often nonlinear and multidimensional, in some instances rendering explicit equation-... | Wikipedia - Empirical dynamic modeling - Description | 309 | 1,695 | null |
Section: Methods. EDM is continuing to evolve. As of 2022, the main algorithms are Simplex projection, Sequential locally weighted global linear maps (S-Map) projection, Multivariate embedding in Simplex or S-Map, Convergent cross mapping (CCM), and Multiview Embeding, described below. Nearest neighbors are found accor... | Wikipedia - Empirical dynamic modeling - Methods | 194 | 509 | null |
Find k {\displaystyle k} nearest neighbor: N k ← NN ( y , X , k ) {\displaystyle N_{k}\gets {\text{NN}}(y,X,k)} Define the distance scale: d ← ‖ X N 1 E − y ‖ {\displaystyle d\gets \|X_{N_{1}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ( − ‖ X N i E − y ‖ / d ) {\displayst... | Wikipedia - Empirical dynamic modeling - Methods > Simplex | 280 | 550 | null |
Section: Methods > S-Map. S-Map extends the state-space prediction in Simplex from an average of the E + 1 {\displaystyle E+1} nearest neighbors to a linear regression fit to all neighbors, but localised with an exponential decay kernel. The exponential localisation function is F ( θ ) = exp ( − θ d / D ) {\displaystyl... | Wikipedia - Empirical dynamic modeling - Methods > S-Map | 259 | 1,159 | null |
Find k {\displaystyle k} nearest neighbor: N ← NN ( y , X , k ) {\displaystyle N\gets {\text{NN}}(y,X,k)} Sum of distances: D ← 1 k ∑ i = 1 k ‖ X N i E − y ‖ {\displaystyle D\gets {\frac {1}{k}}\sum _{i=1}^{k}\|X_{N_{i}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ( − θ ‖ X... | Wikipedia - Empirical dynamic modeling - Methods > S-Map | 343 | 685 | null |
&X_{N_{1}-E+1}\\1&X_{N_{2}}&X_{N_{2}-1}&\dots &X_{N_{2}-E+1}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&X_{N_{k}}&X_{N_{k}-1}&\dots &X_{N_{k}-E+1}\end{bmatrix}}} Weighted design matrix: A ← W A {\displaystyle A\gets WA} Response vector at T p {\displaystyle Tp} : b ← [ X N 1 + T p X N 2 + T p ⋮ X N k + T p ] {\display... | Wikipedia - Empirical dynamic modeling - Methods > S-Map | 350 | 632 | null |
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