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Loss functions for classification : For proper loss functions, the loss margin can be defined as μ ϕ = − ϕ ′ ( 0 ) ϕ ″ ( 0 ) =- and shown to be directly related to the regularization properties of the classifier. Specifically a loss function of larger margin increases regularization and produces better estimates of the... |
Loss functions for classification : While more commonly used in regression, the square loss function can be re-written as a function ϕ ( y f ( x → ) ) )) and utilized for classification. It can be generated using (2) and Table-I as follows ϕ ( v ) = C [ f − 1 ( v ) ] + ( 1 − f − 1 ( v ) ) C ′ [ f − 1 ( v ) ] = 4 ( 1 2 ... |
Loss functions for classification : The logistic loss function can be generated using (2) and Table-I as follows ϕ ( v ) = C [ f − 1 ( v ) ] + ( 1 − f − 1 ( v ) ) C ′ [ f − 1 ( v ) ] = 1 log ( 2 ) [ − e v 1 + e v log e v 1 + e v − ( 1 − e v 1 + e v ) log ( 1 − e v 1 + e v ) ] + ( 1 − e v 1 + e v ) [ − 1 log ( 2... |
Loss functions for classification : The exponential loss function can be generated using (2) and Table-I as follows ϕ ( v ) = C [ f − 1 ( v ) ] + ( 1 − f − 1 ( v ) ) C ′ [ f − 1 ( v ) ] = 2 ( e 2 v 1 + e 2 v ) ( 1 − e 2 v 1 + e 2 v ) + ( 1 − e 2 v 1 + e 2 v ) ( 1 − 2 e 2 v 1 + e 2 v e 2 v 1 + e 2 v ( 1 − e 2 v 1 + e 2 ... |
Loss functions for classification : The Savage loss can be generated using (2) and Table-I as follows ϕ ( v ) = C [ f − 1 ( v ) ] + ( 1 − f − 1 ( v ) ) C ′ [ f − 1 ( v ) ] = ( e v 1 + e v ) ( 1 − e v 1 + e v ) + ( 1 − e v 1 + e v ) ( 1 − 2 e v 1 + e v ) = 1 ( 1 + e v ) 2 . (v)]+(1-f^(v))C'[f^(v)]=\left(\right)\left(1-\... |
Loss functions for classification : The Tangent loss can be generated using (2) and Table-I as follows ϕ ( v ) = C [ f − 1 ( v ) ] + ( 1 − f − 1 ( v ) ) C ′ [ f − 1 ( v ) ] = 4 ( arctan ( v ) + 1 2 ) ( 1 − ( arctan ( v ) + 1 2 ) ) + ( 1 − ( arctan ( v ) + 1 2 ) ) ( 4 − 8 ( arctan ( v ) + 1 2 ) ) = ( 2 arctan ... |
Loss functions for classification : The hinge loss function is defined with ϕ ( υ ) = max ( 0 , 1 − υ ) = [ 1 − υ ] + , where [ a ] + = max ( 0 , a ) =\max(0,a) is the positive part function. V ( f ( x → ) , y ) = max ( 0 , 1 − y f ( x → ) ) = [ 1 − y f ( x → ) ] + . ),y)=\max(0,1-yf())=[1-yf()]_. The hinge loss provi... |
Loss functions for classification : The generalized smooth hinge loss function with parameter α is defined as f α ∗ ( z ) = ^(z)\;=\;-z&z\leq 0\\z^-z+&0<z<1\\0&z\geq 1\end, where z = y f ( x → ) . ). It is monotonically increasing and reaches 0 when z = 1 . |
Loss functions for classification : Differentiable programming Scoring function == References == |
Manifold alignment : Manifold alignment is a class of machine learning algorithms that produce projections between sets of data, given that the original data sets lie on a common manifold. The concept was first introduced as such by Ham, Lee, and Saul in 2003, adding a manifold constraint to the general problem of corr... |
Manifold alignment : Manifold alignment assumes that disparate data sets produced by similar generating processes will share a similar underlying manifold representation. By learning projections from each original space to the shared manifold, correspondences are recovered and knowledge from one domain can be transferr... |
Manifold alignment : The algorithm described above requires full pairwise correspondence information between input data sets; a supervised learning paradigm. However, this information is usually difficult or impossible to obtain in real world applications. Recent work has extended the core manifold alignment algorithm ... |
Manifold alignment : The algorithm described above performs a "one-step" alignment, finding embeddings for both data sets at the same time. A similar effect can also be achieved with "two-step" alignments , following a slightly modified procedure: Project each input data set to a lower-dimensional space independently, ... |
Manifold alignment : Manifold alignment can be used to find linear (feature-level) projections, or nonlinear (instance-level) embeddings. While the instance-level version generally produces more accurate alignments, it sacrifices a great degree of flexibility as the learned embedding is often difficult to parameterize.... |
Manifold alignment : Manifold alignment is suited to problems with several corpora that lie on a shared manifold, even when each corpus is of a different dimensionality. Many real-world problems fit this description, but traditional techniques are not able to take advantage of all corpora at the same time. Manifold ali... |
Manifold alignment : Manifold hypothesis |
Manifold alignment : Xiong, L.; F. Wang; C. Zhang (2007). "Semi-definite manifold alignment". Proceedings of the 18th European Conference on Machine Learning. CiteSeerX 10.1.1.91.7346. Wang, Chang; Sridhar Mahadevan (2009). "A General Framework for Manifold Alignment" (PDF). AAAI Fall Symposium on Manifold Learning and... |
Minimum redundancy feature selection : Minimum redundancy feature selection is an algorithm frequently used in a method to accurately identify characteristics of genes and phenotypes and narrow down their relevance and is usually described in its pairing with relevant feature selection as Minimum Redundancy Maximum Rel... |
Minimum redundancy feature selection : Peng, H.C., Long, F., and Ding, C., "Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 27, No. 8, pp. 1226–1238, 2005. Chris Ding and Hanchuan Peng, "M... |
Mixture of experts : Mixture of experts (MoE) is a machine learning technique where multiple expert networks (learners) are used to divide a problem space into homogeneous regions. MoE represents a form of ensemble learning. They were also called committee machines. |
Mixture of experts : MoE always has the following components, but they are implemented and combined differently according to the problem being solved: Experts f 1 , . . . , f n ,...,f_ , each taking the same input x , and producing outputs f 1 ( x ) , . . . , f n ( x ) (x),...,f_(x) . A weighting function (also known ... |
Mixture of experts : The previous section described MoE as it was used before the era of deep learning. After deep learning, MoE found applications in running the largest models, as a simple way to perform conditional computation: only parts of the model are used, the parts chosen according to what the input is. The ea... |
Mixture of experts : Product of experts Mixture models Mixture of gaussians Ensemble learning |
Mixture of experts : Before deep learning era McLachlan, Geoffrey J.; Peel, David (2000). Finite mixture models. Wiley series in probability and statistics applied probability and statistics section. New York Chichester Weinheim Brisbane Singapore Toronto: John Wiley & Sons, Inc. ISBN 978-0-471-00626-8. Yuksel, S. E.; ... |
Multi expression programming : Multi Expression Programming (MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is a Genetic Programming variant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have ... |
Multi expression programming : MEP chromosomes are arrays of instructions represented in Three-address code format. Each instruction contains a variable, a constant, or a function. If the instruction is a function, then the arguments (given as instruction's addresses) are also present. |
Multi expression programming : When the chromosome is evaluated it is unclear which instruction will provide the output of the program. In many cases, a set of programs is obtained, some of them being completely unrelated (they do not have common instructions). For the above chromosome, here is the list of possible pro... |
Multi expression programming : Which expression will represent the chromosome? Which one will give the fitness of the chromosome? In MEP, the best of them (which has the lowest error) will represent the chromosome. This is different from other GP techniques: In Linear genetic programming the last instruction will give ... |
Multi expression programming : Genetic programming Cartesian genetic programming Gene expression programming Grammatical evolution Linear genetic programming |
Multi expression programming : Multi Expression Programming website Multi Expression Programming source code |
Multiple kernel learning : Multiple kernel learning refers to a set of machine learning methods that use a predefined set of kernels and learn an optimal linear or non-linear combination of kernels as part of the algorithm. Reasons to use multiple kernel learning include a) the ability to select for an optimal kernel a... |
Multiple kernel learning : Multiple kernel learning algorithms have been developed for supervised, semi-supervised, as well as unsupervised learning. Most work has been done on the supervised learning case with linear combinations of kernels, however, many algorithms have been developed. The basic idea behind multiple ... |
Multiple kernel learning : Available MKL libraries include SPG-GMKL: A scalable C++ MKL SVM library that can handle a million kernels. GMKL: Generalized Multiple Kernel Learning code in MATLAB, does ℓ 1 and ℓ 2 regularization for supervised learning. (Another) GMKL: A different MATLAB MKL code that can also perform e... |
Neural radiance field : A neural radiance field (NeRF) is a method based on deep learning for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications of novel view synthesis, scene geometry reconstruction, and obtaining the reflectance pro... |
Neural radiance field : The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network (DNN). The network predicts a volume density and view-dependent emitted radiance given the spatial location (x, y, z) and viewing direction in Euler angles (θ, Φ) of the camera. By sampling many point... |
Neural radiance field : Early versions of NeRF were slow to optimize and required that all input views were taken with the same camera in the same lighting conditions. These performed best when limited to orbiting around individual objects, such as a drum set, plants or small toys. Since the original paper in 2020, man... |
Neural radiance field : NeRFs have a wide range of applications, and are starting to grow in popularity as they become integrated into user-friendly applications. |
Non-negative matrix factorization : Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative ... |
Non-negative matrix factorization : In chemometrics non-negative matrix factorization has a long history under the name "self modeling curve resolution". In this framework the vectors in the right matrix are continuous curves rather than discrete vectors. Also early work on non-negative matrix factorizations was perfor... |
Non-negative matrix factorization : Let matrix V be the product of the matrices W and H, V = W H . =\mathbf \mathbf \,. Matrix multiplication can be implemented as computing the column vectors of V as linear combinations of the column vectors in W using coefficients supplied by columns of H. That is, each column of ... |
Non-negative matrix factorization : NMF has an inherent clustering property, i.e., it automatically clusters the columns of input data V = ( v 1 , … , v n ) =(v_,\dots ,v_) . More specifically, the approximation of V by V ≃ W H \simeq \mathbf \mathbf is achieved by finding W and H that minimize the error funct... |
Non-negative matrix factorization : There are several ways in which the W and H may be found: Lee and Seung's multiplicative update rule has been a popular method due to the simplicity of implementation. This algorithm is: initialize: W and H non negative. Then update the values in W and H by computing the following, w... |
Non-negative matrix factorization : In Learning the parts of objects by non-negative matrix factorization Lee and Seung proposed NMF mainly for parts-based decomposition of images. It compares NMF to vector quantization and principal component analysis, and shows that although the three techniques may be written as fac... |
Non-negative matrix factorization : The factorization is not unique: A matrix and its inverse can be used to transform the two factorization matrices by, e.g., W H = W B B − 1 H =\mathbf ^\mathbf If the two new matrices W ~ = W B =WB and H ~ = B − 1 H =\mathbf ^\mathbf are non-negative they form another parame... |
Non-negative matrix factorization : Current research (since 2010) in nonnegative matrix factorization includes, but is not limited to, Algorithmic: searching for global minima of the factors and factor initialization. Scalability: how to factorize million-by-billion matrices, which are commonplace in Web-scale data min... |
Non-negative matrix factorization : Multilinear algebra Multilinear subspace learning Tensor Tensor decomposition Tensor software |
NSynth : NSynth (a portmanteau of "Neural Synthesis") is a WaveNet-based autoencoder for synthesizing audio, outlined in a paper in April 2017. |
NSynth : The model generates sounds through a neural network based synthesis, employing a WaveNet-style autoencoder to learn its own temporal embeddings from four different sounds. Google then released an open source hardware interface for the algorithm called NSynth Super, used by notable musicians such as Grimes and ... |
NSynth : In 2018 Google released a hardware interface for the NSynth algorithm, called NSynth Super, designed to provide an accessible physical interface to the algorithm for musicians to use in their artistic production. Design files, source code and internal components are released under an open source Apache License... |
NSynth : Despite not being publicly available as a commercial product, NSynth Super has been used by notable artists, including Grimes and YACHT. Grimes reported using the instrument in her 2020 studio album Miss Anthropocene. YACHT announced an extensive use of NSynth Super in their album Chain Tripping. Claire L. Eva... |
NSynth : Engel, Jesse; Resnick, Cinjon; Roberts, Adam; Dieleman, Sander; Eck, Douglas; Simonyan, Karen; Norouzi, Mohammad (2017). "Neural Audio Synthesis of Musical Notes with WaveNet Autoencoders". arXiv:1704.01279 [cs.LG]. |
NSynth : Official Nsynth Super site Official Magenta site In-browser emulation of the Nsynth algorithm |
Online machine learning : In computer science, online machine learning is a method of machine learning in which data becomes available in a sequential order and is used to update the best predictor for future data at each step, as opposed to batch learning techniques which generate the best predictor by learning on the... |
Online machine learning : In the setting of supervised learning, a function of f : X → Y is to be learned, where X is thought of as a space of inputs and Y as a space of outputs, that predicts well on instances that are drawn from a joint probability distribution p ( x , y ) on X × Y . In reality, the learner neve... |
Online machine learning : In statistical learning models, the training sample ( x i , y i ) ,y_) are assumed to have been drawn from the true distribution p ( x , y ) and the objective is to minimize the expected "risk" I [ f ] = E [ V ( f ( x ) , y ) ] = ∫ V ( f ( x ) , y ) d p ( x , y ) . [V(f(x),y)]=\int V(f(x),y)... |
Online machine learning : Continual learning means constantly improving the learned model by processing continuous streams of information. Continual learning capabilities are essential for software systems and autonomous agents interacting in an ever changing real world. However, continual learning is a challenge for m... |
Online machine learning : The paradigm of online learning has different interpretations depending on the choice of the learning model, each of which has distinct implications about the predictive quality of the sequence of functions f 1 , f 2 , … , f n ,f_,\ldots ,f_ . The prototypical stochastic gradient descent algor... |
Online machine learning : Vowpal Wabbit: Open-source fast out-of-core online learning system which is notable for supporting a number of machine learning reductions, importance weighting and a selection of different loss functions and optimisation algorithms. It uses the hashing trick for bounding the size of the set o... |
Online machine learning : Learning paradigms Incremental learning Lazy learning Offline learning, the opposite model Reinforcement learning Multi-armed bandit Supervised learning General algorithms Online algorithm Online optimization Streaming algorithm Stochastic gradient descent Learning models Adaptive Resonance Th... |
Online machine learning : 6.883: Online Methods in Machine Learning: Theory and Applications. Alexander Rakhlin. MIT |
Out-of-bag error : Out-of-bag (OOB) error, also called out-of-bag estimate, is a method of measuring the prediction error of random forests, boosted decision trees, and other machine learning models utilizing bootstrap aggregating (bagging). Bagging uses subsampling with replacement to create training samples for the m... |
Out-of-bag error : When bootstrap aggregating is performed, two independent sets are created. One set, the bootstrap sample, is the data chosen to be "in-the-bag" by sampling with replacement. The out-of-bag set is all data not chosen in the sampling process. When this process is repeated, such as when building a rando... |
Out-of-bag error : Since each out-of-bag set is not used to train the model, it is a good test for the performance of the model. The specific calculation of OOB error depends on the implementation of the model, but a general calculation is as follows. Find all models (or trees, in the case of a random forest) that are ... |
Out-of-bag error : Out-of-bag error and cross-validation (CV) are different methods of measuring the error estimate of a machine learning model. Over many iterations, the two methods should produce a very similar error estimate. That is, once the OOB error stabilizes, it will converge to the cross-validation (specifica... |
Out-of-bag error : Out-of-bag error is used frequently for error estimation within random forests but with the conclusion of a study done by Silke Janitza and Roman Hornung, out-of-bag error has shown to overestimate in settings that include an equal number of observations from all response classes (balanced samples), ... |
Out-of-bag error : Boosting (meta-algorithm) Bootstrap aggregating Bootstrapping (statistics) Cross-validation (statistics) Random forest Random subspace method (attribute bagging) == References == |
Prefrontal cortex basal ganglia working memory : Prefrontal cortex basal ganglia working memory (PBWM) is an algorithm that models working memory in the prefrontal cortex and the basal ganglia. It can be compared to long short-term memory (LSTM) in functionality, but is more biologically explainable. It uses the primar... |
Prefrontal cortex basal ganglia working memory : The prefrontal cortex has long been thought to subserve both working memory (the holding of information online for processing) and "executive" functions (deciding how to manipulate working memory and perform processing). Although many computational models of working memo... |
Prefrontal cortex basal ganglia working memory : First, there are multiple separate stripes (groups of units) in the prefrontal cortex and striatum layers. Each stripe can be independently updated, such that this system can remember several different things at the same time, each with a different "updating policy" of w... |
Prefrontal cortex basal ganglia working memory : State–action–reward–state–action Sammon Mapping Constructing skill trees == References == |
Prescription monitoring program : In the United States, prescription monitoring programs (PMPs) or prescription drug monitoring programs (PDMPs) are state-run programs which collect and distribute data about the prescription and dispensation of federally controlled substances and, depending on state requirements, other... |
Prescription monitoring program : Prescription drug monitoring programs, or PDMPs, are an example of one initiative proposed to alleviate effects of the opioid crisis. The programs are designed to restrict prescription drug abuse by limiting a patient's ability to obtain similar prescriptions from multiple providers (i... |
Prescription monitoring program : Most health care workers support PMPs which intend to assist physicians, physician assistants, nurse practitioners, dentists and other prescribers, the pharmacists, chemists and support staff of dispensing establishments, as well as law-enforcement agencies. The collaboration supports ... |
Prescription monitoring program : Many doctors and researchers support the idea of PDMPs as a tool in combatting the opioid epidemic. Opioid prescribing, opioid diversion and supply, opioid misuse, and opioid-related morbidity and mortality are common elements in data entered into PDMPs. Prescription Monitoring Program... |
Prototype methods : Prototype methods are machine learning methods that use data prototypes. A data prototype is a data value that reflects other values in its class, e.g., the centroid in a K-means clustering problem. |
Prototype methods : The following are some prototype methods K-means clustering Learning vector quantization (LVQ) Gaussian mixtures |
Prototype methods : While K-nearest neighbor's does not use prototypes, it is similar to prototype methods like K-means clustering. == References == |
PVLV : The primary value learned value (PVLV) model is a possible explanation for the reward-predictive firing properties of dopamine (DA) neurons. It simulates behavioral and neural data on Pavlovian conditioning and the midbrain dopaminergic neurons that fire in proportion to unexpected rewards. It is an alternative ... |
Randomized weighted majority algorithm : The randomized weighted majority algorithm is an algorithm in machine learning theory for aggregating expert predictions to a series of decision problems. It is a simple and effective method based on weighted voting which improves on the mistake bound of the deterministic weight... |
Randomized weighted majority algorithm : Imagine that every morning before the stock market opens, we get a prediction from each of our "experts" about whether the stock market will go up or down. Our goal is to somehow combine this set of predictions into a single prediction that we then use to make a buy or sell deci... |
Randomized weighted majority algorithm : In machine learning, the weighted majority algorithm (WMA) is a deterministic meta-learning algorithm for aggregating expert predictions. In pseudocode, the WMA is as follows: initialize all experts to weight 1 for each round: add each expert's weight to the option they predicte... |
Randomized weighted majority algorithm : The randomized weighted majority algorithm is an attempt to improve the dependence of the mistake bound of the WMA on m . Instead of predicting based on majority vote, the weights, are used as probabilities for choosing the experts in each round and are updated over time (hence... |
Randomized weighted majority algorithm : Let W t denote the total weight of all experts at round t . Also let F t denote the fraction of weight placed on experts which predict the wrong answer at round t . Finally, let N be the total number of rounds in the process. By definition, F t is the probability that the ... |
Randomized weighted majority algorithm : Recall that the motivation for the randomized weighted majority algorithm was given by an example where the best expert makes a mistake 20% of the time. Precisely, in N = 100 rounds, with n = 10 experts, where the best expert makes m = 20 mistakes, the deterministic weighted ... |
Randomized weighted majority algorithm : The Randomized Weighted Majority Algorithm can be used to combine multiple algorithms in which case RWMA can be expected to perform nearly as well as the best of the original algorithms in hindsight. Note that the RWMA can be generalized to solve problems which do not have binar... |
Randomized weighted majority algorithm : Multi-armed bandit problem. Efficient algorithm for some cases with many experts. Sleeping experts/"specialists" setting. |
Randomized weighted majority algorithm : Machine learning Weighted majority algorithm Game theory Multi-armed bandit |
Randomized weighted majority algorithm : Weighted Majority & Randomized Weighted Majority Avrim Blum (2004) machine learning theory Rob Schapire 2006 Foundations of Machine Learning Predicting From Experts Advice Uri Feige, Robi Krauthgamer, Moni Naor. Algorithmic Game Theory Nika Haghtalab 2020 Theoretical Foundations... |
Repeated incremental pruning to produce error reduction (RIPPER) : In machine learning, repeated incremental pruning to produce error reduction (RIPPER) is a propositional rule learner proposed by William W. Cohen as an optimized version of IREP. |
Rule-based machine learning : Rule-based machine learning (RBML) is a term in computer science intended to encompass any machine learning method that identifies, learns, or evolves 'rules' to store, manipulate or apply. The defining characteristic of a rule-based machine learner is the identification and utilization of... |
Rule-based machine learning : Rules typically take the form of an ' expression', (e.g. , or as a more specific example, ). An individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Therefore rule-based machine learning methods typically comprise a set of rules, or k... |
Skill chaining : Skill chaining is a skill discovery method in continuous reinforcement learning. It has been extended to high-dimensional continuous domains by the related Deep skill chaining algorithm. |
Skill chaining : Konidaris, George; Andrew Barto (2009). "Skill discovery in continuous reinforcement learning domains using skill chaining". Advances in Neural Information Processing Systems 22. Bagaria, Akhil; George Konidaris (2020). "Option discovery using deep skill chaining". International Conference on Learning ... |
Sparse PCA : Sparse principal component analysis (SPCA or sparse PCA) is a technique used in statistical analysis and, in particular, in the analysis of multivariate data sets. It extends the classic method of principal component analysis (PCA) for the reduction of dimensionality of data by introducing sparsity structu... |
Sparse PCA : Consider a data matrix, X , where each of the p columns represent an input variable, and each of the n rows represents an independent sample from data population. One assumes each column of X has mean zero, otherwise one can subtract column-wise mean from each element of X . Let Σ = 1 n − 1 X ⊤ X X^X ... |
Sparse PCA : As most sparse problems, variable selection in SPCA is a computationally intractable non-convex NP-hard problem, therefore greedy sub-optimal algorithms are often employed to find solutions. Note also that SPCA introduces hyperparameters quantifying in what capacity large parameter values are penalized. Th... |
Sparse PCA : Several alternative approaches (of Eq. 1) have been proposed, including a regression framework, a penalized matrix decomposition framework, a convex relaxation/semidefinite programming framework, a generalized power method framework an alternating maximization framework forward-backward greedy search and e... |
Sparse PCA : amanpg - R package for Sparse PCA using the Alternating Manifold Proximal Gradient Method elasticnet – R package for Sparse Estimation and Sparse PCA using Elastic-Nets epca – R package for exploratory principal component analysis for large-scale dataset, including sparse principal component analysis and s... |
Sparse PCA : == References == |
State–action–reward–state–action : State–action–reward–state–action (SARSA) is an algorithm for learning a Markov decision process policy, used in the reinforcement learning area of machine learning. It was proposed by Rummery and Niranjan in a technical note with the name "Modified Connectionist Q-Learning" (MCQ-L). T... |
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