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Measure of algorithm accuracy
machine learning and statistical learning theory, generalization error (also known as the out-of-sample error or the risk) is a measure of how accurately an
Generalization_error
Conclusion made on the basis of one or few instances of a phenomenon
on insufficiently large samples under an implied margin of error. A faulty generalization often follows the following format: The proportion Q of the
Faulty_generalization
Machine learning algorithm
to bound the generalization error of these classifiers. These bounds are frequently shown using the VC dimension. The generalization error bound in boosting
Margin_classifier
subdivided into categories such as improper presumption, faulty generalization, error in assigning causation, and relevance, among others. The use of
List_of_fallacies
Machine learning paradigm
generalize from the training examples, a quality measured by its generalization error. Supervised learning is commonly used for tasks like classification
Supervised_learning
Set of methods for supervised statistical learning
general the larger the margin, the lower the generalization error of the classifier. A lower generalization error means that the implementer is less likely
Support_vector_machine
Property of a model
expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting
Bias–variance_tradeoff
Method in machine learning
model's fit to the training data comes at the expense of increased generalization error. Early stopping rules provide guidance as to how many iterations
Early_stopping
Framework for mathematical analysis of machine learning
probability (the "probably" part), the selected function will have low generalization error (the "approximately correct" part). The learner must be able to learn
Probably approximately correct learning
Probably_approximately_correct_learning
Technique to make a model more generalizable and transferable
modifications to the algorithm. It is always intended to reduce the generalization error, i.e. the error score with the trained model on the evaluation set (testing
Regularization_(mathematics)
Measure of complexity of real-valued functions
that the true error of a classifier is not much higher than its estimated error, and so selecting a classifier that has low estimated error will ensure
Rademacher_complexity
Type of kernel induced by artificial neural networks
describing the expected generalization error of high-dimensional kernel regression; these results immediately explain the generalization of sufficiently wide
Neural_tangent_kernel
Phase transition in machine learning
("model‑wise"), and the authors report "model‑wise grokking". Overfitting Generalization error Double descent Neural tangent kernel Feature learning Reward hacking
Grokking_(machine_learning)
Statistical model validation technique
selection of the best set of hyperparameters and for error estimation (and assessment of generalization capacity), a nested cross-validation is required.
Cross-validation_(statistics)
Tree-based ensemble machine learning methods
of random forests, in particular: Using out-of-bag error as an estimate of the generalization error. Measuring variable importance through permutation
Random_forest
Concept in machine learning
; Sompolinsky, Haim (2020-12-01). "High-dimensional dynamics of generalization error in neural networks". Neural Networks. 132: 428–446. doi:10.1016/j
Double_descent
Statistics and machine learning technique
MacReady, William G. (1999). "An Efficient Method to Estimate Bagging's Generalization Error" (PDF). Machine Learning. 35 (1): 41–55. Bibcode:1999MLear..35..
Ensemble_learning
Digit necessary to represent a quantity
significant figures, resulting in 12345 g as the accurate value. The rounding error (in this example, 0.25 g) approximates the numerical resolution or precision
Significant_figures
Flaw in mathematical modelling
thus insufficiently be able to predict future data results (see Generalization error). As shown in Figure 5, the linear line could not represent all the
Overfitting
Technique to solve partial differential equations
Mishra, Siddhartha; Molinaro, Roberto (2021-04-01). "Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class
Physics-informed neural networks
Physics-informed_neural_networks
Number of balls of a given size needed to cover a given space
the generalization error of learning functions from K {\displaystyle K} , relative to the squared loss: Prob [ sup h ∈ K | GeneralizationError ( h )
Covering_number
Computer scientist
Constructive Prediction of the Generalization Error Across Scales, an ICLR 2020 paper on predicting neural-network generalization error across model and data scales
Yonatan_Belinkov
Expressions for approximation accuracy
the order increases, but the order does not directly indicate the percent error of the approximation. See Taylor's theorem for more on this. For example
Order_of_approximation
Software for understanding biological data
classification or regression. As random forests give an internal estimate of generalization error, cross-validation is unnecessary. In addition, they produce proximities
Machine learning in bioinformatics
Machine_learning_in_bioinformatics
Computational model used in machine learning
over-training and select appropriate hyperparameters to minimize generalization error. Regularization in a probabilistic (Bayesian) framework can be performed
Neural network (machine learning)
Neural_network_(machine_learning)
Technique in information theory
information bottleneck is one way to control generalization error in deep learning. Namely, the generalization error is proven to scale as O ~ ( I ( X , T )
Information_bottleneck_method
Notion in computational learning theory
stability of a learning algorithm and showed that it implies low generalization error. Uniform hypothesis stability, however, is a strong condition that
Stability_(learning_theory)
Hypersurface used by a classification algorithm
boundary. Decision boundary instability can be incorporated with generalization error as a standard for selecting the most accurate and stable classifier
Decision_boundary
Machine learning strategy
the current model. Expected error reduction: label those points that would most reduce the model's generalization error. Exponentiated Gradient Exploration
Active learning (machine learning)
Active_learning_(machine_learning)
Overview of and topical guide to machine learning
emulator Gene prediction General Architecture for Text Engineering Generalization error Generalized canonical correlation Generalized filtering Generalized
Outline_of_machine_learning
Method of logical reasoning
differences in how their results are regarded. A generalization (more accurately, an inductive generalization) proceeds from premises about a sample to a conclusion
Inductive_reasoning
List of concepts in artificial intelligence
similar. generalization error For supervised learning applications in machine learning and statistical learning theory, generalization error (also known
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Describes approximate behavior of a function
In mathematical analysis, including calculus, Big O notation bounds the error when truncating a power series and expresses the quality of approximation
Big_O_notation
Mathematical concept
The approximation error in a given data value represents the significant discrepancy that arises when an exact, true value is compared against some approximation
Approximation_error
Linguistic category tracking areal features of European languages
linguistics created a substantial SAE-centric bias, leading to generalization errors, such as mistaking linguistic features idiosyncratic to the SAE
Standard_Average_European
Deviation from the apparently intended form of an utterance
mental lexicon is also organized in terms of sound. Four generalizations about speech errors have been identified: Interacting elements tend to come from
Speech_error
Informal logical fallacy
Bradley Dowden explains the fallacy as an "ad hoc rescue" of a refuted generalization attempt. The following is a simplified rendition of the fallacy: Person
No_true_Scotsman
Process in quantum computing
Quantum error correction (QEC) comprises a set of techniques used in quantum memory and quantum computing to protect quantum information from errors arising
Quantum_error_correction
Estimation method that minimizes the mean square error
processing, a minimum mean square error estimator (MMSE estimator) is an estimation method which minimizes the mean square error (MSE), which is a common measure
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Error in numerical data
In science and engineering, convention dictates that unless a margin of error is explicitly stated, the number of significant figures used in the presentation
False_precision
Method for estimating new data within known data points
methods also produce smoother interpolants. Polynomial interpolation is a generalization of linear interpolation. Note that the linear interpolant is a linear
Interpolation
Technique to reduce dimensionality of points in Euclidean space
ISBN 978-1-4244-2246-3. S2CID 206563812. Li, Xiaoyun; Li, Ping (2019). "Generalization error analysis of quantized compressive learning". 33rd International Conference
Random_projection
Description of limiting behavior in probabilistic algorithms
process for machine-learning in which the learned function has low generalization-error WHP. Gossip protocols: a communication protocol used in distributed
With_high_probability
Boosting algorithm
the final classifier is learned from the non-noisy examples, the generalization error of the final classifier may be much better than if learned from noisy
BrownBoost
Method for model fitting in statistics
least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of
Weighted_least_squares
Argument that uses faulty reasoning
renders the argument invalid, while an informal fallacy originates in an error in reasoning other than an improper logical form. Arguments containing informal
Fallacy
Curve simplification algorithm
successful algorithms developed for cartographic generalization. It produces the most accurate generalization, but it is also more time-consuming. The starting
Ramer–Douglas–Peucker algorithm
Ramer–Douglas–Peucker_algorithm
Process of mapping a continuous set to a countable set
input value and its quantized value (such as round-off error) is referred to as quantization error, noise or distortion. A device or algorithmic function
Quantization (signal processing)
Quantization_(signal_processing)
Probability distribution
Gaussian q-distribution above. The Kaniadakis κ-Gaussian distribution is a generalization of the Gaussian distribution which arises from the Kaniadakis statistics
Normal_distribution
Statistical technique
dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied
Total_least_squares
Statistical modeling method
with multivariate linear regression). Multiple linear regression is a generalization of simple linear regression to the case of more than one independent
Linear_regression
Concept in regression analysis mathematics
correlated variables. Least squares Regularization in mathematics. Generalization error, one of the reasons regularization is used. Tikhonov regularization
Regularized_least_squares
Mathematical problem in cryptography
In cryptography, learning with errors (LWE) is a mathematical problem that is widely used to create secure encryption algorithms. It is based on the idea
Learning_with_errors
Function that is holomorphic on the whole complex plane
meromorphic functions can be viewed as a generalization of rational functions, entire functions can be viewed as a generalization of polynomials. In particular,
Entire_function
Statistical confidence interval for success counts
formulas, showing that the calculation for weighted data is a direct generalization of them. If the weights in question are the complex sampling design
Binomial proportion confidence interval
Binomial_proportion_confidence_interval
Cognitive bias
categorization and generalization to members of this group (boys). The fundamental attribution error is similar to the group attribution error in that it refers
Group_attribution_error
Quantum Information Science
in quantum error-correcting code, discrete AdS/CFT correspondence, AdS/CMT correspondence, and more. It is the multipartite generalization of the bipartite
Absolutely maximally entangled state
Absolutely_maximally_entangled_state
Topological quantum error correcting code
able to demonstrate the error correction properties of the code. For realizations of the toric code and its generalizations with a Hamiltonian, much
Surface_code
Statistical technique used to correct for multiple comparisons
detection of the Higgs boson. In such cases, one can apply a continuous generalization of the Bonferroni correction by employing Bayesian logic to relate the
Bonferroni_correction
Regression models accounting for possible errors in independent variables
In statistics, an errors-in-variables model or a measurement error model is a regression model that accounts for measurement errors in the independent
Errors-in-variables_model
Tasks in machine learning
therefore a set of examples used only to assess the performance (i.e. generalization) of a specified classifier on unseen data. To do this, the model is
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
Problem-solving technique in applied mathematics using order-of-magnitude approximations
notation Curve fitting False precision Significant figures Other fundamentals Approximation Generalization error Taylor polynomial Scientific modelling v t e
Scale_analysis_(mathematics)
Type of fallacious argument (logical fallacy)
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is
Affirming_the_consequent
Similar to the basis of a vector space, but not necessarily linearly independent
In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology
Frame_(linear_algebra)
ITU-T Recommendation
the generalization error is the main concern in applying any kind of Supervised Learning (SL) approach, which can be high even if the test error is kept
Y.3181
Statistical measure of how far values spread from their average
the expected absolute deviation, and, together with variance and its generalization covariance, is used frequently in theoretical statistics; however the
Variance
Middle quantile of a data set or probability distribution
statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a
Median
Approximation of a function by a polynomial
of Taylor's theorem, some giving explicit estimates of the approximation error of the function by its Taylor polynomial. Taylor's theorem is named after
Taylor's_theorem
Number with a real and an imaginary part
field theory.) Complex numbers are essential to spinors, which are a generalization of the tensors used in relativity. The field C {\displaystyle \mathbb
Complex_number
In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code. They were conceived
Concatenated error correction code
Concatenated_error_correction_code
Mathematical operation on vectors in 3D space
represent quantities such as multi-dimensional space-time. (See § Generalizations below for other dimensions.) The cross product of two vectors a and
Cross_product
Ensemble learning method
large. This is due to high intra class variability and the need for generalization across variations of objects within the same category. Objects within
Boosting_(machine_learning)
Type of modal logic
logic that results from the combining of K, T, 4, 5, and the Knowledge Generalization Rule, is primarily known as S5. This is why the properties of knowledge
Epistemic_modal_logic
Notion in calculus
familiar error rules of summation, multiplication, etc. are derived, e.g.: Let f ( a , b ) = a b {\displaystyle f(a,b)=ab} . Then the finite error can be
Differential_of_a_function
Discrete Fourier transform algorithm
simplest non-row-column FFT is the vector-radix FFT algorithm, which is a generalization of the ordinary Cooley–Tukey algorithm where one divides the transform
Fast_Fourier_transform
Probability of shared birthdays
possible dates (the birthday problem), the answer is 2365. Another generalization is to ask for the probability of finding at least one pair in a group
Birthday_problem
Theorem related to ordinary least squares
reduced the assumptions to the form stated above. A further generalization to non-spherical errors was given by Alexander Aitken. Suppose we are given two
Gauss–Markov_theorem
Part of the process of building a statistical model
following: R2, Bayes factor, and the likelihood-ratio test together with its generalization relative likelihood. For more on this topic, see statistical model selection
Statistical model specification
Statistical_model_specification
Type of block code
belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Let
Cyclic_code
Form of incorrect argument in natural language
are a type of incorrect argument in natural language. The source of the error is not necessarily due to the form of the argument, as is the case for formal
Informal_fallacy
Error correction code
systematic binary BCH code is used only for error-detection purposes, we see that BCH codes are just a generalization of the mathematics of cyclic redundancy
BCH_code
Multi-dimensional version of a confidence interval
multi-dimensional generalization of a confidence interval. For a bivariate normal distribution, it is an ellipse, also known as the error ellipse. More generally
Confidence_region
Non-parametric classification method
original (PDF) on 2018-12-23. Retrieved 2018-05-24. This scheme is a generalization of linear interpolation. Hastie, Trevor. (2001). The elements of statistical
K-nearest_neighbors_algorithm
Approximation method in statistics
statistical degrees of freedom; see effective degrees of freedom for generalizations. C is the covariance matrix. If the probability distribution of the
Least_squares
Reinforcement learning method
collection of input-output pairs to facilitate the process of generalization. The widely utilized error backpropagation learning algorithm is known as GeneRec
Error-driven_learning
Scientific study of digital information
entropy and the Tsallis entropy (generalizations of the concept of entropy), differential entropy (a generalization of quantities of information to continuous
Information_theory
Iraqi mathematician
recognized for his contributions to Shannon Sampling Theory, Its Generalizations, Error Analysis, and Historical Reviews, and in particular his establishment
Abdul_Jerri
Instantaneous rate of change (mathematics)
of order n {\displaystyle n} . As has been discussed above, the generalization of derivative of a function f {\displaystyle f} may be denoted as
Derivative
Internet rage incitement technique
2020. sfn error: no target: CITEREFKarim2020 (help) Dempsey 2022. sfn error: no target: CITEREFDempsey2022 (help) Piccardi 2025. sfn error: no target:
Rage-baiting
Type of activation function
derivative of the rectifier, the Heaviside step function. The multivariable generalization of single-variable softplus is the LogSumExp with the first argument
Rectified_linear_unit
Technique for training recurrent neural networks
Engineering Department. CUED/F-INFENG/TR.1. Werbos, Paul J. (1988). "Generalization of backpropagation with application to a recurrent gas market model"
Backpropagation_through_time
Study of mathematical algorithms for optimization problems
within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes
Mathematical_optimization
Mathematical concept
inequality follows from evaluating the integrals. (See below for a generalization.) A second proof is via Jensen's inequality: Proof The claim is certainly
Young's inequality for products
Young's_inequality_for_products
Theorem that tells the maximum rate at which information can be transmitted
capacity for such a communication link, a bound on the maximum amount of error-free information per time unit that can be transmitted with a specified
Shannon–Hartley_theorem
Algorithm that estimates unknowns from a series of measurements over time
unless all noise processes are assumed to be Gaussian. Extensions and generalizations of the method have also been developed, such as the extended Kalman
Kalman_filter
Algorithm for solving systems of linear equations
Buchberger's algorithm is a generalization of Gaussian elimination to systems of polynomial equations. This generalization depends heavily on the notion
Gaussian_elimination
Problem in computer science
\epsilon } . In words, there is a positive error rate for which any algorithm will do worse than that error rate arbitrarily often, even as the size of
Halting_problem
Matrix equal to its conjugate-transpose
{\displaystyle A.} Hermitian matrices can be understood as the complex generalization of symmetric real matrices. The Hermitian property of a matrix A {\displaystyle
Hermitian_matrix
variety Height zeta function of a variety Hurwitz zeta function, a generalization of the Riemann zeta function Igusa zeta function Ihara zeta function
List_of_zeta_functions
On triangles inscribed in a circle with a diameter as an edge
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle
Thales's_theorem
GENERALIZATION ERROR
GENERALIZATION ERROR
Boy/Male
Shakespearean
The Comedy of Errors' Twin brothers, both named Antipholus, sons to Aemelia and Aegion....
Boy/Male
Hindu
Errorless
Boy/Male
Shakespearean
The Comedy of Errors' Twin brothers, both named Dromio, attendants on the twin Antipholuses....
Boy/Male
Indian
Perfect, Complete, Generalization
Boy/Male
Shakespearean
The Comedy of Errors' Father to the twin brothers Antipholus of Ephesus, and Antipholus of Syracuse.
Girl/Female
Indian
Goddess Aadisakti: She who Maintains the Rules of Justice without the Slightest Error
Boy/Male
Shakespearean
The Comedy of Errors' A merchant.
Boy/Male
Indian
Perfect, Complete, Generalization
Female
Hebrew
(×ֲבִיש×Ö·×’) Variant spelling of Hebrew Abiyshag, AVISHAG means "my father is a wanderer" or "father of error." In the bible, this is the name of a young girl who cared for David in his old age.Â
Girl/Female
Hindu, Indian
Without Error
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Error-less
Boy/Male
Tamil
Errorless
Boy/Male
Shakespearean
The Comedy of Errors' A merchant of Syracuse.
Girl/Female
Shakespearean
The Comedy of Errors' Adriana's servant.
Boy/Male
Shakespearean
The Comedy of Errors' A schoolmaster.
Female
Hebrew
(×ֲבִיש×Ö·×’) Hebrew name ABIYSHAG means "my father is a wanderer" or "father of error." In the bible, this is the name of a young girl who cared for David in his old age. Also spelled Avishag.
Boy/Male
Muslim
Perfect, Complete, Generalization
Surname or Lastname
English
English : of uncertain derivation. The first recorded instance seems to be William Cleike (Yorkshire 1176), but this may well be an error for Clerke. In subsequent records the name is concentrated in Devon; it seems to have been originally a habitational name connected with a piece of land in the parish of Ermington near Plymouth, first recorded in 1278 as Clekeland(e), and still known as Clickland; the names John de Clakelond and Robert Cleaklond occur in this parish in 1332 and 1337 respectively. The place name may be from Old English cleaca ‘stepping stone’, ‘boundary stone’ (of Celtic origin) + land ‘territory’. Compare Clack.Americanized spelling of German Glück (see Gluck).
Boy/Male
Shakespearean
The Comedy of Errors' Duke of Ephesus.
Boy/Male
Muslim
Perfect, Complete, Generalization
GENERALIZATION ERROR
GENERALIZATION ERROR
Girl/Female
Tamil
A river, Darkness
Girl/Female
Arabic, Muslim
Girl Slave
Boy/Male
French Gaelic English
Strong.
Boy/Male
Indian, Punjabi, Sikh
Of Nine Hundred Thousand
Surname or Lastname
English, French, German, Dutch, Spanish (Simón), Czech and Slovak (Šimon), Slovenian, Hungarian, and Jewish (Ashkenazic)
English, French, German, Dutch, Spanish (Simón), Czech and Slovak (Å imon), Slovenian, Hungarian, and Jewish (Ashkenazic) : from the personal name, Hebrew Shim‘on, which is probably derived from the verb sham‘a ‘to hearken’. In the Vulgate and in many vernacular versions of the Old Testament, this is usually rendered Simeon. In the Greek New Testament, however, the name occurs as SimÅn, as a result of assimilation to the pre-existing Greek byname SÄ«mÅn (from sÄ«mos ‘snub-nosed’). Both Simon and Simeon were in use as personal names in western Europe from the Middle Ages onward. In Christendom the former was always more popular, at least in part because of its associations with the apostle Simon Peter, the brother of Andrew. In Britain there was also confusion from an early date with Anglo-Scandinavian forms of Sigmund (see Siegmund), a name whose popularity was reinforced at the Conquest by the Norman form Simund.The earliest documented bearer of the surname Simon in New France came from the Saintonge region of France and was in Montreal by 1655. Another, from Paris, is recorded in Quebec City in 1659 with the secondary surname Lapointe.
Boy/Male
Hindu, Indian, Sanskrit
The Yajur Veda
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Sanskrit, Telugu, Traditional
Eternally Pure
Female
Egyptian
, the wife of Nakht-ankh.
Girl/Female
Indian, Telugu
The Garland in the Neck of God - Sai Baba
Girl/Female
Arabic, Muslim
Proud
GENERALIZATION ERROR
GENERALIZATION ERROR
GENERALIZATION ERROR
GENERALIZATION ERROR
GENERALIZATION ERROR
n.
A false step; a stumble; a misstep; a loss of footing or balance. Fig.: An error; a failure; a mistake.
n.
A general notion, or a conception formed by generalization.
n.
The conversion of a cell wall into a material of a stony nature.
n.
The difference between the observed value of a quantity and that which is taken or computed to be the true value; -- sometimes called residual error.
n.
Fig.: That which preserves from corruption or error; that which purifies; a corrective; an antiseptic; also, an allowance or deduction; as, his statements must be taken with a grain of salt.
n.
One who encourages and propagates error; one who holds to error.
v. t.
To recite (a lesson) or pass (an examination) without an error.
n.
The state or condition of being central; the combination of several parts into one whole; centralization.
a.
Committing no mistake; incapable or error or failure certain; sure; unfailing; as, the unerring wisdom of God.
a.
Full of error; wrong.
n.
The process of mineralizing, or forming a mineral by combination of a metal with another element; also, the process of converting into a mineral, as a bone or a plant.
n.
The addition of a differentia to a concept or notion, thus limiting its extent; -- the opposite of generalization.
n.
The act or process of centralizing, or the state of being centralized; the act or process of combining or reducing several parts into a whole; as, the centralization of power in the general government; the centralization of commerce in a city.
n.
A general inference.
n.
The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning.
n.
A wandering or deviation from the right course or standard; irregularity; mistake; inaccuracy; something made wrong or left wrong; as, an error in writing or in printing; a clerical error.
n.
A defect; a fault; an error; a blemish; an imperfection; as, the vices of a political constitution; the vices of a horse.
n.
The act or process of generalizing; the act of bringing individuals or particulars under a genus or class; deduction of a general principle from particulars.
n.
The act of impregnating with a mineral, as water.