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Approximate inference methods make it possible to learn realistic models from big data by trading off computation time for accuracy, when exact learning
Approximate_inference
Computational method in Bayesian statistics
epidemiology, and phylogeography. Approximate Bayesian computation can be understood as a kind of Bayesian version of indirect inference. Several efficient Monte
Approximate Bayesian computation
Approximate_Bayesian_computation
Programming paradigm
that they support in polynomial time. Since the cost of inference may be very high, approximate algorithms have been developed. They either compute subsets
Probabilistic logic programming
Probabilistic_logic_programming
Hypothesis in neuroscience
accuracy of its predictions. This principle approximates an integration of Bayesian inference with active inference, where actions are guided by predictions
Free_energy_principle
Probabilistic graphical representation of causal relationships
approximate probabilistic inference to within an absolute error ɛ < 1/2. Second, they proved that no tractable randomized algorithm can approximate probabilistic
Bayesian_network
Branch of statistics
system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable
Causal_inference
Method for estimating the parameters of economic models
unsuitable for formal modeling. Approximate Bayesian computation can be understood as a kind of Bayesian version of indirect inference. Given a dataset of real
Indirect_inference
Statistical model
generalized linear model Breslow, N. E.; Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models", Journal of the American Statistical
Generalized linear mixed model
Generalized_linear_mixed_model
Probabilistic logic
Wang, Jue (2017). "Scalable learning and inference in Markov logic networks". International Journal of Approximate Reasoning. 82: 39–55. doi:10.1016/j.ijar
Markov_logic_network
Deep learning method
Already in the original paper1⁄1/, the authors noted that "Learned approximate inference can be performed by training an auxiliary network to predict z {\displaystyle
Generative adversarial network
Generative_adversarial_network
Process of using data analysis for predicting population data from sample data
Statistical inference is the process of using data analysis to infer properties of an underlying probability distribution. Inferential statistical analysis
Statistical_inference
Method of statistical inference
Bayesian inference (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is a method of statistical inference in which Bayes' theorem is used to calculate a probability
Bayesian_inference
Theory and paradigm of statistics
a good model for the data is central in Bayesian inference. In most cases, models only approximate the true process, and may not take into account certain
Bayesian_statistics
Supervised machine learning techniques
variables, the processes of model training and inference are often computationally infeasible, so approximate inference and learning methods are used. An example
Structured_prediction
Analytical expression in statistics
Integrated nested Laplace approximation (INLA) is a method for approximate Bayesian inference based on Laplace's approximation. It is designed for a class
Laplace's_approximation
Machine learning algorithm
propagation is used when an approximate solution is needed instead of the exact solution. It is an approximate inference. Cutset conditioning: Used with
Junction_tree_algorithm
Set of methods for supervised statistical learning
Wenzel; Matthäus Deutsch; Théo Galy-Fajou; Marius Kloft; ”Scalable Approximate Inference for the Bayesian Nonlinear Support Vector Machine” Ferris, Michael
Support_vector_machine
Probabilistic graphical model
license) libDAI: C++ library that provides implementations of various (approximate) inference methods for discrete graphical models; supports arbitrary factor
Dynamic_Bayesian_network
Type of machine learning model
reverse-engineering may lead to the discovery of algorithms that approximate inferences performed by an LLM. For instance, the authors trained small transformers
Large_language_model
Type of stochastic recurrent neural network
expectations and approximate the expected sufficient statistics by using Markov chain Monte Carlo (MCMC). This approximate inference, which must be done
Boltzmann_machine
Approximate interference technique in Bayesian networks
Variational message passing (VMP) is an approximate inference technique for continuous- or discrete-valued Bayesian networks, with conjugate-exponential
Variational_message_passing
Inference seeking the simplest and most likely explanation
Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion
Abductive_reasoning
Deep learning generative model to encode data representation
Shakir; Wierstra, Daan (2014-06-18). "Stochastic Backpropagation and Approximate Inference in Deep Generative Models". International Conference on Machine
Variational_autoencoder
Square root of the determinant of a skew-symmetric square matrix
arXiv:math/0406301. Globerson, Amir; Jaakkola, Tommi (2007). "Approximate inference using planar graph decomposition" (PDF). Advances in Neural Information
Pfaffian
Monte Carlo algorithm
Gibbs sampling is commonly used as a means of statistical inference, especially Bayesian inference. It is a randomized algorithm (i.e. an algorithm that makes
Gibbs_sampling
Type of artificial neural network
single framework. Its inference system corresponds to a set of fuzzy IF–THEN rules that have learning capability to approximate nonlinear functions. Hence
Adaptive neuro fuzzy inference system
Adaptive_neuro_fuzzy_inference_system
Statistical theory
formalism the Gibbs free energy can be calculated, which permits the (approximate) inference of the posterior mean field via a numerical robust functional minimization
Information_field_theory
American scientist (born 1956)
also prominent in the formalisation of variational methods for approximate inference and the popularisation of the expectation–maximization algorithm
Michael_I._Jordan
Israeli computer scientist (born 1960)
algebraic systems in vision and learning, primal/dual optimization for approximate inference in MRF and Graphical models, and (since 2014) deep layered networks
Amnon_Shashua
Mathematical rule for inverting probabilities
of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of observations
Bayes'_theorem
Mathematical theory
Solomonoff's theory of inductive inference purportedly proves that, under its assumptions (axioms), the best possible scientific model is the shortest
Solomonoff's theory of inductive inference
Solomonoff's_theory_of_inductive_inference
Method of logical reasoning
prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded. A generalization
Inductive_reasoning
Cognitive science prize
I. Jordan Latent Dirichlet allocation, variational methods for approximate inference, expectation-maximization algorithm University of California, Berkeley
Rumelhart_Prize
Computation of nearly accurate results
Raha, Arnab; Raghunathan, Vijay (2023-07-24). "Energy-Efficient Approximate Edge Inference Systems". ACM Transactions on Embedded Computing Systems. 22 (4):
Approximate_computing
Range to estimate an unknown parameter
According to frequentist inference, a confidence interval (CI) is a range of values which is likely to contain (in repeated sampling) the true value of
Confidence_interval
Lower bound on the log-likelihood of some observed data
called amortized inference. All in all, we have found a problem of variational Bayesian inference. A basic result in variational inference is that minimizing
Evidence_lower_bound
Mathematical methods used in Bayesian inference and machine learning
Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used
Variational_Bayesian_methods
Class of statistical modeling methods
algorithms yield exact solutions. If exact inference is impossible, several algorithms can be used to obtain approximate solutions. These include: Loopy belief
Conditional_random_field
Algorithm for statistical inference on graphical models
sum–product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields
Belief_propagation
American speed skater
Computer Science at Stanford University with a PhD Thesis titled, Fast Approximate Inference: Shifting the Pareto Frontier via Adaptation - advised by Stefano
Jonathan_Kuck
Calculation of complex statistical distributions
Gibbs sampling highly resembles that of the coordinate ascent variational inference in that both algorithms utilize the full-conditional distributions in
Markov_chain_Monte_Carlo
Probabilistic programming language for Bayesian inference
algorithms for Bayesian inference, stochastic, gradient-based variational Bayesian methods for approximate Bayesian inference, and gradient-based optimization
Stan_(software)
Probabilistic programming library for the Python programming language
algorithms for Bayesian inference and stochastic, gradient-based variational Bayesian methods for approximate Bayesian inference. MCMC-based algorithms:
PyMC
Compilation of software used to produce phylogenetic trees
pair group method with arithmetic mean (UPGMA), Bayesian phylogenetic inference, maximum likelihood, and distance matrix methods. List of phylogenetic
List of phylogenetics software
List_of_phylogenetics_software
Habits of working
in London in 1888 Modus ponens – Rule of logical inference Modus tollens – Rule of logical inference Modus vivendi – Arrangement that allows conflicting
Modus_operandi
Mental ability to track moving objects with attention
"Explaining human multiple object tracking as resource-constrained approximate inference in a dynamic probabilistic model". In Bengio, Y.; Schuurmans, D
Multiple_object_tracking
Results about asymptotic posterior normality
In Bayesian inference, the Bernstein–von Mises theorem provides the basis for using Bayesian credible sets for confidence statements in parametric models
Bernstein–von_Mises_theorem
Statistical model written in multiple levels
theorem. This simple expression encapsulates the technical core of Bayesian inference which aims to deconstruct the probability, P ( θ ∣ y ) {\displaystyle
Bayesian hierarchical modeling
Bayesian_hierarchical_modeling
Machine learning and inference framework
A constrained conditional model (CCM) is a machine learning and inference framework that augments the learning of conditional (probabilistic or discriminative)
Constrained_conditional_model
Statistical interpretation with many tests
rate (FWER). The larger the number of inferences made in a series of tests, the more likely erroneous inferences become. Several statistical techniques
Multiple_comparisons_problem
Statistical method for molecular phylogenetics
Bayesian inference of phylogeny combines the information in the prior and in the data likelihood to create the so-called posterior probability of trees
Bayesian inference in phylogeny
Bayesian_inference_in_phylogeny
Bayesian statistical inference method
Empirical Bayes methods are procedures for statistical inference in which the prior probability distribution is estimated from the data. This approach
Empirical_Bayes_method
perform approximate inference. Approaches that use collective classification can make use of relational information when performing inference. Examples
Collective_classification
Principle in Bayesian statistics
should be considered a particular application of a general tool of logical inference and information theory. In most practical cases, the stated prior data
Principle_of_maximum_entropy
Canadian statistician
the Guy medal in Gold "for her pioneering work on higher-order approximate inference which provides a foundational basis for optimal information extraction
Nancy_Reid
Type of investigation
implications and the approximate forms of inference hang on the properties that derive from these. In describing the various types of inference the following
Inquiry
Statistical Markov model
resort to variational approximations to Bayesian inference, e.g. Indeed, approximate variational inference offers computational efficiency comparable to
Hidden_Markov_model
American technology company
Groq announced an agreement reportedly valued at approximately US$20 billion to license Groq's AI inference technology and to transfer several senior Groq
Groq
Formal fallacy in statistical interpretation
ecological inference fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the
Ecological_fallacy
Derivation of the laws of probability theory
(2003). "Constructing a logic of plausible inference: A guide to Cox's theorem". International Journal of Approximate Reasoning. 34: 3–24. doi:10.1016/S0888-613X(03)00051-3
Cox's_theorem
Rating system supporting games with more than 2 players
performances and observed outcomes as a factor graph. Inference is then framed as the computation of approximate single-variable marginals by message passing using
TrueSkill
Semiring defined over probabilities
Hidden Markov Model". Gimpel, Kevin; Smith, Noah A. "Cube Summing, Approximate Inference with Non-Local Features, and Dynamic Programming without Semirings"
Viterbi_semiring
Method of estimating the parameters of a statistical model, given observations
flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for
Maximum_likelihood_estimation
Online vector quantization algorithm
language model inference and high-dimensional search: Product quantization – a vector quantization technique widely used for approximate nearest-neighbor
TurboQuant
Equation to approximate pooled degrees of freedom
Behrens–Fisher problem. The result can be used to perform approximate statistical inference tests. The simplest application of this equation is in performing
Welch–Satterthwaite_equation
Aspect of statistics
regression. There are two approaches to statistical inference: model-based inference and design-based inference. Both approaches rely on some statistical model
Statistical_assumption
Probabilistic theory of knowledge
conditionalization governs the dynamic aspects as a form of probabilistic inference. The most characteristic Bayesian expression of these principles is found
Bayesian_epistemology
Intelligence of machines
decision support, knowledge discovery (mining "interesting" and actionable inferences from large databases), and other areas. A knowledge base is a body of
Artificial_intelligence
Applications of logic under uncertainty
logic. Just as in courtroom reasoning, the goal of employing uncertain inference is to gather evidence to strengthen the confidence of a proposition, as
Probabilistic_logic
Type of statistical inference
possible motivation of transduction arises through the need to approximate. If exact inference is computationally prohibitive, one may at least try to make
Transduction (machine learning)
Transduction_(machine_learning)
Evidence indirectly supporting conclusion
Circumstantial evidence is evidence that relies on an inference to connect it to a conclusion of fact, such as a fingerprint at the scene of a crime.
Circumstantial_evidence
Proposition in statistics
because it is inconsistent with the mainstream frequentist approach to inference. While the likelihood function is important to frequentists, they do not
Likelihood_principle
Thought experiment, to justify Bayesian probability
approximation Integrated nested Laplace approximations Variational inference Approximate Bayesian computation Estimators Bayesian estimator Credible interval
Dutch_book_arguments
Approach to artificial intellegence
based on the Approximate Analogical Reasoning Scheme POPFNN-CRI(S), which is based on commonly accepted fuzzy Compositional Rule of Inference POPFNN-TVR
Neuro-fuzzy
Classification algorithm in statistics
approximation Integrated nested Laplace approximations Variational inference Approximate Bayesian computation Estimators Bayesian estimator Credible interval
Bayes_classifier
Theory and paradigm of statistics
of statistical inference, while others make inferences based on likelihood, but without using Bayesian inference or frequentist inference. Likelihoodism
Likelihoodist_statistics
Study of collection and analysis of data
experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population
Statistics
Interval bounded by an upper and a lower limit statistics
prior, much like confidence intervals. Fiducial inference is a less common form of statistical inference. The founder, R.A. Fisher, who had been developing
Interval_estimation
In probability theory, a rule for assigning epistemic probabilities
approximation Integrated nested Laplace approximations Variational inference Approximate Bayesian computation Estimators Bayesian estimator Credible interval
Principle_of_indifference
Statistical law in machine learning
training cost. Some models also exhibit performance gains by scaling inference through increased test-time compute (TTC), extending neural scaling laws
Neural_scaling_law
Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to
Algorithmic_inference
Method for numerical integration
nested sampling algorithm was developed by John Skilling specifically to approximate these marginalization integrals, and it has the added benefit of generating
Nested_sampling_algorithm
Statistical method
to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or
Bootstrapping_(statistics)
Field of statistics
Causal Inference – it is impossible to directly observe causal effects. A major goal of scientific experiments and statistical methods is to approximate as
Causal_analysis
Research Workers. Oliver and Boyd. Mehta, C.R.; Patel, N.R. (1998). "Exact Inference for Categorical Data". In P. Armitage and T. Colton, eds., Encyclopedia
Exact_test
rule or Bayesian updating Empirical Bayes method – Bayesian statistical inference method Evidence under Bayes theorem Hierarchical Bayes model – Type of
List of things named after Thomas Bayes
List_of_things_named_after_Thomas_Bayes
Type of statistic
interval estimation by eliminating procedures based on asymptotic and approximate statistical methods. The main characteristic of exact methods is that
Exact_statistics
computational convenience – they do not change the process of Bayesian inference, but simply allow one to more easily describe and compute with the prior
Hyperprior
Type of mathematical model
generally, statistical models are part of the foundation of statistical inference. A statistical model is usually specified as a mathematical relationship
Statistical_model
Field of study in artificial intelligence
This reduces retraining time even within a shard. Aggregation occurs at inference, when the model is queried. It combines the outputs of each shard to determine
Machine_unlearning
Method of estimating the parameters of a statistical model
characterized by the use of distributions to summarize data and draw inferences: thus, Bayesian methods tend to report the posterior mean or median instead
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Probabilistic problem-solving algorithm
random sample from the posterior distribution in Bayesian inference. This sample then approximates and summarizes all the essential features of the posterior
Monte_Carlo_method
Type of information retrieval using LLMs
model with a non-parametric external memory accessed through retrieval at inference time. LLMs can provide incorrect information. For example, when Google
Retrieval-augmented generation
Retrieval-augmented_generation
Information conveyed verbally yet not literally
many other researchers. Entailment, or implication, in logic Free choice inference Indirect speech act Presupposition Davis (2019, section 14) Grice (1975:24–26)
Implicature
Rewriting system and type of formal grammar
represents a significant advancement in L-system inference, introducing the Plant Model Inference Tools (PMIT) suite. Despite the name, this tool is
L-system
Method for approximate evaluation of integrals
Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form ∫ a b e M f ( x ) d x , {\displaystyle \int _{a}^{b}e^{Mf(x)}\
Laplace's_method
British-Iranian computer researcher (born 1970)
Bayesian machine learning (particularly variational methods for approximate Bayesian inference), as well as graphical models and computational neuroscience
Zoubin_Ghahramani
Topics referred to by the same term
to: Integrated nested Laplace approximations, a method for approximate Bayesian inference InlA, one form of the Internalin surface protein found on Listeria
INLA
Social media platform owned by Meta
trial or case-control, meaning they were incapable of drawing causal inferences. The WSJ reported that Instagram can worsen poor body image of young people
Netherlands-based chip company
at simplifying deployment of AI inference at the edge. In 2025 Axelera AI introduced Europa, a next-generation inference processor targeting edge servers
Axelera_AI
APPROXIMATE INFERENCE
APPROXIMATE INFERENCE
Boy/Male
Scandinavian
Royalty title approximately equivalent to the English Earl.
Surname or Lastname
English
English : topographic name for someone who lived by an enclosure of some kind, Middle English yard(e) (Old English geard; compare Garth).English : nickname from Middle English yard ‘rod’, ‘stick’ (Old English (Anglian) gerd), probably with reference to a rod or staff carried as a symbol of authority.English : from the same word as in 2, used to denote a measure of land. The surname probably denoted someone who held this quantity of land, and as it was quite a large amount (varying at different periods and in different places, but generally approximately 30 acres, a quarter of a hide), such a person would have been a reasonably prosperous farmer.
Girl/Female
Tamil
Inference
Surname or Lastname
English
English : habitational name from any of the various places so called. The majority, with examples in at least fourteen counties, get the name from Old English hÅh ‘ridge’, ‘spur’ (literally ‘heel’) + tÅ«n ‘enclosure’, ‘settlement’. Haughton in Nottinghamshire also has this origin, and may have contributed to the surname. A smaller group of Houghtons, with examples in Lancashire and South Yorkshire, have as their first element Old English halh ‘nook’, ‘recess’. In the case of isolated examples in Devon and East Yorkshire, the first elements appear to be unattested Old English personal names or bynames, of which the forms approximate to Huhha and Hofa respectively, but the meanings are unknown.
Girl/Female
Indian
Inference
Surname or Lastname
English
English : metonymic occupational name for a maker and seller of gloves or a nickname for a wearer of particularly fine gloves, from Middle English cuffe ‘glove’ (of uncertain origin; attested in this sense from the 14th century, with the modern meaning first in the 16th century).Irish : Anglicized form of Gaelic Mac Dhuibh, a variant of Mac Duibh ‘son of the black one’ (see Duff).Irish : approximate translation of Gaelic Ó DoirnÃn (see Dornan).Cornish : nickname from Cornish cuf ‘dear’, ‘kind’.
APPROXIMATE INFERENCE
APPROXIMATE INFERENCE
Boy/Male
English
Surname.'beloved.
Girl/Female
English
Modernand Laurie referring to the laurel tree or sweet bay tree symbolic of honor and victory.
Boy/Male
Hindu, Indian, Malayalam, Marathi, Tamil
Light; The Earliest; Lord Shiva
Surname or Lastname
English
English : variant spelling of Frizzell.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Gift
Boy/Male
Tamil
Vajinath | வாஜீநாத
Lord Shiva
Girl/Female
Welsh
Just; upright. Feminine of Justin.
Male
English
Anglicized form of Hebrew Mowab, MOAB means "water," i.e. "seed," hence "of his father." In the bible, this is the name of a son of Lot.
Girl/Female
Tamil
Silk
Boy/Male
Hindu, Indian, Tamil
Ritual
APPROXIMATE INFERENCE
APPROXIMATE INFERENCE
APPROXIMATE INFERENCE
APPROXIMATE INFERENCE
APPROXIMATE INFERENCE
v. t.
To come near to; to approach.
a.
Nearest; next immediately preceding or following.
a.
Proximate.
v. i.
To approximate to the surface; to head; -- said of an abscess.
a.
Nearly or approximately square; almost square.
a.
Near correctness; nearly exact; not perfectly accurate; as, approximate results or values.
a.
Approximately polygonal; somewhat or almost polygonal.
n.
One who, or that which, approximates.
a.
Obtained by trial, by measurements, etc.; approximate; empirical. See the 2d Note under Geometric.
imp. & p. p.
of Approximate
a.
Imperfectly cylindrical; approximately cylindrical.
a.
Nearly or approximately pentangular; almost pentangular.
a.
Approaching; proximate; nearly resembling.
adv.
With approximation; so as to approximate; nearly.
a.
Approaching; approximate.
v. t.
To carry or advance near; to cause to approach.
prep.
Near; not far from; -- determining approximately time, size, quantity.
v. i.
To draw; to approach.
superl.
Not proximate or acting directly; primary; distant.
p. pr. & vb. n.
of Approximate