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PyMC
PyMC (formerly known as PyMC3) is a Python package for Bayesian statistical modeling and probabilistic machine learning which focuses on advanced Markov chain Monte Carlo and variational fitting algorithms. It is a rewrite from scratch of the previous version of the PyMC software. Unlike PyMC2, which had used Fortran extensions for performing computations, PyMC relies on Aesara, a Python library that allows to define, optimize, and efficiently evaluate mathematical expressions involving multi-dimensional arrays. From version 3.8 PyMC relies on ArviZ to handle plotting, diagnostics, and statistical checks. PyMC and Stan are the two most popular probabilistic programming tools. PyMC is an open source project, developed by the community and fiscally sponsored by NumFOCUS. PyMC has been used to solve inference problems in several scientific domains, including astronomy, epidemiology, molecular biology, crystallography, chemistry, ecology and psychology. Previous versions of PyM ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic Programming
Probabilistic programming (PP) is a programming paradigm in which probabilistic models are specified and inference for these models is performed automatically. It represents an attempt to unify probabilistic modeling and traditional general purpose programming in order to make the former easier and more widely applicable.Pfeffer, Avrom (2014), ''Practical Probabilistic Programming'', Manning Publications. p.28. It can be used to create systems that help make decisions in the face of uncertainty. Programming languages used for probabilistic programming are referred to as "probabilistic programming languages" (PPLs). Applications Probabilistic reasoning has been used for a wide variety of tasks such as predicting stock prices, recommending movies, diagnosing computers, detecting cyber intrusions and image detection. However, until recently (partially due to limited computing power), probabilistic programming was limited in scope, and most inference algorithms had to be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theano (software)
Theano is a Python library and optimizing compiler for manipulating and evaluating mathematical expressions, especially matrix-valued ones. In Theano, computations are expressed using a NumPy-esque syntax and compiled to run efficiently on either CPU or GPU architectures. Theano is an open source project primarily developed by the Montreal Institute for Learning Algorithms (MILA) at the Université de Montréal. The name of the software references the ancient philosopher Theano, long associated with the development of the golden mean. On 28 September 2017, Pascal Lamblin posted a message from Yoshua Bengio, Head of MILA: major development would cease after the 1.0 release due to competing offerings by strong industrial players. Theano 1.0.0 was then released on 15 November 2017. On 17 May 2018, Chris Fonnesbeck wrote on behalf of the PyMC development team that the PyMC developers will officially assume control of Theano maintenance once they step down. On 29 January 2021, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ArviZ
ArviZ ( ) is a Python package for exploratory analysis of Bayesian models. When working with Bayesian models there are a series of related tasks that need to be addressed besides inference itself: * Diagnoses of the quality of the inference, this is needed when using numerical methods such as Markov chain Monte Carlo techniques * Model criticism, including evaluations of both model assumptions and model predictions * Comparison of models, including model selection or model averaging * Preparation of the results for a particular audience All these tasks are part of the Exploratory analysis of Bayesian models approach, and successfully performing them is central to the iterative and interactive modeling process. These tasks require both numerical and visual summaries. ArviZ offers data structures for manipulating data common in Bayesian analysis, like numerical samples from the posterior, prior predictive and posterior predictive distributions as well as observed data. Addition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximate Bayesian Computation
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior distributions of model parameters. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain Monte Carlo
In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm. Application domains MCMC methods are primarily used for calculating numerical approximations of multi-dimensional integrals, for example in Bayesian statistics, computational physics, computational biology and computational linguistics. In Bayesian statistics, the recent development of MCMC methods has made it possible to compute large hierarchical models that require integrations over hundreds to thousands of unknown parameters. In rare even ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently ranks as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, it has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. As of June 2022, GitHub reported having over 83 million developers and more than 200 million repositories, including at least 28 million public repositories. It is the largest source code host . History GitHub.com Development of the GitHub.com platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett and Scott Chacon after it had been made available for a few months prior as a beta release. GitHub has an annual keynote called GitHub Universe. Organizational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numba
Numba is an open-source JIT compiler that translates a subset of Python and NumPy into fast machine code using LLVM, via the llvmlite Python package. It offers a range of options for parallelising Python code for CPUs and GPUs, often with only minor code changes. Numba was started by Travis Oliphant in 2012 and has since been under active development at https://github.com/numba/numba with frequent releases. The project is driven by developers at Anaconda, Inc., with support by DARPA, the Gordon and Betty Moore Foundation, Intel, Nvidia and AMD, and a community of contributors on GitHub. Example Numba can be used by simply applying the numba.jit decorator to a Python function that does numerical computations: import numba import random @numba.jit def monte_carlo_pi(n_samples: int): acc = 0 for i in range(n_samples): x = random.random() y = random.random() if (x**2 + y**2) >> monte_carlo_pi(1000000) 3.14 The Numba website at https://numba.pyd ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Bayesian Methods
Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as might be described by a graphical model. As typical in Bayesian inference, the parameters and latent variables are grouped together as "unobserved variables". Variational Bayesian methods are primarily used for two purposes: #To provide an analytical approximation to the posterior probability of the unobserved variables, in order to do statistical inference over these variables. #To derive a lower bound for the marginal likelihood (sometimes called the ''evidence'') of the observed data (i.e. the marginal probability of the data given the model, with marginalization performed over unobserved v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Machine Learning Research
The ''Journal of Machine Learning Research'' is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). History The journal was established as an open-access alternative to the journal ''Machine Learning''. In 2001, forty editorial board members of ''Machine Learning'' resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the ''Journal of Machine Learning Research'' allows authors to publish articles for free and retain copyright, while archives are freely available online. Print editions of the journal were published by MIT Press until 2004 and by Microtome Publishing thereafter. From its inception, the journal received no revenue from the pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neuroscience
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developmental biology, cytology, psychology, physics, computer science, chemistry, medicine, statistics, and Mathematical Modeling, mathematical modeling to understand the fundamental and emergent properties of neurons, glia and neural circuits. The understanding of the biological basis of learning, memory, behavior, perception, and consciousness has been described by Eric Kandel as the "epic challenge" of the Biology, biological sciences. The scope of neuroscience has broadened over time to include different approaches used to study the nervous system at different scales. The techniques used by neuroscientists have expanded enormously, from molecular biology, molecular and cell biology, cellular studies of individual neurons to neuroimaging, imaging ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hybrid Monte Carlo
The Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random samples which converge to being distributed according to a target probability distribution for which direct sampling is difficult. This sequence can be used to estimate integrals with respect to the target distribution (expected values). Hamiltonian Monte Carlo corresponds to an instance of the Metropolis–Hastings algorithm, with a Hamiltonian dynamics evolution simulated using a time-reversible and volume-preserving numerical integrator (typically the leapfrog integrator) to propose a move to a new point in the state space. Compared to using a Gaussian random walk proposal distribution in the Metropolis–Hastings algorithm, Hamiltonian Monte Carlo reduces the correlation between successive sampled states by proposing moves to distant states which maintain a high probability of acceptance due to the approximate energy conservin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
