Why use variational inference?
In some cases, we will even have bounds on their accuracy. In practice, variational inference methods often scale better and are more amenable to techniques like stochastic gradient optimization, parallelization over multiple processors, and acceleration using GPUs.
What is variational inference in machine learning?
Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications.
What is stochastic variational inference?
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.
Is variational inference Bayesian?
One such approximate inference technique that has gained popularity in recent times is the Variational Bayes (VB). Having a relatively low computational cost and a good empirical approximation has propelled it to drive the intuition behind successful models like the Variational Auto-encoders and more.
What does variational mean in statistics?
It means using variational inference (at least for the first two). In short, it’s an method to approximate maximum likelihood when the probability density is complicated (and thus MLE is hard).
Why is variational inference called?
The term variational is used because you pick the best q in Q — the term derives from the “calculus of variations,” which deals with optimization problems that pick the best function (in this case, a distribution q).
Why is variational inference called variational?
What is black box variational inference?
Essentially black box VI is a method that yields an estimator for the gradient of the ELBO with respect to the variational parameters with very little constraint on the form of the posterior or the variational distribution.
Is variational inference exact?
However, variational inference approximates the solution rather than finding the exact solution. Indeed, it is unlikely that our solution will be exact.
Why is it called variational inference?
What are variational parameters?
The basic idea of the variational method is to guess a “trial” wavefunction for the problem, which consists of some adjustable parameters called “variational parameters. ” These parameters are adjusted until the energy of the trial wavefunction is minimized.
What does it mean to say that a theoretical model is variational?
In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate or ground state, and some excited states. This allows calculating approximate wavefunctions such as molecular orbitals. The basis for this method is the variational principle.
What is stochastic in statistics?
The adjective “stochastic” implies the presence of a random variable; e.g. stochastic variation is variation in which at least one of the elements is a variate and a stochastic process is one wherein the system incorporates an element of randomness as opposed to a deterministic system.
What is stochastic process in statistics?
A stochastic process means that one has a system for which there are observations at certain times, and that the outcome, that is, the observed value at each time is a random variable.
What is the meaning of stochasticity?
1 : random specifically : involving a random variable a stochastic process. 2 : involving chance or probability : probabilistic a stochastic model of radiation-induced mutation.
What is the difference between statistical and stochastic?
In “statistics” we are given the probability of a number of events and want to determine the probability distribution. “Stochastic”, on the other hand, is an adjective while both “probability” and “statistics” are nouns, denoting fields of study.
What is variational inference?
This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this article, we review variational inference (VI), a method from machine learning that approximates probability densities through optimization.
Is variational inference useful in modern Bayesian statistics?
Modern Bayesian statistics relies on models for which the posterior is not easy to compute and corresponding algorithms for approximating them. In this paper, we review variational inference (vi), a method from machine learning for approximating probability densities (Jordan et al., 1999; Wainwright and Jordan, 2008) .
What is the open research problem in variational inference?
A final open research problem is to understand variational inference as an estimator and to understand its statistical profile relative to the exact posterior. 26 A Bayesian Linear Regression with Automatic Relevance Determination Consider a dataset ofy=y1:n2Rnoutputs andx=x1:n2R(n D)D-dimensional inputs, where eachxi2RD.
What is the inference problem in statistics?
The inference problem is to compute the conditional density of the latent variables given the observations,p(zjx). This conditional can be used to produce point or interval estimates of the latent variables, form predictive densities of new data, and more.