Relevance vector machine

Key takeaways

Relevance vector machine belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Relevance vector machine to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Relevance vector machine from memory before moving on to harder problems.

Reference excerpt

In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. A greedy optimisation procedure and thus fast version were subsequently developed. The RVM has an identical functional form to the support vector machine, but provides probabilistic classification. It is actually equivalent to a Gaussian process model with covariance function:

k ( x , x ′ ) = ∑ j = 1 N 1 α j φ ( x , x j ) φ ( x ′ , x j ) {\displaystyle k(\mathbf {x} ,\mathbf {x'} )=\sum _{j=1}^{N}{\frac {1}{\alpha _{j}}}\varphi (\mathbf {x} ,\mathbf {x} _{j})\varphi (\mathbf {x} ',\mathbf {x} _{j})}

where φ {\displaystyle \varphi } is the kernel function (usually Gaussian), α j {\displaystyle \alpha _{j}} are the variances of the prior on the weight vector

w ∼ N ( 0 , α − 1 I ) {\displaystyle w\sim N(0,\alpha ^{-1}I)} , and x 1 , … , x N {\displaystyle \mathbf {x} _{1},\ldots ,\mathbf {x} _{N}} are the input vectors of the training set. Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based post-optimizations). However RVMs use an expectation maximization (EM)-like learning method and are therefore at risk of local minima. This is unlike the standard sequential minimal optimization (SMO)-based algorithms employed by SVMs, which are guaranteed to find a global optimum (of the convex problem). The relevance vector machine was patented in the United States by Microsoft (patent expired September 4, 2019).

See also Kernel trick Platt scaling: turns an SVM into a probability model

References

Worked examples

Example 1 — a first encounter with Relevance vector machine

Start with the simplest possible case. Write down what Relevance vector machine claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Relevance vector machine before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Relevance vector machine ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Relevance vector machine

In research: Relevance vector machine appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Relevance vector machine in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Relevance vector machine is common in secondary-school and first-year university syllabi. It links to neighbouring topics Classification algorithms, Kernel methods for machine learning, Nonparametric Bayesian statistics, so understanding it makes those chapters shorter.
In everyday life: Look for Relevance vector machine outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Relevance vector machine in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Relevance vector machine means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Relevance vector machine out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Relevance vector machine in simple terms?

In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. A greedy optimisation procedure and thus fast version were subsequently developed.

Why does Relevance vector machine matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Relevance vector machine?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Relevance vector machine.