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Parity learning

Parity learning is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Parity learning rather than just read about it. In short: Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ƒ, given some samples (x, ƒ(x)) and the assurance that ƒ computes the parity of bits at some fixed locations.

Key takeaways

  • Parity learning 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 Parity learning to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Parity learning from memory before moving on to harder problems.

Reference excerpt

Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ƒ, given some samples (x, ƒ(x)) and the assurance that ƒ computes the parity of bits at some fixed locations. The samples are generated using some distribution over the input. The problem is easy to solve using Gaussian elimination provided that a sufficient number of samples (from a distribution which is not too skewed) are provided to the algorithm.

Noisy version ("Learning Parity with Noise") In Learning Parity with Noise (LPN), the samples may contain some error. Instead of samples (x, ƒ(x)), the algorithm is provided with (x, y), where for random boolean b ∈ { 0 , 1 } {\displaystyle b\in \{0,1\}}

y = { f ( x ) , if b 1 − f ( x ) , otherwise {\displaystyle y={\begin{cases}f(x),&{\text{if }}b\\1-f(x),&{\text{otherwise}}\end{cases}}}

The noisy version of the parity learning problem is conjectured to be hard and is widely used in cryptography.

See also Learning with errors

References

Avrim Blum, Adam Kalai, and Hal Wasserman, “Noise-tolerant learning, the parity problem, and the statistical query model,” J. ACM 50, no. 4 (2003): 506–519. Adam Tauman Kalai, Yishay Mansour, and Elad Verbin, “On agnostic boosting and parity learning,” in Proceedings of the 40th annual ACM symposium on Theory of computing (Victoria, British Columbia, Canada: ACM, 2008), 629–638, http://portal.acm.org/citation.cfm?id=1374466. Oded Regev, “On lattices, learning with errors, random linear codes, and cryptography,” in Proceedings of the thirty-seventh annual ACM symposium on Theory of computing (Baltimore, MD, USA: ACM, 2005), 84–93, http://portal.acm.org/citation.cfm?id=1060590.1060603.

Worked examples

Example 1 — a first encounter with Parity learning

Start with the simplest possible case. Write down what Parity learning 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 Parity learning 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 Parity learning 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 Parity learning

In research
Parity learning 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 Parity learning 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
Parity learning is common in secondary-school and first-year university syllabi. It links to neighbouring topics Applied mathematics stubs, Machine learning, Machine learning stubs, so understanding it makes those chapters shorter.
In everyday life
Look for Parity learning 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.

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How to study Parity learning in 20 minutes

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

Frequently asked questions

What is Parity learning in simple terms?

Parity learning is a problem in machine learning. An algorithm that solves this problem must find a function ƒ, given some samples (x, ƒ(x)) and the assurance that ƒ computes the parity of bits at some fixed locations.

Why does Parity learning 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 Parity learning?

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 Parity learning.

Tags

  • Applied mathematics stubs
  • Machine learning
  • Machine learning stubs

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