mathematics

Uncertain data

Uncertain data is a mathematics 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 Uncertain data rather than just read about it. In short: In computer science, uncertain data is data that contains noise that makes it deviate from the correct, intended or original values. In the age of big data, uncertainty or data veracity is one of the defining characteristics of data.

Key takeaways

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

Reference excerpt

In computer science, uncertain data is data that contains noise that makes it deviate from the correct, intended or original values. In the age of big data, uncertainty or data veracity is one of the defining characteristics of data. Data is constantly growing in volume, variety, velocity and uncertainty (1/veracity). Uncertain data is found in abundance today on the web, in sensor networks, within enterprises both in their structured and unstructured sources. For example, there may be uncertainty regarding the address of a customer in an enterprise dataset, or the temperature readings captured by a sensor due to aging of the sensor. In 2012 IBM called out managing uncertain data at scale in its global technology outlook report that presents a comprehensive analysis looking three to ten years into the future seeking to identify significant, disruptive technologies that will change the world. In order to make confident business decisions based on real-world data, analyses must necessarily account for many different kinds of uncertainty present in very large amounts of data. Analyses based on uncertain data will have an effect on the quality of subsequent decisions, so the degree and types of inaccuracies in this uncertain data cannot be ignored. Uncertain data is found in the area of sensor networks; text where noisy text is found in abundance on social media, web and within enterprises where the structured and unstructured data may be old, outdated, or plain incorrect; in modeling where the mathematical model may only be an approximation of the actual process. When representing such data in a database, an appropriate uncertain database model needs to be selected.

Example data model for uncertain data One way to represent uncertain data is through probability distributions. Let us take the example of a relational database. There are three main ways to do represent uncertainty as probability distributions in such a database model. In attribute uncertainty, each uncertain attribute in a tuple is subject to its own independent probability distribution. For example, if readings are taken of temperature and wind speed, each would be described by its own probability distribution, as knowing the reading for one measurement would not provide any information about the other. In correlated uncertainty, multiple attributes may be described by a joint probability distribution. For example, if readings are taken of the position of an object, and the x- and y-coordinates stored, the probability of different values may depend on the distance from the recorded coordinates. As distance depends on both coordinates, it may be appropriate to use a joint distribution for these coordinates, as they are not independent. In tuple uncertainty, all the attributes of a tuple are subject to a joint probability distribution. This covers the case of correlated uncertainty, but also includes the case where there is a probability of a tuple not belonging in the relevant relation, which is indicated by all the probabilities not summing to one. For example, assume we have the following tuple from a probabilistic database:

Then, the tuple has 10% chance of not existing in the database.

References

Habich Volk; Clemens Utzny; Ralf Dittmann; Wolfgang Lehner. "Error-Aware Density-Based Clustering of Imprecise Measurement Values". Seventh IEEE International Conference on Data Mining Workshops, 2007. ICDM Workshops 2007. IEEE. Volk Rosentahl; Martin Hahmann; Dirk Habich; Wolfgang Lehner. "Clustering Uncertain Data With Possible Worlds". Proceedings of the 1st Workshop on Management and mining Of Uncertain Data in conjunction with the 25th International Conference on Data Engineering, 2009. IEEE.

Worked examples

Example 1 — a first encounter with Uncertain data

Start with the simplest possible case. Write down what Uncertain data claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Uncertain data 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 Uncertain data 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 Uncertain data

In research: Uncertain data appears in mathematics 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 Uncertain data 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: Uncertain data is common in secondary-school and first-year university syllabi. It links to neighbouring topics Data mining, Machine learning, Statistical theory, so understanding it makes those chapters shorter.
In everyday life: Look for Uncertain data 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 Uncertain data in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Uncertain data 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 Uncertain data out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Uncertain data in simple terms?

Why does Uncertain data matter?

Because it connects several mathematics 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 Uncertain data?

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 Uncertain data.