Professional Skills in Computer Science Lecture 8: Induction (2)

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1 Professional Skills in Computer Science Lecture 8: Induction (2) Ullrich Hustadt Department of Computer Science School of Electrical Engineering, Electronics, and Computer Science University of Liverpool Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 1

2 Ind. generalisation Statistical syllogism Ind. reasoning in CS Contents 1 Inductive generalisation Definition Hasty generalisation Overgeneralisation Biased sample Observation 2 Statistical syllogism Definition and examples Fallacy by accident Arguments from authority Fallacy by appeal to inappropriate authority Arguments from consensus 3 Inductive Reasoning in Computer Science Machine Learning Data Mining Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 2

3 Ind. generalisation Statistical syllogism Ind. reasoning in CS Today... Relevant learning outcomes: 1 Ability to describe and discuss economic, historic, organisational, research, and social aspects of computing as a discipline and computing in practice 2 To effectively retrieve information including the use of library and web sources and the evaluation of information retrieved from such sources 3 To recognise and employ sound reasoning and argumentation techniques as part of conducting basic research Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 3

4 Ind. generalisation Statistical syllogism Ind. reasoning in CS Causal induction / Causal inference Mill s five methods of induction / five methods of experimental inquiry 1 Method of agreement 2 Method of difference 3 Joint method of agreement and difference 4 Method of concomitant variations 5 Method of residue are methods for causal induction (or causal inference) Causal induction draws a conclusion about a causal connection based on the circumstances of the occurrence of an effect Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 4

5 Ind. generalisation Statistical syllogism Ind. reasoning in CS Causal induction: Example In 1695, Edmond Halley was computing the orbits of a set of comets for inclusion in Newton s Principia Mathematica He noticed that comets that were observed in 1531, 1607, and 1682 took very similar paths across the sky Also, the observations were years apart (suggesting a regular interval) Newton had already established (by induction) that comets follow certain paths, e.g. a parabolic path or an elliptic orbit Halley inferred by induction that the three sightings were caused by the same comet orbiting the sun on a highly elliptic orbit Note: This could be seen as hasty generalisation, but we now know that the comet has been observed since 240 BC by Chinese and Babylonian astronomers (Source: T. L. Griffiths and J. B. Tenenbaum: Theory-Based Causal Induction. Psychological Review 116(4): , 2009.) Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 5

6 Ind. generalisation Statistical syllogism Ind. reasoning in CS Other forms of inductive reasoning Causal induction is only one form of inductive reasoning In particular, we were looking for reasoning that from observations like draws a conclusion like All the crows I ve ever seen were black All crows are black This does not appear to be causal induction Instead this form of inductive reasoning is based on 1 Inductive generalisation 2 Statistical syllogism Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 6

7 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Hasty Overgeneral Bias Observation Inductive generalisation An inductive generalisation takes a sample of a population and draws a conclusion about the entire population: Proportion X of sample S have property P therefore Proportion X of the entire population have property P Example: You have a box with 100 balls in it, some black, some white You draw a sample of 5 balls out of the box, 4 of them are black, i.e., 80%, and 1 is white, i.e., 20% Inductive generalisation: 80% of all the balls in the box are black and 20% are white Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 7

8 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Hasty Overgeneral Bias Observation Inductive generalisation A special case of inductive generalisation occurs when the proportion X of the sample represents the whole sample: Every instance of sample S has property P therefore Every instance of the entire population has property P Example: Every crow that I have ever seen was black therefore Every crow in the entire world is black This was exactly the kind of inductive reasoning that we were looking for Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 8

9 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Hasty Overgeneral Bias Observation Hasty generalisation Inductive generalisation requires a sample that is sufficiently large and unbiased A sample that is too small can lead to a hasty generalisation Example: You have a box with 100 balls in it, some black, some white, some red You draw a sample of 2 balls out of the box, 1 of them is black, i.e., 50%, and 1 is white, i.e., 50% Generalisation: 50% of all the balls in the box are black and 50% are white, there are no red balls in the box A sample of 2 balls could never have been representative given that there are 3 colours involved Note that this generalisation might still be correct! Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 9

10 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Hasty Overgeneral Bias Observation Overgeneralisation A special instance of hasty generalisation is overgeneralisation Overgeneralisation occurs if you draw an overly-general conclusion that is unwarranted by the sample Instances Salad Fish Meat Chicken Sick Andy yes yes yes yes yes Dave yes yes yes Frank yes yes yes yes Eve yes yes yes Jack yes yes yes yes Betty yes yes yes Causal induction: This particular salad makes you sick Overgeneralisation: Salad is bad for you Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 10

11 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Hasty Overgeneral Bias Observation Biased sample A biased sample occurs when a sample is collected in such a way that some members of the intended population are less likely to be included than others A biased sample is again not a sound basis for inductive generalisation Example: The average age of people studying or working at the University is 28 years Generalisation: The average age of the UK population is 28 years In reality, the average age of the UK population is 38 years The sample of people studying and working at the University is biased towards younger people Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 11

12 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Hasty Overgeneral Bias Observation Insufficient Range of Observational Circumstances Example: We observe that a fellow student, Michael, is grumpy on Wednesday, 2nd November, Wednesday, 9th November, Wednesday, 16th November, Wednesday, 23rd November We conclude that Michael is always grumpy on Wednesdays We failed to recognise that these dates coincide with COMP101 coursework deadlines and that this is the cause for Michael s grumpiness As soon as COMP101 is over Michael will be grumpy on a different day of the week Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 12

13 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Accident Authority Statistical syllogism A statistical syllogism proceeds from a generalisation to a conclusion about an individual Proportion X of the population have property P (where X is large) Individual I is a member of that population Therefore, I has property P Syllogism means conclusion or inference Beware: Some dictionaries define a syllogism as a deductive scheme or deductive reasoning Statistical syllogism is not a form of deductive reasoning It is a form of inductive reasoning Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 13

14 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Accident Authority Statistical syllogism A statistical syllogism proceeds from a generalisation to a conclusion about an individual Proportion X of the population have property P (where X is large) Individual I is a member of that population Therefore, I has property P Example: 90% of university students have above average intelligence You are a university student Therefore, you have above average intelligence Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 14

15 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Accident Authority Statistical syllogism: Fallacy by accident Fallacy by accident: a generalisation is applied when circumstances suggest that there should be an exception Example: Exceeding the speed limit is (almost always) an offence The driver of an ambulance has exceeded the speed limit Therefore, the driver has committed an offence Obviously, we should realise that an ambulance may be exempted from obeying the speed limit Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 15

16 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Accident Authority Statistical syllogism: Arguments from authority Arguments from authority can be seen as a version of statistical syllogism: Statistical syllogism Proportion X of the population have property P (where X is large) Individual I is a member of that population Therefore, I has property P Argument from authority Most of what authority A says on subject matter S is correct X is something that A says in the context of S Therefore, X is true Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 16

17 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Accident Authority Arguments from authority: Appeal to inappropriate authority Arguments from authority are best avoided in science If you still feel the need to use such an argument, make sure that you avoid the fallacy of appeal to inappropriate authority where the authority and subject matter does not satisfy all of the following conditions: 1 The authority is a recognised expert on the subject matter 2 There is general agreement among authorities on questions / statements relating to that subject matter 3 There is no good reason to suspect that the authority is biased on the subject matter or the particular question Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 17

18 Ind. generalisation Statistical syllogism Ind. reasoning in CS Definition Accident Authority Statistical syllogism: Arguments from consensus Arguments from consensus can be seen as a version of statistical syllogism: Argument from consensus Most of the claims that most of the people agree upon are true X is a claim that most people agree upon Therefore, X is true Even worse than arguments from authority But admissible when the subject matter is public opinion or strongly influenced by public opinion Example: If opinion polls suggest that a considerable majority believes that there will be a change of government at the next election, then there will be a change of government Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 18

19 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Inductive reasoning: Summary and applications Our motivation for considering inductive reasoning was the question What is the right proto-theory/hypothesis/model in a particular situation? We have seen that, for example, the method of difference may also help us with the question What is the right experiment to conduct? Both of these questions relate to the conduct of Research in general and the conduct of Computer Science Research in particular A central question of Computer Science Research is So, a natural question is What can be (efficiently) automated (described as an algorithmic process)? Can inductive reasoning be automated? Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 19

20 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Computational Scientific Discovery Can inductive reasoning be automated? Computational Scientific Discovery is the branch of Artificial Intelligence that is concerned with providing answers to this question An early example of a scientific discovery system is Meta-Dendral B. G. Buchanan and E. A. Feigenbaum: Dendral and Meta-Dendral. Artificial Intelligence 11(1 2):5 24, 1978 System for rule discovery in the area of chemical analysis via mass spectrometry Motivated by applications in space exploration Experiments and analysis may need to be conducted without human involvement Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 20

21 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining BACON Another early example of a scientific discovery system is BACON (Langley et al, ) Named after Francis Bacon ( ), a pioneer of the scientific method BACON was a system for the discovery of (scientific) numeric laws, that is, laws of the form y = F (x) BACON was able to rediscover Ohm s law, Boyle s gas law, Kepler s law of planetary motion, Galileo s law of uniform acceleration Uses the plan-generate-test approach using a number of simple inference rules / rules of thumb for the generation of F Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 21

22 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining BACON: Example We have the following data for the period of revolution (P) of four of Jupiter s moons in relation to their mean distance (D) to the planet Moon Distance (D) Period (P) A B C D The task is to find a function F linking P to D Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 22

23 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining BACON: Example We have the following data for the period of revolution (P) of four of Jupiter s moons in relation to their mean distance (D) to the planet Moon Distance (D) Period (P) (D/P) (D 2 /P) (D 3 /P 2 ) A B C D The task is to find a function F linking P to D Solution: D 3 /P 2 = or D 3 / = P We have rediscovered Kepler s third law: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 23

24 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Robot Scientist Developed by the University of Aberystwyth Experiments can be designed by intelligent software and executed by the robot The results are analysed automatically by the software and are fed back into the next round of hypothesis formation and experimentation Theory generation uses inductive reasoning Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 24

25 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Machine Learning Inductive reasoning is not only useful for research, but for learning in general Machine Learning is the branch of Artificial Intelligence that is concerned with the development of algorithms that learn rules, behaviours, etc using inductive reasoning based on data (or using abductive reasoning) Important subcategories of machine learning: Learning to classify Pattern recognition Example applications: Recognition of faces, crop blights, mal-manufactured items Intelligent non-player characters in computer games Classification of DNA sequences Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 25

26 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Data Mining Machine learning is a key component of Data Mining Typically associated with the analysis of large amounts of data Additionally involves storing large amounts of data, data cleansing, data visualisation Aims to find previously unknown patterns (cluster analysis) unusual data records (anomaly detection) interdependencies in the data (association rule mining) Example applications: Advertising: To which offer/advertisement is a potential customer most likely to respond Basket analysis: What items are customers most likely to buy together Sensitive data: Finding a user s religious affiliations, political leanings, sexual orientation via analysis of social networking data Serious privacy concerns Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 26

27 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Data Mining: Example (People Analytics) Google applied data mining to the question Answer: 1 Be a good coach What makes a good team leader? 2 Empower your teams and don t micromanage 3 Express interest in team member s success and personal well-being 4 Don t be a sissy: be productive and results orientated 5 Be a good communicator and listen to your team 6 Help your employees with career development 7 Have a clear vision and strategy for the team 8 Have key technical skills so you can help your team ( 8 ) is the only surprise contradicts that good managers can manage anything also contradicts that technicals skills are the most important skills for a manager Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 27

28 Ind. generalisation Statistical syllogism Ind. reasoning in CS Machine Learning Data Mining Further reading For more on Inductive Reasoning see W. Hughes, J. Lavery, and K. Doran: Critical Thinking: An Introduction to the Basic Skills (6th revised ed). Broadview Press, Chapter 10 Ullrich Hustadt COMP110 Professional Skills in Computer Science L8 28