Utilising software to enhance your research

1. Utilising software to enhance your research Eamonn Hynes 5th November, 2012

2. Basic statistics and some parallel computing

3. Basic statistics • Probability • Mean • Standard deviation • Simple examples: • Probability of just one six from three throws of a die? • Probability of winning the Lotto • Tougher problems: • Transcribing speech into words • Poker robot that plays optimally

4. Hands on Mean of column 1? Mean of row 4? Standard deviation of column 3?

5. Standard deviation 13.6%

6. A billion numbers? • Single-core • Multi-core Memory Memory Eight cores Single core

7. More interesting example • Again, a large sequence of numbers • Speech signal • ~56 Different sounds • Task is to calculate the most likely sequence of words • Over 50 years of research

8. Moore’s Law

9. Demise of Moore’s Law • Reality

10. Moore’s Law • The solution: • Parallel architectures • Hybrid architectures • New software – harder to write • New programming paradigms • Dedicated hardware • Beyond silicon

11. Amdhal’s Law • Limitations on parallel code • Thankfully a large number of problems are parallel in nature (rendering 3D graphics, weather prediction, image processing, DNA matching) • But many problems are sequential in nature! • e.g. card game, legal process, ordering a laptop, etc. • Nothing we can do except increase clock rate!

12. Clustering

13. Clustering • Categorise data into groups • Important in many fields – speech, medical statistics, data mining, etc. • Very loose algorithm (k-means clustering): • Let each point be a cluster centroid • Pick a random point • Get point closest to this chosen point • Calculate centroid • Repeat until just kcentroids • Big limitation: k must be specified in advance… • Example

14. Clustering • Not just for points on a 2d surface • Pixels of an image • Example

15. Support Vector Machines • Support vector machines (SVMs) • Popular in the 1990s/2000s (Vapnik et al. 1992) • Non-linear classification • Beautiful maths • Find a nonlinear boundary between k sets of points • Example

16. Text analysis

17. Text analysis • Searching documents task • Naïve search: • SQL query: “SELECT * FROM articles WHERE body LIKE '%$keyword%';” • Works fine for small document collections • Large databases: Better to index all documents • tf-idf

18. Text analysis • Process each document • Calculate the frequency of each word • Store the index, not the entire document • Much faster document retrieval • Intuitive to pick document with highest term count • Must weight each document by the inverse document frequency

19. Text analysis • Example: Simple Boolean logic • Searching for “rose” • If word appears, then document is relevant

20. Text analysis • Taking term frequencies into account

21. Text analysis TFIDF = TF * IDF where: TF = C/T where C = number of times a given word appears in a document and T = total number of words in a document IDF = D/DF where D = total number of documents in a corpus, and DF = total number of documents containing a given word

22. Text analysis • Natural language follows a Zipfian distribution

23. Finally

24. Deep belief networks • Given a document, how to find similar documents? • Deep belief networks (DBNs) • State-of-the-art in machine learning • More advanced than Latent Semantic Analysis (LSA) Principal Component Analysis (PCA) and clustering

25. Deep belief networks • 2000 most common word stems fed into base layer • Gradual reduction in number of neurons • Left with a 30-digit binary representation of a document with 2000-dimension feature vector • Super fast document retrieval (“semantic hashing”) Images from G. Hinton, Science (2006)

26. Images from G. Hinton, Science (2006)