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

Basic statistics and some parallel computing

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

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

Standard deviation 13.6%

A billion numbers? Single-core Multi-core Eight cores Single core Memory

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

Moore’s Law

Demise of Moore’s Law Reality

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

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!

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 k centroids Big limitation: k must be specified in advance… Example

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

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

Text analysis

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

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

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

Text analysis Taking term frequencies into account

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

Text analysis Natural language follows a Zipfian distribution

Finally

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

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)