Monday, 11 August 2025
The Fresh Air of Mathematics
Machine Learny Language: Exchangeable RVs
The concept of exchangeable random variables is commonplace but the terminology might seem new.
An exchangeable sequence of random variables is one in which any re-ordering of any finite sequence results in the same joint probability function.
An alternative phrasing of this is the joint distribution is invariant to finite permutation.
The term exchangeable was a neologism at the time of its inception in the 1920s in a book on Logic written by an alumnus of Kings College, Cambridge, where said coiner of said term studied mathematics.
Tuesday, 5 August 2025
The Kantarovich Paradox, Expressed in FAAM
Wednesday, 9 July 2025
Revisiting Map Reduce
Map reduce is very prevalent in distributed data processing.
It's an idea from functional programming. The basic idea is you have a map function that can apply a filter to a list, and then apply a summary operation, which is the reduce.
A Mickey Mouse example to bring this to life could be - you have list of fishing vessels, you want to filter for foreign flags, and then you want to add them all up, and you want to do this every 6 hours and create a time series database of this data.
A popular open source implementation is Apache Hadoop.
Thursday, 3 July 2025
The Autoregressive Nature of LLM Operations
LLMs are AUTOREGRESSIVE generative models.
An autoregression is a regression of a variable against its own lagged values.
For example, an AR(1) predicts the current value based on the immediately preceding value, AR(n) uses the n most recent values.
One remarkable feature of these models is in-context learning, which has been hypothesised as being Bayesian in nature.
The Python Datasets library
Hugging Face has a Python datasets library which has natural language training data sets amongst others.
Tuesday, 11 March 2025
Designing an Experiment - Single and Double Blind Trials
Single-blind and double-blind trials relate to how experiments are set up.
- Double-blind - where neither subjects nor experimenters know who is in TEST or CONTROL group
- Single-blind - only the subjects (e.g.. patients in a medical study) know which group they are in
Tuesday, 4 March 2025
Coding with Bilinear Maps
When Pycryptonistas advance beyond the familiar realm of linear algebra to the new realm of multilinear algebra there are terms that must be mastered post haste to make sense of the new environs.
Amongst these terms is the term bilinear map a simple sounding term but oddly not widely socialised even among linear algebra aficionados.
A bilinear map is a function that combines elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments. Matrix multiplication is an example.
To be confident in bilinear maps you should be able to product multiple examples of bilinear maps from basic mathematics.