Abel Jansma
In a recent paper, I proposed to study complex systems through a mereological lens by applying the Möbius inversion theorem. I also covered this in a recent blogpost. Here, I will collect some of the most important applications of Möbius transformations in the sciences. I will update this table as...
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Preamble Probably, one of the most fundamental issue in classical statistical mechanics is extending reversible dynamics to many-particle systems that behaves irreversibly. In other words, how time's arrow appears even though constituted systems evolves in reversible dynamics. This is the main...
Abel Jansma
In my PhD thesis, I developed a method and software package to infer interactions and cell states from gene expression data. Both the software and the research are now published! The software is called Stator, and comprises the Stator Nextflow pipeline, as well as a bespoke Shiny app developed by...
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Dominos in motion (Wikipedia)Preamble The definition of weighted directed graphs (wDAGs) provides a great opportunity to express causal relationships among given variates. Usually this is expressed as SCMs, Structural Causal Model or in more generally causal model. A given causal model can be...
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Preamble David Hume (Wikipedia)Experimental design is not a new concept and randomised control trials (RCTs) are our solid gold standard of doing quantitative research, when no apparent physical laws are available to validate observations. However, it is very expensive to design RCTs, not ethical...
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Preamble Fractal Tree (Wikipedia)A quiet causal inference revolution is underway in industry. We see immense success of transformers deep learning architectures. However their success should also be attributed to causal modelling. Large Language Models (LLMs), specially closed-sourced ones,...
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Boltzmann (Wikipedia)Post covers the papers: H-theorem do-conjecture, M. Süzen, arxiv:2310.01458 (2023) PreambleProbably the most important achievement for humans is the ability to produce scientific discoveries, that helps us objectively understand how nature works and build artificial tools...
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Preamble Babylonian Tablet for square root of 2. (Wikipedia)Prediction implies a mechanics, as in knowing a form of a trajectory over time. Strictly speaking a predictive system implies knowing a solution to the path, set of variable depending on time, time evolution of the system under...
Abel Jansma
Generative models, in particular energy-based models, are often used to sample from conditional distributions–a process known as inpainting. One of the most fundamental kinds of generative energy-based models is called a restricted Boltzmann machine (RBM), which is essentially a bipartite, glassy...
Aram’s Lair of Mad Science
Apologies for taking so long to follow up on the probability post. I was floored by its engagement on Hacker News, with over 200 thoughtful comments! I’ve revised the post to incorporate all your feedback. Now to unveil the secret behind that post: it was a part of my preparation for a very...
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Preamble George Boole (Wikipedia)Agent, AI agent or an intelligent agent is used often to describe algorithms or AI systems that are released by research teams recently. However, the definition of an intelligent agent (IA) is a bit opaque. Naïvely thinking, it is nothing more than a decision...
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Domino OR-gate (Wikipedia)PreambleA trained model may provide predictions about input values it may never seen before but it isn't an inference, at least for 'classical' supervised learning. In reality it provides an interpolation from the training-set, i.e., via function...
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Preamble One of the main tenants of practical data science is performing statistical inference on data sets which are assumed to be representations of populations of activity, natural or man-made. A specific case is called causal inference, which probably the core interest of decision makers...