Mastodawn

Our paper on "Central subspace data depth" is posted in arXiv at https://arxiv.org/abs/2601.14947
#StatisticalDataDepth
#CentralSubspace
#Symmetry
#Statistics
#DimensionReduction
#ProjectionPursuit

Central subspace data depth

Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the data and as input to further statistical analysis. An important property of data depth is related to symmetric distributions as the point with the highest depth value, the center, coincides with the point of symmetry. However, there are applications in which it is more natural to consider symmetry with respect to a subspace of a certain dimension rather than to a point, i.e. a subspace of dimension zero. We provide a general framework to construct statistical data depths which attain maximum value in a subspace, providing a center-outward ordering from that subspace. We refer to these data depths as central subspace data depths. Moreover, if the distribution is symmetric with respect to a subspace, then the depth is maximized at that subspace. We introduce general notions of symmetry about a subspace for distributions, study the properties of central subspace data depths and provide asymptotic convergence for the corresponding sample versions. Additionally, we discuss connections with projection pursuit and dimension reduction. An application based on custom data fraud detection shows the importance of the proposed approach and strengthens its potential.

arXiv.org

Victoria Stuart 🇨🇦 🏳️‍⚧️Apr 29, 2025

Minimal Genetic Circuit for Cellular Anticipation
https://www.biorxiv.org/content/10.1101/2025.04.22.649979v1?rss=1

Circuit design in biology and machine learning. I. Random networks and dimensional reduction
https://arxiv.org/abs/2408.09604

Steven A. Frank
https://stevefrank.org/
https://en.wikipedia.org/wiki/Steven_Frank_(biologist)
https://en.wikipedia.org/wiki/Reservoir_computing

Biological circuit to anticipate trend
https://academic.oup.com/evlett/article/8/5/719/7697097

#SyntheticBiology #SyntheticCircuits #ReservoirComputing #EvolutionTheory #ML #DimensionReduction #biocomputing #SteveFrank

A Minimal Genetic Circuit for Cellular Anticipation

Living systems have evolved cognitive complexity to reduce environmental uncertainty, enabling them to predict and prepare for future conditions. Anticipation, distinct from simple prediction, involves active adaptation before an event occurs and is a key feature of both neural and non-neural biological agents. Recent work by Steven Frank proposed a minimal anticipatory mechanism based on the moving average convergence-divergence principle from financial markets. Here, we implement this principle using synthetic biology to design and evaluate minimal genetic circuits capable of anticipating environmental trends. Through deterministic and stochastic analyses, we demonstrate that these motifs achieve robust anticipatory responses under a wide range of conditions. Our findings suggest that simple genetic circuits could be naturally exploited by cells to prepare for future events, providing a foundation for engineering predictive biological systems. ### Competing Interest Statement The authors have declared no competing interest.

bioRxiv

Dick Smiths Fair Go Supporters Feb 16, 2022

How would you do DimensionReduction #AI in #FOSS?

Do you find the minimal number of examples of a thing (eg. for #computerVision 1000 photos of a thing that best represents it) for #dimensionReduction and supply those with the #sourceCode?

Is the reduced dimension result enough?

We would assume that the former is needed, for it to be FOSS.