Density Estimation via Measure Transport: Applications in Biological Sciences

Główne pojęcia

Measure transport methods offer a unified framework for processing and analyzing data distributed according to various probability measures, with applications in biological sciences.

Streszczenie

The content discusses the advantages of measure transport methods for density estimation in biological sciences. It presents computational studies on using triangular transport maps to support research in radiation biology. The article outlines the benefits of adaptive transport maps and their potential in uncovering hidden information in limited sample data sets. Various measure transport techniques are explored, including normalizing flows, gradient flows, and invertible neural networks.

1. Introduction

   • Density estimation is crucial across scientific fields.
   • Known parametric density functions may not capture complex data features.

2. Optimal Measure Transport

   • Minimizes cost of transporting one measure to another.
   • Offers explicit formulas for unknown probability densities.

3. Triangular Transport Maps

   • Efficiently compute sparse transport maps.
   • Useful for conditional density estimation and sampling.

4. Application to Gene Expression Data

   • Utilizes gene pathways from KEGG database to construct Bayesian networks.
   • Incorporates prior knowledge into sparse transport map construction.

5. Experimental Results

   • Classification results using sparse transport maps informed by gene relationships.

6. Conclusion

   • Adaptive transport maps offer flexibility when prior knowledge is uncertain or lacking.

Statystyki

"18 are in the zero-dose category, 87 are in the low-dose category, and 16 are in the high-dose category."
"121 human blood samples"
"5 gene pathways from the KEGG database"

Cytaty

"A measure transport approach offers a unified density estimation framework capable of characterizing a diverse range of properties."
"Adaptive transport maps provide more flexibility when prior knowledge about gene relationships is lacking or uncertain."

Kluczowe wnioski z

Density Estimation via Measure Transport

by Vanessa Lope... o arxiv.org 03-26-2024

https://arxiv.org/pdf/2309.15366.pdf

Głębsze pytania

How can measure transport methods be applied beyond biological sciences

Measure transport methods can be applied beyond biological sciences in various fields such as finance, climate science, image processing, and natural language processing. In finance, measure transport techniques can be used for risk assessment and portfolio optimization by modeling the distribution of financial data. In climate science, these methods can help analyze complex weather patterns and model changes in environmental variables. In image processing, measure transport can aid in tasks like image registration and object recognition by aligning images from different sources or time points. Lastly, in natural language processing, these techniques can assist in text analysis and machine translation by mapping distributions of words or phrases.

What are potential drawbacks or limitations of enforcing sparsity patterns based on prior knowledge

Enforcing sparsity patterns based on prior knowledge may have limitations when the relationships between variables are not well understood or when there is uncertainty about the structure of the target probability space. If the imposed sparsity pattern does not accurately capture all relevant dependencies among genes or variables, it could lead to biased results and hinder the ability to uncover new insights from the data. Additionally, enforcing strict sparsity patterns may limit the flexibility of the model to adapt to unexpected relationships or interactions within the data set.

How can adaptive transport maps contribute to understanding complex relationships between genes

Adaptive transport maps offer a flexible approach to understanding complex relationships between genes by allowing for an exploration of different dependence structures without imposing preconceived notions about variable interactions. By dynamically adjusting to the underlying data distribution during training, adaptive transport maps can capture intricate dependencies that may not be captured by fixed sparsity patterns based on prior knowledge alone. This adaptability enables researchers to uncover hidden gene relationships and dynamics under specific conditions like radiation exposure without being constrained by predefined assumptions about gene interactions.