ishanu chattopadhyay

Digital Twin of the Human Microbiome

University of Chicago Medicine

Nicholas Sizemore

Kaitlyn Oliphant

Erika Claud

pip install qbiome

import qbiome
from qbiome.data_formatter import DataFormatter
from qbiome.quantizer import Quantizer
from qbiome.qnet_orchestrator import QnetOrchestrator
from qbiome.forecaster import Forecaster

mathematics

computer science

social science

medicine

AI/ML learning theory and applications

Complex systems

Implication of AI in Future of Societay

University of Chicago Medicine

The Laboratory for Zero Knowledge Discovery

THE PROBLEM

Can microbial assay from gut actionably

pre-empt developmental markers?

Assuming a 1000 species ecosystem, and 1 successful experiment every day to discern a single two-way relationship, we would need 1,368 years to go through all possibilities. If we look for 3 way interactions, we would need 454,844 years

This is a general method!

\Phi_i:\prod_{j \neq i} \Sigma_j \rightarrow \mathcal{D}(\Sigma_i)

E-Net

recursive forest

E-distance

a biologically informed, adaptive distance between strains

\theta(x,y) \triangleq \\ \mathbf{E}_i \left ( \mathbb{J}^{\frac{1}{2}} \left (\Phi_i^P(x_{-i}) , \Phi_i^Q(y_{-i})\right ) \right )

This distance is "special"

smaller distances imply a quatitatively high probability of spontaneous jump

$$J \textrm{ is the Jensen-Shannon divergence }$$

Sanov's Theorem & Pinsker's Inequality

Theorem

\left \vert \ln \frac{Pr(x \rightarrow y ) }{Pr( y \rightarrow y)} \right \vert \leqq \beta \theta(x,y)

\left \vert \ln \frac{Pr(x_a \rightarrow x_h ) }{Pr( x_h \rightarrow x_h)} \right \vert \approx 0 \\ \Rightarrow Pr(x_a \rightarrow x_h ) \approx Pr(x_h \rightarrow x_h ) \\ \color{green}\Rightarrow Pr(x_a \rightarrow x_h ) \approx 1

stable profile $x_{h}$, "well-adapted" $\Rightarrow Pr(x_h\rightarrow x_h) \approx 1 $

For "new" profile $x_{a}$, $ \displaystyle \theta(x_{a},x_{h}) \approx 0 $

Assume:

Then, we have:

we can tell if new profile will be stable

A Math Solution to a Hard Biological Problem

Biology-aware Perturbations to "reconstruct" missing data