Ishanu Chattopadhyay PRO
ML | Data Science Biomedical Informatics | Social Science | Assistant Professor
Large Science Models:
A General Framework for Generative Modeling of Microbiome-Metabolome systems
Ishanu Chattopadhyay, PhD
Assistant Professor of Biomedical Informatics & Computer Science
University of Kentucky
What is a healthy Microbiome/ Metabolome?
Can gut microbiota pre-empt developmental deficits?
High Abundance Classes
Complex Interdependecies Exist over time and taxonomic strata
quantized output levels
Purely wet-lab investigations are insufficient to understand complex ecosystems
We need to scale up!
We need a digital twin
of the dataset
-
Learn from uncurated data
-
understand non-trvial cross-dependencies between entities, without prior knowledge
-
can explore valid perturbations of the overall system
-
can identify deviations from "normal" behavior
-
Can model out-of-box targeted and untargeted metabolites (or uncharacterized microbes)
Can microbial assay from gut actionably
pre-empt developmental deficit?
Study Set-up
Predicting neurodevelopmental deficits
Forecasting ecosystem trajectories
Build classifiers
Ability to "fill in" missing data is equivalent to making trajectory forecasts
Forecast ecosystem fluctuations
Large Science Models
- Consider a large number (\(n\)) of coupled observables
- We dont know potential couplings a priori
- Compute all \(x_i \vert x_1,\cdots,x_{i-1},x_{i+1},\cdots, x_n\) conditionals
-
Estimate the joint distribution of all variables
Brook’s lemma*
*Brook, D. (1964). On the distinction between the conditional probability and the joint probability distribution. Journal of the Royal Statistical Society. Series B (Methodological), 26(2), 295–307.
perfect inference of these conditionals gives us a unique joint
The central problem of ML is computing joint distributions or estimates thereof
hard!
How Complex Are These Models?
Hundreds of thousands to 10s of millions of features
The Goal: Create a digital twin which can reveal valid perturbations
\psi_0
\psi_t
Completely uninformative state
Observed state
?
\rho(x) =\frac{\theta_\mathcal{H}(\psi_0,x)}{\theta_\mathcal{D}(\psi_0,x)}
Risk
Geometric Interpretation
LSM-based Risk
- Infer LSM for typical development
- Infer LSM for disease trajectories
\mathcal{H}
\mathcal{D}
How different are the individual estimators for typical and dysbiotic models?
Bacilli 30
typical
deficit
Coriobacteria 32
typical
deficit
Gammaproteobacteria 32
typical
deficit
All Patients
Feeding Variables added
Forecasting of class abundance variations both
in-sample (\( R^2 \ge 95\%\))
and out-of sample (\(R^2\ge 72\%\))
Forecasting of class abundance variations both
in-sample (\( R^2 \ge 95\%\))
and out-of sample (\(R^2\ge 72\%\))
Building classifier based on LSM metric
moving the top drivers impact risk of deficit maximally
Understanding Key Drivers via LSM perturbations
Just add those microbes back?
No! The LSM indicates that supplantations need to be patient specific
No transplantation is guaranteed to work reliably
Predicted to reduce
risk reliably
Predicted to reduce
risk reliably
Network Interpretations? We see clear differences between two cases
Typical
Deficit
Integrating Clinical Features
IBD Metabolomics: Preliminary Results
Dataset from Metabolomics Workbench
| Study ID | ST000923 |
|---|---|
| Study Title | Longitudinal Metabolomics of the Human Microbiome in Inflammatory Bowel Disease |
| Institute | Broad Institute of MIT and Harvard |
|---|---|
| Last Name | Avila-Pacheco |
| First Name | Julian |
| Submit Date | 2017-11-14 |
| Num Groups | 3 |
| Total Subjects | 546 |
| Num Males | 276 |
| Num Females | 270 |
| Analysis Type Detail | LC-MS |
State-of-art microbiome based Classification (~10 species) *
| IBD vs UC | 0.82 |
| IBD vs CD | 0.76 |
*Zheng, J., et al. (2024). Noninvasive, microbiome-based diagnosis of inflammatory bowel disease. Nature Medicine, 30(12), 3555–3567. https://doi.org/10.1038/s41591-024-03280-4
| IBD vs non IBD | 0.85 |
Gut-Metabolome based Classification (~36 metabolites) *
Application 2
Large Science Models
1. How will proposer form and maintain a computationally tractable LSM tree structure given, as proposed, hundreds to thousands of observable variables?
\(\checkmark\)
- Each predictor is inferred independently
- Can scale up to thousands of variables in Python implementation
- Further scale-up \(10^6 - 10^8\) needs C/C++ implementation
https://34.66.189.202/data/trees_mbol_UC
Full Example of Hyperlinked Trees
Metabolomics
LSM model
- No. parameters: 70 million
- Out of sample n=150
- Uses all names and unnamed metabolites (>81K features)
| AUC (out of sample) | |
|---|---|
| Healthy vs IBD | 96.1% |
| Healthy vs UC | 92% |
| UC vs CD | 99% |
| Healthy vs CD | 99% |
Metabolomics
LSM model
- No. parameters: 70 million
- Out of sample n=150
- Uses all names and unnamed metabolites (>81K features)
| AUC (out of sample) | |
|---|---|
| Healthy vs IBD | 96.1% |
| Healthy vs UC | 92% |
| UC vs CD | 99% |
| Healthy vs CD | 99% |
Metabolomics
Insight: the discriminating hypersurface is 2d (almost 1d)
| Number of metabolites | 5,280 | 85% untargeted metabolites |
|---|---|---|
| Number of parameters | 4,002,306 | |
| Average Tree Depth | 38.62 | |
| Number of constraints inferred | 108,884 | ~83% involve untargeted metabolites |
| Number of samples used | 180 | (no clinical phenotype information used) |
-
Using all samples of metabolite profiles
-
Not using clinical phenotypes and replicates
Application 3
ASD Metabolics: Preliminary Results
R_{\mathcal A}(y)
:=
\|L(y)\|_2
=
\left(
\sum_{k=1}^K
\bigl[-\log \Pr(a_k\to y)\bigr]^2
\right)^{1/2}
ASD Metabolics: Preliminary Results
ASD sample profile
ASD samples from same patient
sample profile of new patient \(y\)
Pr(a \rightarrow y)
Need one patient!
Predictive Performance
| AUC | Sensitivity at 95% spec | |
|---|---|---|
| LSM | 92.7% | 74% |
| MCHAT/F | 67% | 39% |
| ADOS-2 | 90-97% | 85% |
getting close to the gold standard
1 false positive
1 false negative
10% flag in TBD (expected 8.3% positives)
Predictive Performance
Top risk drivers mapped to known pathways
P_x(m_j) = \frac{\partial R(x)}{\partial m_j}
Patient specific driver profile
\displaystyle P(m_j) = \frac{1}{N} \sum_x P_x(m_j)
Average driver profile
Top 30 risk drivers (targeted met.)
Tissue and Serum Metabolomics (Targeted and Untargeted) in Fibrotic Interstitial Lung Disease (F-ILD)
Uncovering latent geometry separating disease phenotypes
Application 4
Tissue and Serum Metabolomics (Targeted and Untargeted) in Fibrotic Interstitial Lung Disease (F-ILD)
Learn LSM with tissue samples -> Can disambiguate serum samples
LSM model for healthy profiles
What is a healthy Microbiome/ Metabolome?
\mathcal{H}
Any profile generated by \(\mathcal{H}\) is a healthy profile, while they might be different from one another
A Universal Risk Index
\theta_\mathcal{H}(\psi_\star,x)
average healthy profile
A New Paradigm of AI-driven Discovery in Metabolome Biology
Supplantation MUST be bacteroidia
Supplantation MUST be Actinobacteria
No risk-decreasing supplantation
*Hothorn, Torsten, Kurt Hornik, and Achim Zeileis. "Unbiased recursive partitioning: A conditional inference framework." Journal of Computational and Graphical statistics 15, no. 3 (2006): 651-674.
LSM Forest of Conditional Inference Trees*
Revealing Emergent Cross-talk between mutations in a viral protein (Influenza A HA)
Component predictor (Conditional Inference Tree*)
Example: Influenza A HA protein
Large Science Models: Properties
LSM-Distance Metric*
\theta(\psi,\psi') \triangleq \frac{1}{N}\sum_{i=1}^{N} \sqrt{D_{JS}\Bigl(\phi^i(\psi^{-i}) \vert \vert \phi^i(\psi'^{-i})\Bigr)}
where \(D_{JS}(P\vert \vert Q)\) is the Jensen-Shannon divergence.
g_{ij}(\psi) \;=\; \frac{1}{2}\,\frac{\partial^2}{\partial \psi^i\,\partial \psi^j}\,\theta^2(\psi,\psi')\Biggr|_{\psi'=\psi}
\left \lvert \ln \frac{\Pr(\psi\to \psi')}{\Pr(\psi' \rightarrow \psi')}\right \rvert \le \beta\,\theta(\psi,\psi')
Large Deviation Bound*
Induced Riemannian metric tensor
This bound connects ``closeness'' of samples to the odds of perturbing from one to the other, bridging geometry to dynamics
Ergodic Projection
\psi_\star \triangleq \bigotimes_{i=1}^N\phi^i\left (\prod_{1}^{N-1}\varnothing\right )
(Sanov's Theorem, Pinkser's Inequality)
\(\psi\)
\(\psi'\)
\(\theta\)
"spatial average": average of all plausible worldviews or states
* Sizemore, Nicholas, Kaitlyn Oliphant, Ruolin Zheng, Camilia R. Martin, Erika C. Claud, and Ishanu Chattopadhyay. "A digital twin of the infant microbiome to predict neurodevelopmental deficits." Science Advances 10, no. 15 (2024): eadj0400. https://www.science.org/doi/full/10.1126/sciadv.adj0400
persistence probability
Ergodic dispersion
\Psi_\star = \theta(\psi,\psi_\star)
Central to Model Drift Quantification
Start with opinion vector with all entries missing
This is a standard Physics construct, quantifying curvature of the underlying latent geometry
Pr(\psi \rightarrow \psi')
Easily computable in LSM framework!
Apply \(\phi^i\)
Random variable quantifying dispersion around the spatial average of worlviews
const. scaling as \(N^2\)
Digital Twin Inference
- Consider ecosystem of many inbitants
- The abundunce of each entity is a variable
- The variables interact in complex ways
- We are going to model this cross-talk
The LSM Framework
\Phi_i:\prod_{j \neq i} \Sigma_j \rightarrow \mathcal{D}(\Sigma_i)
Q-Net
recursive forest
Proposed Concept
- Develop Foundation models of complex systems with
- hundreds to thousands of evolving variables with apriori unknown cross-talk
- no governing equations are know a priori
- reflexivity: system changes if observed
- Learn intrinsic system geometry from data
- Derive equations of motion with variational principles (stationary action on Lagrangian).
- Inference under data sparsity
- Detect data (in)sufficiency, adapt to model drift
- Support forward simulation and perturbation analysis
Data inference boundaries & limitations
Alignment validation
Complex phenomena
Adaptation to model obsolence
Precise validation protocols to assess process drift triggering re-calibration/training
Built-in flexibility for changing contexts and non-ergodicity
Scalable to thousands to millions of variables, intrinsic reflexivity
Component LSM predictors enforce statistical significance of splits in recursive partitioning, ensuring precise uncertainty quantification
*Hothorn, Torsten, Kurt Hornik, and Achim Zeileis. "Unbiased recursive partitioning: A conditional inference framework." Journal of Computational and Graphical statistics 15, no. 3 (2006): 651-674.
emergent macro-structure
Component predictor (Conditional Inference Tree*)
Example: Influenza A HA protein
Recursive
LSM
forest
LSM Forest of Conditional Inference Trees*
Revealing Emergent Cross-talk
Large Science Models: Mathematical Framework
\begin{aligned}
\text{Observables:} \quad & \color{yellow}X = \{x^1, \ldots, x^N\}, \overbrace{x^i \in \Sigma^i}^{\text{finite alphabet}} \\
{\color{gray}\text{Notation:} }\quad & \color{gray} x^{-i} = \{x^j : j \ne i\}\\
\text{Crosstalk:} \quad & \forall i \ P(x^i) = \color{red} f_i(x^{-i}) \\
\text{System state:} \quad & \color{Cyan} \psi = \bigotimes_{i=1}^N \psi^i, \quad \psi^i \in \mathscr{D}(\Sigma^i) \cup \varnothing \\
%\textbf{Degenerate case:} \quad & \psi^i \text{ is a delta distribution (fully observed)} \\
{\color{gray}\text{Notation:} }\quad & \color{gray}\psi^{-i} = \bigotimes_{j \ne i} \psi^j
\end{aligned}
| reliten | gunlaw | abany | --- | grass | |
|---|---|---|---|---|---|
| Person 1 | |||||
| Person 2 | |||||
| --- | |||||
| Person m |
observables
samples
Distributions over alphabet \(\Sigma^i\)
\phi = \bigotimes_{i=1}^N \phi^i, \quad \phi^i(\psi^{-i}) \in \mathscr{D}(\Sigma^i) \\
Individual Predictor (CIT)
cross-talk
\phi(\psi) \vert \vert \psi
Tension between predicted and observed distribution drives change
Example
GSS topic: There should be more gun-control
\(\psi^i\)
| strongly agree | agree | neutral | disagree | strongly disagree |
\Sigma^i
Digital Twin
\phi^i(\psi^{-i}) \sim \widetilde{\psi}^i
\(\phi\) estimates \(\psi\)
Examples: GSS, ANES, WVS, ESS, Eurobarometer, Afrobarometer, Asian Barometer etc
group
individual
estimate is always a non-empty non-degenerate distribution
missing observation
Large Science Models: Properties
LSM-Distance Metric*
\theta(\psi,\psi') \triangleq \frac{1}{N}\sum_{i=1}^{N} \sqrt{D_{JS}\Bigl(\phi^i(\psi^{-i}) \vert \vert \phi^i(\psi'^{-i})\Bigr)}
where \(D_{JS}(P\vert \vert Q)\) is the Jensen-Shannon divergence.
g_{ij}(\psi) \;=\; \frac{1}{2}\,\frac{\partial^2}{\partial \psi^i\,\partial \psi^j}\,\theta^2(\psi,\psi')\Biggr|_{\psi'=\psi}
\left \lvert \ln \frac{\Pr(\psi\to \psi')}{\Pr(\psi' \rightarrow \psi')}\right \rvert \le \beta\,\theta(\psi,\psi')
Large Deviation Bound*
Induced Riemannian metric tensor
This bound connects ``closeness'' of samples to the odds of perturbing from one to the other, bridging geometry to dynamics
Ergodic Projection
\psi_\star \triangleq \bigotimes_{i=1}^N\phi^i\left (\prod_{1}^{N-1}\varnothing\right )
(Sanov's Theorem, Pinkser's Inequality)
\(\psi\)
\(\psi'\)
\(\theta\)
"spatial average": average of all plausible worldviews or states
* Sizemore, Nicholas, Kaitlyn Oliphant, Ruolin Zheng, Camilia R. Martin, Erika C. Claud, and Ishanu Chattopadhyay. "A digital twin of the infant microbiome to predict neurodevelopmental deficits." Science Advances 10, no. 15 (2024): eadj0400. https://www.science.org/doi/full/10.1126/sciadv.adj0400
persistence probability
Ergodic dispersion
\Psi_\star = \theta(\psi,\psi_\star)
Central to Model Drift Quantification
Start with opinion vector with all entries missing
This is a standard Physics construct, quantifying curvature of the underlying latent geometry
Pr(\psi \rightarrow \psi')
Easily computable in LSM framework!
Apply \(\phi^i\)
Random variable quantifying dispersion around the spatial average of worlviews
const. scaling as \(N^2\)
Digital Twin & Fidelity of Simulation
\mathcal{N}_\epsilon(\psi) \triangleq \big\{ \psi': {\color{red}\forall i \ \psi'_i \sim \phi^i\left ( \psi^{-i}\right )}
\wedge {\color{yellow} \theta(\psi,\psi') \leqq \epsilon }\big \}
Sample predicted distributions
perturbed state within \(\epsilon\) of \(\psi\)
Digital Twin
-Neighborhood of state \(\psi\)
\epsilon
Definition
Sample neighborhood to impute missing data
\psi
\epsilon
}
LSM sampling: sampling the \(\epsilon\)-neighborhood of a state or worldview allows reconstruction of censored opinions
Predictive ability of LSM quantified as ability to reconstruct censored out-of-sample observations
{\color{Tomato}\psi_\star }\rightarrow \psi \rightarrow \cdots \rightarrow \psi'
Null state (all missing observations)
Valid perturbations/ simulations
LSM sampling allows simulating opinion perturbations
Global Emergent Structure via Clusters & Poles
2018 GSS
\theta_t(\psi_+,\psi_-)
Polar separation over time
2016 Presidential Election Vote Prediction
2004
| abany | no | yes |
| abdefctw | always wrong | not wrong at all |
| abdefect | no | yes |
| abhlth | no | yes |
| abnomore | no | yes |
| abpoor | no | yes |
| abpoorw | always wrong | not wrong at all |
| abrape | no | yes |
| absingle | no | yes |
| bible | inspired word | book of fables |
| colcom | fired | not fired |
| colmil | not fired | not allowed |
| comfort | strongly agree | strongly disagree |
| conlabor | hardly any | a great deal |
| godchnge | believe now, always have | don't believe now, never have |
| grass | not legal | legal |
| gunlaw | oppose | favor |
| intmil | very interested | not at all interested |
| libcom | remove | not remove |
| libmil | not remove | remove |
| maboygrl | true | false |
| owngun | yes | no |
| pillok | agree | strongly agree |
| pilloky | strongly disagree | strongly agree |
| polabuse | no | yes |
| pray | several times a day | never |
| prayer | disapprove | approve |
| prayfreq | several times a day | never |
| religcon | strongly disagree | strongly agree |
| religint | strongly disagree | strongly agree |
| reliten | strong | no religion |
| rowngun | yes | no |
| shotgun | yes | no |
| spkcom | not allowed | allowed |
| spkmil | allowed | not allowed |
| taxrich | about right | much too low |
conservative pole
\psi_+
liberal pole
\psi_-
Clustering LSM distance \(\theta(x,y)\) between out-of-sample individuals
conservative
liberal
poles:
partial states aligning with extreme opposing worldviews
- Compare across time and different GSS surveys
- Derived features for individuals (ideology index)
I(x) = \frac{\theta(x,\psi_+) - \theta(x,\psi_-)}{\theta(\psi_+,\psi_-)}
Predict 2016 votes using ideology index
Emergent global structure
Reflexivity and State Collapse on Observation
Emergent Equations of Motion
L \triangleq \frac{1}{2} \sum_i g_{kl} P^k_p \dot{\psi}^p_i P^l_n \dot{\psi}^n_i - \theta(\psi, \phi)
Define Lagrangian*
\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{\psi}^m_i} \right) - \frac{\partial L}{\partial \psi^m_i} = 0
Via the Euler-Lagrange Equations\(^\dag\):
\ddot{\psi}^m_i = -g^{km} P^k_m \frac{1}{2N} \sum_j \frac{1}{\sqrt{D_{JS}(\psi^m_j \| \phi^m_j)}} \left[ \ln\left( \frac{2e\psi^m_j}{\psi^m_j + \phi^m_j} \right) - \frac{1}{2(\psi^m_j + \phi^m_j)} \right]
Over-damped Gradient flow Equation*
where \(-g^{km}\) is the inverse metric tensor
kinetic energy
state collapse
strongly agree
agree
neutral
disagree
strongly disagree
strongly agree
agree
neutral
disagree
strongly disagree
Query/
Observation
\(X_i\)
Non-local Influence propagation on measurement/observation (QM-like)
\phi^i(\psi^{-i})
potential energy
* Einstein notation used
Goldstein, Herbert, et al. Classical Mechanics. 3rd ed., Pearson, 2002.
\(^\dag\)
Principle of stationary action
Dynamics
Local potential field eqn
Local Potential Fields
Stable
(captured by local extrema)
Free to move locally towards extrema
GSS 2018 individuals and neighborhoods
Influenza C : strains and their neighborhoods
Observation: This lineage (Mississippi lineage) is now extinct since 2022/23
stable lineage
Local potential fields can be computed given the LSM and dynamical considerations, which reveal future evolution
Data Sufficiency via Conservation of Complexity
%K(x) = K(S) + K(x \vert S_\star) + O(1) = K(S') + K(x \vert S'_\star) +O(1)
K(x \vert S_\star) = O(1) = K(S \vert x_\star)
The No-cheating Thorem: Generative models cannot cheat on complexity
Kolmogorov Complexity
Optimal Generative Model
compressed data representation
compressed model representation
Theorem
K(\textrm{data}) = K(\textrm{LSM}) +O(1)
Conservation Law arising from the continuous symmetry of typicality*
\mu_0(X) \triangleq \frac{\delta(\vert \langle S(X) \rangle \vert)}{\delta(\vert \langle X \rangle \vert)} \leq 1
Saturation relation:
Data Sufficiency Statistic \(\mu_0\)
We need LSM-sampling to calculate this
*Noether's Theorem
For every continuous symmetry of a physical system, there exists a corresponding conserved quantity
\vert \langle X' \rangle \vert \approx \max\{1,\mu_0(X)\} \vert \langle X \rangle \vert
How much more data do we need?
Data saturation
Data deficient
Needed
Current
Empirical Validation
Model Drift Quantification
Ergodic dispersion
\Delta_\star = \theta(\Psi,\psi_\star)
z(\Delta_\star) = \frac{\Delta_\star^{[t]} - \langle \Delta_\star^{[t]} \rangle}{\sigma(\Delta_\star^{[t]} )}
Z-value of dispersion
Do new samples (survey respondents) still conform to the model?
GSS Model drift
ergodic projection (all missing values)
A random belief state (with possibly missing entries)
random variable
normal variate
\zeta(M) = \vert z(\Delta_\star^0) - z(\Delta_\star^{[t]}) \vert
Model drift stochastic process (\(\zeta\))
\mathbf{E}(\zeta(M) )
assess if \(\zeta\) is stationary: if not then new samples are not conforming to model
Example for GSS LSM inferred for year 2000
Large Science Models & Ergodicity
\(\checkmark\) 4. Address whether your approach makes assumptions regarding ergodicity, and if so, how these assumptions affect the model's applicability to non-ergodic systems.
No Convergence
(~50% belief mismatch between pairs)
2018 GSS survey belief vectors simulated via LSM sampling
- No ergodicity assumption: LSMs are built for non-ergodic systems
- Sampling and simuation "remembers" the start point (No convergence), demonstrating non-ergodic learned structure
- Local potential fields vary across the space
- Potential wells may arise, driven by the dynamics at hand, not via assumptions
- "change" is driven by non-equilibrium (dissonance)
Embedded Social Theories in LSM
When applied to Social Modeling and Opinion Dynamics
-
Belief about topic iii is expected to align with beliefs about other topics \(\displaystyle\psi^{-i}\).
Deviations are exponentially improbable \(\Rightarrow \) people/groups seek internal coherence. -
Theory Link:
-
Cognitive consistency theory – Abelson et al. (1968)
-
Constraint satisfaction in beliefs – Read & Marcus-Newhall (1993)
-
-
Beliefs evolve to minimize tension between actual state and “expected” state.
Reflexive gradient flow — system reduces internal contradiction. -
Theory Link:
-
Cognitive Dissonance Theory – Festinger (1957)
-
Homeostatic belief adjustment – Gawronski & Strack (2004)
-
-
Observing a belief changes it and affects all conditionals.
Direct encoding of feedback loops central to human systems. -
Theory Link:
-
Reflexivity in social systems – Giddens (1984), Soros (1994)
-
Theory of mind / mutual modeling – Premack & Woodruff (1978)
-
Validation of Social Theory Questions:
- Perception changes reality, which changes perception
- The Constitution of Society
- The Alchemy of Finance
- Does a chimpanzee have a theory of mind?
- Our system “wants” to reach a low-energy (low-dissonance) state — a direct computational analog of Festinger’s theory.
- People strive to align beliefs and attitudes across related domains. Inconsistencies create cognitive discomfort, prompting adjustments across belief clusters to restore harmony.
| Exploratory: Belief systems react measurably to exogenous events and shocks |
Exploratory: Cross-dependencies between beliefs have observable effects on societal resilience.
Is Polarization an Inevitable Attractor?
Social Identity Theory vs. Belief Proximity
Large Science Models: Broader Applications
A General Framework for modeling Complex Systems
Genomic database: Missing heritability problem
Personalized Clinical Digital Twin, Virtual Patients
Any structured interview, PTSD fabrication
Assess sysmptom data and co-pathologies
Predict future mutations; which animal strain is closest to jumping to humans
Mental health diagnosis
Microbiome Analysis**
Algorithmic lie detector
Viral emergence
Teomims
Opinion Dynamics
Darkome
Generative model of complex microbial ecosystems, and their impact on health and disease
Data requirements
- Tabular data
- Potentially large number of features/covariates (\(10^2 - 10^8 \))
- Sufficient number of samples (\(10^3 - 10^6\))
- Small number of longitudinal samples (currently, \( < 100\))
| Limitation | Mitigation / Response |
|---|---|
| Conventional time series is currently out-of-scope | Focus on cross-sectional interdependencies and belief geometry; time handled via drift |
| LSMs model statistical interdependence, not causal mechanisms | Use perturbation-based simulations to infer plausible influence pathways |
| Limited by observed belief variables | Integrate multiple surveys; use latent proxies and test sensitivity of digital twins |
| Social theory connections and interpretability may be challenging | Anchor dynamics with theory-driven constructs (e.g., ToM, cognitive dissonance) |
LSMs for complex systems
**preliminary study published (https://www.science.org/doi/10.1126/sciadv.adj0400)
LSM-metabolomics
By Ishanu Chattopadhyay
LSM-metabolomics
DARPA-EA-25-02-05-MAGICS-PA-025
