Causal Discovery with Single-Parent Decoding for Temporal Data: An Identifiable Causal Representation Learning Approach

Centrala begrepp

Causal Discovery with Single-parent Decoding (CDSD) is a novel method for learning causal representations from temporal data by leveraging a sparsity assumption (single-parent decoding) to achieve identifiability of both the latent representation and the causal graph over these latents.

Sammanfattning

• Bibliographic Information: Brouillard, P., Lachapelle, S., Kaltenborn, J., Gurwicz, Y., Sridhar, D., Drouin, A., Nowack, P., Runge, J., & Rolnick, D. (2024). Causal Representation Learning in Temporal Data via Single-Parent Decoding. arXiv preprint arXiv:2410.07013v1.
• Research Objective: This paper introduces CDSD, a differentiable causal discovery method that learns both latent variables and their causal graph from time series data by leveraging a single-parent decoding assumption, where each observed variable is affected by only one latent variable.
• Methodology: CDSD utilizes a variational autoencoder (VAE) framework with a constrained optimization problem to enforce the single-parent decoding structure. It parameterizes the latent-to-observable graph using a weighted adjacency matrix constrained to be non-negative with orthonormal columns. The causal graph over latent variables is learned through continuous optimization using a Bernoulli distribution parameterized by learnable parameters. The model is trained end-to-end using stochastic gradient descent.
• Key Findings: The authors prove theoretically that the single-parent decoding assumption enables the identification of the latent representation up to permutation and coordinate-wise transformations, as well as the temporal causal graph over the latents. Empirical evaluations on synthetic data demonstrate CDSD's superior performance compared to Varimax-PCMCI, especially in scenarios with nonlinear relationships between latents and observables. Additionally, CDSD outperforms identifiable representation methods like iVAE and DMS on synthetic data adhering to the single-parent decoding assumption. In a real-world climate science application using NOAA's MSLP dataset, CDSD successfully recovers spatially coherent regions corresponding to known climate phenomena and infers plausible causal links between them.
• Main Conclusions: CDSD presents a promising approach for causal representation learning from temporal data, particularly in scientific domains where identifying meaningful latent structures and their causal relationships is crucial. The single-parent decoding assumption, while strong, proves valuable for achieving identifiability and leads to interpretable results in practical applications.
• Significance: This work contributes significantly to causal representation learning by introducing a novel method with theoretical guarantees for identifiability. It demonstrates the potential of leveraging sparsity assumptions for disentangling causal relationships in complex systems and offers a valuable tool for scientific discovery.
• Limitations and Future Research: The study acknowledges limitations regarding assumptions like stationarity and single-parent decoding, which might not always hold in real-world scenarios. Future research could explore the robustness of CDSD to violations of these assumptions. Additionally, developing methods for automatically determining hyperparameters like the number of latent variables and the order of the stationary process would enhance the method's practicality.

Statistik

CDSD achieves a high MCC ≥0.95 in all linear settings.
Varimax-PCMCI requires over 24 hours for a single experiment with nonlinear dynamics and 1000 samples.
Varimax-PCMCI fails to recover the latent representation with nonlinear decoding, achieving poor MCC and SHD.
CDSD successfully clusters climate variables into geographically connected regions, unlike models without constraints.

Citat

"The challenge is that this task, called causal representation learning, is highly underdetermined from observational data alone, requiring other constraints during learning to resolve the indeterminacies."
"In this work, we consider a temporal model with a sparsity assumption, namely single-parent decoding: each observed low-level variable is only affected by a single latent variable."
"A key innovation of this paper is that, with our sparse mapping assumption, we can identify the latents up to some benign indeterminacies (e.g., permutations) as well as the temporal causal graph over the latents."

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Causal Representation Learning in Temporal Data via Single-Parent Decoding

by Phil... på arxiv.org 10-10-2024

https://arxiv.org/pdf/2410.07013.pdf

Djupare frågor

How could CDSD be adapted to handle non-stationary temporal data, where the underlying causal relationships might change over time?

Adapting CDSD to handle non-stationary temporal data, where the causal relationships themselves change over time, presents a fascinating challenge and a valuable direction for future research. Here are a few potential strategies:

Sliding Window Approach: Instead of assuming a single global causal graph G, we could employ a sliding window approach. This would involve learning separate causal graphs G(t) for different time segments. The size of the window would need careful consideration, balancing the need to capture local stationarity with the ability to adapt to changing dynamics.

Time-Varying Graph Parameters: We could allow the parameters of the causal graph G to vary over time. For instance, instead of a fixed adjacency matrix Γ, we could have Γ(t), where the entries evolve according to some function of time. This function could be parameterized and learned alongside the other model parameters. Techniques like recurrent neural networks (RNNs) or temporal convolutional networks (TCNs) could be incorporated to capture temporal dependencies in the evolution of Γ(t).

Changepoint Detection: Integrate changepoint detection algorithms into the CDSD framework. These algorithms could identify potential points in time where the underlying causal structure might have shifted. The model could then be re-trained or adapted on segments defined by these changepoints.

State-Space Models: Explore the integration of state-space models, such as Hidden Markov Models (HMMs) or their nonlinear counterparts, into the CDSD framework. These models provide a natural way to represent systems with both observed and hidden states, where the hidden states can govern the evolution of the causal structure over time.

Each of these approaches comes with its own set of challenges and trade-offs. For example, introducing more flexibility to handle non-stationarity might increase the complexity of the model and require more data for robust learning.

While the single-parent decoding assumption offers identifiability benefits, could it be overly restrictive in certain domains, and are there alternative sparsity constraints that could be explored?

You are right, while the single-parent decoding assumption is powerful for identifiability in CDSD, it can indeed be overly restrictive in domains where observations are influenced by multiple latent factors.
Here's why it can be limiting and some alternative sparsity constraints:
Limitations of Single-Parent Decoding:

Complex Interactions: In many real-world systems, observed variables are a result of complex interplay between multiple underlying factors. Forcing a single latent parent might oversimplify the true generative process.
Loss of Information: Enforcing a one-to-one mapping from latent to observed variables (in the extreme case) could lead to a loss of information, especially if the dimensionality of the latent space is much smaller than that of the observed space.
Alternative Sparsity Constraints:

Sparse Multi-Parent Decoding: Instead of limiting each observed variable to a single parent, allow a small, fixed number of latent parents. This could be implemented by modifying the orthogonality constraint on W to allow for a limited number of non-zero entries per row.
Group Sparsity: Encourage the latent variables to influence distinct groups of observed variables. This could be achieved by adding a group sparsity-inducing regularizer, such as the Group LASSO, to the objective function during the learning of W.
Hierarchical Sparsity: Explore hierarchical sparsity structures, where latent variables at different levels of a hierarchy influence increasingly larger groups of observed variables. This could be suitable for domains with inherent hierarchical structures.
Structure Learning on F: Instead of imposing a fixed sparsity pattern on F, learn the structure of F alongside G. This would provide more flexibility but might require additional assumptions or regularization to ensure identifiability.

Trade-offs to Consider:
The choice of sparsity constraint involves a trade-off between identifiability, model flexibility, and computational complexity. Relaxing the single-parent assumption might make the model more expressive but could also make it more challenging to guarantee identifiability.

Considering the successful application of CDSD in climate science, what other scientific fields could benefit from this approach to uncover hidden causal structures and advance our understanding of complex systems?

The success of CDSD in climate science, particularly in identifying spatially localized regions of influence, suggests its potential applicability to a wide range of scientific fields grappling with complex systems and high-dimensional data. Here are a few promising areas:

Neuroscience:

Brain Imaging Analysis: CDSD could be used to analyze fMRI or EEG data to identify functional brain regions (analogous to climate zones) and uncover causal relationships between them during cognitive tasks.
Neural Population Dynamics: Understanding how different groups of neurons interact and influence each other is crucial for deciphering brain function. CDSD could help disentangle these complex interactions from recordings of neural activity.

Genomics:

Gene Regulatory Networks: CDSD could be applied to gene expression data to infer causal relationships between genes and identify regulatory modules, providing insights into cellular processes and disease mechanisms.
Single-Cell Analysis: With the rise of single-cell sequencing technologies, CDSD could help uncover causal dependencies within individual cells, leading to a deeper understanding of cellular heterogeneity and function.

Ecology:

Ecosystem Dynamics: CDSD could be used to model the complex interactions between species within an ecosystem, identifying keystone species and predicting the effects of environmental changes.
Spatial Ecology: Similar to its application in climate science, CDSD could help analyze spatial patterns in ecological data, identifying regions of influence and understanding how species distributions are causally linked.

Social Sciences:

Social Network Analysis: CDSD could be adapted to analyze social network data, identifying influential individuals or groups and understanding how information or opinions spread through the network.
Causal Inference in Observational Studies: In fields like economics or sociology, where controlled experiments are often not feasible, CDSD could offer a way to infer causal relationships from observational data.

Finance:

Market Dynamics: CDSD could be applied to financial time series data to identify groups of assets that exhibit similar behavior and uncover causal relationships between them, potentially leading to improved risk management and investment strategies.

These are just a few examples, and the potential applications of CDSD extend to many other fields where understanding causal relationships in complex systems is paramount.