# 🔬 deep_causality_algorithms 🔬
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A collection of computational causality algorithms used in
the [DeepCausality](https://github.com/deepcausality-rs/deep_causality) project. This crate provides tools for analyzing
and decomposing causal relationships in complex systems.
The cornerstone of this crate is `surd_states`, a high-performance Rust implementation of the **SURD-states algorithm**.
Based on the paper "Observational causality by states and interaction type for scientific discovery" (
martínezsánchez2025), this algorithm decomposes the mutual information between a set of source variables and a target
variable into its fundamental components: **S**ynergistic, **U**nique, and **R**edundant (**SURD**).
This decomposition allows for a deep, nuanced understanding of causal structures, moving beyond simple correlations to
reveal the nature of multi-variable interactions.
## Key Features
* **Faithful & Performant Implementation**: A high-performance, mathematically faithful Rust port of the SURD-states
algorithm, optimized for speed and memory efficiency.
* **Rich Causal Decomposition**: Decomposes the total causal influence into:
* **Redundant (R)**: Overlapping information provided by multiple sources.
* **Unique (U)**: Information provided by a single source independently.
* **Synergistic (S)**: New information that emerges only from the combination of sources.
* **State-Dependent Analysis**: Provides detailed state-dependent maps that reveal how causal influences change based on
the system's current state.
* **Information Leak Quantification**: Explicitly calculates the "information leak," which quantifies the influence of
unobserved variables or inherent randomness in the system.
* **Robust Incomplete Data Handling (CDL Variant)**: The `surd_states_cdl` function provides a variant of the
SURD-states algorithm specifically designed to gracefully manage missing or undefined probability values (`None` in
`CausalTensor<Option<f64>>`). This is crucial for real-world datasets where data incompleteness is common, allowing
for meaningful causal insights even with partial information by ignoring `None` values in calculations and propagating
uncertainty.
* **Minimum Redundancy Maximum Relevance (mRMR) Feature Selection**: Implements the mRMR algorithm to select features that are maximally relevant to a target variable and minimally redundant among themselves. The algorithm now returns a ranked list of features along with their normalized importance scores (between 0.0 and 1.0), providing a clear indication of each feature's contribution.
* **Performance Optimized**:
* **Algorithmic Capping**: Use the `MaxOrder` enum to limit the analysis to a tractable number of interactions (
e.g., pairwise), reducing complexity from exponential `O(2^N)` to polynomial `O(N^k)`.
* **Parallel Execution**: When compiled with the `parallel` feature flag, the main decomposition loop of the SURD algorithm and the feature selection loops of the mRMR algorithm run in parallel across all available CPU cores using `rayon`.
## Installation
```bash
cargo add deep_causality_algorithms
```
## Usage
The primary function is `surd_states`, which takes a `CausalTensor` representing a joint probability distribution and
returns a `SurdResult`.
```rust
use deep_causality_algorithms::{surd_states, MaxOrder};
use deep_causality_data_structures::CausalTensor;
// Create a joint probability distribution for a target and 2 source variables.
// Shape: [target_states, source1_states, source2_states] = [2, 2, 2]
let data = vec![
0.1, 0.2, // P(T=0, S1=0, S2=0), P(T=0, S1=0, S2=1)
0.0, 0.2, // P(T=0, S1=1, S2=0), P(T=0, S1=1, S2=1)
0.3, 0.0, // P(T=1, S1=0, S2=0), P(T=1, S1=0, S2=1)
0.1, 0.1, // P(T=1, S1=1, S2=0), P(T=1, S1=1, S2=1)
];
let p_raw = CausalTensor::new(data, vec![2, 2, 2]).unwrap();
// Perform a full decomposition (k=N=2)
let full_result = surd_states(&p_raw, MaxOrder::Max).unwrap();
// Print the detailed decomposition
println!("{}", &full_result);
// Access specific results
println!("Information Leak: {:.3}", full_result.info_leak());
// Synergistic information for the pair of variables {1, 2}
if let Some(synergy) = full_result.synergistic_info().get(&vec![1, 2]) {
println!("Synergistic Info for {{1, 2}}: {:.3}", synergy);
}
```
### Handling Incomplete Data with `surd_states_cdl`
For datasets containing missing or incomplete information, the `surd_states_cdl` function provides a robust solution. It
operates on `CausalTensor<Option<f64>>`, gracefully handling `None` values by ignoring them in calculations and
propagating uncertainty, allowing for causal discovery even with partial data.
```rust
use deep_causality_algorithms::{surd_states_cdl, MaxOrder};
use deep_causality_data_structures::CausalTensor;
// Create a joint probability distribution with missing data (None values).
// Shape: [target_states, source1_states, source2_states] = [2, 2, 2]
let data_with_nones = vec![
Some(0.1), Some(0.2), // P(T=0, S1=0, S2=0), P(T=0, S1=0, S2=1)
None, Some(0.2), // P(T=0, S1=1, S2=0) is missing, P(T=0, S1=1, S2=1)
Some(0.3), None, // P(T=1, S1=0, S2=0), P(T=1, S1=0, S2=1) is missing
Some(0.1), Some(0.1), // P(T=1, S1=1, S2=0), P(T=1, S1=1, S2=1)
];
let p_raw_with_nones = CausalTensor::new(data_with_nones, vec![2, 2, 2]).unwrap();
// Perform a full decomposition with None handling
let full_result_cdl = surd_states_cdl(&p_raw_with_nones, MaxOrder::Max).unwrap();
// Print the detailed decomposition
println!("CDL Result: {}", &full_result_cdl);
// Access specific results
println!("CDL Information Leak: {:.3}", full_result_cdl.info_leak());
```
### Minimum Redundancy Maximum Relevance (mRMR) Feature Selection
The mRMR algorithm is a powerful tool for selecting a subset of features that are maximally relevant to a target
variable and minimally redundant among themselves. This helps in reducing dimensionality and focusing causal analysis on
the most informative variables. The implementation now returns a ranked list of features along with their normalized importance scores (between 0.0 and 1.0).
```rust
use deep_causality_algorithms::mrmr::mrmr_features_selector;
use deep_causality_tensor::CausalTensor;
let data = vec![
10.0, 12.0, 1.0, 11.0,
20.0, 21.0, 5.0, 22.0,
30.0, 33.0, 2.0, 31.0,
40.0, 40.0, 8.0, 43.0,
50.0, 55.0, 3.0, 52.0,
];
let mut tensor = CausalTensor::new(data, vec![5, 4]).unwrap();
// Select 2 features, with the target variable in column 3.
let selected_features_with_scores = mrmr_features_selector(&mut tensor, 2, 3).unwrap();
println!("Selected Features and Scores: {:?}", selected_features_with_scores);
```
A higher mRMR score (and thus a higher normalized importance score)
indicates that the feature is not only highly relevant to the target but also
provides new, non-redundant information compared to the features already
chosen. It's a measure of a feature's unique and strong contribution to
predicting the target within the context of the selected feature set.
## From Discovery to Model: Connecting SURD to DeepCausality
The `surd_states` algorithm serves as a bridge from observational data to executable causal models with the
DeepCausality.
### 1. Mapping Causal Links to `CausaloidGraph` Structure
The aggregate SURD results inform the structure of the `CausaloidGraph`.
* A strong **unique** influence from `S1` to `T` suggests a direct edge: `Causaloid(S1) -> Causaloid(T)`.
* A strong **synergistic** influence from `S1` and `S2` onto `T` suggests a many-to-one connection where `Causaloid(S1)`
and `Causaloid(S2)` both point to `Causaloid(T)`.
* A high **information leak** suggests that the `Causaloid` for `T` should model a high degree of internal randomness or
dependency on an unobserved `Context`.
### 2. Mapping State-Dependency to `Causaloid` Logic
The state-dependent maps provide the exact conditional logic for a `Causaloid`'s `causal_fn`. For example, if SURD shows
that `S1`'s influence on `T` is strong only when `S1 > 0`, this condition can be programmed directly into the
`Causaloid`.
### 3. Modeling Multiple Causes with `CausaloidCollection`
SURD's ability to detect multi-causal relationships is perfectly complemented by the `CausaloidCollection`, which models
the interplay of multiple factors. The SURD results guide the choice of the collection's `AggregateLogic`:
* **Strong SYNERGY** (e.g., A and B are required for C) maps to `AggregateLogic::All` (Conjunction).
* **Strong UNIQUE or REDUNDANT** influences (e.g., A or B can cause C) maps to `AggregateLogic::Any` (Disjunction).
* **Complex mixed influences** (e.g., any two of three factors cause C) maps to `AggregateLogic::Some(k)` (Threshold).
In summary, `surd_states` provides the data-driven evidence to identify multi-causal structures, and the DeepCausality
primitives provide the formal mechanisms to build an executable model of that precise structure.
## Example: Decomposing Causal Structure
The crate includes a detailed example (`example_surd`) that demonstrates how to use the `surd_states` algorithm and,
more importantly, how to interpret its rich output. It runs through several test cases with different underlying causal
structures (e.g., synergistic, noisy, random) and explains what each part of the output means.
To run the example:
```bash
cargo run --example example_surd
```
For a detailed walkthrough of the output, see the [example's README](examples/README.md).
## 👨💻👩💻 Contribution
Contributions are welcomed especially related to documentation, example code, and fixes.
If unsure where to start, just open an issue and ask.
Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in deep_causality by you,
shall be licensed under the MIT licence, without any additional terms or conditions.
## 📜 Licence
This project is licensed under the [MIT license](LICENSE).
## 👮️ Security
For details about security, please read
the [security policy](https://github.com/deepcausality-rs/deep_causality/blob/main/SECURITY.md).
## 💻 Author
* [Marvin Hansen](https://github.com/marvin-hansen).
* Github GPG key ID: 369D5A0B210D39BC
* GPG Fingerprint: 4B18 F7B2 04B9 7A72 967E 663E 369D 5A0B 210D 39BC