Causal Discovery using Compression-Complexity Measures

Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences X and Y. We present a framework which relies on lossless compressors for inferring context-free grammars (CFGs) from sequence pairs and quantifies the extent to which the grammar inferred from one sequence compresses the other sequence. We infer X causes Y if the grammar inferred from X better compresses Y than in the other direction. To put this notion to practice, we propose three models that use the Compression-Complexity Measures (CCMs) - Lempel-Ziv (LZ) complexity and Effort-To-Compress (ETC) to infer CFGs and discover causal directions. We evaluate these models on synthetic and real-world benchmarks and empirically observe performances competitive with current state-of-the-art methods. Lastly, we present a unique application of the proposed models for causal inference directly from pairs of genome sequences belonging to the SARS-CoV-2 virus. Using a large number of sequences, we show that our models capture directed causal information exchange between sequence pairs, presenting novel opportunities for addressing key issues such as contact-tracing, motif discovery, evolution of virulence and pathogenicity in future applications.

A Neurochaos Learning Architecture for Genome Classification

There has been empirical evidence of presence of non-linearity and chaos at the level of single neurons in biological neural networks. The properties of chaotic neurons inspires us to employ them in artificial learning systems. Here, we propose a Neurochaos Learning (NL) architecture, where the neurons used to extract features from data are 1D chaotic maps. ChaosFEX+SVM, an instance of this NL architecture, is proposed as a hybrid combination of chaos and classical machine learning algorithm. We formally prove that a single layer of NL with a finite number of 1D chaotic neurons satisfies the Universal Approximation Theorem with an exact value for the number of chaotic neurons needed to approximate a discrete real valued function with finite support. This is made possible due to the topological transitivity property of chaos and the existence of uncountably infinite number of dense orbits for the chosen 1D chaotic map. The chaotic neurons in NL get activated under the presence of an input stimulus (data) and output a chaotic firing trajectory. From such chaotic firing trajectories of individual neurons of NL, we extract Firing Time, Firing Rate, Energy and Entropy that constitute ChaosFEX features. These ChaosFEX features are then fed to a Support Vector Machine with linear kernel for classification. The effectiveness of chaotic feature engineering performed by NL (ChaosFEX+SVM) is demonstrated for synthetic and real world datasets in the low and high training sample regimes. Specifically, we consider the problem of classification of genome sequences of SARS-CoV-2 from other coronaviruses (SARS-CoV-1, MERS-CoV and others). With just one training sample per class for 1000 random trials of training, we report an average macro F1-score > 0.99 for the classification of SARS-CoV-2 from SARS-CoV-1 genome sequences. Robustness of ChaosFEX features to additive noise is also demonstrated.