Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the underlying causal graph is acyclic. While this is a convenient framework for developing theoretical developments about causal reasoning and inference, the underlying modeling assumption is likely to be violated in real systems, because feedback loops are common (e.g., in biological systems). Although a few methods search for cyclic causal models, they usually rely on some form of linearity, which is also limiting, or lack a clear underlying probabilistic model. In this work, we propose a novel framework for learning nonlinear cyclic causal graphical models from interventional data, called NODAGS-Flow. We perform inference via direct likelihood optimization, employing techniques from residual normalizing flows for likelihood estimation. Through synthetic experiments and an application to single-cell high-content perturbation screening data, we show significant performance improvements with our approach compared to state-of-the-art methods with respect to structure recovery and predictive performance.
@inproceedings{sethuraman2023nodags,booktitle={Twenty Sixth International Conference on Artificial Intelligence and Statistics (AISTATS)},title={NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning},author={Sethuraman, Muralikrishnna G. and Lopez, Romain and Mohan, Rahul and Fekri, Faramarz and Biancalani, Tommaso and Hütter, Jan-Christian},year={2023},selected={true},pdf={https://proceedings.mlr.press/v206/sethuraman23a/sethuraman23a.pdf},code={https://github.com/Genentech/nodags-flows},video={https://youtu.be/IUE5TFnzLpg},bibtex_show={true}}
A Density Evolution Framework for Recovery of Covariance and Causal Graphs from Compressed Measurements
Sethuraman, Muralikrishnna G., Zhang, Hang, and Fekri, Faramarz
In Fifty Ninth Annual Allerton Conference on Communication, Control, and Computing 2023
In this paper, we propose a general framework for designing sensing matrix A, for estimation of sparse covariance matrix from compressed measurements of the form y = Ax + n. By viewing covariance recovery as inference over factor graphs via message passing algorithm, ideas from coding theory, such as Density evolution (DE), are leveraged to construct a framework for the design of the sensing matrix. The proposed framework can handle both (1) regular sensing, i.e., equal importance is given to all entries of the covariance, and (2) preferential sensing, i.e., higher importance is given to a part of the covariance matrix. Through experiments, we show that the sensing matrix designed via density evolution can match the state-of-the-art for covariance recovery in the regular sensing paradigm and attain improved performance in the preferential sensing regime. Additionally, we study the feasibility of causal graph structure recovery using the estimated covariance matrix obtained from the compressed measurements.
@inproceedings{allerton,booktitle={Fifty Ninth Annual Allerton Conference on Communication, Control, and Computing},url={https://arxiv.org/abs/2203.09636},author={Sethuraman, Muralikrishnna G. and Zhang, Hang and Fekri, Faramarz},title={A Density Evolution Framework for Recovery of Covariance and Causal Graphs from Compressed Measurements},year={2023},copyright={Creative Commons Attribution 4.0 International},bibtex_show={true},selected={true},pdf={allerton_final_version.pdf},supp={supplementary_notes_allerton.pdf},slides={allerton-presentation.pdf}}
2022
2021
Visual Question Answering based on Formal Logic
Sethuraman, Muralikrishnna G., Payani, Ali, Fekri, Faramarz, and Kerce, J. Clayton
In 2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA) 2021
Visual question answering (VQA) has been gaining a lot of traction in the machine learning community in the recent years due to the challenges posed in understanding information coming from multiple modalities (i.e., images, language). In VQA, a series of questions are posed based on a set of images and the task at hand is to arrive at the answer. To achieve this, we take a symbolic reasoning based approach using the framework of formal logic. The image and the questions are converted into symbolic representations on which explicit reasoning is performed. We propose a formal logic framework where (i) images are converted to logical background facts with the help of scene graphs, (ii) the questions are translated to first-order predicate logic clauses using a transformer based deep learning model, and (iii) perform satisfiability checks, by using the background knowledge and the grounding of predicate clauses, to obtain the answer. Our proposed method is highly interpretable and each step in the pipeline can be easily analyzed by a human. We validate our approach on the CLEVR and the GQA dataset. We achieve near perfect accuracy of 99.6% on the CLEVR dataset comparable to the state of art models, showcasing that formal logic is a viable tool to tackle visual question answering. Our model is also data efficient, achieving 99.1% accuracy on CLEVR dataset when trained on just 10% of the training data
@inproceedings{9680048,author={Sethuraman, Muralikrishnna G. and Payani, Ali and Fekri, Faramarz and Kerce, J. Clayton},booktitle={2021 20th IEEE International Conference on Machine Learning and Applications (ICMLA)},title={Visual Question Answering based on Formal Logic},year={2021},volume={},number={},pages={952-957},doi={10.1109/ICMLA52953.2021.00157},pdf={https://ieeexplore.ieee.org/abstract/document/9680048},bibtex_show={true},selected={true},supp={supplementary_materials_v1.pdf}}
2018
Batch Look Ahead Orthogonal Matching Pursuit
G.S., Muralikrishnna, Ambat, Sooraj K., and Hari, K.V.S.
In 2018 Twenty Fourth National Conference on Communications (NCC) 2018
Compressed sensing (CS) is a sampling paradigm that enables sampling signals at sub Nyquist rates by exploiting the sparse nature of signals. One of the main concerns in CS is the reconstruction of the signal after sampling. Many reconstruction algorithms have been proposed in the literature for the recovery of the sparse signals - Basis Pursuit, Orthogonal Matching Pursuit (OMP), Look Ahead Orthogonal Matching Pursuit (LAOMP) are some of the popular reconstruction algorithms. LAOMP, a modification of OMP, improves the reconstruction accuracy of OMP by employing a look ahead procedure. But LAOMP suffers from the drawback of being very expensive in terms of the computational time. In this paper we propose a modified version of the LAOMP algorithm called Batch-LAOMP which has a lesser computational complexity and also gives better performance in terms of reconstruction accuracy as seen from the results of the numerical experiments.
@inproceedings{8600087,author={G.S., Muralikrishnna and Ambat, Sooraj K. and Hari, K.V.S.},booktitle={2018 Twenty Fourth National Conference on Communications (NCC)},title={Batch Look Ahead Orthogonal Matching Pursuit},year={2018},volume={},number={},pages={1-5},doi={10.1109/NCC.2018.8600087},pdf={https://ieeexplore.ieee.org/abstract/document/8600087},bibtex_show={true}}