Malik Shahid Sultan

Malik Shahid Sultan, Samuel Horvath, Hernando Ombao

Dependence between nodes in a network is an important concept that pervades many areas including finance, politics, sociology, genomics and the brain sciences. One way to characterize dependence between components of a multivariate time series data is via Granger Causality (GC). Standard traditional approaches to GC estimation / inference commonly assume linear dynamics, however such simplification does not hold in many real-world applications where signals are inherently non-linear. In such cases, imposing linear models such as vector autoregressive (VAR) models can lead to mis-characterization of true Granger Causal interactions. To overcome this limitation, Tank et al (IEEE Transactions on Pattern Analysis and Machine Learning, 2022) proposed a solution that uses neural networks with sparse regularization penalties. The regularization encourages learnable weights to be sparse, which enables inference on GC. This paper overcomes the limitations of current methods by leveraging advances in machine learning and deep learning which have been demonstrated to learn hidden patterns in the data. We propose novel classes of models that can handle underlying non-linearity in a computationally efficient manner, simultaneously providing GC and lag order selection. Firstly, we present the Learned Kernel VAR (LeKVAR) model that learns kernel parameterized by a shared neural net followed by penalization on learnable weights to discover GC structure. Secondly, we show one can directly decouple lags and individual time series importance via decoupled penalties. This is important as we want to select the lag order during the process of GC estimation. This decoupling acts as a filtering and can be extended to any DL model including Multi-Layer Perceptrons (MLP), Recurrent Neural Networks (RNN), Long Short Term Memory Networks (LSTM), Transformers etc, for simultaneous GC estimation and lag selection.

Sarbojit Roy, Malik Shahid Sultan, Hernando Ombao

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which can be restrictive for real-world applications. In this article, we propose a model-based approach for classifying high-dimensional stationary time series by assuming sparsity in the difference between inverse SDMs. Our approach emphasizes the interpretability of model parameters, making it especially suitable for fields like neuroscience, where understanding differences in brain network connectivity across various states is crucial. The estimators for model parameters demonstrate consistency under appropriate conditions. We further propose using standard deep learning optimizers for parameter estimation, employing techniques such as mini-batching and learning rate scheduling. Additionally, we introduce a method to screen the most discriminatory frequencies for classification, which exhibits the sure screening property under general conditions. The flexibility of the proposed model allows the significance of covariates to vary across frequencies, enabling nuanced inferences and deeper insights into the underlying problem. The novelty of our method lies in the interpretability of the model parameters, addressing critical needs in neuroscience. The proposed approaches have been evaluated on simulated examples and the `Alert-vs-Drowsy' EEG dataset.

Md Nurul Muttakin, Malik Shahid Sultan, Robert Hoehndorf et al.

Generative Adversarial Networks are used for generating the data using a generator and a discriminator, GANs usually produce high-quality images, but training GANs in an adversarial setting is a difficult task. GANs require high computation power and hyper-parameter regularization for converging. Projected GANs tackle the training difficulty of GANs by using transfer learning to project the generated and real samples into a pre-trained feature space. Projected GANs improve the training time and convergence but produce artifacts in the generated images which reduce the quality of the generated samples, we propose an optimized architecture called Stylized Projected GANs which integrates the mapping network of the Style GANs with Skip Layer Excitation of Fast GAN. The integrated modules are incorporated within the generator architecture of the Fast GAN to mitigate the problem of artifacts in the generated images.

Malik Shahid Sultan, Hernando Ombao

Granger Causality (GC) offers an elegant statistical framework to study the association between multivariate time series data. Linear Vector Autoregressive models (VAR) though have nice interpretation properties but have limited practical application due to underlying assumptions on the kind of associations that can be captured by these models. Numerous attempts have already been made in the literature that exploit the functional approximation power of Deep Neural Networks (DNNs) for the task of GC estimation. These methods however treat GC as a variable selection problem. We present a novel paradigm for approaching GC. We present this idea that GC is essentially linked with prediction and if a deep learning model is used to model the time series collectively or jointly, a well regularized model may learn the true granger causal structure from the data, given that there is enough training data. We propose to uncover the learned GC structure by comparing the model uncertainty or distribution of the residuals when the past of everything is used as compared to the one where a specific time series component is dropped from the model. We also compare the effect of input layer dropout on the ability of a neural network to learn granger causality from the data. We show that a well regularized model infact can learn the true GC structure from the data without explicitly adding terms in the loss function that guide the model to select variables or perform sparse regression.