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Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
Temporal causal analysis means understanding the underlying causes behind observed variables over time. Deep learning based methods such as transformers are increasingly used to capture temporal dynamics and causal relationships beyond mere…
Graph topology inference of network processes with co-evolving and interacting time-series is crucial for network studies. Vector autoregressive models (VAR) are popular approaches for topology inference of directed graphs; however, in…
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. However, we show that the current SRG analysis suffers from a pitfall that limits its applicability in analyzing…
The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
Traditionally, statistical and causal inference on human subjects rely on the assumption that individuals are independently affected by treatments or exposures. However, recently there has been increasing interest in settings, such as…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
Despite the great successes of deep learning, the effectiveness of deep neural networks has not been understood at any theoretical depth. This work is motivated by the thrust of developing a deeper understanding of recurrent neural…
Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…
Time series forecasting is difficult. It is difficult even for recurrent neural networks with their inherent ability to learn sequentiality. This article presents a recurrent neural network based time series forecasting framework covering…
We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a…
When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent…
In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…
Modeling inter-dependencies between time-series is the key to achieve high performance in anomaly detection for multivariate time-series data. The de-facto solution to model the dependencies is to feed the data into a recurrent neural…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. There have been recent efforts to generalize SRG analysis to Multiple-Input Multiple-Output (MIMO) systems. However,…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
While it is widely recognised that linear (structural) VARs may fail to capture important aspects of economic time series, the use of nonlinear SVARs has to date been almost entirely confined to the modelling of stationary time series,…