arXiv subjects

Mishfad Shaikh Veedu

Publications and source records attributed to Mishfad Shaikh Veedu.

4 recordsLinked to original sources

arXiv2025

Uncovering the Influence Flow Model of Transistor Amplifiers, Its Reconstruction and Application

Multistage transistor amplifiers can be effectively modeled as network of dynamic systems where individual amplifier stages interact through couplings that are dynamic in nature. Using circuit analysis techniques, we show that a large class of transistor amplifiers can be modeled as Linear Dynamic Influence Model (LDIM), where the interactions between different amplifier stages are modeled as linear dynamic equations. LDIM modeling of transistor circuits leads to application of data-driven network reconstruction techniques to characterize stage interactions and identify faults and critical circuit parameters efficiently. Employing graphical modeling techniques and Wiener filtering, we demonstrate that the network structure can be reconstructed solely from voltage time-series measurements sampled at specified points in the circuit. The efficacy of these network reconstruction methods in multistage amplifiers is demonstrated through extensive simulations involving multiple amplifier circuits in Cadence, as well as experimental results on physical hardware. The ability to infer network structure directly from measurement data offers designers and users efficient tools to design, analyze, and debug amplifier circuits. To demonstrate the utility of network reconstruction in multistage amplifier circuits, a fault diagnosis method leveraging these techniques is presented.

eess.SY↗

arXiv2024

Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphs

In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG (DDAG). In particular, we consider a DDAG where the nodal dynamics are driven by unobserved exogenous noise sources that are wide-sense stationary (WSS) in time but are mutually uncorrelated, and have the same {power spectral density (PSD)}. Inspired by the static DAG setting, a metric and an algorithm based on the PSD matrix of the observed time series are proposed to reconstruct the DDAG. It is shown that the optimal sample complexity (or length of state trajectory) needed to learn the DDAG is $n=Θ(q\log(p/q))$, where $p$ is the number of nodes and $q$ is the maximum number of parents per node. To prove the sample complexity upper bound, a concentration bound for the PSD estimation is derived, under two different sampling strategies. A matching min-max lower bound using generalized Fano's inequality also is provided, thus showing the order optimality of the proposed algorithm.

stat.ML↗

arXiv2023

Causal Structure Recovery of Linear Dynamical Systems: An FFT based Approach

Learning causal effects from data is a fundamental and well-studied problem across science, especially when the cause-effect relationship is static in nature. However, causal effect is less explored when there are dynamical dependencies, i.e., when dependencies exist between entities across time. Identifying dynamic causal effects from time-series observations is computationally expensive when compared to the static scenario. We demonstrate that the computational complexity of recovering the causation structure for the vector auto-regressive (VAR) model is $O(Tn^3N^2)$, where $n$ is the number of nodes, $T$ is the number of samples, and $N$ is the largest time-lag in the dependency between entities. We report a method, with a reduced complexity of $O(Tn^3 \log N)$, to recover the causation structure to obtain frequency-domain (FD) representations of time-series. Since FFT accumulates all the time dependencies on every frequency, causal inference can be performed efficiently by considering the state variables as random variables at any given frequency. We additionally show that, for systems with interactions that are LTI, do-calculus machinery can be realized in the FD resulting in versions of the classical single-door (with cycles), front and backdoor criteria. We demonstrate, for a large class of problems, graph reconstruction using multivariate Wiener projections results in a significant computational advantage with $O(n)$ complexity over reconstruction algorithms such as the PC algorithm which has $O(n^q)$ complexity, where $q$ is the maximum neighborhood size. This advantage accrues due to some remarkable properties of the phase response of the frequency-dependent Wiener coefficients which is not present in any time-domain approach.

cs.LG↗

arXiv2023

Topology Identification under Spatially Correlated Noise

This article addresses the problem of reconstructing the topology of a network of agents interacting via linear dynamics, while being excited by exogenous stochastic sources that are possibly correlated across the agents, from time-series measurements alone. It is shown, under the assumption that the correlations are affine in nature, such network of nodal interactions is equivalent to a network with added agents, represented by nodes that are latent, where no corresponding time-series measurements are available; however, here all exogenous excitements are spatially (that is, across agents) uncorrelated. Generalizing affine correlations, it is shown that, under polynomial correlations, the latent nodes in the expanded networks can be excited by clusters of noise sources, where the clusters are uncorrelated with each other. The clusters can be replaced with a single noise source if the latent nodes are allowed to have non-linear interactions. Finally, using the sparse plus low-rank matrix decomposition of the imaginary part of the inverse power spectral density matrix (IPSDM) of the time-series data, the topology of the network is reconstructed. Under non conservative assumptions, the correlation graph is retrieved.

eess.SY↗