Related papers: Evolutionary State-Space Model and Its Application…
In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude…
The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
Electrophysiological brain signals, such as electroencephalography (EEG), exhibit both periodic and aperiodic components, with the latter often modeled as 1/f noise and considered critical to cognitive and neurological processes. Although…
Objective: Mixtures of temporally nonstationary signals are very common in biomedical applications. The nonstationarity of the source signals can be used as a discriminative property for signal separation. Herein, a semi-blind source…
Extracellular electrical potentials (EEP) recorded from the brain are an active manifestation of all cellular processes that propagate within a volume of brain tissue. A standard approach for their quantification are power spectral analyses…
Bayesian experimental design (BED) provides a principled framework for optimizing data collection by choosing experiments that are maximally informative about unknown parameters. However, existing methods cannot deal with the joint…
We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function with the…
Event cameras unlock new frontiers that were previously unthinkable with standard frame-based cameras. One notable example is low-latency motion estimation (optical flow), which is critical for many real-time applications. In such…
This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome…
Electromagnetic transient (EMT) simulation is a crucial tool for power system dynamic analysis because of its detailed component modeling and high simulation accuracy. However, it suffers from computational burdens for large power grids…
We perform approximate inference in state-space models with nonlinear state transitions. Without parameterizing a generative model, we apply Bayesian update formulas using a local linearity approximation parameterized by neural networks.…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
Recent State Space Models (SSMs) such as S4, S5, and Mamba have shown remarkable computational benefits in long-range temporal dependency modeling. However, in many sequence modeling problems, the underlying process is inherently modular…
Many modern time-series datasets contain large numbers of output response variables sampled for prolonged periods of time. For example, in neuroscience, the activities of 100s-1000's of neurons are recorded during behaviors and in response…
We investigate nonlinear prediction/regression in an online setting and introduce a hybrid model that effectively mitigates, via a joint mechanism through a state space formulation, the need for domain-specific feature engineering issues of…
This paper presents an examination of State Space Models (SSM) and Koopman-based deep learning methods for modelling the dynamics of both linear and non-linear stiff strings. Through experiments with datasets generated under different…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
Large Audio Language Models (LALM) combine the audio perception models and the Large Language Models (LLM) and show a remarkable ability to reason about the input audio, infer the meaning, and understand the intent. However, these systems…