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This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a…

State-space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several…

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…

Handling sparse and unstructured geometric data, such as point clouds or event-based vision, is a pressing challenge in the field of machine vision. Recently, sequence models such as Transformers and state-space models entered the domain of…

State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…

Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The…

If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in the constrained discrete-time state-space estimation, the state…

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

We propose a fine-grained hypergraph model for sparse matrix-matrix multiplication (SpGEMM), a key computational kernel in scientific computing and data analysis whose performance is often communication bound. This model correctly describes…

A state-space model is a statistical framework for inferring latent states from observed time-series data. However, inference with nonlinear and high-dimensional state-space models remains challenging. To this end, an approach based on…

Accurate representation of non-Gaussian distributions of quantities of interest in nonlinear dynamical systems is critical for estimation, control, and decision-making, but can be challenging when forward propagations are expensive to carry…

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Bayesian methods are increasingly being applied to parameterize mechanistic process models used in environmental prediction and forecasting. In particular, models describing ecosystem dynamics with multiple states that are linear and…

This work attempts to approximate a linear Gaussian system with a finite-state hidden Markov model (HMM), which is found useful in solving sophisticated event-based state estimation problems. An indirect modeling approach is developed,…

In this paper, we consider linear state-space models with compressible innovations and convergent transition matrices in order to model spatiotemporally sparse transient events. We perform parameter and state estimation using a dynamic…

Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power…