Related papers: A State-Space Approach to Nonstationary Discrimina…

A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…

We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical…

Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly-adopted ES method that employs the Kalman formula, that is, ES$_\text{(K)}$, does not perform…

Dynamic structural equation models (DSEMs) combine time-series modeling of within-person processes with hierarchical modeling of between-person differences and differences between timepoints, and have become very popular for the analysis of…

Data assimilation (DA) integrates observations with a dynamical model to estimate states of PDE-governed systems. Model-driven methods (e.g., Kalman, particle) presuppose full knowledge of the true dynamics, which is not always satisfied in…

Most environmental phenomena, such as wind profiles, ozone concentration and sunlight distribution under a forest canopy, exhibit nonstationary dynamics i.e. phenomenon variation change depending on the location and time of occurrence.…

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

Non-Gaussian state-space models arise in several applications, and within this framework the binary time series setting provides a relevant example. However, unlike for Gaussian state-space models - where filtering, predictive and smoothing…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…

Forecasting driving behavior or other sensor measurements is an essential component of autonomous driving systems. Often real-world multivariate time series data is hard to model because the underlying dynamics are nonlinear and the…

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

In this paper, we propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples in a weighted…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…

In this paper, adaptive prescribed finite time stabilization of uncertain single-input and single-output nonlinear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric…

System identification methods for multivariate time-series, such as neural and behavioral recordings, have been used to build models for predicting one from the other. For example, Preferential Subspace Identification (PSID) builds a…

We present an approach for efficiently training Gaussian Mixture Model (GMM) by Stochastic Gradient Descent (SGD) with non-stationary, high-dimensional streaming data. Our training scheme does not require data-driven parameter…