相关论文: Finite Sample Analysis of Tensor Decomposition for…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…

Encoding time-series with Linear Dynamical Systems (LDSs) leads to rich models with applications ranging from dynamical texture recognition to video segmentation to name a few. In this paper, we propose to represent LDSs with…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…

We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of…

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing…

We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the…

We study the task of learning latent-variable models. A common algorithmic technique for this task is the method of moments. Unfortunately, moment-based approaches are hampered by the fact that the moment tensors of super-constant degree…