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We provide an overview of high dimensional dynamical systems driven by random matrices, focusing on applications to simple models of learning and generalization in machine learning theory. Using both cavity method arguments and path…
Multivariate time series are routinely encountered in real-world applications, and in many cases, these time series are strongly correlated. In this paper, we present a deep learning structural time series model which can (i) handle…
A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is a multi-layer connection of many low-dimensional fuzzy systems, where the input variables to the low-dimensional fuzzy systems are selected through a moving…
Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…
We present the collaborative Kalman filter (CKF), a dynamic model for collaborative filtering and related factorization models. Using the matrix factorization approach to collaborative filtering, the CKF accounts for time evolution by…
Synthetic data is essential for training foundation models for time series (FMTS), but most generators assume static correlations, and are typically missing realistic inter-channel dependencies. We introduce DynLMC, a Dynamic Linear Model…
Dynamic conditional correlation (DCC) is a method that estimates the correlation between two time series across time. Although used primarily in finance so far, DCC has been proposed recently as a model-based estimation method for…
In this paper we study state-space realizations of Linear and Time-Invariant (LTI) systems. Motivated by biochemical reaction networks, Gon\c{c}alves and Warnick have recently introduced the notion of a {\em Dynamical Structure Functions}…
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space…
Federated learning is designed to enhance data security and privacy, but faces challenges when dealing with heterogeneous data in long-tailed and non-IID distributions. This paper explores an overlooked scenario where tail classes are…
Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade. A significant amount of attention has been given to develop NMF algorithms that are suitable to model time series…
Integrating deep learning with latent state space models has the potential to yield temporal models that are powerful, yet tractable and interpretable. Unfortunately, current models are not designed to handle missing data or multiple data…
Dynamic Mode Decomposition (DMD) is a powerful, data-driven method for diagnosing complex dynamics. Various DMD algorithms allow one to fit data with a low-rank model that decomposes it into a sum of coherent spatiotemporal patterns.…
In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…
Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…
Conventional time series classification approaches based on bags of patterns or shapelets face significant challenges in dealing with a vast amount of feature candidates from high-dimensional multivariate data. In contrast, deep neural…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
Long-term time series forecasting (LTSF) offers broad utility in practical settings like energy consumption and weather prediction. Accurately predicting long-term changes, however, is demanding due to the intricate temporal patterns and…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…