Related papers: Learning Nonlinear Regime Transitions via Semi-Par…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…
Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
The low-frequency variability of the mid-latitude atmosphere involves complex nonlinear and chaotic dynamical processes posing predictability challenges. It is characterized by sporadically recurring, often long-lived patterns of…
Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…
We consider probabilistic systems with hidden state and unobservable transitions, an extension of Hidden Markov Models (HMMs) that in particular admits unobservable {\epsilon}-transitions (also called null transitions), allowing state…
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
We consider filtering for a hidden Markov model that evolves with multiple time scales in the hidden states. In particular, we consider the case where one of the states is a scaled Ornstein-Uhlenbeck process with fast reversion to a…
We propose a novel framework for exploring generalization errors of transfer learning through the lens of differential calculus on the space of probability measures. In particular, we consider two main transfer learning scenarios,…
Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…
Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…
Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal…
By using straightforward frequency arguments we classify transformations of probabilities which can be generated by transition from one preparation procedure (context) to another. There are three classes of transformations corresponding to…
This paper deals with the identification of piecewise affine state-space models. These models are obtained by partitioning the state or input domain into a finite number of regions and by considering affine submodels in each region. The…
We introduce a class of semiparametric time series models by assuming a quasi-likelihood approach driven by a latent factor process. More specifically, given the latent process, we only specify the conditional mean and variance of the time…
A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by…