Related papers: Markov-Modulated Linear Regression
We consider a spectrally-negative Markov additive process as a model of a risk process in random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
Dropout represents a typical issue to be addressed when dealing with longitudinal studies. If the mechanism leading to missing information is non-ignorable, inference based on the observed data only may be severely biased. A frequent…
We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole…
In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the…
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…
Latent Markov (LM) models represent an important class of models for the analysis of longitudinal data (Bartolucci et. al., 2013), especially when response variables are categorical. These models have a great potential of application for…
Systems with stochastic time delay between the input and output present a number of unique challenges. Time domain noise leads to irregular alignments, obfuscates relationships and attenuates inferred coefficients. To handle these…
Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…
We introduce and analyze a new class of monotone stochastic recursions in a regenerative environment which is essentially broader than that of Markov chains. We prove stability theorems and apply our results {to three canonical models in…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…