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Recommender systems help users find relevant items of interest based on the past preferences of those users. In many domains, however, the tastes and preferences of users change over time due to a variety of factors and recommender systems…
This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
We propose a Neural Hidden Markov Model (HMM) with Adaptive Granularity Attention (AGA) for high-frequency order flow modeling. The model addresses the challenge of capturing multi-scale temporal dynamics in financial markets, where…
Land use land cover changes (LULCC) are generally modeled using multi-scale spatio-temporal variables. Recently, Markov Chain (MC) has been used to model LULCC. However, the model is derived from the proportion of LULCC observed over a…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
The hidden Markov model (HMM) is a widely-used generative model that copes with sequential data, assuming that each observation is conditioned on the state of a hidden Markov chain. In this paper, we derive a novel algorithm to cluster HMMs…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
We focus on the parametric estimation of the distribution of a Markov environment from the observation of a single trajectory of a one-dimensional nearest-neighbor path evolving in this random environment. In the ballistic case, as the…
The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…
Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models…
Territorial control is a key aspect shaping the dynamics of civil war. Despite its importance, we lack data on territorial control that are fine-grained enough to account for subnational spatio-temporal variation and that cover a large set…
We address the problem of detecting an anomalous process among a large number of processes. At each time t, normal processes are in state zero (normal state), while the abnormal process may be in either state zero (normal state) or state…
Extending classical probabilistic reasoning using the quantum mechanical view of probability has been of recent interest, particularly in the development of hidden quantum Markov models (HQMMs) to model stochastic processes. However, there…
Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may…
The need for long-term multi-object tracking (MOT) is growing due to the demand for analyzing individual behaviors in videos that span several minutes. Unfortunately, due to identity switches between objects, the tracking performance of…
Variable order sequence modeling is an important problem in artificial and natural intelligence. While overcomplete Hidden Markov Models (HMMs), in theory, have the capacity to represent long-term temporal structure, they often fail to…
Understanding behavioural responses to disturbances is vital for wildlife conservation. For example, in the Arctic, the decrease in sea ice has opened new shipping routes, increasing the need for impact assessments that quantify the…
Data collected from wearable devices and smartphones can shed light on an individual's pattern of behavioral and circadian routine. Phone use can be modeled as alternating event process, between the state of active use and the state of…