Related papers: Equations for hidden Markov models
A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden…
Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…
Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…
We propose a simple tractable pair hidden Markov model for pairwise sequence alignment that accounts for the presence of short tandem repeats. Using the framework of gain functions, we design several optimization criteria for decoding this…
Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a…
We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers…
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…
This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
This paper intends to apply the Hidden Markov Model into stock market and and make predictions. Moreover, four different methods of improvement, which are GMM-HMM, XGB-HMM, GMM-HMM+LSTM and XGB-HMM+LSTM, will be discussed later with the…
We extend the Markov chain tree theorem to general commutative semirings, and we generalize the state reduction algorithm to commutative semifields. This leads to a new universal algorithm, whose prototype is the state reduction algorithm…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm for hidden Markov models, in a…
In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.
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…
Forecasting tasks using large datasets gathering thousands of heterogeneous time series is a crucial statistical problem in numerous sectors. The main challenge is to model a rich variety of time series, leverage any available external…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…