Measuring the Influence of Observations in HMMs Through the Kullback-Leibler Distance
نویسندگان
چکیده
We measure the influence of individual observations on the sequence of the hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler distance (KLD). Namely, we consider the KLD between the conditional distribution of the hidden states’ chain given the complete sequence of observations and the conditional distribution of the hidden chain given all the observations but the one under consideration. We introduce a linear complexity algorithm for computing the influence of all the observations. As an illustration, we investigate the application of our algorithm to the problem of detecting meaningful observations in HMM data series.
منابع مشابه
Using Kullback-Leibler distance for performance evaluation of search designs
This paper considers the search problem, introduced by Srivastava cite{Sr}. This is a model discrimination problem. In the context of search linear models, discrimination ability of search designs has been studied by several researchers. Some criteria have been developed to measure this capability, however, they are restricted in a sense of being able to work for searching only one possibl...
متن کاملModel Confidence Set Based on Kullback-Leibler Divergence Distance
Consider the problem of estimating true density, h(.) based upon a random sample X1,…, Xn. In general, h(.)is approximated using an appropriate in some sense, see below) model fƟ(x). This article using Vuong's (1989) test along with a collection of k(> 2) non-nested models constructs a set of appropriate models, say model confidence set, for unknown model h(.).Application of such confide...
متن کاملPotential Statistical Evidence in Experiments and Renyi Information
Recently Habibi et al. (2006) defined a pre-experimental criterion for the potential strength of evidence provided by an experiment, based on Kullback-Leibler distance. In this paper, we investigate the potential statistical evidence in an experiment in terms of Renyi distance and compare the potential statistical evidence in lower (upper) record values with that in the same number of ii...
متن کاملComparison of Kullback-Leibler, Hellinger and LINEX with Quadratic Loss Function in Bayesian Dynamic Linear Models: Forecasting of Real Price of Oil
In this paper we intend to examine the application of Kullback-Leibler, Hellinger and LINEX loss function in Dynamic Linear Model using the real price of oil for 106 years of data from 1913 to 2018 concerning the asymmetric problem in filtering and forecasting. We use DLM form of the basic Hoteling Model under Quadratic loss function, Kullback-Leibler, Hellinger and LINEX trying to address the ...
متن کاملExact Computation of Kullback-Leibler Distance for Hidden Markov Trees and Models
We suggest new recursive formulas to compute the exact value of the Kullback-Leibler distance (KLD) between two general Hidden Markov Trees (HMTs). For homogeneous HMTs with regular topology, such as homogeneous Hidden Markov Models (HMMs), we obtain a closed-form expression for the KLD when no evidence is given. We generalize our recursive formulas to the case of HMMs conditioned on the observ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Signal Process. Lett.
دوره 20 شماره
صفحات -
تاریخ انتشار 2013