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A novel solution of the inverse Frobenius-Perron problem for constructing semi-Markov chaotic maps with prescribed statistical properties is presented. The proposed solution uses recursive Markov state disaggregation to construct an ergodic map with a piecewise constant invariant density function that approximates an arbitrary probability distribution over a compact interval. The solution is novel...
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized...
In this paper, we apply probability density function (PDF) projection to arrive at an exact closed-form expression for the marginal distribution of the visible data of a restricted Boltzmann machine (RBM) without requiring integrating over the distribution of the hidden variables or needing to know the partition function. We express the visible data marginal as a projected PDF based on a set of sufficient...
In this paper, a generalization of the Misspecified Cramér-Rao Bound (MCRB) and of the Constrained MCRB (CMCRB) to complex parameter vectors is presented. Our derivation aims at providing lower bounds on the Mean Square Error (MSE) for both circular and non-circular, MS-unbiased, mismatched estimators. A simple toy example is also presented to clarify the theoretical findings.
Independent vector analysis (IVA) can thoretically avoid the permutation problem in frequency domain blind source separation by using a multivariate source prior to retain the dependency between different frequency bins of each source. The performance of the IVA method is however very dependent upon the choice of source prior. Recently, a fixed combination of the original super Gaussian, previously...
In this paper, we consider the problem of estimating an unknown random scalar observed by two modalities. We study two scenarios using mutual information and mean square error. In the first scenario, we consider that the noise correlation is known and examine its impact on the information content of two modalities. In the second scenario we quantify the information loss when the considered value of...
In the field of automatic speech recognition (ASR), it is common practice to augment features with time-derivatives, which we call derivative-augmented features (DAF). Although the method is effective for modeling the dynamic behavior of features and produces signiicantly lower clas-siication error, it violates the assumption of conditional independence of the observations. The traditional approach...
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