In this paper we present a statistical transliteration technique that is language independent. This technique uses Hidden Markov Model (HMM) alignment and Conditional Random Fields (CRF), a discriminative model. HMM alignment maximizes the probability of the observed (source, target) word pairs using the expectation maximization algorithm and then the character level alignments (n-gram) are set...

In this paper, we use a general mathematical and experimental methodology to analyze image deconvolution. The main procedure is to use an example image convolving it with a know Gaussian point spread function and then develop algorithms to recover the image. Observe the deconvolution process by adding Gaussian and Poisson noise at different signal to noise ratios. In addition, we will describe ...

This note represents my attempt at explaining the EM algorithm (Hartley, 1958; Dempster et al., 1977; McLachlan and Krishnan, 1997). This is just a slight variation on TomMinka’s tutorial (Minka, 1998), perhaps a little easier (or perhaps not). It includes a graphical example to provide some intuition. 1 Intuitive Explanation of EM EM is an iterative optimizationmethod to estimate some unknown ...

In this paper, a new iterative pilot-aided algorithm based on expectation conditional maximization (ECM) for joint estimation of Wiener phase noise (PHN) and carrier frequency offset (CFO) in orthogonal frequency division multiplexing (OFDM) systems is proposed. Next, a new expression for the hybrid Cramér-Rao lower bound (HCRB) for joint estimation of PHN and CFO in OFDM systems is derived. Nu...

in which f(·|·) denotes conditional density function. Maximizing (2) over Φ yields the maximum likelihood estimate Φ̂. Since Φ is a 20-dimensional vector and the functions pt (Φ) and q ∗ i,t(Φ) have to be computed recursively for 1 ≤ t ≤ n, direct maximization of (2) may be computationally expensive due to the curse of dimensionality. An alternative approach is to use the EM algorithm which expl...

The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudolikelihood defined by adding a component with improper constant density for accommodating outliers to a Gaussian mixture. A special case of the RIMLE is MLE for multivariate finite Gaussian mixture models. In this paper we trea...

Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the late...

We propose a new model for dynamic volatilities and correlations of skewed and heavytailed data. Our model endows the Generalized Hyperbolic distribution with time-varying parameters driven by the score of the observation density function. The key novelty in our approach is the fact that the skewed and fat-tailed shape of the distribution directly affects the dynamic behavior of the time-varyin...

Alex Pentland MIT Media Lab Cambridge, MA 02139 [email protected] Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning. Its applications therein include the EM algorithm, Bayesian estimation and Bayesian inference. Jensen computes simple lower bounds on otherwise intractable quantities such as products of sums and latent log-likelihoods. This s...