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Results for “penalized likelihood maximization”

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PubMed1997

Weighted least-squares reconstruction methods for positron emission tomography.

We present unpenalized and penalized weighted least-squares (WLS) reconstruction methods for positron emission tomography (PET), where the weights are based on the covariance of a model error and depend on the unknown parameters. The penalty function for the latter method is chosen so that certain a priori information is incorporated. The algorithms used to minimize the WLS objective functions guarantee nonnegative estimates and, experimentally, they converged faster than the maximum likelihood expectation-maximization (ML-EM) algorithm and produced images that had significantly better resolution and contrast. Although simulations suggest that the proposed algorithms are globally convergent, a proof of convergence has not yet been found. Nevertheless, we are able to show that the unpenalized method produces estimates that decrease the objective function monotonically with increasing iterations.

Algorithms↗

PubMed2001

Robust full Bayesian learning for radial basis networks.

We propose a hierarchical full Bayesian model for radial basis networks. This model treats the model dimension (number of neurons), model parameters, regularization parameters, and noise parameters as unknown random variables. We develop a reversible-jump Markov chain Monte Carlo (MCMC) method to perform the Bayesian computation. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible-jump MCMC simulated annealing algorithm to optimize neural networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima to a large extent. We show that by calibrating the full hierarchical Bayesian prior, we can obtain the classical Akaike information criterion, Bayesian information criterion, and minimum description length model selection criteria within a penalized likelihood framework. Finally, we present a geometric convergence theorem for the algorithm with homogeneous transition kernel and a convergence theorem for the reversible-jump MCMC simulated annealing method.

Journal Article↗

PubMed1997

Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction.

This paper presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. 1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. 2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. 3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.

Algorithms↗

PubMed2006

On weighting clustering.

Recent papers and patents in iterative unsupervised learning have emphasized a new trend in clustering. It basically consists of penalizing solutions via weights on the instance points, somehow making clustering move toward the hardest points to cluster. The motivations come principally from an analogy with powerful supervised classification methods known as boosting algorithms. However, interest in this analogy has so far been mainly borne out from experimental studies only. This paper is, to the best of our knowledge, the first attempt at its formalization. More precisely, we handle clustering as a constrained minimization of a Bregman divergence. Weight modifications rely on the local variations of the expected complete log-likelihoods. Theoretical results show benefits resembling those of boosting algorithms and bring modified (weighted) versions of clustering algorithms such as k-means, fuzzy c-means, Expectation Maximization (EM), and k-harmonic means. Experiments are provided for all these algorithms, with a readily available code. They display the advantages that subtle data reweighting may bring to clustering.

Algorithms↗