Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

The organisation and expression of the genes encoding the mitochondrial glycine decarboxylase complex and serine hydroxymethyltransferase in pea (Pisum sativum)

Restriction fragment length polymorphisms have been used to determine the chromosomal location of the genes encoding the glycine decarboxylase complex (GDC) and serine hydroxymethyltransferase (SHMT) of pea leaf mitochondria. The genes encoding the H subunit of GDC and the genes encoding SHMT both show linkage to the classical group I marker i. In addition, the genes for the P protein of GDC show linkage to the classic group I marker a. The genes for the L and T proteins of GDC are linked to one another and are probably situated on the satellite of chromosome 7. The mRNAs encoding the five polypeptides that make up GDC and SHMT are strongly induced when dark-grown etiolated pea seedlings are placed in the light. Similarly, when mature plants are placed in the dark for 48 h, the levels of both GDC protein and SHMT mRNAs decline dramatically and then are induced strongly when these plants are returned to the light. During both treatments a similar pattern of mRNA induction is observed, with the mRNA encoding the P protein of GDC being the most rapidly induced and the mRNA for the H protein the slowest. Whereas during the greening of etiolated seedlings the polypeptides of GDC and SHMT show patterns of accumulation similar to those of the corresponding mRNAs, very little change in the level of the polypeptides is seen when mature plants are placed in the dark and then re-exposed to the light.

A novel ACVR1 mutation in the glycine/serine-rich domain found in the most benign case of a fibrodysplasia ossificans progressiva variant reported to date

Fibrodysplasia Ossificans Progressiva (FOP) is a rare, autosomal dominant condition, classically characterised by heterotopic ossification beginning in childhood and congenital great toe malformations; occurring in response to a c.617 G>A ACVR1 mutation in the functionally important glycine/serine-rich domain of exon 6. Here we describe a novel c.587 T>C mutation in the glycine/serine-rich domain of ACVR1, associated with delayed onset of heterotopic ossification and an exceptionally mild clinical course. Absence of great toe malformations, the presence of early ossification of the cervical spine facets joints, plus mild bilateral camptodactyly of the 5th fingers, together with a novel ACVR1 mutation, are consistent with the 'FOP-variant' syndrome. The c.587 T>C mutation replaces a conserved leucine with proline at residue 196. Modelling of the mutant protein reveals a steric clash with the kinase domain that will weaken interactions with FKBP12 and induce exposure of the glycine/serine-rich repeat. The mutant receptor is predicted to be hypersensitive to ligand stimulation rather than being constitutively active, consistent with the mild clinical phenotype. This case extends our understanding of the 'FOP-variant' syndrome.