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.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Compilation of somatic mutations of the CDKN2 gene in human cancers : non-random distribution of base substitutions

The CDKN2 gene, encoding the cyclin-dependent kinase inhibitor p16, is a tumour suppressor gene that maps to chromosome band 9p21-p22. The most common mechanism of inactivation of this gene in human cancers is through homozygous deletion; however, in a smaller proportion of tumours and tumour cell lines intragenic mutations occur. In this study we have compiled a database of over 120 published point mutations in the CDKN2 gene from a wide variety of tumour types. A further 50 deletions, insertions, and splice mutations in CDKN2 have also been compiled. Furthermore, we have standardised the numbering of all mutations according to the full-length 156 amino acid form of p16. From this study we are able to define several hot spots, some of which occur at conserved residues within the ankyrin domains of p16. While many of the hotspots are shared by a number of cancers, the relative importance of each position varies, possibly reflecting the role of different carcinogens in the development of certain tumours. As reported previously, the mutational spectrum of CDKN2 in melanomas differs from that of internal malignancies and supports the involvement of UV in melanoma tumorigenesis. Notably, 52% of all substitutions in melanoma-derived samples occurred at just six nucleotide positions. Nonsense mutations comprise a comparatively high proportion of mutations present in the CDKN2 gene, and possible explanations for this are discussed.

Sequential fusion of decisions from adaptive and random samples for controlled verification of errors

Fusion techniques have received considerable attention for achieving performance improvement with biometrics. While a multi-sample fusion architecture reduces false rejects, it also increases false accepts. This impact on performance also depends on the nature of subsequent attempts, i.e., random or adaptive. Expressions for error rates are presented and experimentally evaluated in this work by considering the multi-sample fusion architecture for text-dependent speaker verification using HMM based digit dependent speaker models. Analysis incorporating correlation modeling demonstrates that the use of adaptive samples improves overall fusion performance compared to randomly repeated samples. For a text dependent speaker verification system using digit strings, sequential decision fusion of seven instances with three random samples is shown to reduce the overall error of the verification system by 26% which can be further reduced by 6% for adaptive samples. This analysis novel in its treatment of random and adaptive multiple presentations within a sequential fused decision architecture, is also applicable to other biometric modalities such as finger prints and handwriting samples.

Modeling random effect and excess zeros in road traffic accident prediction

Poisson distribution has often been used for count like accident data. Negative Binomial (NB) distribution has been adopted in the count data to take care of the over-dispersion problem. However, Poisson and NB distributions are incapable of taking into account some unobserved heterogeneities due to spatial and temporal effects of accident data. To overcome this problem, Random Effect models have been developed. Again another challenge with existing traffic accident prediction models is the distribution of excess zero accident observations in some accident data. Although Zero-Inflated Poisson (ZIP) model is capable of handling the dual-state system in accident data with excess zero observations, it does not accommodate the within-location correlation and between-location correlation heterogeneities which are the basic motivations for the need of the Random Effect models. This paper proposes an effective way of fitting ZIP model with location specific random effects and for model calibration and assessment the Bayesian analysis is recommended.

Document clustering evaluation : Divergence from a random baseline

Divergence from a random baseline is a technique for the evaluation of document clustering. It ensures cluster quality measures are performing work that prevents ineffective clusterings from giving high scores to clusterings that provide no useful result. These concepts are defined and analysed using intrinsic and extrinsic approaches to the evaluation of document cluster quality. This includes the classical clusters to categories approach and a novel approach that uses ad hoc information retrieval. The divergence from a random baseline approach is able to differentiate ineffective clusterings encountered in the INEX XML Mining track. It also appears to perform a normalisation similar to the Normalised Mutual Information (NMI) measure but it can be applied to any measure of cluster quality. When it is applied to the intrinsic measure of distortion as measured by RMSE, subtraction from a random baseline provides a clear optimum that is not apparent otherwise. This approach can be applied to any clustering evaluation. This paper describes its use in the context of document clustering evaluation.

Comparison of PCR, nested PCR, and random amplified polymorphic DNA PCR for detection and typing of Ureaplasma urealyticum in specimens from pregnant women

A PCR assay, using three primer pairs, was developed for the detection of Ureaplasma urealyticum, parvo biovar, mba types 1, 3, and 6, in cultured clinical specimens. The primer pairs were designed by using the polymorphic base positions within a 310- to 311-bp fragment of the 5* end and upstream control region of the mba gene. The specificity of the assay was confirmed with reference serovars 1, 3, 6, and 14 and by the amplified-fragment sizes (81 bp for mba 1, 262 bp for mba 3, and 193 bp for mba 6). A more sensitive nested PCR was also developed. This involved a first-step PCR, using the primers UMS-125 and UMA226, followed by the nested mba-type PCR described above. This nested PCR enabled the detection and typing of small numbers of U. urealyticum cells, including mixtures, directly in original clinical specimens. By using random amplified polymorphic DNA (RAPD) PCR with seven arbitrary primers, we were also able to differentiate the two biovars of U. urealyticum and to identify 13 RAPD-PCR subtypes. By applying these subtyping techniques to clinical samples collected from pregnant women, we established that (i) U. urealyticum is often a persistent colonizer of the lower genital tract from early midtrimester until the third trimester of pregnancy, (ii) mba type 6 was isolated significantly more often (P 5 0.048) from women who delivered preterm than from women who delivered at term, (iii) no particular ureaplasma subtype(s) was associated with placental infections and/or adverse pregnancy outcomes, and (iv) the ureaplasma subtypes most frequently isolated from women were the same subtypes most often isolated from infected placentas.

On the probability density function of the product of Rayleigh distributed random variables

In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.