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3. HHCART: An Oblique Decision Tree

Author

Wickramarachchi, D. C., Robertson, B. L., Reale, M., Price, C. J., and Brown, J.

Subjects
Statistics - Machine Learning, Computer Science - Learning
Abstract

Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using axis parallel splits. When the true decision boundaries are not aligned with the feature axes, this approach can produce a complicated boundary structure. Oblique decision trees use oblique decision boundaries to potentially simplify the boundary structure. The major limitation of this approach is that the tree induction algorithm is computationally expensive. In this article we present a new decision tree algorithm, called HHCART. The method utilizes a series of Householder matrices to reflect the training data at each node during the tree construction. Each reflection is based on the directions of the eigenvectors from each classes' covariance matrix. Considering axis parallel splits in the reflected training data provides an efficient way of finding oblique splits in the unreflected training data. Experimental results show that the accuracy and size of the HHCART trees are comparable with some benchmark methods in the literature. The appealing feature of HHCART is that it can handle both qualitative and quantitative features in the same oblique split., Comment: 13 Pages, 1 Figure, 4 Tables, 1 Algorithm

Published
2015

7. Language Control in the Bilingual Brain

Author

Crinion, J., Turner, R., Grogan, A., Hanakawa, T., Noppeney, U., Devlin, J. T., Aso, T., Urayama, S., Fukuyama, H., Stockton, K., Usui, K., Green, D. W., and Price, C. J.

Published
2006

21. A primal–dual penalty method via rounded weighted-ℓ1 Lagrangian duality.

Author

Burachik, R. S., Kaya, C. Y., and Price, C. J.

Subjects
CONSTRAINED optimization, KISSING
Abstract

We propose a new duality scheme based on a sequence of smooth minorants of the weighted- ℓ 1 penalty function, interpreted as a parametrized sequence of augmented Lagrangians, to solve non-convex constrained optimization problems. For the induced sequence of dual problems, we establish strong asymptotic duality properties. Namely, we show that (i) the sequence of dual problems is convex and (ii) the dual values monotonically increase to the optimal primal value. We use these properties to devise a subgradient based primal–dual method, and show that the generated primal sequence accumulates at a solution of the original problem. We illustrate the performance of the new method with three different types of test problems: A polynomial non-convex problem, large-scale instances of the celebrated kissing number problem, and the Markov–Dubins problem. Our numerical experiments demonstrate that, when compared with the traditional implementation of a well-known smooth solver, our new method (using the same well-known solver in its subproblem) can find better quality solutions, i.e. 'deeper' local minima, or solutions closer to the global minimum. Moreover, our method seems to be more time efficient, especially when the problem has a large number of constraints. [ABSTRACT FROM AUTHOR]

Published
2022
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34. RELEASE: A protocol for a systematic review based, individual participant data, meta- and network meta-analysis, of complex speech-language therapy interventions for stroke-related aphasia

Author

Brady, M. C., Ali, M., VandenBerg, K., Williams, L. J., Williams, L. R., Abo, M., Becker, F., Bowen, A., Brandenburg, C., Breitenstein, C., Bruehl, S., Copland, D., Cranfill, T. B., de Pietro-Bachmann, M., Enderby, P., Fillingham, J., Galli, F., Gandolfi, M., Glize, B., Godecke, E., Hawkins, N., Hilari, K., Hinckley, J., Horton, S., Howard, D., Jaecks, P., Jefferies, E., Jesus, L.M.T., Kambanaros, M., Laganaro, M., Lambon Ralph, M. A., Laska, A., Leemann, B., Leff, A.P., Lima, R., Lorenz, A., MacWhinney, B., Shisler Marshall, R., Mattioli, F., Mavis, I., Meinzer, M., Nilipour, R., Noe, E., Paik, N-J., Palmer, R., Papathanasiou, I., Patrício, B., Pavao Martins, I., Price, C. J., Prizl Jakovac, T., Rochon, E., Rose, M., Rosso, C., Rubi-Fessen, I., Ruiter, M. B., Snell, C., Stahl, B., Szaflarski, J., Thomas, S., van de Sandt-Koenderman, M., van der Meulen, I., Visch-Brink, E., Worrall, L., and Harris Wright, H.

Subjects
P1
Abstract

Background: Speech and language therapy (SLT) benefits people with aphasia following stroke. Group level summary statistics from randomised controlled trials hinder exploration of highly complex SLT interventions and a clinically relevant heterogeneous population. Creating a database of individual participant data (IPD) for people with aphasia aims to allow exploration of individual and therapy-related predictors of recovery and prognosis. \ud \ud Aim: To explore the contribution that individual participant characteristics (including stroke and aphasia profiles) and SLT intervention components make to language recovery following stroke.\ud \ud Methods and procedures: We will identify eligible IPD datasets (including randomised controlled trials, non-randomised comparison studies, observational studies and registries) and invite their contribution to the database. Where possible, we will use metaand network meta-analysis to explore language performance after stroke and predictors of recovery as it relates to participants who had no SLT, historical SLT or SLT in the primary research study. We will also examine the components of effective SLT interventions.\ud \ud Outcomes and results: Outcomes include changes in measures of functional communication, overall severity of language impairment, auditory comprehension, spoken language (including naming), reading and writing from baseline. Data captured on assessment tools will be collated and transformed to a standardised measure for each of the outcome domains.\ud \ud Conclusion: Our planned systematic-review-based IPD meta- and network meta-analysis is a large scale, international, multidisciplinary and methodologically complex endeavour. It will enable hypotheses to be generated and tested to optimise and inform development of interventions for people with aphasia after stroke.\ud \ud Systematic review registration: The protocol has been registered at the International Prospective Register of Systematic Reviews (PROSPERO; registration number: CRD42018110947

Published
2019

39. Direct search nonsmooth constrained optimization via rounded ℓ1 penalty functions.

Author

Price, C. J.

Subjects
*CONSTRAINED optimization, *CONTINUOUS functions, *QUASI-Newton methods, *NONSMOOTH optimization
Abstract

A class of direct search methods for locally minimizing a Lipschitz continuous black-box function f subject to locally Lipschitz constraints is presented. A sequence of smoothed ℓ 1 penalty functions is used. Each smoothed penalty function is approximately minimized in turn. The smoothing is reduced after each minimization, exposing the ℓ 1 exact penalty function in the limit. Convergence to a constrained Clarke stationary point is shown under appropriate regularity conditions. Convergence to one or more KKT points is shown under similar conditions when f and all active constraints are strictly differentiable at each limit point. An implementation of one method in this class is numerically tested and shown to be effective in practice. The implementation uses a discrete quasi-Newton step when possible. Otherwise a global direction search is used to locate a descent direction. Theoretical convergence properties are independent of the quasi-Newton step. [ABSTRACT FROM AUTHOR]

Published
2022
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