title: Random projections as regularizers: learning a linear discriminant ensemble from fewer observations than dimensions

authors: Durrant, Robert J.

subjects: ensemble classifiers

abstract: We examine the performance of an ensemble of randomly-projected Fisher Linear Discriminant classifiers, focusing on the case when there are fewer training observations than data dimensions. Our ensemble is learned from a sequence of randomly-projected representations of the original high dimensional data and therefore for this approach data can be collected, stored and processed in such a compressed form. The specific form and simplicity of this ensemble permits a direct and much more detailed analysis than existing generic tools in previous works. In particular, we are able to derive the exact form of the generalization error of our ensemble, conditional on the training set, and based on this we give theoretical guarantees which directly link the performance of the ensemble to that of the corresponding linear discriminant learned in the full data space. To the best of our knowledge these are the first theoretical results to prove such an explicit link for any classifier and classifier ensemble pair. Furthermore we show that the randomly-projected ensemble is equivalent to implementing a sophisticated regularization scheme to the linear discriminant learned in the original data space and this prevents overfitting in conditions of small sample size where pseudo-inverse FLD learned in the data space is provably poor.

text: Random projections as regularizers: learning a linear discriminant ensemble from fewer observations than dimensions We examine the performance of an ensemble of randomly-projected Fisher Linear Discriminant classifiers, focusing on the case when there are fewer training observations than data dimensions. Our ensemble is learned from a sequence of randomly-projected representations of the original high dimensional data and therefore for this approach data can be collected, stored and processed in such a compressed form. The specific form and simplicity of this ensemble permits a direct and much more detailed analysis than existing generic tools in previous works. In particular, we are able to derive the exact form of the generalization error of our ensemble, conditional on the training set, and based on this we give theoretical guarantees which directly link the performance of the ensemble to that of the corresponding linear discriminant learned in the full data space. To the best of our knowledge these are the first theoretical results to prove such an explicit link for any classifier and classifier ensemble pair. Furthermore we show that the randomly-projected ensemble is equivalent to implementing a sophisticated regularization scheme to the linear discriminant learned in the original data space and this prevents overfitting in conditions of small sample size where pseudo-inverse FLD learned in the data space is provably poor.

year: 2013-11-13

title: Relational random forests based on random relational rules

authors: Anderson, Grant

subjects: computer science

abstract: Random Forests have been shown to perform very well in propositional learning. FORF is an upgrade of Random Forests for relational data. In this paper we investigate shortcomings of FORF and propose an alternative algorithm, R⁴F, for generating Random Forests over relational data. R⁴F employs randomly generated relational rules as fully self-contained Boolean tests inside each node in a tree and thus can be viewed as an instance of dynamic propositionalization. The implementation of R⁴F allows for the simultaneous or parallel growth of all the branches of all the trees in the ensemble in an efficient shared, but still single-threaded way. Experiments favorably compare R⁴F to both FORF and the combination of static propositionalization together with standard Random Forests. Various strategies for tree initialization and splitting of nodes, as well as resulting ensemble size, diversity, and computational complexity of R⁴F are also investigated.

text: Relational random forests based on random relational rules Random Forests have been shown to perform very well in propositional learning. FORF is an upgrade of Random Forests for relational data. In this paper we investigate shortcomings of FORF and propose an alternative algorithm, R⁴F, for generating Random Forests over relational data. R⁴F employs randomly generated relational rules as fully self-contained Boolean tests inside each node in a tree and thus can be viewed as an instance of dynamic propositionalization. The implementation of R⁴F allows for the simultaneous or parallel growth of all the branches of all the trees in the ensemble in an efficient shared, but still single-threaded way. Experiments favorably compare R⁴F to both FORF and the combination of static propositionalization together with standard Random Forests. Various strategies for tree initialization and splitting of nodes, as well as resulting ensemble size, diversity, and computational complexity of R⁴F are also investigated.

year: 2009

title: Te ahi tawhito, te ahi tipua, te ahi nā Mahuika: Re-igniting native women’s ceremony

authors: Murphy, Ngahuia Aroha Grace

subjects: Native women's ceremony

abstract: This research examines the multiple ways in which Māori, and Hawai’ian and Native American women, are re-activating feminine ceremonial forms and recovering sacred relationships with customary feminine deities. Attention is focused on the creation of personal ritual practices that respond to contemporary decolonising and ecological contexts.
A mana wahine theoretical and methodological framework motivated by emancipatory agendas that seek to facilitate transformation is used. Key to mana wahine projects is the creation of space for Native women to define themselves and their own stories and knowledges. This is important because Native women’s voices, knowledge and ritual histories continue to be marginalised. Furthermore, debased colonial renditions of femininity, which have been reproduced, perpetuate patriarchal and colonial politics that engender discord in Native communities today.  
The study used a suite of complimentary methods to engage 45 Native women and men. Interviews and kōrero (discussion), ceremony, mana wahine wānanga (women’s sacred learning space), Native sacred site visits, solicited journals, collaboration in ritual theatre productions, and analysis of mana wahine artworks as discursive texts were employed to gather stories of spiritual continuation that are unique and largely unchartered in academia. 
The empirical material is organised around four themes in four different chapters. The first of these empirical chapters re-interprets colonial ethnographic material alongside karakia (incantations), mōteatea (songs), cosmological and tribal stories, to reveal bold examples of Māori female ritual leadership. The second empirical chapter comprises an analysis of key colonial processes that have attempted to erase Native women’s ritual ontologies and the strident expressions of Native women’s resistance to colonial imperatives. The third empirical chapter investigates the multiple channels through which Native women are restoring their ceremonial lives. The fourth chapter investigates rerenga atua (menstruation) rituals that celebrate the Native feminine body as a cosmological site of communion with feminine deities. 
The rich weave of Native women’s stories of ceremony, old and new, threads into decolonising Indigenous scholarship around the world that also seeks to recover the sacred feminine as a key site of Native sovereignty. These discussions reveal a self-renewing Native belief system based on vibrant and evolving rituals that respond directly to current socio-political, spiritual and ecological realities.

text: Te ahi tawhito, te ahi tipua, te ahi nā Mahuika: Re-igniting native women’s ceremony This research examines the multiple ways in which Māori, and Hawai’ian and Native American women, are re-activating feminine ceremonial forms and recovering sacred relationships with customary feminine deities. Attention is focused on the creation of personal ritual practices that respond to contemporary decolonising and ecological contexts.
A mana wahine theoretical and methodological framework motivated by emancipatory agendas that seek to facilitate transformation is used. Key to mana wahine projects is the creation of space for Native women to define themselves and their own stories and knowledges. This is important because Native women’s voices, knowledge and ritual histories continue to be marginalised. Furthermore, debased colonial renditions of femininity, which have been reproduced, perpetuate patriarchal and colonial politics that engender discord in Native communities today.  
The study used a suite of complimentary methods to engage 45 Native women and men. Interviews and kōrero (discussion), ceremony, mana wahine wānanga (women’s sacred learning space), Native sacred site visits, solicited journals, collaboration in ritual theatre productions, and analysis of mana wahine artworks as discursive texts were employed to gather stories of spiritual continuation that are unique and largely unchartered in academia. 
The empirical material is organised around four themes in four different chapters. The first of these empirical chapters re-interprets colonial ethnographic material alongside karakia (incantations), mōteatea (songs), cosmological and tribal stories, to reveal bold examples of Māori female ritual leadership. The second empirical chapter comprises an analysis of key colonial processes that have attempted to erase Native women’s ritual ontologies and the strident expressions of Native women’s resistance to colonial imperatives. The third empirical chapter investigates the multiple channels through which Native women are restoring their ceremonial lives. The fourth chapter investigates rerenga atua (menstruation) rituals that celebrate the Native feminine body as a cosmological site of communion with feminine deities. 
The rich weave of Native women’s stories of ceremony, old and new, threads into decolonising Indigenous scholarship around the world that also seeks to recover the sacred feminine as a key site of Native sovereignty. These discussions reveal a self-renewing Native belief system based on vibrant and evolving rituals that respond directly to current socio-political, spiritual and ecological realities.

year: 2019