Learning from Geometry

Subspaces and manifolds are two powerful models for high dimensional signals. Subspaces model linear correlation and are a good fit to signals generated by physical systems, such as frontal images of human faces and multiple sources impinging at an antenna array. Manifolds model sources that are not linearly correlated, but where signals are determined by a small number of parameters. Examples are images of human faces under different poses or expressions, and handwritten digits with varying styles. However, there will always be some degree of model mismatch between the subspace or manifold model and the true statistics of the source. This dissertation exploits subspace and manifold models as prior information in various signal processing and machine learning tasks.

A near-low-rank Gaussian mixture model measures proximity to a union of linear or affine subspaces. This simple model can effectively capture the signal distribution when each class is near a subspace. This dissertation studies how the pairwise geometry between these subspaces affects classification performance. When model mismatch is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the model mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. This linear transformation, termed TRAIT, also preserves some specific features in each class, being complementary to a recently developed Low Rank Transform (LRT). Moreover, when the model mismatch is more significant, TRAIT shows superior performance compared to LRT.

The manifold model enforces a constraint on the freedom of data variation. Learning features that are robust to data variation is very important, especially when the size of the training set is small. A learning machine with large numbers of parameters, e.g., deep neural network, can well describe a very complicated data distribution. However, it is also more likely to be sensitive to small perturbations of the data, and to suffer from suffer from degraded performance when generalizing to unseen (test) data.

From the perspective of complexity of function classes, such a learning machine has a huge capacity (complexity), which tends to overfit. The manifold model provides us with a way of regularizing the learning machine, so as to reduce the generalization error, therefore mitigate overfiting. Two different overfiting-preventing approaches are proposed, one from the perspective of data variation, the other from capacity/complexity control. In the first approach, the learning machine is encouraged to make decisions that vary smoothly for data points in local neighborhoods on the manifold. In the second approach, a graph adjacency matrix is derived for the manifold, and the learned features are encouraged to be aligned with the principal components of this adjacency matrix. Experimental results on benchmark datasets are demonstrated, showing an obvious advantage of the proposed approaches when the training set is small.

Stochastic optimization makes it possible to track a slowly varying subspace underlying streaming data. By approximating local neighborhoods using affine subspaces, a slowly varying manifold can be efficiently tracked as well, even with corrupted and noisy data. The more the local neighborhoods, the better the approximation, but the higher the computational complexity. A multiscale approximation scheme is proposed, where the local approximating subspaces are organized in a tree structure. Splitting and merging of the tree nodes then allows efficient control of the number of neighbourhoods. Deviation (of each datum) from the learned model is estimated, yielding a series of statistics for anomaly detection. This framework extends the classical {\em changepoint detection} technique, which only works for one dimensional signals. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.

Learning from Incredible Commitments: Evolution and Impact of Bilateral Investment Treaties

Ostensibly, BITs are the ideal international treaty. First, until just recently, they almost uniformly came with explicit dispute resolution mechanisms through which countries could face real costs for violation (Montt 2009). Second, the signing, ratification, and violation of them are easily accessible public knowledge. Thus countries presumably would face reputational costs for violating these agreements. Yet, these compliance devices have not dissuaded states from violating these agreements. Even more interestingly, in recent years, both developed and developing countries have moved towards modifying the investor-friendly provisions of these agreements. These deviations from the expectations of the credible commitment argument raise important questions about the field's assumptions regarding the ability of international treaties with commitment devices to effectively constrain state behavior.

Other Than a Citizen: Vernacular Poetics in Postwar America

Few symbols of 1950s-1960s America remain as central to our contemporary conception of Cold War culture as the iconic ranch-style suburban home. While the house took center stage in the Nixon/Khrushchev kitchen debates as a symbol of modern efficiency and capitalist values, its popularity depended largely upon its obvious appropriation of vernacular architecture from the 19th century, those California haciendas and Texas dogtrots that dotted the American west. Contractors like William Levitt modernized the historical common houses, hermetically sealing their porous construction, all while using the ranch-style roots of the dwelling to galvanize a myth of an indigenous American culture. At a moment of intense occupational bureaucracy, political uncertainty and atomized social life, the rancher gave a self-identifying white consumer base reason to believe they could master their own plot in the expansive frontier. Only one example of America’s mid-century love affair with commodified vernacular forms, the ranch-style home represents a broad effort on the part of corporate and governmental interest groups to transform the vernacular into a style that expresses a distinctly homogenous vision of American culture. “Other than a Citizen” begins with an anatomy of that transformation, and then turns to the work of four poets who sought to reclaim the vernacular from that process of standardization and use it to countermand the containment-era strategies of Cold War America.

In four chapters, I trace references to common speech and verbal expressivity in the poetry and poetic theory of Charles Olson, Robert Duncan, LeRoi Jones/Amiri Baraka and Gwendolyn Brooks, against the historical backdrop of the Free-Speech Movement and the rise of mass-culture. When poets frame nonliterary speech within the literary page, they encounter the inability of writing to capture the vital ephemerality of verbal expression. Rather than treat this limitation as an impediment, the writers in my study use the poem to dramatize the fugitivity of speech, emphasizing it as a disruptive counterpoint to the technologies of capture. Where critics such as Houston Baker interpret the vernacular strictly in terms of resistance, I take a cue from the poets and argue that the vernacular, rooted etymologically at the intersection of domestic security and enslaved margin, represents a gestalt form, capable at once of establishing centralized power and sparking minor protest. My argument also expands upon Michael North’s exploration of the influence of minstrelsy and regionalism on the development of modernist literary technique in The Dialect of Modernism. As he focuses on writers from the early 20th century, I account for the next generation, whose America was not a culturally inferior collection of immigrants but an imperial power, replete with economic, political and artistic dominance. Instead of settling for an essentially American idiom, the poets in my study saw in the vernacular not phonetic misspellings, slang terminology and fragmented syntax, but the potential to provoke and thereby frame a more ethical mode of social life, straining against the regimentation of citizenship.

My attention to the vernacular argues for an alignment among writers who have been segregated by the assumption that race and aesthetics are mutually exclusive categories. In reading these writers alongside one another, “Other than a Citizen” shows how the avant-garde concepts of projective poetics and composition by field develop out of an interest in black expressivity. Conversely, I trace black radicalism and its emphasis on sociality back to the communalism practiced at the experimental arts college in Black Mountain, North Carolina, where Olson and Duncan taught. In pressing for this connection, my work reveals the racial politics embedded within the speech-based aesthetics of the postwar era, while foregrounding the aesthetic dimension of militant protest.

Not unlike today, the popular rhetoric of the Cold War insists that to be a citizen involves defending one’s status as a rightful member of an exclusionary nation. To be other than a citizen, as the poets in my study make clear, begins with eschewing the false certainty that accompanies categorical nominalization. In promoting a model of mutually dependent participation, these poets lay the groundwork for an alternative model of civic belonging, where volition and reciprocity replace compliance and self-sufficiency. In reading their lines, we become all the more aware of the cracks that run the length of our load-bearing walls.

Development and Testing of An Automatic Lung IMRT Planning Algorithm

Knowledge-based radiation treatment is an emerging concept in radiotherapy. It

mainly refers to the technique that can guide or automate treatment planning in

clinic by learning from prior knowledge. Dierent models are developed to realize

it, one of which is proposed by Yuan et al. at Duke for lung IMRT planning. This

model can automatically determine both beam conguration and optimization ob-

jectives with non-coplanar beams based on patient-specic anatomical information.

Although plans automatically generated by this model demonstrate equivalent or

better dosimetric quality compared to clinical approved plans, its validity and gener-

ality are limited due to the empirical assignment to a coecient called angle spread

constraint dened in the beam eciency index used for beam ranking. To eliminate

these limitations, a systematic study on this coecient is needed to acquire evidences

for its optimal value.

To achieve this purpose, eleven lung cancer patients with complex tumor shape

with non-coplanar beams adopted in clinical approved plans were retrospectively

studied in the frame of the automatic lung IMRT treatment algorithm. The primary

and boost plans used in three patients were treated as dierent cases due to the

dierent target size and shape. A total of 14 lung cases, thus, were re-planned using

the knowledge-based automatic lung IMRT planning algorithm by varying angle

spread constraint from 0 to 1 with increment of 0.2. A modied beam angle eciency

index used for navigate the beam selection was adopted. Great eorts were made to assure the quality of plans associated to every angle spread constraint as good

as possible. Important dosimetric parameters for PTV and OARs, quantitatively

re

ecting the plan quality, were extracted from the DVHs and analyzed as a function

of angle spread constraint for each case. Comparisons of these parameters between

clinical plans and model-based plans were evaluated by two-sampled Students t-tests,

and regression analysis on a composite index built on the percentage errors between

dosimetric parameters in the model-based plans and those in the clinical plans as a

function of angle spread constraint was performed.

Results show that model-based plans generally have equivalent or better quality

than clinical approved plans, qualitatively and quantitatively. All dosimetric param-

eters except those for lungs in the automatically generated plans are statistically

better or comparable to those in the clinical plans. On average, more than 15% re-

duction on conformity index and homogeneity index for PTV and V40, V60 for heart

while an 8% and 3% increase on V5, V20 for lungs, respectively, are observed. The

intra-plan comparison among model-based plans demonstrates that plan quality does

not change much with angle spread constraint larger than 0.4. Further examination

on the variation curve of the composite index as a function of angle spread constraint

shows that 0.6 is the optimal value that can result in statistically the best achievable

plans.

Spic'ing into Existence: Epitaph, Epithet, and the Ethnopoetic Imagination

Quién Es, Quién Somos? Spic’ing into Existence claims a four-fold close-reading: first, analysis of texts: from theoretical meditations to (prison) memoir and film. Second, a half dozen central figures appear, largely Latinx and black American. They cut across a score of registers, socio-economics, ideological reservations, but all are, as Carl Carlton sang, poetry in motion. Writers, poets, theologians, pathologists, artists, comedians, actors, students whose vocation is invocation, the inner surge of their calling. Third, the manuscript draws from a series of historical moments—from radical liberation of the late 60s, to contemporary student activism. Finally, this body of work is movement, in all its social, gestural, and kinesthetic viscera. From this last heading, we peel away layers of what I call the ethnopoet, the fascia undoing that reveals its bio-political anatomy, dressing its bare life with kinship speech. First, the social revolutions of the Civil Rights, Black Power, abolitionism, the Black Panthers and Young Lords, boycotts and jarring artistic performances. These events are superficial not in vain sense, but key epicenters of underground murmurings, the workings of a cunning assailant. She robs not lavish estates, but another day to breathe. Gesturally, as perhaps the interlocutor, lies this author, interspersing his own diatribes to conjure her presence. The final branch is admittedly the most intangible. Kinesthetically, we map the nimbleness, footwork lígera of what I call the ethnopoet. Ethnopoet is no mere aggregate of ethnicity and poetry, but like chemical reaction, the descriptor for its behavior under certain pressures, temperatures, and elements. Elusive and resisting confinement, and therefore definition, the ethnopoet is a shapeshifting figure of how racialized bodies [people of color] respond to hegemonic powers. She is, at bottom, however, a native translator, the plural-lensed subject whose loyalty is only to the imagination of a different world, one whose survival is not contingent upon her exploitation. The native translator’s constant re-calibrations of oppressive power apparatuses seem taxing at best, and near-impossible, at worst. To effectively navigate through these polarized loci, she must identify ideologies that in turn seek “affective liberatory sances” in relation to the dominant social order (43). In a kind of performative contradiction, she must marshall the knowledge necessary to “break with ideology” while speaking within it. Chicana Studies scholar, Chela Sandoval, describes this dual movement as “meta-ideologizing”: the appropriation of hegemonic ideological forms in order to transform them (82). Nuestros padres se subieron encima de La Bestia, y por eso somos pasageros a ese tren. Y ya, dentro su pansa, tenemos que ser vigilantes cuando plantamos las bombas. In Methodology of the Oppressed, Sandoval schematizes this oppositional consciousness around five principle categories: “equal rights,” “revolutionary,” “supremacist,” “separatist,” and “differential.” Taken by themselves, the first four modes appear mutually exclusive, incapable of occupying the same plane, until a fifth pillar emerges. Cinematographic in nature, differential consciousness, as Sandoval defines it, is “a kinetic motion that maneuvers, poetically transfigures, and orchestrates while demanding alienation, perversion, and reformation in both spectators and practitioners” (44). For Sandoval, then, differential consciousness is a methodology that privileges an incredible sense mobility, one reaching artistic sensibilities. Our fourth and final analytic of movement serves an apt example of this dual meaning. Lexically speaking, ‘movement’ may be regarded as a political mobilization of aggrieved populations (through sustained efforts), or the process of moving objects (people or otherwise) from one location to another. Praxis-wise, it is both action and ideal, content and form. Thus, an ethnic poetics must be regarded less as a series of stanzas, shortened lyric, or even arrangement of language, but as a lens through which peripheralized peoples kaleidecope ideological positions in an “original, eccentric, and queer sight” (43). Taking note of the advantages of postponing identifications, the thesis stands its ground on the term ethnopoet. Its abstraction is not dewey-eyed philosophy, but an anticipation of poetic justice, of what’s to come from callused hands. This thesis is divided into 7.5 chapters. The first maps out the ethnopoet’s cartographies of struggle. By revisiting that alleged Tío Tomas, Richard Rodriguez, we unearth the tensions that negatively, deny citizenship to one silo, but on the flipside, engender manifold ways of seeing, hearing, and moving . The second, through George Jackson’s prison memoirs, pans out from this ethnography of power, groping for an apparatus that feigns an impervious prestige: ‘the aesthetic regime of coercion.’ In half-way cut, the thesis sidesteps to spic into existence, formally announcing, through Aime Cesaire, myself, and Pedro Pietri, the poeticization of trauma. Such uplift denies New Age transcendence of self, but a rehearsal of our entrapment in these mortal envelopes. Thirdly, conscious of the bleeding ethnic body, we cut open the incipient corpse to observe her pathologist. Her native autopsies offer the ethnic body’s posthumous recognition, the ethnopoetics ability to speak for and through the dead. Chapter five examines prolific black artists—Beyonce and Kendrick Lamar—to elide the circumvention of their consumption via invoking radical black hi/her-stories, ones fragmenting the black body. Sixth, the paper compares the Black Power Salute of the 1968 Mexico City Olympics to Duke’s Mi Gente Boycott of their Latino Student Recruitment Weekend. Both wielded “silent gestures,” that shrewdly interfered with white noise of numbed negligence. Finally, ‘taking the mask off’ that are her functionalities, the CODA expounds on ethnopoet’s interiority, particularly after the rapid re-calibration of her politics. Through a rerun of El Chavo del Ocho, one of Mexican television’s most cherished shows, we tune into the heart-breaking indigence of barrio residents, only to marvel at the power of humor to, as Friday’s John Witherspoon put it, “fight another day.” This thesis is the tip of my tongue. Y por una vez, déjala que cante.

The Diary of Mary McKeon, an Irish American Domestic Servant in Nineteenth Century America

What did young, single, unaccompanied Irish women experience when immigrating to the United States in the late nineteenth century? In this final project, I will explore primary and secondary sources that address their experiences, focusing on a diary written in 1883 by a young Irish domestic servant working in New Haven, Connecticut. Mary McKeon, a sixteen-year-old girl from County Leitrim, Ireland, recorded her experiences as a domestic servant for two different families, as well as her own personal thoughts. Mary wrote down her personal experiences, providing a glimpse of what her life was like both inside and outside of her employer’s home. Though much of my research will show that many young women like Mary would be subjected to prejudice and discrimination due to their lack of understanding middle-class American values, which would give rise to the “Bridget” stereotype of a brutish, ill-mannered and incompetent domestic servant, not all Irish women experienced that discrimination and prejudice. Mary is one example of a domestic servant that was treated kindly by her employers and her story documents a more positive and supportive environment for this newly arrived young, single immigrant. Her diary also reveals her to be a young woman who worked to improve her language skills and her situation. And, through her diary, we get a glimpse of her strategies for ensuring an active social life, including access to courtship and marriage. By analyzing Mary’s diary and sharing my results in this final project, I hope to provide a more comprehensive view into the lives of these young women.