VictorJuiz/thesis huggingface dataset:
A modern maximum likelihood theory for high-dimensional logistic regression

Logistic regression is arguably the most widely used and studied non-linear model in statistics. Classical maximum-likelihood theory based statistical inference is ubiquitous in this context. This theory hinges on well-known fundamental results: (1) the maximum-likelihood-estimate (MLE) is asymptotically unbiased and normally distributed, (2) its variability can be quantified via the inverse Fisher information, and (3) the log-likelihood ratio (LLR) statistic is asymptotically a Chi-Squared. This thesis uncovers that in the common modern setting where the number of features and the sample size are both large and comparable, classical results are far from accurate. In fact, (1) the MLE is biased, (2) its variability is far greater than classical results, and (3) the LLR statistic is not distributed as a Chi-Square. Consequently, p-values obtained based on classical theory are completely invalid in such settings. This thesis provides a modern perspective on classical maximum likelihood theory in the context of logistic regression (developed jointly by the author and her collaborators). The contributions here are two-fold: first, it discovers a phase transition in the existence of the MLE and explicitly pins down the phase transition curve; second, in the regime where the MLE is finite, it characterizes the asymptotic behavior of the MLE and the LLR for a class of covariate distributions, under the aforementioned high-dimensional regime. Empirical evidence demonstrates that this asymptotic theory provides accurate inference in finite samples and is robust to certain violations of the underlying assumptions. Practical implementation of these results necessitates the estimation of a single scalar, the overall signal strength---a procedure for estimating this parameter is also discussed. This asymptotic theory can be extended to characterize distributions of penalized maximum likelihood estimators in some settings. Along the way, this thesis surveys relevant works in the field of high-dimensional inference, particularly those developing methodology for valid inference in high-dimensional regression problems.

Keywords: Statistics.
Advisor: Candès Emmanuel J. (Emmanuel Jean) 
Johnstone Iain 
Montanari Andrea
Modern methods in extremal combinatorics

In this thesis, we apply modern probabilistic and algebraic techniques to different problems in extremal combinatorics. One of the most recent algebraic techniques is the new polynomial method which Croot, Lev and Pach introduced in 2016. This method has lead to the spectacular breakthrough of Ellenberg and Gijswijt on the cap-set problem, and has had many more applications in additive number theory and extremal combinatorics. In Chapter 2, we use various tools that resulted from the Croot-Lev-Pach polynomial method, combined with probabilistic and combinatorial arguments, to prove new upper bounds on the Erdos-Ginzburg-Ziv constant of F_p^n for a fixed prime p \geq 5 and large n. Chapter 3 also relies on developments arising from the Croot-Lev-Pach polynomial method as well as new combinatorial ideas. We prove a polynomial bound relating the parameters in Green's arithmetic k-cycle removal lemma in F_p^n for all k \geq 3. The special case of k = 3 was previously proved by Fox and Lovasz and is used as the base case of an induction on k in our proof for all k \geq 3. In Chapter 4, we use methods from algebraic geometry (and basic differential topology) to prove an asymptotically tight lower bound for the number of graphs of a certain form where the edges are defined algebraically by the signs of a finite list of polynomials. We present many applications of this result, in particular to counting intersection graphs and containment orders for various families of geometric objects (e.g. segments of disks in the plane). Using probabilistic methods, we prove the so-called Edge-statistics conjecture of Alon, Hefetz, Krivelevich and Tyomkyn in Chapter 5. In a certain range of the parameters, this conjecture already follows from a result of Kwan, Sudakov and Tran. We solve the other cases, and thereby establish the full conjecture. Finally, in Chapter 6 we prove a conjecture of Erdos, Faudree, Rousseau and Schelp from 1990 concerning subgraphs of minimum degree k.

Keywords: Mathematics.
Advisor: Fox Jacob
Soundararajan Kannan
Vondrak Ján (Mathematician)
Modern probabilistic models for human choices and rankings

As datasets capturing human choices and rankings grow in richness and scale, particularly in online domains, there is an increasing need for more flexible models of ranking and choice. I introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, which escapes traditional choice-theoretic axioms such as regularity and stochastic transitivity while remaining inferentially tractable. PCMC still satisfies the axiom of uniform expansion, a considerably weaker assumption than Luce's choice axiom, and PCMC retains the Multinomial Logit (MNL) as a special case. Using the notion of a choice representation to break a ranking into a sequence of choices, I develop a framework for turning models for discrete choice into models for ranking data, generalizing the idea used to build the seminal Plackett-Luce (PL) model from MNL. This framework allows us to leverage our progress in choice into novel models for ranking data and allows us to build flexible yet tractable models for complete and partial rankings from recent advances in choice models. I also discuss methods and subtleties of shrinkage estimation for choice data and demonstrate the efficacy of the models I propose in prediction tasks from a broad range of domains including transportation, competitions, voting, and sushi.

Keywords: Management Science and Engineering.
Advisor: Ugander Johan 
Goel Ashish 
Johari Ramesh
Modern statistical approaches for randomized experiments under interference

This thesis presents new methodology for handling interference in randomized experiments. Interference, a phenomenon in which individuals interact with each other, is widely prevalent in the social and natural sciences, and has major implications for how experiments are optimally designed and analyzed. I first provide an introduction to interference, including examples and a relevant brief history of causal inference. Next, I demonstrate how researchers can use Stein's method to establish limiting distributional results for estimators under interference. The modern tools afforded by Stein's method allow one to analyze certain regimes of arbitrarily dense interference, which goes beyond the analysis capabilities of existing tools. In the subsequent chapter, I develop new model-based, adjustment estimators for estimating the global average treatment effect. The adjustment variables can be constructed from functions of the treatment assignment vector, and the researcher can use a collection of any functions correlated with the response, turning the problem of detecting interference into a feature engineering problem. The final chapter proposes new methods for designing and analyzing stochastic seeding strategies, which are an appealing way of leveraging network structure for marketing, public health, and behavioral interventions. New importance sampling estimators adapted to this setting can greatly improve precision over existing approaches. This thesis is interdisciplinary in nature. Stein's method (Chapter 2), regression adjustments (Chapter 3), and importance sampling (Chapter 4) all command spheres of influence in certain sectors of the literature, and are here repurposed in new domains. I hope that my work shows how existing statistical technology can arise in new arenas of application while simultaneously giving rise to new methodological questions and problems, and in this way, I hope my work is useful for both practitioners and methodologists.

Keywords: Statistics.
Advisor: Ugander Johan 
Palacios Roman Julia Adela 
Walther Guenther
Moduli spaces of bundles via motivic probabilities

We give formulas for the classes in the completed Grothendieck ring of varieties of the moduli stacks of principal bundles for the special linear or symplectic groups over a curve X in terms of the motivic zeta function of X. The answers agree with predictions of Behrend and Dhillon. The computations rely on interpreting certain classes in the Grothendieck ring in a probabilistic way, using work of Margaret Bilu and Sean Howe.

Keywords: Mathematics.
Advisor: Vakil Ravi 
Bump Daniel
Kemeny Michael
Molecular counting analysis of infectious disease

Infectious diseases have a profound impact on humankind, influencing the course of wars and the fate of nations. The case for applying next-generation sequencing (NGS) in clinical microbiology is becoming increasingly clear. A flood of recent studies have shown how this powerful technology can address pressing modern problems in infectious diseases, including resistance, rare infections, and outbreaks. In this thesis, we show that molecular counting of pathogen-derived cell-free DNA is a new diagnostic paradigm for infectious disease. We built a pipeline for counting pathogen-derived cell-free molecules in human plasma and a web appli- cation for browsing the resulting data. We applied these tools to thousands of clin- ical samples collected from hundreds of patients at Stanford hospital. We further processed thousands of clinical test records in order to show that this method can be broadly applied for non-invasive monitoring of viral, bacterial, and fungal infec- tions in deep tissues. Finally, we show that unbiased pathogen monitoring using this technique can track infections that escape hypothesis-centric clinical testing. As well as demonstrating this new diagnostic application of NGS, we show how NGS technology can be used to understand infectious disease mechanism. We de- veloped a pipeline for counting of sequencing reads derived from RNA-protein in- teractions in vivo. We show that this method (CLIP-seq) can be applied to viruses that have infected human cells and use it to reveal novel interactions between the Hepatitis-C virus (HCV) genome and human protein PCBP2. We also applied this method to HERV-K, an endogenous retrovirus. We showed that human embryo development occurs in the presence of retroviral products, which may protect the embryo from exogenous infection and help regulate early development. We highlight three separate ways to validate results from mechanistic CLIP-seq experiments, including comparative analysis, replicate matching, and functional studies. We also developed a multiplexed RNA-protein interaction assay that is compatible with the scale of CLIP-seq experiments and exceeds the throughput of common biochemical assays. We applied this technology to a model RNA-protein interaction (histone stem-loop and stem loop binding protein), recapitulating two decades of biochemistry and revealing novel features of the interaction. In summary, we built computational tools that apply molecular counting to in- fectious disease diagnostics and mechanism. For validation of these results, we developed a novel microfluidic tool for high-throughput biophysical measurements.

Keywords: Bioengineering.
Advisor: Chang Howard Y. (Howard Yuan-Hao)
Quake Stephen Ronald 
Sarnow P. (Peter)
Molecular principles to engineer plant microbiomes

The microbes that live in and on plants (the plant microbiome) are critical for plant health, and exert their influence by facilitating nutrient acquisition, regulating plant hormone levels, and helping to withstand pathogen attack. Due to these potential benefits, the plant microbiome has become an appealing target for engineering sustainable improvements in crop productivity. However, the lack of a mechanistic understanding for plant-microbiome interactions at the molecular level has impeded engineering efforts. In this dissertation, I address the role of plant-derived specialized molecules in shaping the composition of the root microbiome, and that of microbe-produced molecules in influencing plant health. Using broadly-applicable experimental platforms that allow for hypothesis-driven mechanistic studies, along with previously developed reverse genetic tools in the model plant Arabidopsis, I discovered a novel mechanism of action for coumarins (root-exuded, specialized small molecules) in assembling the microbiome of plant roots. Additionally, I describe a role for Pseudomanas-derived pyrroloquinoline quinone (a redox-active small molecule) in improving plant growth under iron-limiting conditions -- a nutrient deficiency prevalent in one-third of the world's soils. Finally, I highlight a serendipitous discovery made while engineering plants to modulate the root microbiome using opines -- unusual conjugates of two common plant metabolites that can be catabolized by select microbes. The microbes inciting the production of opines, Agrobacterium species, hijack the plant cell's splicing machinery as part of its pathogenic lifestyle. This novel finding could be exploited to improve transgene expression in plants, and to survey bacterial genomes for genes that are horizontally transferred across the kingdoms of life. These contributions, which provide mechanistic roles for both plant and microbe-derived small molecules within the phytobiome, offer concrete strategies for engineering phytobiomes to improve agricultural systems.

Keywords: Bioengineering.
Advisor: Sattely Elizabeth 
Long Sharon R. 
Smolke Christina D.
Molecularly confined polymer nanocomposites

Molecular polymer confinement can be achieved in hybrid nanocomposites where individual polymer molecules are confined by a nanoporous matrix to dimensions comparable to or less than the molecular size of the polymer. Such molecular confinement can induce changes in a wide variety of properties of the confined polymer and the nanocomposite. In this dissertation, I focus on the mobility of the molecularly confined polymers as well as the thermal and fracture properties of the nanocomposite. In my first project, I show that the polymer mobility and the nanocomposite thermal and mechanical properties can be significantly influenced by the interaction of the molecularly confined polymer with the pore surface, which can be manipulated by surface chemical functionalization of the pores. Polyimide nanocomposites hold great promise for applications demanding fracture resistance at high temperature. In my second project, I discuss the strategy of improving fracture resistance of polyimide nanocomposites by increasing polymer fill level and polymer-surface interaction.

Keywords: Chemistry.
Advisor: Dauskardt R. H. (Reinhold H.) 
Chidsey Christopher E. D. (Christopher Elisha Dunn)
Xia Yan
More than Medical Records: Uncovering how Childhood Cancer Survivors learn about and interact with their Cancer Histories

From 1971 to 2010 the combined 5-year childhood cancer survival rate has increased from 40 percent to 82 percent (Cancer Research UK, 2015). With more children surviving cancer, more adults will live with the long-term effects of cancer treatments. 70 percent of childhood cancer survivors (CCS) are at risk of physical, psychological, and social late effects of treatment and 66 percent reported living with at least one chronic health condition 30 years post diagnosis (Hewitt, Weiner, & Simone, 2003). Amplifying the likelihood of poor health outcomes, CCS with limited access to their health histories have greater risk for poor health outcomes (Hóven, Lannering, Gustaffson, & Bownman, 2018). To limit some of this risk for poor health outcomes and to properly manage their healthcare, CCS need access to their health histories. Despite the importance for survivors to understand their health histories, research neglects to explore how CCS learn about and interact with their cancer histories as young adults. To fill this gap in the literature I interviewed 9 CCS between the ages of 18 and 29 that were treated for cancer at 10 years of age or younger. With these interviews I conducted a content analysis to identify common themes. I present how CCS learned about and continue to learn about their cancer histories. CCS reported using the following resources to learn about their cancer histories: parents, healthcare professionals knowledgeable of their cancer histories, scientific literature, summer camps for CCS, and survivor clinics. Although participants each reported using some of these resources, many of them still have questions about their cancer histories and relevant long-term effects. CCS interact with their cancer histories through feelings of uncertainty, fearing long-term side effects, feeling fortunate for good health, and feeling guilty for their limited knowledge of their cancer histories. The research reveals needed improvements in health education programs for CCS.

Keywords:  department of Science
Childhood cancer survivor
cancer
survivor
cancer histories
cancer narratives
Science Technology and Society
Stanford University
Thesis
Advisor: Dr. Lochlann S. Jain
Dr. Kyoko Sato
Movement representation in human motor cortex and applications to brain-computer interface control

Intracortical brain-computer interfaces (iBCIs) have largely built upon work investigating the neural representation of overt reaching movements in nonhuman primates (NHPs). However, in people with paralysis, iBCIs leverage neural features related to attempted movement of paralyzed limbs, which may differ substantially from that of overt movement of unparalyzed limbs. To understand how paralysis affects movement representation in the motor cortex, we first compared direction- and distance-related neural tuning of a human participant's attempted arm movements and overt head movements to that of NHP overt arm movements. The participant's neural activity during overt head movement was most similar to NHP overt arm movement with strongest tuning to distance. To further clarify how attempted movement-related neural activity translates into iBCI control, the participant controlled a cursor using a series of different attempted movement strategies. We found that neural activity changes during iBCI control, becoming more similar across different strategies. Applying these gained insights, we designed and demonstrated a discrete neural decoding system which leveraged the neural representation of both overt and attempted movements to enable classification of up to 32 discrete movements across the body. The attempt to move a paralyzed limb also differs from overt movement of an unparalyzed limb in that haptic feedback normally accompanying the movement is lost or diminished. To better understand how haptic stimulation affects motor cortical neurons and iBCI control, we integrated a haptic feedback device into our iBCI system, which provided skin-shear haptic stimulation at the back of the participant's neck. We found motor cortical units that exhibited sensory responses to the stimuli, some of which were significantly tuned to the stimuli and well modeled by cosine-shaped functions. We also demonstrated online iBCI cursor control with continuous skin-shear feedback driven by decoded command signals. Cursor control performance increased slightly but significantly when the participant was given haptic feedback as compared to the visual feedback condition. This work deepens our understanding of how paralysis affects movement representation, delivers a novel discrete neural decoding system leveraging the movement representation of both paralyzed and unparalyzed limbs, provides insight into how motor cortical units respond to haptic stimulation, and shows how this stimulation affects iBCI control performance. These results can help guide and inform the design of future neural prostheses.

Keywords: Mechanical Engineering.
Advisor: Okamura Allison 
Follmer Sean 
Shenoy Krishna V. (Krishna Vaughn)
Multi-dimensional imaging of immune response

Improvements in our understanding of the immune system have led to radical paradigm shifts in medicine including the advent of vaccines and cancer immunotherapy. New "high-dimensional" techniques promise to guide the next generation of immune based therapies, yet thus far, have failed to fully predict patient response or elucidate therapeutic mechanism of action. For this, a "multi-dimensional" approach is needed, as immunity occurs across space, time, and scale (e.g. cells to organ systems). To realize this goal, an immuno-imaging toolbox capable of multi-dimensional interrogation of immune response was built. This dissertation describes engineering principles learned and biological insights gained from developing imaging probes capable of non-invasively monitoring whole body immune response across space and time. This dissertation discusses how to select and validate appropriate imaging biomarkers of immune response, and provides several examples of applications for immuno-imaging in monitoring cancer immunotherapies. Some of the approaches and imaging probes developed in this work are currently being clinically translated for applications from selecting the right cancer patients for immune checkpoint inhibitors, to diagnosing and preventing immune-mediated organ transplant rejection. The state-of-art immuno-imaging toolbox described herein provides a previously unprecedented "multi-dimensional" view of the immune system in action and has the potential to guide future patient care.

Keywords: Bioengineering.
Advisor: Gambhir Sanjiv Sam 
Levin Craig 
Lin Michael Z.
Multi-Disciplinary Argument for Recognition of Term: Immigration Detention-Industrial Complex and A Case for its Abolition

A case for the abolition of immigration detention centers in the United States using the framework of prison abolition studies. This paper presents an argument using evidence from legal, historical, psychological, and cultural perspectives across various mediums to acknowledge the institutionalization of an immigration detention-industrial complex modeled and proliferated along the better recognized prison-industrial complex. Research across academic disciplines reveal a disproportionate imprisonment of black and brown people in relation to population---residue of buried histories of racial violence that procreated structures to sustain and proliferate a punitive society post formal recognition of slavery. A critical understanding of the role race plays in law enforcement can inform development of new resources and institutions in tune with local communities’ specific needs to protect communities most persecuted by law enforcement efforts. An intercommunity accountability system phases out the need to cage adults and children to death.

Keywords: immigration detention-industrial complex
prison-industrial complex
abolition
prison abolition
immigration
race
black
brown
Stanford University
Center for Latin American Studies
Thesis