Most of the efforts in human genetics are directed towards identifying and characterizing genetic variants that impact human traits, achieved by examining relationships between traits and variants. A Genome Wide Association Study (GWAS) quantifies statistical association between genetic variation and phenotypes. These statistical associations can tell us about the biological mechanisms affecting the phenotype and can allow us to predict the phenotype from genetic information in a clinical setting. However, the majority of GWAS datasets have been generated with commodity genotype arrays of single-nucleotide polymorphism (SNP) that fail to explain the majority of heritability for many complex traits even with large sample sizes.

One compelling hypothesis explaining the missing heritability dilemma is that complex variants, such as multi-allelic repeats not in strong linkage with common SNPs, are important drivers of complex traits but are largely invisible to current analyses. Short tandem repeats (STRs), consisting of repeated motifs of 1–6bp in tandem, comprise more than 3% of the human genome. Multiple lines of evidence support a role of STRs in complex traits, particularly in neurological and psychiatric phenotypes. However, existing technologies have not allowed for systematic STR association studies.

To overcome these challenges, we recently generated a reference STR+SNP haplotype panel that enables imputation of STR genotypes into SNP genotypes available for most GWAS cohorts. Our imputation pipeline achieves a high concordance and can be used to impute nearly 500,000 STRs genome-wide. Next, we leveraged our reference haplotype panel to impute STRs into GWAS data for more than 50,000 samples from the Psychiatric Genomics Consortium (PGC) to perform a genome-wide analysis of associations between STR lengths and schizophrenia.

In this dissertation, I demonstrate an end-to-end pipeline for conducting large biobank scale GWAS using STRs that serves as one of the initial studies which researchers can find useful for incorporating complex variants into their analysis.

Coordination failure reduces match quality among employers and candidates in the job market, resulting in a large number of unfilled positions and/or unstable, short-term employment. Centralized job search engines provide a platform that connects directly employers with job-seekers. However, they require users to disclose a significant amount of personal data, i.e., build a user profile, in order to provide meaningful recommendations. In this paper, we present PrivateJobMatch -- a privacy-oriented deferred multi-match recommender system -- which generates stable pairings while requiring users to provide only a partial ranking of their preferences. PrivateJobMatch explores a series of adaptations of the game-theoretic Gale-Shapley deferred-acceptance algorithm which combine the flexibility of decentralized markets with the intelligence of centralized matching. We identify the shortcomings of the original algorithm when applied to a job market and propose novel solutions that rely on machine learning techniques. Experimental results on real and synthetic data confirm the benefits of the proposed algorithms across several quality measures. Over the past year, we have implemented a PrivateJobMatch prototype and deployed it in an active job market economy. Using the gathered real-user preference data, we find that the match-recommendations are superior to a typical decentralized job market---while requiring only a partial ranking of the user preferences.

Previous papers have tested efficient risk sharing under the assumption of identical risk preferences. In this paper we show that, if in the data households have heterogeneous risk preferences, the tests proposed in the past reject efficiency even if households share risk efficiently. To address this issue we propose a method that enables one to test efficiency even when households have different preferences for risk. The method is composed of three tests. The first one can be used todetermine whether in the data under investigation households have homogeneous risk preferences. The second and third test can be used to evaluate efficient risk sharing when the hypothesis of homogeneous risk preferences is rejected. We use this method to test efficient risk sharing in rural India. Using the first test, we strongly reject the hypothesis of identical risk preferences. We then test efficiency with and without the assumption of preference homogeneity. In the first case we reject efficient risk sharing at the village and caste level. In the second case we still reject efficiency at the village level, but we cannot reject this hypothesis at the caste level. This finding suggests that the relevant risk-sharing unit in rural India is the caste and not the village.

South American populations have a complex admixture history. The earliest Native Americans are known to have migrated into the Americas as early as 14000 years ago. The region saw large scale migrations from European colonial powers starting early 1500s. In just a couple of centuries the entire Western hemisphere came under the control of these European powers. These colonial powers brought millions of Africans across the Atlantic between the 1500s and 1800s through the slave trade which led to further admixture of African populations into the Americans. Due to multiple migrations events, presence of different colonial powers that followed different slave trade practices, South Americans populations have a highly heterogeneous genetic composition. We investigate the admixture history of one of the South American populations living in Cerro de Pasco, a high altitude mining town in the Andes region of Peru. Studying the admixture history of this population can give us important insights into the origins of several selection forces at play in this population. We found the Andean population to have lesser proportions of European and African ancestry as compared to the other South American populations. The timing of European and African admixture into this population was also found to be significantly different from other populations, which could be a direct result of lower European and African ancestry proportion. These results indicate a higher level of segregation between the Native Americans and the European/African populations in Peru as compared to other regions.

Deep Neural Networks are now the most prominent tool in Machine Learning with a wide array of societal applications ranging from computer vision and natural language processing to drug discovery and material engineering and much more. With the increasing pervasiveness of deep learning in daily lives especially in areas of critical important it becomes increasingly necessary to understand the mechanisms and dynamics behind how these models work. This is important not only in engendering confidence in the public at large but to also ensure fairness and accountability.This thesis focuses on developing approaches that can help us visualise and compare representations inside deep neural networks. We start with a coupled factorisation framework where we try to embed Features, Neurons and Input Instances themselves into a common shared space. This enables us to compute direction comparisons and correlations between the 3 entities and visualise a network by analysing the subspaces in this common projected space. We build upon this by then utilising tools from subspace clustering literature to develop a more architecture agnostic framework for comparing representations of a neural network. In doing so we discover that deeper and more overparameterised networks have large blocks of layers that are similar to each other. For a network with a given depth, phenomena also occurs when the network is trained on much less data and also earlier in its training. Additionally we also discover that earlier layer of the network are quicker to converge to their final state than later layers. Next we perform a similar study for networks in the domain of time series classification. In this study we focus on analysing how different architectural choices affect the way these networks learn. We take ResNets and Temporal Convolution Networks (TCNs), which are architecturally identical but for the causality of the convolution filter used. We demonstrate that this causes the 2 architectures to have very different dynamics of learning representations in their internal layers. This is the first such study for univariate time series networks. Finally, we analyse how neural networks evolve self-expressive structures in their internal representations by comparing networks trained in different loss regimes. We also demonstrate their predictive power when compared to linear probes trained on representations in the same space. We also use the information encoded in the self-expressive structures to differentiate between networks which generalise and memorise and observe that the effects of memorisation tend to appear in the final layers of a network and how these effects change when using a different non linear activations over neurons.