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**1 - 4**of**4**### The Budgeted Biomarker Discovery Problem

"... Researchers conduct association studies to discover biomarkers in order to gain new biological insight on complex diseases and phenotypes. Although most researchers have intuitions about what defines a biomarker and how to assess the results of an association study, there is neither a formal definit ..."

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Researchers conduct association studies to discover biomarkers in order to gain new biological insight on complex diseases and phenotypes. Although most researchers have intuitions about what defines a biomarker and how to assess the results of an association study, there is neither a formal definition for what a biomarker is, nor objective goal for association studies. As a result, the literature is full of association studies with conflicting results – e.g., studies on the same phenotype that produce lists of biomarkers with little to no overlap. This thesis presents the “Budgeted Biomarker Discovery (BBD) problem”, which clearly defines (1) what a biomarker is, and (2) rewards for correctly identifying biomarkers and penalties for incorrectly identifying biomarkers. Furthermore, the BBD problem allows researchers to use a mixture of high- and low-throughput tech-nologies. In the context of discovering biomarkers from gene expression data, we show how future association studies can use both microarrays and qPCR data to objectively find the genes that are biomarkers in a cost efficient manner. We present several algorithms for solving the BBD problem, and show that good algorithms must make use of both microarrays and qPCR. Also, they must be able to adapt to the data as it is collected. For example, when solving a new BBD problem, we must begin by collecting microarrays because we do not yet know how many biomarkers we expect to identify, or which qPCR arrays would be most informative. Thus, we use the high-throughput microarrays to survey the problem, until we can identify which specific low-throughput qPCR arrays to use for focusing on those genes that are potentially biomarkers. To identify when this transition should occur, we present the problem of estimating the density of univariate statistics in high-throughput data, and we present our Fused Density Estimation (FDE) algorithm as ii a solution. We use FDE as the backbone of our adaptive algorithms for solving BBD problems. In a series of experiments on real microarray data and realistic synthetic data, we show that our BBD1 algorithm is the most robust solution, amongst those considered, to the BBD problem. iii

### An Incentive Compatible Multi-Armed-Bandit Crowdsourcing Mechanism with Quality Assurance

, 2014

"... Consider a requester who wishes to crowdsource a series of identical binary labeling tasks from a pool of workers so as to achieve an assured accuracy for each task, in a cost optimal way. The workers are heterogeneous with unknown but fixed qualities and moreover their costs are private. The proble ..."

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Consider a requester who wishes to crowdsource a series of identical binary labeling tasks from a pool of workers so as to achieve an assured accuracy for each task, in a cost optimal way. The workers are heterogeneous with unknown but fixed qualities and moreover their costs are private. The problem is to select an optimal subset of the workers to work on each task so that the outcome obtained from aggregating labels from them guarantees a target accuracy. This problem is challenging because the requester not only has to learn the qualities of the workers but also elicit their true costs. We develop a novel multi-armed bandit (MAB) mechanism for solving this problem. We propose a framework, Assured Accuracy Bandit (AAB), which leads to an adaptive, exploration separated MAB algorithm, Strategic Constrained Confidence Bound (CCB-S). We derive an upper bound on the number of exploration steps which depends on the target accuracy and true qualities. We show that our CCB-S algorithm produces an ex-post monotone allocation rule which can be transformed into an ex-post incentive compatible and ex-post individually rational mechanism that learns qualities of the workers and guarantees the target accuracy in a cost optimal way. 1

### Optimal Resource Allocation with Semi-Bandit Feedback

"... We study a sequential resource allocation prob-lem involving a fixed number of recurring jobs. At each time-step the manager should distribute available resources among the jobs in order to maximise the expected number of completed jobs. Allocating more resources to a given job in-creases the probab ..."

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We study a sequential resource allocation prob-lem involving a fixed number of recurring jobs. At each time-step the manager should distribute available resources among the jobs in order to maximise the expected number of completed jobs. Allocating more resources to a given job in-creases the probability that it completes, but with a cut-off. Specifically, we assume a linear model where the probability increases linearly until it equals one, after which allocating additional re-sources is wasteful. We assume the difficulty of each job is unknown and present the first algo-rithm for this problem and prove upper and lower bounds on its regret. Despite its apparent sim-plicity, the problem has a rich structure: we show that an appropriate optimistic algorithm can im-prove its learning speed dramatically beyond the results one normally expects for similar problems as the problem becomes resource-laden. 1

### The Cost of Interference in Evolving Systems?

"... Abstract. We study the situation of a decision-maker who aims to encourage the players of an evolutionary game theoretic system to follow certain desired behaviours. To do so, she can interfere in the system to reward her preferred behaviour patterns. However, this action requires certain cost (e.g. ..."

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Abstract. We study the situation of a decision-maker who aims to encourage the players of an evolutionary game theoretic system to follow certain desired behaviours. To do so, she can interfere in the system to reward her preferred behaviour patterns. However, this action requires certain cost (e.g., resource consumption). Given this, her main goal is to maintain an efficient trade-off between achieving the desired system status and minimising the total cost spent. Our initial numerical results reveal interesting observations, which in fact imply that further investigations in the future are required. 1