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**1 - 6**of**6**### Research Statement

"... Summary I am interested in (1) the design of intelligent agents and systems, primarily guided by machine learning; (2) modeling and understanding collective dynamics that result from intelligent individual behavior; and (3) using this understanding to inform the design of venues where people and aut ..."

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Summary I am interested in (1) the design of intelligent agents and systems, primarily guided by machine learning; (2) modeling and understanding collective dynamics that result from intelligent individual behavior; and (3) using this understanding to inform the design of venues where people and automated agents come together to interact. A central focus of my research is on understanding how information flows through systems, how it can be best used by intelligent agents, and how its presence, absence, or the form in which it is available impacts decisions at the individual and systemic levels. My work can be categorized into four broad themes. 1: Collective intelligence I am interested in both modeling and understanding the dynamics of collective intelligence, and in designing algorithms that allow us to use the power of collective wisdom to make better decisions. I have been working on the foundations of a rigorous theory of how information grows in novel social media like Wikipedia and the blogosphere, and on information aggregation and dissemination in prediction markets. In recent work, we have documented some remarkable regularities in the life cycles of average Wikipedia pages and blog posts [26, 27]. They exhibit a concave rise to an editing / commenting peak, followed by decay at a 1/t rate over time. We have proposed a simple model of information creation that matches the data

### A BAYESIAN APPROACH TO STOCHASTIC ROOT FINDING

"... A stylized model of one-dimensional stochastic root-finding involves repeatedly querying an oracle as to whether the root lies to the left or right of a given point x. The oracle answers this question, but the received answer is incorrect with probability 1 − p(x). A Bayesian-style algorithm for thi ..."

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A stylized model of one-dimensional stochastic root-finding involves repeatedly querying an oracle as to whether the root lies to the left or right of a given point x. The oracle answers this question, but the received answer is incorrect with probability 1 − p(x). A Bayesian-style algorithm for this problem that assumes knowledge of p(·) repeatedly updates a density giving, in some sense, one’s belief about the location of the root. We demonstrate how the algorithm works, and provide some results that shed light on its performance, both when p(·) is constant and when p(·) varies with x. 1

### BISECTION SEARCH WITH NOISY RESPONSES

"... Abstract. Bisection search is the most efficient algorithm for locating a unique point X ∗ ∈ [0, 1] when we are able to query an oracle only about whether X ∗ lies to the left or right of a point x of our choosing. We study a noisy version of this classic problem, where the oracle’s response is cor ..."

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Abstract. Bisection search is the most efficient algorithm for locating a unique point X ∗ ∈ [0, 1] when we are able to query an oracle only about whether X ∗ lies to the left or right of a point x of our choosing. We study a noisy version of this classic problem, where the oracle’s response is correct only with probability p. The Probabilistic Bisection Algorithm (PBA) introduced in Horstein (1963) can be used to locate X ∗ in this setting. While the method works extremely well in practice, very little is known about its theoretical properties. In this paper, we provide several key findings about the PBA, which lead to the main conclusion that the expected absolute residuals of successive search results, i.e., E[|X ∗ − Xn|], converge to 0 at a geometric rate.

### SEQUENTIAL SCREENING: A BAYESIAN DYNAMIC PROGRAMMING ANALYSIS OF OPTIMAL GROUP-SPLITTING

"... Sequential screening is the problem of allocating simulation effort to identify those input factors that have an important effect on a simulation’s output. In this problem, sophisticated algorithms can be substantially more efficient than simulating one factor at a time. We consider this problem in ..."

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Sequential screening is the problem of allocating simulation effort to identify those input factors that have an important effect on a simulation’s output. In this problem, sophisticated algorithms can be substantially more efficient than simulating one factor at a time. We consider this problem in a Bayesian framework, in which each factor is important independently and with a known probability. We use dynamic programming to compute the Bayes-optimal method for splitting factors among groups within a sequential bifurcation procedure (Bettonvil & Kleijnen 1997). We assume importance can be tested without error. Numerical experiments suggest that existing group-splitting rules are optimal, or close to optimal, when factors have homogeneous importance probability, but that substantial gains are possible when factors have heterogeneous probability of importance. 1

### Learning to Discover: A Bayesian Approach

"... Generalized binary search is a natural framework for modeling interactive search. This is the first paper that studies this problem under the assumption that the user’s searched items are drawn from an unknown probability distribution. We propose an algorithm that efficiently learns how to quickly d ..."

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Generalized binary search is a natural framework for modeling interactive search. This is the first paper that studies this problem under the assumption that the user’s searched items are drawn from an unknown probability distribution. We propose an algorithm that efficiently learns how to quickly discover the user’s searched items over time as the user interacts with the search engine, show that it is Bayesian optimal, and prove that its regret increases only sublinearly with time. 1

### A COLLABORATIVE 20 QUESTIONS MODEL FOR TARGET SEARCH WITH HUMAN-MACHINE INTERACTION

"... We consider the problem of 20 questions with noise for collaborative players under the minimum entropy criterion [1] in the setting of stochastic search, with application to target localization. First, assuming conditionally independent collaborators, we characterize the structure of the optimal pol ..."

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We consider the problem of 20 questions with noise for collaborative players under the minimum entropy criterion [1] in the setting of stochastic search, with application to target localization. First, assuming conditionally independent collaborators, we characterize the structure of the optimal policy for constructing the sequence of questions. This generalizes the single player probabilistic bisection method [1, 2] for stochastic search problems. Second, we prove a separation theorem showing that optimal joint queries achieve the same performance as a greedy sequential scheme. Third, we establish convergence rates of the mean-square error (MSE). Fourth, we derive upper bounds on the MSE of the sequential scheme. This framework provides a mathematical model for incorporating a human in the loop for active machine learning systems. Index Terms — optimal query selection, human-machine interaction, target localization, convergence rate, minimum entropy. 1.