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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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Cited by 10 (2 self)
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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.
An Optimal Policy for Target Localization with Application to Electron Microscopy
"... This paper considers the task of finding a target location by making a limited number of sequential observation. Each observation results from evaluating an imperfect classifier of a chosen cost and accuracy on an interval of chosen length and position. Within a Bayesian framework, we study the prob ..."
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Cited by 9 (5 self)
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This paper considers the task of finding a target location by making a limited number of sequential observation. Each observation results from evaluating an imperfect classifier of a chosen cost and accuracy on an interval of chosen length and position. Within a Bayesian framework, we study the problem of minimizing an objective that combines the entropy of the posterior distribution with the cost of the questions asked. In this problem, we show that the onestep lookahead policy is Bayesoptimal for any arbitrary time horizon. Moreover, this onestep lookahead policy is easy to compute and implement. We then use this policy in the context of localizing mitochondria in electron microscope images, and experimentally show that significant speed ups in acquisition can be gained, while maintaining near equal image quality at target locations, when compared to current policies. Proceedings of the 30 th
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
SEQUENTIAL SCREENING: A BAYESIAN DYNAMIC PROGRAMMING ANALYSIS OF OPTIMAL GROUPSPLITTING
"... 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 Bayesoptimal 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 groupsplitting 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
Optimal Sequential Experimental Design for Stochastic Rootfinding in Drug Development
, 2011
"... Metritis is a bacterial infection of the uterus. It is a leading cause of loss of milk production and fertility in dairy cows. It also occurs in other animals and people. The treatments developed may also be useful for other problematic bacterial infections, in both animals and people (e.g. MRSA). C ..."
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Metritis is a bacterial infection of the uterus. It is a leading cause of loss of milk production and fertility in dairy cows. It also occurs in other animals and people. The treatments developed may also be useful for other problematic bacterial infections, in both animals and people (e.g. MRSA). Current Treatment: BroadSpectrum Antibiotics Metritis is caused primarily by E. coli and A. pyogenes bacteria. Antibiotics are used to treat metritis in sick cows. Antibiotics are also given to well cows as a preventative measure. Causes to be concerned about the indiscriminate use of broadspectrum antibiotics: 1 Bacteria develop resistance to antibiotics if they are used too widley. 2 Releasing large quantities of antibiotics into the environment via farm effluent may have negative environmental effects. An Alternative Treatment: Bacteriophages Bacteriophages (abbreviated phages) are viruses that kill bacteria. Can we treat bacterial infections with phages instead of antibiotics? Bacteriophagebased Treatments: Advantages Reduced risk of bacterial resistance Phages are a new type of treatment. Each phage would be used against a few bacteria, limiting its use. Increasing the number of available treatments, and limiting their use, mitigates the problem of bacterial resistance. Reduced environmental impact: Each phage kills a few very specific strains of bacteria, and nothing else. In contrast, each type of antibiotic kills a wide variety of bacteria. Phages already exist naturally at dairy farms.
1Collaborative 20 Questions for Target Localization
"... We consider the problem of 20 questions with noise for multiple players under the minimum entropy criterion [1] in the setting of stochastic search, with application to target localization. Each player yields a noisy response to a binary query governed by a certain error probability. First, we propo ..."
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We consider the problem of 20 questions with noise for multiple players under the minimum entropy criterion [1] in the setting of stochastic search, with application to target localization. Each player yields a noisy response to a binary query governed by a certain error probability. First, we propose a sequential policy for constructing questions that queries each player in sequence and refines the posterior of the target location. Second, we consider a joint policy that asks all players questions in parallel at each time instant and 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. Third, we prove an equivalence between the two schemes showing that, despite the fact that the sequential scheme has access to a more refined filtration, the joint scheme performs just as well on average. Fourth, we establish convergence rates of the meansquare error (MSE) and derive error exponents. Lastly, we obtain an extension to the case of unknown error probabilities. This framework provides a mathematical model for incorporating a human in the loop for active machine learning systems. Index Terms Optimal query selection, machinemachineinteraction, target localization, convergence rate, minimum entropy, humanaided decision making. I.