Fatemeh Navidi - Academia.edu (original) (raw)

Papers by Fatemeh Navidi

We study a general stochastic ranking problem where an algorithm needs to adaptively select a seq... more We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario is captured by an individual submodular function, where the scenario is said to be covered when its function value goes above a given threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible (unless P=NP). This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning. The approximation ratio of our algorithm either matches or improves the best result known in each of these special cases. Furthermore, we extend our results to an adaptive vehicle routing problem, where costs are determined by an underlying metric. This routing problem is a significant generalization of the previously-studied adaptive travel...

A fundamental task in active learning involves performing a sequence of tests to identify an unkn... more A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of...

We study a general adaptive ranking problem where an algorithm needs to perform a sequence of act... more We study a general adaptive ranking problem where an algorithm needs to perform a sequence of actions on a random user, drawn from a known distribution, so as to "satisfy" the user as early as possible. The satisfaction of each user is captured by an individual submodular function, where the user is said to be satisfied when the function value goes above some threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible. The adaptive ranking problem has many applications in active learning and ranking: it significantly generalizes previously-studied problems such as optimal decision trees, equivalence class determination, decision region determination and submodular cover. We also present some preliminary experimental results based on our algorithm.

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template... more Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.

We consider the a priori traveling repairman problem, which is a stochastic version of the classi... more We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem (also called the traveling deliveryman or minimum latency problem). Given a metric (V,d) with a root r∈ V, the traveling repairman problem (TRP) involves finding a tour originating from r that minimizes the sum of arrival-times at all vertices. In its a priori version, we are also given independent probabilities of each vertex being active. We want to find a master tour τ originating from r and visiting all vertices. The objective is to minimize the expected sum of arrival-times at all active vertices, when τ is shortcut over the inactive vertices. We obtain the first constant-factor approximation algorithm for a priori TRP under non-uniform probabilities. Previously, such a result was only known for uniform probabilities.

Operations Research

Many applications of stochastic optimization involve making sequential decisions until some stopp... more Many applications of stochastic optimization involve making sequential decisions until some stopping criterion is satisfied. For example, in medical diagnosis, a doctor needs to perform an adaptive sequence of tests on a patient in order to diagnose a disease. Being adaptive allows the doctor to choose the next test based on the outcomes of prior tests. Given an a priori probability distribution over diseases, the goal is to minimize the expected cost of tests. In “Adaptive Submodular Ranking and Routing,” Navidi, Kambadur, and Nagarajan formulate a general stochastic optimization problem in which the stopping criterion corresponds to covering a submodular function. Such problems arise in many applications, including active learning, robotics, and disaster management. The authors obtain efficient algorithms with best possible performance guarantees. These results also extend to a vehicle-routing setting, in which one needs to plan an adaptive route based on information observed at n...

Operations Research Letters

Operations Research, Apr 7, 2020

We study a general stochastic ranking problem where an algorithm needs to adaptively select a seq... more We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario is captured by an individual submodular function, where the scenario is said to be covered when its function value goes above a given threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible (unless P = N P). This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning. The approximation ratio of our algorithm either matches or improves the best result known in each of these special cases. Furthermore, we extend our results to an adaptive vehicle routing problem, where costs are determined by an underlying metric. This routing problem is a significant generalization of the previously-studied adaptive traveling salesman and traveling repairman problems. Our approximation ratio nearly matches the best bound known for these special cases. Finally, we present experimental results for some applications of adaptive ranking.

BioMed Research International, 2015

The rapidly expanding eld of big data analytics has started to play a pivotal role in the evoluti... more The rapidly expanding eld of big data analytics has started to play a pivotal role in the evolution of healthcare practices and research. It has provided tools to accumulate, manage, analyze and assimilate large volumes of disparate, structured and unstructured data produced by current healthcare systems. Big data analytics has been recently applied towards aiding the process of care delivery and disease exploration.

We study a general stochastic ranking problem where an algorithm needs to adaptively select a seq... more We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario is captured by an individual submodular function, where the scenario is said to be covered when its function value goes above a given threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible (unless P=NP). This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning. The approximation ratio of our algorithm either matches or improves the best result known in each of these special cases. Furthermore, we extend our results to an adaptive vehicle routing problem, where costs are determined by an underlying metric. This routing problem is a significant generalization of the previously-studied adaptive travel...

A fundamental task in active learning involves performing a sequence of tests to identify an unkn... more A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of...

We study a general adaptive ranking problem where an algorithm needs to perform a sequence of act... more We study a general adaptive ranking problem where an algorithm needs to perform a sequence of actions on a random user, drawn from a known distribution, so as to "satisfy" the user as early as possible. The satisfaction of each user is captured by an individual submodular function, where the user is said to be satisfied when the function value goes above some threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible. The adaptive ranking problem has many applications in active learning and ranking: it significantly generalizes previously-studied problems such as optimal decision trees, equivalence class determination, decision region determination and submodular cover. We also present some preliminary experimental results based on our algorithm.

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template... more Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.

We consider the a priori traveling repairman problem, which is a stochastic version of the classi... more We consider the a priori traveling repairman problem, which is a stochastic version of the classic traveling repairman problem (also called the traveling deliveryman or minimum latency problem). Given a metric (V,d) with a root r∈ V, the traveling repairman problem (TRP) involves finding a tour originating from r that minimizes the sum of arrival-times at all vertices. In its a priori version, we are also given independent probabilities of each vertex being active. We want to find a master tour τ originating from r and visiting all vertices. The objective is to minimize the expected sum of arrival-times at all active vertices, when τ is shortcut over the inactive vertices. We obtain the first constant-factor approximation algorithm for a priori TRP under non-uniform probabilities. Previously, such a result was only known for uniform probabilities.

Operations Research

Many applications of stochastic optimization involve making sequential decisions until some stopp... more Many applications of stochastic optimization involve making sequential decisions until some stopping criterion is satisfied. For example, in medical diagnosis, a doctor needs to perform an adaptive sequence of tests on a patient in order to diagnose a disease. Being adaptive allows the doctor to choose the next test based on the outcomes of prior tests. Given an a priori probability distribution over diseases, the goal is to minimize the expected cost of tests. In “Adaptive Submodular Ranking and Routing,” Navidi, Kambadur, and Nagarajan formulate a general stochastic optimization problem in which the stopping criterion corresponds to covering a submodular function. Such problems arise in many applications, including active learning, robotics, and disaster management. The authors obtain efficient algorithms with best possible performance guarantees. These results also extend to a vehicle-routing setting, in which one needs to plan an adaptive route based on information observed at n...

Operations Research Letters

Operations Research, Apr 7, 2020

We study a general stochastic ranking problem where an algorithm needs to adaptively select a seq... more We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario is captured by an individual submodular function, where the scenario is said to be covered when its function value goes above a given threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible (unless P = N P). This problem unifies and generalizes many previously studied problems with applications in search ranking and active learning. The approximation ratio of our algorithm either matches or improves the best result known in each of these special cases. Furthermore, we extend our results to an adaptive vehicle routing problem, where costs are determined by an underlying metric. This routing problem is a significant generalization of the previously-studied adaptive traveling salesman and traveling repairman problems. Our approximation ratio nearly matches the best bound known for these special cases. Finally, we present experimental results for some applications of adaptive ranking.

BioMed Research International, 2015

The rapidly expanding eld of big data analytics has started to play a pivotal role in the evoluti... more The rapidly expanding eld of big data analytics has started to play a pivotal role in the evolution of healthcare practices and research. It has provided tools to accumulate, manage, analyze and assimilate large volumes of disparate, structured and unstructured data produced by current healthcare systems. Big data analytics has been recently applied towards aiding the process of care delivery and disease exploration.