On the submodularity of sensor scheduling for estimation of linear dynamical systems
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Bibliographic record
Abstract
In this paper, we study the problem of using an energy constrained sensor network to estimate the state of a linear dynamical system. The state estimate is computed using a Kalman filter and the goal is to choose a subset of sensors at each time step so as to minimize the a posteriori error covariance. Recent work has indicated that the simple greedy algorithm, which chooses the sensor at each time step that maximizes the error covariance reduction, outperforms many other known scheduling algorithms. In addition, it has been suggested that the cost function mapping a sensor sequence to an error covariance cost is submodular; this would imply that the greedy algorithm provides a near optimal sensor schedule. As a negative result, we show that the sensor schedule cost is not, in general, a submodular function. This contradicts an established result. We argue that given a linear dynamical system, it is computationally intractable to determine if it will yield a submodular cost. Thus, we provide sufficient and easily checkable conditions under which the dynamical system yields a submodular cost, and thus performance guarantees for the greedy schedule.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it