Joint Estimation of Trajectory and Dynamics from Paired Comparisons

Canal, Gregory; O’Shaughnessy, Matthew; Rozell, Christopher J.; Davenport, Mark A.

doi:10.1109/camsap45676.2019.9022446

Cited by 2 publications

(2 citation statements)

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“…Researchers have proposed a multitude of models ranging from classical techniques such as the Bradley-Terry model [35,36], Plackett-Luce model [37,38], and Thurstone model [39] to more modern approaches such as preference learning via Siamese networks [40] to fit the myriad of tailored applications of preference learning. In the linear setting, [7,[41][42][43] among others propose passive learning algorithms whereas [5,6,[17][18][19]44] propose adaptive sampling procedures. [20] perform localization from paired comparisons, and [45] employ a Gaussian process approach for learning pairwise preferences from multiple users.…”

Section: B Related Workmentioning

confidence: 99%

“…A common paradigm in metric learning is that by observing distance comparisons, one can learn a linear [10][11][12], kernelized [13,14], or deep metric [15,16] and use it for downstream tasks such as classification. Similarly, it is common in preference learning to use comparisons to learn a ranking or to identify a most preferred item [5,6,[17][18][19]. An important family of these algorithms reduces preference learning to identifying an ideal point for a fixed metric [5,20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

One for All: Simultaneous Metric and Preference Learning over Multiple Users

Canal¹,

Mason²,

Vinayak³

et al. 2022

Preprint

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This paper investigates simultaneous preference and metric learning from a crowd of respondents. A set of items represented by d-dimensional feature vectors and paired comparisons of the form "item i is preferable to item j" made by each user is given. Our model jointly learns a distance metric that characterizes the crowd's general measure of item similarities along with a latent ideal point for each user reflecting their individual preferences. This model has the flexibility to capture individual preferences, while enjoying a metric learning sample cost that is amortized over the crowd. We first study this problem in a noiseless, continuous response setting (i.e., responses equal to differences of item distances) to understand the fundamental limits of learning. Next, we establish prediction error guarantees for noisy, binary measurements such as may be collected from human respondents, and show how the sample complexity improves when the underlying metric is lowrank. Finally, we establish recovery guarantees under assumptions on the response distribution. We demonstrate the performance of our model on both simulated data and on a dataset of color preference judgements across a large number of users.Preprint. Under review.

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