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Portugaly, Elon


Unbiased Estimation of the Value of an Optimized Policy

arXiv.org Machine Learning

Randomized trials, also known as A/B tests, are used to select between two policies: a control and a treatment. Given a corresponding set of features, we can ideally learn an optimized policy P that maps the A/B test data features to action space and optimizes reward. However, although A/B testing provides an unbiased estimator for the value of deploying B (i.e., switching from policy A to B), direct application of those samples to learn the the optimized policy P generally does not provide an unbiased estimator of the value of P as the samples were observed when constructing P. In situations where the cost and risks associated of deploying a policy are high, such an unbiased estimator is highly desirable. We present a procedure for learning optimized policies and getting unbiased estimates for the value of deploying them. We wrap any policy learning procedure with a bagging process and obtain out-of-bag policy inclusion decisions for each sample. We then prove that inverse-propensity-weighting effect estimator is unbiased when applied to the optimized subset. Likewise, we apply the same idea to obtain out-of-bag unbiased per-sample value estimate of the measurement that is independent of the randomized treatment, and use these estimates to build an unbiased doubly-robust effect estimator. Lastly, we empirically shown that even when the average treatment effect is negative we can find a positive optimized policy.


Counterfactual Reasoning and Learning Systems

arXiv.org Artificial Intelligence

This work shows how to leverage causal inference to understand the behavior of complex learning systems interacting with their environment and predict the consequences of changes to the system. Such predictions allow both humans and algorithms to select changes that improve both the short-term and long-term performance of such systems. This work is illustrated by experiments carried out on the ad placement system associated with the Bing search engine.


Noise and the two-thirds power Law

Neural Information Processing Systems

The two-thirds power law, an empirical law stating an inverse nonlinear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant ofupper-limb movement. It has also been shown to exist in eyemotion, locomotionand was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed eitherto smoothness in hand-or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis ofsignal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying thepower-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operatingon the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.


Noise and the two-thirds power Law

Neural Information Processing Systems

The two-thirds power law, an empirical law stating an inverse nonlinear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant of upper-limb movement. It has also been shown to exist in eyemotion, locomotion and was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed either to smoothness in hand-or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis of signal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying the power-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operating on the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.


Noise and the two-thirds power Law

Neural Information Processing Systems

The two-thirds power law, an empirical law stating an inverse nonlinear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant of upper-limb movement. It has also been shown to exist in eyemotion, locomotion and was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed either to smoothness in hand-or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis of signal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying the power-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operating on the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.