We propose a new differentially-private decision forest algorithm that minimizes both the number of queries required, and the sensitivity of those queries. To do so, we build an ensemble of random decision trees that avoids querying the private data except to find the majority class label in the leaf nodes. Rather than using a count query to return the class counts like the current state-ofthe-art, we use the Exponential Mechanism to only output the class label itself.This drastically reduces the sensitivity of the query -often by several orders of magnitude -which in turn reduces the amount of noise that must be added to preserve privacy. Our improved sensitivity is achieved by using "smooth sensitivity", which takes into account the specific data used in the query rather than assuming the worst-case scenario. We also extend work done on the optimal depth of random decision trees to handle continuous features, not just discrete features. This, along with several other improvements, allows us to create a differentially private decision forest with substantially higher predictive power than the current state-of-the-art.
Data mining information about people is becoming increasingly important in the data-driven society of the 21st century. Unfortunately, sometimes there are real-world considerations that conflict with the goals of data mining; sometimes the privacy of the people being data mined needs to be considered. This necessitates that the output of data mining algorithms be modified to preserve privacy while simultaneously not ruining the predictive power of the outputted model. Differential privacy is a strong, enforceable definition of privacy that can be used in data mining algorithms, guaranteeing that nothing will be learned about the people in the data that could not already be discovered without their participation. In this survey, we focus on one particular data mining algorithm—decision trees—and how differential privacy interacts with each of the components that constitute decision tree algorithms. We analyze both greedy and random decision trees, and the conflicts that arise when trying to balance privacy requirements with the accuracy of the model.
A quantitative study of the interaction of the T(0,1) torsional mode with an axial defect in a pipe is presented. The results are obtained from finite element simulations and experiments. The influence of the crack axial extent, depth, excitation frequency, and pipe circumference on the scattering is examined. It is found that the reflection from a defect consists of a series of the wave pulses with gradually decaying amplitudes. Such behavior is caused by the shear waves diffracting from the crack and then repeatedly interacting with the crack due to circumferential propagation. Time-domain reflection coefficient analysis demonstrates that the trend of the reflection strength for different crack lengths, pipe diameters, and frequencies from a through-thickness crack satisfies a simple normalization. The results show that the reflection coefficient initially increases with the crack length at all frequencies but finally reaches an oscillating regime. Also, at a given frequency and crack length the reflection decreases with the increase in pipe circumference. An additional scattering study of the shear wave SH(0) mode at a part-thickness notch in a plate shows that the reflection coefficient, when plotted against depth of the notch, increases with both frequency and notch depth.
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