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We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is proportional to the expected number of points falling within the hypersphere radius. The distance to the $N$-th nearest neighbor alone is then a sufficient statistic for the density. In the non-uniform case the proportionality is distorted. We model this distortion by normalizing hypersphere volumes to the largest one and expressing the resulting distribution in terms of the Legendre polynomials. Using Monte Carlo simulations we show that this approach can be used to effectively address the tradeoff between smoothing bias and estimator variance for sparsely sampled distributions.
We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for n
The observed velocities of the gas in barred galaxies are a combination of the azimuthally-averaged circular velocity and non-circular motions, primarily caused by gas streaming along the bar. These non-circular flows must be accounted for before the
In this paper, we propose an ensemble learning algorithm called textit{under-bagging $k$-nearest neighbors} (textit{under-bagging $k$-NN}) for imbalanced classification problems. On the theoretical side, by developing a new learning theory analysis,
In this paper, we report progress on answering the open problem presented by Pagh~[14], who considered the nearest neighbor search without false negatives for the Hamming distance. We show new data structures for solving the $c$-approximate nearest n
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive random sa