Neural Information Processing Systems http://nips.cc/

In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a general non-parametric setup.

The resolution of intelligence tests, in particular numerical sequences, has been of great interest in the evaluation of AI systems. We present a new computational model called KitBit that uses a reduced set of algorithms and their combinations to build a predictive model that finds the underlying pattern in numerical sequences, such as those included in IQ tests and others of much greater complexity. We present the fundamentals of the model and its application in different cases. First, the system is tested on a set of number series used in IQ tests collected from various sources. Next, our model is successfully applied on the sequences used to evaluate the models reported in the literature. In both cases, the system is capable of solving these types of problems in less than a second using standard computing power. Finally, KitBit's algorithms have been applied for the first time to the complete set of entire sequences of the well-known OEIS database. We find a pattern in the form of a list of algorithms and predict the following terms in the largest number of series to date. These results demonstrate the potential of KitBit to solve complex problems that could be represented numerically.

Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a general non-parametric setup. Specifically, a Wald-type test statistic is obtained based on an iterated estimate produced by functional gradient descent algorithms in a reproducing kernel Hilbert space. A notable contribution is to establish a ``sharp'' stopping rule: when the number of iterations achieves an optimal order, testing optimality is achievable; otherwise, testing optimality becomes impossible. As a by-product, a similar sharpness result is also derived for minimax optimal estimation under early stopping. All obtained results hold for various kernel classes, including Sobolev smoothness classes and Gaussian kernel classes.

Early stopping of iterative algorithms is an algorithmic regularization method to avoid over-fitting in estimation and classification. In this paper, we show that early stopping can also be applied to obtain the minimax optimal testing in a general non-parametric setup. Specifically, a Wald-type test statistic is obtained based on an iterated estimate produced by functional gradient descent algorithms in a reproducing kernel Hilbert space. A notable contribution is to establish a ``sharp'' stopping rule: when the number of iterations achieves an optimal order, testing optimality is achievable; otherwise, testing optimality becomes impossible. As a by-product, a similar sharpness result is also derived for minimax optimal estimation under early stopping. All obtained results hold for various kernel classes, including Sobolev smoothness classes and Gaussian kernel classes.