In machine learning problems a learning algorithm tries to learn the input–output dependency (relationship) of a system from a training dataset. This input–output relationship is usually deformed by a random noise. From experience, simulations, and special case theories, most practitioners...

In the problem of binary classification (or medical diagnosis), the classification rule (or diagnostic test) produces a continuous decision variable which is compared to a critical value (or threshold). Test values above (or below) that threshold are called positive (or negative) for disease....

Productivity growth is essential for economic enhancement of any country. However it is empirically quite perplexing to estimate it. The standard practice is to estimate productivity changes by incorporating a time trend within the production function (Baltagi and Griffin 1988; Kumbhakar and Hesmati...

The problem of determining the size of the training sample needed to achieve sufficiently small misclassification probability is considered. The appropriate sample size is approximated using a stopping rule. The proposed procedure is asymptotically optimal.

A Central Limit Theorem for a triangular array of row-wise independent Hilbert-valued random elements with finite second moment is proved under mild convergence requirements on the covariances of the row sums and the Lindeberg condition along the evaluations at an orthonormal basis. A Central...