Threshold Auto-Tuning Metric Learning

It has been reported repeatedly that discriminative learning of distance metric boosts the pattern recognition performance. A weak point of ITML-based methods is that the distance threshold for similarity/dissimilarity constraints must be determined manually and it is sensitive to generalization performance, although the ITML-based methods enjoy an advantage that the Bregman projection framework can be applied for optimization of distance metric. In this paper, we present a new formulation of metric learning algorithm in which the distance threshold is optimized together. Since the optimization is still in the Bregman projection framework, the Dykstra algorithm can be applied for optimization. A nonlinear equation has to be solved to project the solution onto a half-space in each iteration. Na\"{i}ve method takes $O(LMn^{3})$ computational time to solve the nonlinear equation. In this study, an efficient technique that can solve the nonlinear equation in $O(Mn^{3})$ has been discovered. We have proved that the root exists and is unique. We empirically show that the accuracy of pattern recognition for the proposed metric learning algorithm is comparable to the existing metric learning methods, yet the distance threshold is automatically tuned for the proposed metric learning algorithm

Cognitive Constructivism and the Epistemic Significance of Sharp Statistical Hypotheses in Natural Sciences

This book presents our case in defense of a constructivist epistemological framework and the use of compatible statistical theory and inference tools. The basic metaphor of decision theory is the maximization of a gambler's expected fortune, according to his own subjective utility, prior beliefs an learned experiences. This metaphor has proven to be very useful, leading the development of Bayesian statistics since its XX-th century revival, rooted on the work of de Finetti, Savage and others. The basic metaphor presented in this text, as a foundation for cognitive constructivism, is that of an eigen-solution, and the verification of its objective epistemic status. The FBST - Full Bayesian Significance Test - is the cornerstone of a set of statistical tolls conceived to assess the epistemic value of such eigen-solutions, according to their four essential attributes, namely, sharpness, stability, separability and composability. We believe that this alternative perspective, complementary to the one ofered by decision theory, can provide powerful insights and make pertinent contributions in the context of scientific research.Comment: 453 page