On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem.

A Formulation for Active Learning with Applications to Object Detection

We discuss a formulation for active example selection for function learning problems. This formulation is obtained by adapting Fedorov's optimal experiment design to the learning problem. We specifically show how to analytically derive example selection algorithms for certain well defined function classes. We then explore the behavior and sample complexity of such active learning algorithms. Finally, we view object detection as a special case of function learning and show how our formulation reduces to a useful heuristic to choose examples to reduce the generalization error.

Self-Assembly of Stimuli-Responsive Water-Soluble [60]Fullerene End-Capped Ampholytic Block Copolymer

Well-defined, water-soluble, pH and temperature stimuli-responsive [60]fullerene (C₆₀) containing ampholytic block copolymer of poly((methacrylic acid)-block-(2-(dimethylamino)ethyl methacrylate))-block–C₆₀ (P(MAA-b-DMAEMA)-b-C₆₀) was synthesized by the atom transfer radical polymerization (ATRP) technique. The self-assembly behaviour of the C₆₀ containing polyampholyte in aqueous solution was characterized by dynamic light scattering (DLS), and transmission electron microscopy. This amphiphilic mono-C₆₀ end-capped block copolymer shows enhanced solubility in aqueous medium at room and elevated temperatures and at low and high pH but phase-separates at intermediate pH of between 5.4 and 8.8. The self assembly of the copolymer is different from that of P(MAA-b-DMAEMA). Examination of the association behavior using DLS revealed the co-existence of unimers and aggregates at low pH at all temperatures studied, with the association being driven by the balance of hydrophobic and electrostatic interactions. Unimers and aggregates of different microstructures are also observed at high pH and at temperatures below the lower critical solution temperature (LCST) of PDMAEMA. At high pH and at temperatures above the LCST of PDMAEMA, the formation of micelles and aggregates co-existing in solution is driven by the combination of hydrophobic, electrostatic, and charge-transfer interactions.