This paper considers a modification of a PAC learning theory problem in which each instance of the training data is supplemented with side information. In this case, a transformation, given by a side-information map, of the training instance is also classified. However, the learning algorithm needs only to classify a new instance, not the instance and its value under the side information map. Side information can improve general learning rates, but not always. This paper shows that side information leads to the improvement of standard PAC learning theory rate bounds, under restrictions on the probable overlap between concepts and their images under the side information map.

This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that inputs are generated randomly from a known class consisting of linear combinations of k sinusoidals. The output of the system is classified at some single instant of time. The main result establishes that the number of samples needed for identification with small error and high probability, independently from the distribution of inputs, scales polynomially with n, the system dimension, and logarithmically with k.

The identification of continuous-time control systems is considered as a learning problem. As the general problem is too rich to be learnable, input signals are assumed to have only a finite number k of frequency components. When the system being identified has a dimension at most n, the required sample size scales polynomially with n and logarithmically with k.

We present a method for deriving necessary and sufficient conditions for the local stability of the TCP-RED congestion control. The analysis is based on a system of differential equations modeling the behavior of the system. One equation describes the dynamics of the TCP source population operating in the congestion avoidance phase. The TCP dynamics are driven by another differential equation representing the RED controlled queue, which determines, in the form of a packet loss function, the feedback to the TCP population. The stability of the system is characterized in terms of stability parameters and we illustrate how the physical RED parameters affect the stability. Finally, different stability conditions (sufficient vs. necessary) are compared by analyzing a further simplified TCP model, where the queue feedback is a packet loss function depending only on the aggregate traffic rate of the TCP population.