The problem of predicting the next outcome of an individual binary sequence based on a noisy observation of the past is considered. The goal of the predictor is to perform on each individual sequence (almost) as well as the best ``expert'' in a finite set where the performance is evaluated using a general loss function. This setup is a generalization of that considered extensively by researchers from various disciplines of universal prediction and forecasting for the case where the information regarding the past data, which are corrupted by noise, is incomplete.

In this work we restrict ourselves to the case where the noise corrupting the data is ``white'' (i.e., an i.i.d Bernoulli(p) process) and additive and where its parameter $p$ is assumed known to the predictor. In the expected loss regime, for a given sequence, we define the regret as the difference between the total expected loss of the predictor on the entire sequence and that of the best (i.e., having lowest expected loss on the particular sequence) expert in the comparison class. We generalize and improve the recent order results of Haussler et al. to this noisy setup for a large class of loss functions and show that under certain conditions on the loss functions, the minimax regret is \theta(\log N) while under other conditions it is \theta(\sqrt{n \log N}) where n is the sequence length and N is the cardinality of the expert class. It is also seen that this new setup, which involves a stochastic noise process, gives rise to additional interesting performance criteria by which our predictors are judged and shown to do well.

These results are part of an M.Sc. thesis under the supervision of Neri Merhav.