The exaggerated intonation and special rhythmic properties of infant-directed speech (IDS) have been hypothesized to attract infants' attention to the speech stream. However, there has been little work actually connecting the properties of IDS to models of attentional processing or perceptual learning. A number of such attention models suggest that surprising or novel perceptual inputs attract attention, where novelty can be operationalized as the statistical (un)predictability of the stimulus in the given context. Since prosodic patterns such as F0 contours are accessible to young infants who are also known to be adept statistical learners, the present paper investigates a hypothesis that F0 contours in IDS are less predictable than those in adult-directed speech (ADS), given previous exposure to both speaking styles, thereby potentially tapping into basic attentional mechanisms of the listeners in a similar manner that relative probabilities of other linguistic patterns are known to modulate attentional processing in infants and adults. Computational modeling analyses with naturalistic IDS and ADS speech from matched speakers and contexts show that IDS intonation has lower overall temporal predictability even when the F0 contours of both speaking styles are normalized to have equal means and variances. A closer analysis reveals that there is a tendency of IDS intonation to be less predictable at the end of short utterances, whereas ADS exhibits more stable average predictability patterns across the full extent of the utterances. The difference between IDS and ADS persists even when the proportion of IDS and ADS exposure is varied substantially, simulating different relative amounts of IDS heard in different family and cultural environments. Exposure to IDS is also found to be more efficient for predicting ADS intonation contours in new utterances than exposure to the equal amount of ADS speech. This indicates that the more variable prosodic contours of IDS also generalize to ADS, and may therefore enhance prosodic learning in infancy. Overall, the study suggests that one reason behind infant preference for IDS could be its higher information value at the prosodic level, as measured by the amount of surprisal in the F0 contours. This provides the first formal link between the properties of IDS and the models of attentional processing and statistical learning in the brain. However, this finding does not rule out the possibility that other differences between the IDS and ADS also play a role.