Frey uses probability theory and graphical models to connect information theory and machine learning. Graphical models become useful in identifying and classifying patterns, in understanding nonsequential learning, and in data compression and channel coding. Various examples of graphical models are used in the work, such as Markov random fills, Bayesian networks, chain graphs, and factor graphs. Many of these models have applications in genetics to identify clique, generational, and ancestral relations. Frey believes in the use of these graphical models to develop algorithms for pattern classification, nonsequential learning, data compression, and channel coding. His ultimate goal is to come up with code that will give excellent performance as well as good results.

The use of humor and examples makes this work quite entertaining. The first interesting example is how the United States Postal Service Office of Advanced Technology has worked on the machine identification of handwritten digits in zip codes. With the use of the nearest neighbor classifier and the k-nearest neighbor classifier, they have been able to reduce the misclassification rate to 6.7 percent on a test set of 4000 handwriting patterns. Clearly, pattern classification is possible here.

The second example is the burglar alarm problem of determining whether the alarm was set off by a real burglar and not just tripped by an earthquake. Frey’s discussion of this problem shows how biological systems respond to their environment and how multiple-cause networks can be supervised and trained to identify a pattern even though there may be meaningful hidden causes for the sensory input. The system is then trained to respond to nonsequential learning patterns.

The goal of data compression is to exploit the redundancy in input patterns to represent individual patterns concisely on average. The best result is lossless data compression, whereby the original pattern can be completely recovered despite the compression. The concern of channel coding is to come up with efficient, reliable methods of communicating discrete messages over physical channels that may introduce errors.

The author’s sense of humor is also shown by the use of such witticisms as “A code by any other network would not decode as sweetly” or “Just toss the graphical model in a bag and shake.” By interspersing his mathematical and graphical presentations with examples and humor, he helped ease the intellectual burden on readers who are less mathematically inclined or have less of a mathematical background.

The author’s emphasis on future research directions is also valuable. He sees this work as part of a larger scientific process, and suggests ways of describing problems and developing useful algorithms that will allow us to treat what are deemed to be complicated problems in simple ways. This would mean improving model structures, as he has tried to do in this work. It could also mean getting into interactive decoding. He believes that coming up with snappy algorithms will bring about faster influence and learning, but he recognizes the researcher’s dilemma: How do you know when to stop? How do you know it is meaningful? According to Frey, solving this could mean “scaling up the brain.”