Vol. 9, No. 2
In Search of the Statistical Brain
Javier R. Movellan
Department of Cognitive Science
University of California, San Diego
The brain is a fantastic random number generator and its operating principles are inherrently statistical. I refer to this conceptual framework as "The Statistical Brain". This approach to understanding the brain and human information processing is not new. In my case, it was inspired by the work of signal-detection theorists in psychology, the PDP work on harmony theory, and the ideas of the late von Neumann, the designer of the digital computer.
According to von Neummann, a crucial difference between the brain and the digital computer is that the brain is statistical in nature whereas digital computers are deterministic. Digital computers were designed with an eye on reliability: At a hardware level, natural noise is cancelled by the use of digital technology, and at a functional level, computation is grounded on deterministic Boolean logic. Contrary to the digital computer, brains are designed to operate in natural environments, where uncertainty rules. They are made of massive numbers of simple stochastic processors and their representations are probabilistic and flexible, as required by the enoromous variability present in real-life situations.
But what are the designing principles of these natural stochastic computers? Can we envision new computers based on the same statistical principles as the brain? I am trying to address these questions in two ways: 1) analyzing the formal properties of stochastic networks, 2) studying how humans combine different sources of uncertain information in perceptual tasks.
With respect to the study of stochastic networks, the goal here is to find a formal framework to better understand how stochastic dynamical systems work. At this level, analysis is grounded on continuous stochastic calculus, a generalization of ordinary calculus. One of the things we learn from these network models is the need to think in terms of probability distributions evolving through time. When we initialize these networks, probability concentrates in particular states and, as time progresses, probability, and thus information, evolves according to well defined diffusion principles. From this point of view, one can think of the statistical brain as a continuous representational web and of probability as a substance diffusing through this web in response to internal and external forces. Understanding network dynamics in probability space may give us important insights about the way the statistical brain operates.
I am also trying to understand the designing principles of the statistical brain by studying how humans combine different sources of information (stimulus, context and prior knowledge) in perceptual tasks. The task I am working on now is audio-visual (AV) speech perception.
We know that the brain uses both visual and acoustic information to recognize speech. For example, when acoustic information for the syllable /ba/ is synchronized with video images of lip movements for /ga/, subjects report hearing /da/ or /ta/. This phenomenon, known as the McGurk-McDonald effect, raises crucial questions about the way the brain combines information from different sources: What kind of representations facilitate this intermodal integration? Is bimodal speech perception based on relatively unmodified and independent elements from each modality? Is it based on non-independent amodal representations? What are the temporal dynamics of information integration?
I like to approach these problems first from an engineering point of view. If I had to develop an optimal system to recognize speech, how would I go about it? Here is where I find probability theory in general and pattern recognition theory in particular so useful. In pattern recognition ideal optimal systems are called "Bayesian classifiers", or maximum posterior classifiers (MAP). A system that follows the MAP principles is guaranteed to achieve minimum error rates. MAP is a very useful framework to understand the type of problems that the brain needs to solve in real life. MAP tells us in a general way how information needs to be combined to achieve optimal performance. However, MAP itself does not tell us about specifics, unless we are willing to make assumptions. Here is where modeling results from human experiments may help: Is the human data consistent with the assumtions we are making?
Experimental psychologists have studied the problem of AV speech recognition with some success but their approach has been too limiting. In my opinion current psychological models have two major shortcomings:
1) Lack of temporal dynamics: Current models of speech perception typically do not pay attention to the temporal dynamics of the visual and acoustic signals. Figure 1, for example, shows preliminary results from an ongoing experiment in my laboratory. The figure shows the percentage of fused AV responses in a McGurck-like experiment as a function of the temporal delay between the visual and acoustic signals. The blue curve is for a high-volume acoustic signal, and the red curve for a low-volume signal. As the figure indicates, synchrony between the visual and acoustic signals plays a well defined role in the percentage of combined responses. This type of temporal dynamics is ignored in present psychological models but needs to be addressed if we want to develop realistic models of information integration.
Figure 1: Click on the Image to receive a .ps Version
2) Insufficient specification of computational mechanisms: Current
psychological models are typically built from the top-down. Based on
the response confusions made by humans, simple representational models
are developed that generate the same type of confusions that humans
do. This top-down approach typically used in psychology (from
responses to representations) is insufficient; it needs to be
complemented with a bottom-up approach (from physical stimuli to
internal representations). The bottom-up approach to modeling
emphasizes the importance of models capable of processing
physical signals through time. For example, in the AV speech
recognition case, we may start with images and acoustic signals,
process them with biologically inspired models of the acoustic and
visual system and train models of AV speech integration that would
actually work in real-life situations. Once we have a model built from
the bottom-up we can test whether the responses generated by
the system match the data obtained from humans. This strategy has the
advantage of forcing us to be very specific about hidden
assumptions in our models. Moreover, it allows us to visualize the
kind of representations that may be sufficient to solve the task under
Figure 2 shows an example of this bottom-up approach. The figure shows typical representations learned by a purely visual synthetic speech recognizer developed in my laboratory. The system is based on a simple stochastic network trained to recognize the first four digits in English. Each column is a different digit, starting with "one." Each row represents different time steps. The two pictures within each cell are related to intensity and to intensity derivatives, a crude measure of flow. The network uses dynamic probability distributions to represent possible ways in which people say the digits in English. Since we cannot visualize entire probability distributions evolving through time, the figure just shows the most-likely paths. The fact that the network representations are entire probability distributions, not just fixed patterns, allows it to be robust to variations in the way people look and act when they say things.
This particular system achieved a 89.5% correct generalization, which compares well with the 89.9% correct obtained by untrained humans. However, trained lip-readers achieved a 95% correct rate, indicating that there is still room for improvement. Interestingly the type of mistakes made by humans and by the synthetic system had a 0.99 correlation (98% of the variance in human confusions can be accounted for by the artificial model). This suggests that the probability distribution of representational states learned by the artificial system is a reasonable model of the stochastic representational space used by humans.
Presently we are developing a combined audio-visual system. The acoustic signal will be handled by a biologically inspired model of the auditory system, that converts the incoming waveform into a statistical representation of the pattern of activity in the cochlea. The visual input will be handled by a model of the MST, a center in the brain related to optical flow computation. This model, which was developed by Sereno and Zhang in our Department, computes optic flow in a robust and inexpensive way. Learning and information integration will be handled by a stochastic neural network. One of the most exciting aspects of this project is that it will help us find optimal ways to combine visual and acoustic representations. Is it a good idea to do low-level integration of the representations and base perceptual decisions on these multimodal representations? Is it better to keep the two channels separate and base the perceptual decisions on independent modal representations? This project will provide answers to these questions.
This is just an example of the possibilities opened by integrating the study of the brain, human information processing and computational analysis. In my case, probability theory and statistics are invaluable tools to guide my research and to bridge the gaps between these three fields. Hopefully our quest to understand the designing principles of the stochastic brain will take us to new, unexplored territories.
If you are interested on the specifics of the AV speech recognition project at my lab, you may contact me at email@example.com. I conclude with pointers to interesting sites related to speech recognition and to pattern recognition in general. I include a pointer to my home page, where you can get copies of papers related to our AV speech recognition project.