Integration of relational and hierarchical network information for protein function prediction

BACKGROUND:In the current climate of high-throughput computational biology, the inference of a protein's function from related measurements, such as protein-protein interaction relations, has become a canonical task. Most existing technologies pursue this task as a classification problem, on a term-by-term basis, for each term in a database, such as the Gene Ontology (GO) database, a popular rigorous vocabulary for biological functions. However, ontology structures are essentially hierarchies, with certain top to bottom annotation rules which protein function predictions should in principle follow. Currently, the most common approach to imposing these hierarchical constraints on network-based classifiers is through the use of transitive closure to predictions.RESULTS:We propose a probabilistic framework to integrate information in relational data, in the form of a protein-protein interaction network, and a hierarchically structured database of terms, in the form of the GO database, for the purpose of protein function prediction. At the heart of our framework is a factorization of local neighborhood information in the protein-protein interaction network across successive ancestral terms in the GO hierarchy. We introduce a classifier within this framework, with computationally efficient implementation, that produces GO-term predictions that naturally obey a hierarchical 'true-path' consistency from root to leaves, without the need for further post-processing.CONCLUSION:A cross-validation study, using data from the yeast Saccharomyces cerevisiae, shows our method offers substantial improvements over both standard 'guilt-by-association' (i.e., Nearest-Neighbor) and more refined Markov random field methods, whether in their original form or when post-processed to artificially impose 'true-path' consistency. Further analysis of the results indicates that these improvements are associated with increased predictive capabilities (i.e., increased positive predictive value), and that this increase is consistent uniformly with GO-term depth. Additional in silico validation on a collection of new annotations recently added to GO confirms the advantages suggested by the cross-validation study. Taken as a whole, our results show that a hierarchical approach to network-based protein function prediction, that exploits the ontological structure of protein annotation databases in a principled manner, can offer substantial advantages over the successive application of 'flat' network-based methods.

A Distributed Outstar Network for Spatial Pattern Learning

The distributed outstar, a generalization of the outstar neural network for spatial pattern learning, is introduced. In the outstar, signals from a source node cause weights to learn and recall arbitrary patterns across a target field of nodes. The distributed outstar replaces the outstar source node with a source field of arbitrarily many nodes, whose activity pattern may be arbitrarily distributed or compressed. Learning proceeds according to a principle of atrophy due to disuse, whereby a path weight decreases in joint proportion to the transmitted path signal and the degree of disuse of the target node. During learning, the total signal to a target node converges toward that node's activity level. Weight changes at a node are apportioned according to the distributed pattern of converging signals. Three synaptic transmission functions, by a product rule, a capacity rule, and a threshold rule, are examined for this system. The three rules are computationally equivalent when source field activity is maximally compressed, or winner-take-all. When source field activity is distributed, catastrophic forgetting may occur. Only the threshold rule solves this problem. Analysis of spatial pattern learning by distributed codes thereby leads to the conjecture that the unit of long-term memory in such a system is an adaptive threshold, rather than the multiplicative path weight widely used in neural models.

ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network

This article introduces a new neural network architecture, called ARTMAP, that autonomously learns to classify arbitrarily many, arbitrarily ordered vectors into recognition categories based on predictive success. This supervised learning system is built up from a pair of Adaptive Resonance Theory modules (ARTa and ARTb) that are capable of self-organizing stable recognition categories in response to arbitrary sequences of input patterns. During training trials, the ARTa module receives a stream {a^(p)} of input patterns, and ARTb receives a stream {b^(p)} of input patterns, where b^(p) is the correct prediction given a^(p). These ART modules are linked by an associative learning network and an internal controller that ensures autonomous system operation in real time. During test trials, the remaining patterns a^(p) are presented without b^(p), and their predictions at ARTb are compared with b^(p). Tested on a benchmark machine learning database in both on-line and off-line simulations, the ARTMAP system learns orders of magnitude more quickly, efficiently, and accurately than alternative algorithms, and achieves 100% accuracy after training on less than half the input patterns in the database. It achieves these properties by using an internal controller that conjointly maximizes predictive generalization and minimizes predictive error by linking predictive success to category size on a trial-by-trial basis, using only local operations. This computation increases the vigilance parameter ρa of ARTa by the minimal amount needed to correct a predictive error at ARTb· Parameter ρa calibrates the minimum confidence that ARTa must have in a category, or hypothesis, activated by an input a^(p) in order for ARTa to accept that category, rather than search for a better one through an automatically controlled process of hypothesis testing. Parameter ρa is compared with the degree of match between a^(p) and the top-down learned expectation, or prototype, that is read-out subsequent to activation of an ARTa category. Search occurs if the degree of match is less than ρa. ARTMAP is hereby a type of self-organizing expert system that calibrates the selectivity of its hypotheses based upon predictive success. As a result, rare but important events can be quickly and sharply distinguished even if they are similar to frequent events with different consequences. Between input trials ρa relaxes to a baseline vigilance pa When ρa is large, the system runs in a conservative mode, wherein predictions are made only if the system is confident of the outcome. Very few false-alarm errors then occur at any stage of learning, yet the system reaches asymptote with no loss of speed. Because ARTMAP learning is self stabilizing, it can continue learning one or more databases, without degrading its corpus of memories, until its full memory capacity is utilized.

A Neural Network Model for the Spatial and Temporal Response of Retinal Ganglion Cells

This article introduces a quantitative model of early visual system function. The model is formulated to unify analyses of spatial and temporal information processing by the nervous system. Functional constraints of the model suggest mechanisms analogous to photoreceptors, bipolar cells, and retinal ganglion cells, which can be formally represented with first order differential equations. Preliminary numerical simulations and analytical results show that the same formal mechanisms can explain the behavior of both X (linear) and Y (nonlinear) retinal ganglion cell classes by simple changes in the relative width of the receptive field (RF) center and surround mechanisms. Specifically, an increase in the width of the RF center results in a change from X-like to Y-like response, in agreement with anatomical data on the relationship between α- and

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.