XCSc: a novel approach to clustering with extended classifier system

In this paper, we propose a novel approach to clustering noisy and complex data sets based on the eXtend Classifier Systems (XCS). The proposed approach, termed XCSc, has three main processes: (a) a learning process to evolve the rule population, (b) a rule compacting process to remove redundant rules after the learning process, and (c) a rule merging process to deal with the overlapping rules that commonly occur between the clusters. In the first process, we have modified the clustering mechanisms of the current available XCS and developed a new accelerate learning method to improve the quality of the evolved rule population. In the second process, an effective rule compacting algorithm is utilized. The rule merging process is based on our newly proposed agglomerative hierarchical rule merging algorithm, which comprises the following steps: (i) all the generated rules are modeled by a graph, with each rule representing a node; (ii) the vertices in the graph are merged to form a number of sub-graphs (i.e. rule clusters) under some pre-defined criteria, which generates the final rule set to represent the clusters; (iii) each data is re-checked and assigned to a cluster that it belongs to, guided by the final rule set. In our experiments, we compared the proposed XCSc with CHAMELEON, a benchmark algorithm well known for its excellent performance, on a number of challenging data sets. The results show that the proposed approach outperforms CHAMELEON in the successful rate, and also demonstrates good stability.     

Designing boosting ensemble of relational fuzzy systems

A method frequently used in classification systems for improving classification accuracy is to combine outputs of several classifiers. Among various types of classifiers, fuzzy ones are tempting because of using intelligible fuzzy if-then rules. In the paper we build an AdaBoost ensemble of relational neuro-fuzzy classifiers. Relational fuzzy systems bond input and output fuzzy linguistic values by a binary relation; thus, fuzzy rules have additional, comparing to traditional fuzzy systems, weights - elements of a fuzzy relation matrix. Thanks to this the system is better adjustable to data during learning. In the paper an ensemble of relational fuzzy systems is proposed. The problem is that such an ensemble contains separate rule bases which cannot be directly merged. As systems are separate, we cannot treat fuzzy rules coming from different systems as rules from the same (single) system. In the paper, the problem is addressed by a novel design of fuzzy systems constituting the ensemble, resulting in normalization of individual rule bases during learning. The method described in the paper is tested on several known benchmarks and compared with other machine learning solutions from the literature.     

The evolution of social learning rules: Payoff-biased and frequency-dependent biased transmission

Humans and other animals do not use social learning indiscriminately, rather, natural selection has favoured the evolution of social learning rules that make selective use of social learning to acquire relevant information in a changing environment. We present a gene-culture coevolutionary analysis of a small selection of such rules (unbiased social learning, payoff-biased social learning and frequency-dependent biased social learning, including conformism and anti-conformism) in a population of asocial learners where the environment is subject to a constant probability of change to a novel state. We define conditions under which each rule evolves to a genetically polymorphic equilibrium. We find that payoff-biased social learning may evolve under high levels of environmental variation if the fitness benefit associated with the acquired behaviour is either high or low but not of intermediate value. In contrast, both conformist and anti-conformist biases can become fixed when environment variation is low, whereupon the mean fitness in the population is higher than for a population of asocial learners. Our examination of the population dynamics reveals stable limit cycles under conformist and anti-conformist biases and some highly complex dynamics including chaos. Anti-conformists can out-compete conformists when conditions favour a low equilibrium frequency of the learned behaviour. We conclude that evolution, punctuated by the repeated successful invasion of different social learning rules, should continuously favour a reduction in the equilibrium frequency of asocial learning, and propose that, among competing social learning rules, the dominant rule will be the one that can persist with the lowest frequency of asocial learning.     

The spatiotemporal learning rule and its efficiency in separating spatiotemporal patterns

The hippocampus plays an important role in the course of establishing long-term memory, i.e., to make short-term memory of spatially and temporally associated input information. In 1996 (Tsukada et al. 1996), the spatiotemporal learning rule was proposed based on differences observed in hippocampal long-term potentiation (LTP) induced by various spatiotemporal pattern stimuli. One essential point of this learning rule is that the change of synaptic weight depends on both spatial coincidence and the temporal summation of input pulses. We applied this rule to a single-layered neural network and compared its ability to separate spatiotemporal patterns with that of other rules, including the Hebbian learning rule and its extended rules. The simulated results showed that the spatiotemporal learning rule had the highest efficiency in discriminating spatiotemporal pattern sequences, while the Hebbian learning rule (including its extended rules) was sensitive to differences in spatial patterns.     

Computational Consequences of Temporally Asymmetric Learning Rules: I. Differential Hebbian Learning

Temporally asymetric learning rules governing plastic changes in synaptic efficacy have recently been identified in physiological studies. In these rules, the exact timing of pre- and postsynaptic spikes is critical to the induced change of synaptic efficacy. The temporal learning rules treated in this article are approximately antisymmetric; the synaptic efficacy is enhanced if the postsynaptic spike follows the presynaptic spike by a few milliseconds, but the efficacy is depressed if the postsynaptic spike precedes the presynaptic spike. The learning dynamics of this rule are studied using a stochastic model neuron receiving a set of serially delayed inputs. The average change of synaptic efficacy due to the temporally antisymmetric learning rule is shown to yield differential Hebbian learning. These results are demonstrated with both mathematical analyses and computer simulations, and connections with theories of classical conditioning are discussed.     

Learning rules for optimal selection in a varying environment: mate choice revisited

The quality of a chosen partner can be one of the most significantfactors affecting an animal's long-term reproductive success.We investigate optimal mate choice rules in an environment wherethere is both local variation in the quality of potential mateswithin each local mating pool and spatial (or temporal) variationin the average quality of the pools themselves. In such a situation,a robust rule that works well across a variety of environmentswill confer a significant reproductive advantage. We formulatea full Bayesian model for updating information in such a varyingenvironment and derive the form of the rule that maximizes expectedreward in a spatially varying environment. We compare the theoreticalperformance of our optimal learning rule against both fixedthreshold rules and simpler near-optimal learning rules andshow that learning is most advantageous when both the localand environmental variances are large. We consider how optimalsimple learning rules might evolve and compare their evolutionwith that of fixed threshold rules using genetic algorithmsas minimal models of the relevant genetics. Our analysis pointsup the variety of ways in which a near-optimal rule can be expressed.Finally, we describe how our results extend to the case of temporallyvarying environments.     

Visual artificial grammar learning: comparative research on humans, kea (Nestor notabilis) and pigeons (Columba livia)

Artificial grammar learning (AGL) provides a useful tool for exploring rule learning strategies linked to general purpose pattern perception. To be able to directly compare performance of humans with other species with different memory capacities, we developed an AGL task in the visual domain. Presenting entire visual patterns simultaneously instead of sequentially minimizes the amount of required working memory. This approach allowed us to evaluate performance levels of two bird species, kea (Nestor notabilis) and pigeons (Columba livia), in direct comparison to human participants. After being trained to discriminate between two types of visual patterns generated by rules at different levels of computational complexity and presented on a computer screen, birds and humans received further training with a series of novel stimuli that followed the same rules, but differed in various visual features from the training stimuli. Most avian and all human subjects continued to perform well above chance during this initial generalization phase, suggesting that they were able to generalize learned rules to novel stimuli. However, detailed testing with stimuli that violated the intended rules regarding the exact number of stimulus elements indicates that neither bird species was able to successfully acquire the intended pattern rule. Our data suggest that, in contrast to humans, these birds were unable to master a simple rule above the finite-state level, even with simultaneous item presentation and despite intensive training.     

Association pattern mining of intron retention events in human based on hybrid learning machine

Alternative splicing is a main component of protein diversity, and aberrant splicing is known to be one of the main causes of genetic disorders such as cancer. Many statistical and computational approaches have identified several major factors that determine the splicing event, such as exon/intron length, splice site strength, and density of splicing enhancers or silencers. These factors may be correlated with one another and thus result in a specific type of splicing, but there has not been a systematic approach to extracting comprehensible association patterns. Here, we attempted to understand the decision making process of the learning machine on intron retention event. We adopted a hybrid learning machine approach using a random forest and association rule mining algorithm to determine the governing factors of intron retention events and their combined effect on decision-making processes. By quantifying all candidate features into five category values, we enhanced the understandability of generated rules. The interesting features found by the random forest algorithm are that only the adenine- and thymine-based triplets such as ATA, TTA, and ATT, but not the known intronic splicing enhancer GGG triplet is shown the significant features. The rules generated by the association rule mining algorithm also show that constitutive introns are generally characterized by high adenine- and thymine-based triplet frequency (level 3 and above), 3' and 5' splice site scores, exonic splicing silencer scores, and intron length, whereas retained introns are characterized by low-level counterpart scores.     

Mirrored STDP Implements Autoencoder Learning in a Network of Spiking Neurons

The autoencoder algorithm is a simple but powerful unsupervised method for training neural networks. Autoencoder networks can learn sparse distributed codes similar to those seen in cortical sensory areas such as visual area V1, but they can also be stacked to learn increasingly abstract representations. Several computational neuroscience models of sensory areas, including Olshausen & Field’s Sparse Coding algorithm, can be seen as autoencoder variants, and autoencoders have seen extensive use in the machine learning community. Despite their power and versatility, autoencoders have been difficult to implement in a biologically realistic fashion. The challenges include their need to calculate differences between two neuronal activities and their requirement for learning rules which lead to identical changes at feedforward and feedback connections. Here, we study a biologically realistic network of integrate-and-fire neurons with anatomical connectivity and synaptic plasticity that closely matches that observed in cortical sensory areas. Our choice of synaptic plasticity rules is inspired by recent experimental and theoretical results suggesting that learning at feedback connections may have a different form from learning at feedforward connections, and our results depend critically on this novel choice of plasticity rules. Specifically, we propose that plasticity rules at feedforward versus feedback connections are temporally opposed versions of spike-timing dependent plasticity (STDP), leading to a symmetric combined rule we call Mirrored STDP (mSTDP). We show that with mSTDP, our network follows a learning rule that approximately minimizes an autoencoder loss function. When trained with whitened natural image patches, the learned synaptic weights resemble the receptive fields seen in V1. Our results use realistic synaptic plasticity rules to show that the powerful autoencoder learning algorithm could be within the reach of real biological networks.     

Stability of complex spike timing-dependent plasticity in cerebellar learning

Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. Constraints are derived for the timing between complex spikes and presynaptic spikes, constraints that result from the stability of the learning dynamics of the learning rule. Potential instabilities in the parallel fiber synaptic learning rule are found to be stabilized by synaptic plasticity at inhibitory synapses if the inhibitory learning rules are stable, and conditions for stability of inhibitory plasticity are given. Combining excitatory with inhibitory plasticity provides a mechanism for minimizing the overall synaptic input. Stable learning rules are shown to be able to sculpt simple-spike patterns by regulating the excitability of neurons in the inferior olive that give rise to climbing fibers.     

Independent Component Analysis in Spiking Neurons

Although models based on independent component analysis (ICA) have been successful in explaining various properties of sensory coding in the cortex, it remains unclear how networks of spiking neurons using realistic plasticity rules can realize such computation. Here, we propose a biologically plausible mechanism for ICA-like learning with spiking neurons. Our model combines spike-timing dependent plasticity and synaptic scaling with an intrinsic plasticity rule that regulates neuronal excitability to maximize information transmission. We show that a stochastically spiking neuron learns one independent component for inputs encoded either as rates or using spike-spike correlations. Furthermore, different independent components can be recovered, when the activity of different neurons is decorrelated by adaptive lateral inhibition.     

Allen's rule revisited: quantitative genetics of extremity length in the common frog along a latitudinal gradient

Ecogeographical rules linking climate to morphology have gained renewed interest because of climate change. Yet few studies have evaluated to what extent geographical trends ascribed to these rules have a genetic, rather than environmentally determined, basis. This applies especially to Allen's rule, which states that the relative extremity length decreases with increasing latitude. We studied leg length in the common frog (Rana temporaria) along a 1500 km latitudinal gradient utilizing wild and common garden data. In the wild, the body size-corrected femur and tibia lengths did not conform to Allen's rule but peaked at mid-latitudes. However, the ratio of femur to tibia length increased in the north, and the common garden data revealed a genetic cline consistent with Allen's rule in some trait and treatment combinations. While selection may have shortened the leg length in the north, the genetic trend seems to be partially masked by environmental effects.     

A burst-based "Hebbian" learning rule at retinogeniculate synapses links retinal waves to activity-dependent refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.     

Slowness: an objective for spike-timing-dependent plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this "temporal stability" or "slowness" approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing-dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the "trace rule." The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.     

A Burst-Based “Hebbian” Learning Rule at Retinogeniculate Synapses Links Retinal Waves to Activity-Dependent Refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.     

Learning rules for social foragers: implications for the producer-scrounger game and ideal free distribution theory

In population games, the optimal behaviour of a forager depends partly on courses of action selected by other individuals in the population. How individuals learn to allocate effort in foraging games involving frequency-dependent payoffs has been little examined. The performance of three different learning rules was investigated in several types of habitats in each of two population games. Learning rules allow individuals to weigh information about the past and the present and to choose among alternative patterns of behaviour. In the producer-scrounger game, foragers use producer to locate food patches and scrounger to exploit the food discoveries of others. In the ideal free distribution game, foragers that experience feeding interference from companions distribute themselves among heterogeneous food patches. In simulations of each population game, the use of different learning rules induced large variation in foraging behaviour, thus providing a tool to assess the relevance of each learning rule in experimental systems. Rare mutants using alternative learning rules often successfully invaded populations of foragers using other rules indicating that some learning rules are not stable when pitted against each other. Learning rules often closely approximated optimal behaviour in each population game suggesting that stimulus-response learning of contingencies created by foraging companions could be sufficient to perform at near-optimal level in two population games.     

LTD windows of the STDP learning rule and synaptic connections having a large transmission delay enable robust sequence learning amid background noise

Spike-timing-dependent synaptic plasticity (STDP) is a simple and effective learning rule for sequence learning. However, synapses being subject to STDP rules are readily influenced in noisy circumstances because synaptic conductances are modified by pre- and postsynaptic spikes elicited within a few tens of milliseconds, regardless of whether those spikes convey information or not. Noisy firing existing everywhere in the brain may induce irrelevant enhancement of synaptic connections through STDP rules and would result in uncertain memory encoding and obscure memory patterns. We will here show that the LTD windows of the STDP rules enable robust sequence learning amid background noise in cooperation with a large signal transmission delay between neurons and a theta rhythm, using a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections. The important element of the present model for robust sequence learning amid background noise is the symmetric STDP rule having LTD windows on both sides of the LTP window, in addition to the loop connections having a large signal transmission delay and the theta rhythm pacing activities of stellate cells. Above all, the LTD window in the range of positive spike-timing is important to prevent influences of noise with the progress of sequence learning.     

Slowness: An Objective for Spike-Timing–Dependent Plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this “temporal stability” or “slowness” approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing–dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the “trace rule.” The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.     

Sleep Promotes the Extraction of Grammatical Rules

Grammar acquisition is a high level cognitive function that requires the extraction of complex rules. While it has been proposed that offline time might benefit this type of rule extraction, this remains to be tested. Here, we addressed this question using an artificial grammar learning paradigm. During a short-term memory cover task, eighty-one human participants were exposed to letter sequences generated according to an unknown artificial grammar. Following a time delay of 15 min, 12 h (wake or sleep) or 24 h, participants classified novel test sequences as Grammatical or Non-Grammatical. Previous behavioral and functional neuroimaging work has shown that classification can be guided by two distinct underlying processes: (1) the holistic abstraction of the underlying grammar rules and (2) the detection of sequence chunks that appear at varying frequencies during exposure. Here, we show that classification performance improved after sleep. Moreover, this improvement was due to an enhancement of rule abstraction, while the effect of chunk frequency was unaltered by sleep. These findings suggest that sleep plays a critical role in extracting complex structure from separate but related items during integrative memory processing. Our findings stress the importance of alternating periods of learning with sleep in settings in which complex information must be acquired.     

Stimulus representation in SOP: II. An application to inhibition of delay

The componential extension of SOP accounts for conditioned response (CR) timing in Pavlovian conditioning by assuming that learning accrues with relative independence to stimulus elements that are differentially occasioned during the duration of the conditioned stimulus (CS). SOP, using a competitive learning rule and the assumption that temporal learning emerges via resolution of what is equivalent to an "AX+BX-" discrimination, predicts a progressive increase in the latency of the CR over training, or what Pavlov refer to as "inhibition of delay." Other componential models, which use noncompetitive learning rules, do not predict inhibition of delay. Either type of model makes the prediction indicated, independently of the length of the CS-unconditioned stimulus (US) interval. We report two experiments that demonstrated inhibition of delay when rabbits were trained with relatively long, but not with short, CS-US intervals. To account for this divergence, we assumed that the SOP stimulus trace involves two kinds of elements, some with a temporally distributed pattern of activity over the duration of the CS duration, and some with a randomly distributed pattern. This stimulus representation, not only allows for inhibition of delay with long but not short CS-US intervals, but in combination with SOP's performance rule deduces CR's with "Weber variability."