Statistical learning theory for geospatial data. Case study: Aral sea

In recent years there has been an explosive growth in the development of adaptive and data driven methods. One of the efficient and data-driven approaches is based on statistical learning theory (Vapnik 1998). The theory is based on Structural Risk Minimisation (SRM) principle and has a solid statistical background. When applying SRM we are trying not only to reduce training error ? to fit the available data with a model, but also to reduce the complexity of the model and to reduce generalisation error. Many nonlinear learning procedures recently developed in neural networks and statistics can be understood and interpreted in terms of the structural risk minimisation inductive principle. A recent methodology based on SRM is called Support Vector Machines (SVM). At present SLT is still under intensive development and SVM find new areas of application (www.kernel-machines.org). SVM develop robust and non linear data models with excellent generalisation abilities that is very important both for monitoring and forecasting. SVM are extremely good when input space is high dimensional and training data set i not big enough to develop corresponding nonlinear model. Moreover, SVM use only support vectors to derive decision boundaries. It opens a way to sampling optimization, estimation of noise in data, quantification of data redundancy etc. Presentation of SVM for spatially distributed data is given in (Kanevski and Maignan 2004).

De la perception à l'apprentissage [From perception to learning]

Dans le domaine de la perception, l'apprentissage est contraint par la présence d'une architecture fonctionnelle constituée d'aires corticales distribuées et très spécialisées. Dans le domaine des troubles visuels d'origine cérébrale, l'apprentissage d'un patient hémi-anopsique ou agnosique sera limité par ses capacités perceptives résiduelles, mais un déficit de reconnaissance visuelle de nature apparemment perceptive, peut également être associé à une altération des représentations en mémoire à long terme. Des réseaux neuronaux distincts pour la reconnaissance - cortex temporal - et pour la localisation des sons - cortex pariétal - ont été décrits chez l'homme. L'étude de patients cérébro-lésés confirme le rôle des indices spatiaux dans un traitement auditif explicite du « where » et dans la discrimination implicite du « what ». Cette organisation, similaire à ce qui a été décrit dans la modalité visuelle, faciliterait les apprentissages perceptifs. Plus généralement, l'apprentissage implicite fonde une grande partie de nos connaissances sur le monde en nous rendant sensible, à notre insu, aux règles et régularités de notre environnement. Il serait impliqué dans le développement cognitif, la formation des réactions émotionnelles ou encore l'apprentissage par le jeune enfant de sa langue maternelle. Le caractère inconscient de cet apprentissage est confirmé par l'étude des temps de réaction sériels de patients amnésiques dans l'acquisition d'une grammaire artificielle. Son évaluation pourrait être déterminante dans la prise en charge ré-adaptative. [In the field of perception, learning is formed by a distributed functional architecture of very specialized cortical areas. For example, capacities of learning in patients with visual deficits - hemianopia or visual agnosia - from cerebral lesions are limited by perceptual abilities. Moreover a visual deficit in link with abnormal perception may be associated with an alteration of representations in long term (semantic) memory. Furthermore, perception and memory traces rely on parallel processing. This has been recently demonstrated for human audition. Activation studies in normal subjects and psychophysical investigations in patients with focal hemispheric lesions have shown that auditory information relevant to sound recognition and that relevant to sound localisation are processed in parallel, anatomically distinct cortical networks, often referred to as the "What" and "Where" processing streams. Parallel processing may appear counterintuitive from the point of view of a unified perception of the auditory world, but there are advantages, such as rapidity of processing within a single stream, its adaptability in perceptual learning or facility of multisensory interactions. More generally, implicit learning mechanisms are responsible for the non-conscious acquisition of a great part of our knowledge about the world, using our sensitivity to the rules and regularities structuring our environment. Implicit learning is involved in cognitive development, in the generation of emotional processing and in the acquisition of natural language. Preserved implicit learning abilities have been shown in amnesic patients with paradigms like serial reaction time and artificial grammar learning tasks, confirming that implicit learning mechanisms are not sustained by the cognitive processes and the brain structures that are damaged in amnesia. In a clinical perspective, the assessment of implicit learning abilities in amnesic patients could be critical for building adapted neuropsychological rehabilitation programs.]

Machine learning for spatial environmental data. Theory, applications and software

The book presents the state of the art in machine learning algorithms (artificial neural networks of different architectures, support vector machines, etc.) as applied to the classification and mapping of spatially distributed environmental data. Basic geostatistical algorithms are presented as well. New trends in machine learning and their application to spatial data are given, and real case studies based on environmental and pollution data are carried out. The book provides a CD-ROM with the Machine Learning Office software, including sample sets of data, that will allow both students and researchers to put the concepts rapidly to practice.

Organization and plasticity of auditory spatial representations

Spatial hearing refers to a set of abilities enabling us to determine the location of sound sources, redirect our attention toward relevant acoustic events, and recognize separate sound sources in noisy environments. Determining the location of sound sources plays a key role in the way in which humans perceive and interact with their environment. Deficits in sound localization abilities are observed after lesions to the neural tissues supporting these functions and can result in serious handicaps in everyday life. These deficits can, however, be remediated (at least to a certain degree) by the surprising capacity of reorganization that the human brain possesses following damage and/or learning, namely, the brain plasticity. In this thesis, our aim was to investigate the functional organization of auditory spatial functions and the learning-induced plasticity of these functions. Overall, we describe the results of three studies. The first study entitled "The role of the right parietal cortex in sound localization: A chronometric single pulse transcranial magnetic stimulation study" (At et al., 2011), study A, investigated the role of the right parietal cortex in spatial functions and its chronometry (i.e. the critical time window of its contribution to sound localizations). We concentrated on the behavioral changes produced by the temporarily inactivation of the parietal cortex with transcranial magnetic stimulation (TMS). We found that the integrity of the right parietal cortex is crucial for localizing sounds in the space and determined a critical time window of its involvement, suggesting a right parietal dominance for auditory spatial discrimination in both hemispaces. In "Distributed coding of the auditory space in man: evidence from training-induced plasticity" (At et al., 2013a), study B, we investigated the neurophysiological correlates and changes of the different sub-parties of the right auditory hemispace induced by a multi-day auditory spatial training in healthy subjects with electroencephalography (EEG). We report a distributed coding for sound locations over numerous auditory regions, particular auditory areas code specifically for precise parts of the auditory space, and this specificity for a distinct region is enhanced with training. In the third study "Training-induced changes in auditory spatial mismatch negativity" (At et al., 2013b), study C, we investigated the pre-attentive neurophysiological changes induced with a training over 4 days in healthy subjects with a passive mismatch negativity (MMN) paradigm. We showed that training changed the mechanisms for the relative representation of sound positions and not the specific lateralization themselves and that it changed the coding in right parahippocampal regions. - L'audition spatiale désigne notre capacité à localiser des sources sonores dans l'espace, de diriger notre attention vers les événements acoustiques pertinents et de reconnaître des sources sonores appartenant à des objets distincts dans un environnement bruyant. La localisation des sources sonores joue un rôle important dans la façon dont les humains perçoivent et interagissent avec leur environnement. Des déficits dans la localisation de sons sont souvent observés quand les réseaux neuronaux impliqués dans cette fonction sont endommagés. Ces déficits peuvent handicaper sévèrement les patients dans leur vie de tous les jours. Cependant, ces déficits peuvent (au moins à un certain degré) être réhabilités grâce à la plasticité cérébrale, la capacité du cerveau humain à se réorganiser après des lésions ou un apprentissage. L'objectif de cette thèse était d'étudier l'organisation fonctionnelle de l'audition spatiale et la plasticité induite par l'apprentissage de ces fonctions. Dans la première étude intitulé « The role of the right parietal cortex in sound localization : A chronometric single pulse study » (At et al., 2011), étude A, nous avons examiné le rôle du cortex pariétal droit dans l'audition spatiale et sa chronométrie, c'est-à- dire le moment critique de son intervention dans la localisation de sons. Nous nous sommes concentrés sur les changements comportementaux induits par l'inactivation temporaire du cortex pariétal droit par le biais de la Stimulation Transcrânienne Magnétique (TMS). Nous avons démontré que l'intégrité du cortex pariétal droit est cruciale pour localiser des sons dans l'espace. Nous avons aussi défini le moment critique de l'intervention de cette structure. Dans « Distributed coding of the auditory space : evidence from training-induced plasticity » (At et al., 2013a), étude B, nous avons examiné la plasticité cérébrale induite par un entraînement des capacités de discrimination auditive spatiale de plusieurs jours. Nous avons montré que le codage des positions spatiales est distribué dans de nombreuses régions auditives, que des aires auditives spécifiques codent pour des parties données de l'espace et que cette spécificité pour des régions distinctes est augmentée par l'entraînement. Dans « Training-induced changes in auditory spatial mismatch negativity » (At et al., 2013b), étude C, nous avons examiné les changements neurophysiologiques pré- attentionnels induits par un entraînement de quatre jours. Nous avons montré que l'entraînement modifie la représentation des positions spatiales entraînées et non-entrainées, et que le codage de ces positions est modifié dans des régions parahippocampales.

On learning dynamics underlying the evolution of learning rules.

In order to understand the development of non-genetically encoded actions during an animal's lifespan, it is necessary to analyze the dynamics and evolution of learning rules producing behavior. Owing to the intrinsic stochastic and frequency-dependent nature of learning dynamics, these rules are often studied in evolutionary biology via agent-based computer simulations. In this paper, we show that stochastic approximation theory can help to qualitatively understand learning dynamics and formulate analytical models for the evolution of learning rules. We consider a population of individuals repeatedly interacting during their lifespan, and where the stage game faced by the individuals fluctuates according to an environmental stochastic process. Individuals adjust their behavioral actions according to learning rules belonging to the class of experience-weighted attraction learning mechanisms, which includes standard reinforcement and Bayesian learning as special cases. We use stochastic approximation theory in order to derive differential equations governing action play probabilities, which turn out to have qualitative features of mutator-selection equations. We then perform agent-based simulations to find the conditions where the deterministic approximation is closest to the original stochastic learning process for standard 2-action 2-player fluctuating games, where interaction between learning rules and preference reversal may occur. Finally, we analyze a simplified model for the evolution of learning in a producer-scrounger game, which shows that the exploration rate can interact in a non-intuitive way with other features of co-evolving learning rules. Overall, our analyses illustrate the usefulness of applying stochastic approximation theory in the study of animal learning.

Drosophila rely on learning while foraging under semi-natural conditions

Learning is predicted to affect manifold ecological and evolutionary processes, but the extent to which animals rely on learning in nature remains poorly known, especially for short-lived non-social invertebrates. This is in particular the case for Drosophila, a favourite laboratory system to study molecular mechanisms of learning. Here we tested whether Drosophila melanogaster use learned information to choose food while free-flying in a large greenhouse emulating the natural environment. In a series of experiments flies were first given an opportunity to learn which of two food odours was associated with good versus unpalatable taste; subsequently, their preference for the two odours was assessed with olfactory traps set up in the greenhouse. Flies that had experienced palatable apple-flavoured food and unpalatable orange-flavoured food were more likely to be attracted to the odour of apple than flies with the opposite experience. This was true both when the flies first learned in the laboratory and were then released and recaptured in the greenhouse, and when the learning occurred under free-flying conditions in the greenhouse. Furthermore, flies retained the memory of their experience while exploring the greenhouse overnight in the absence of focal odours, pointing to the involvement of consolidated memory. These results support the notion that even small, short lived insects which are not central-place foragers make use of learned cues in their natural environments.

A model for the evolution of reinforcement learning in fluctuating games

Many species are able to learn to associate behaviours with rewards as this gives fitness advantages in changing environments. Social interactions between population members may, however, require more cognitive abilities than simple trial-and-error learning, in particular the capacity to make accurate hypotheses about the material payoff consequences of alternative action combinations. It is unclear in this context whether natural selection necessarily favours individuals to use information about payoffs associated with nontried actions (hypothetical payoffs), as opposed to simple reinforcement of realized payoff. Here, we develop an evolutionary model in which individuals are genetically determined to use either trial-and-error learning or learning based on hypothetical reinforcements, and ask what is the evolutionarily stable learning rule under pairwise symmetric two-action stochastic repeated games played over the individual's lifetime. We analyse through stochastic approximation theory and simulations the learning dynamics on the behavioural timescale, and derive conditions where trial-and-error learning outcompetes hypothetical reinforcement learning on the evolutionary timescale. This occurs in particular under repeated cooperative interactions with the same partner. By contrast, we find that hypothetical reinforcement learners tend to be favoured under random interactions, but stable polymorphisms can also obtain where trial-and-error learners are maintained at a low frequency. We conclude that specific game structures can select for trial-and-error learning even in the absence of costs of cognition, which illustrates that cost-free increased cognition can be counterselected under social interactions.

Validation of and comparison between a semidistributed rainfall-runoff hydrological model (PREVAH) and a spatially distributed snow-evolution model (SnowModel) for snow cover prediction in mountain ecosystems

Snow cover is an important control in mountain environments and a shift of the snow-free period triggered by climate warming can strongly impact ecosystem dynamics. Changing snow patterns can have severe effects on alpine plant distribution and diversity. It thus becomes urgent to provide spatially explicit assessments of snow cover changes that can be incorporated into correlative or empirical species distribution models (SDMs). Here, we provide for the first time a with a lower overestimation comparison of two physically based snow distribution models (PREVAH and SnowModel) to produce snow cover maps (SCMs) at a fine spatial resolution in a mountain landscape in Austria. SCMs have been evaluated with SPOT-HRVIR images and predictions of snow water equivalent from the two models with ground measurements. Finally, SCMs of the two models have been compared under a climate warming scenario for the end of the century. The predictive performances of PREVAH and SnowModel were similar when validated with the SPOT images. However, the tendency to overestimate snow cover was slightly lower with SnowModel during the accumulation period, whereas it was lower with PREVAH during the melting period. The rate of true positives during the melting period was two times higher on average with SnowModel with a lower overestimation of snow water equivalent. Our results allow for recommending the use of SnowModel in SDMs because it better captures persisting snow patches at the end of the snow season, which is important when modelling the response of species to long-lasting snow cover and evaluating whether they might survive under climate change.

What can ecosystems learn? Expanding evolutionary ecology with learning theory.

BACKGROUND: The structure and organisation of ecological interactions within an ecosystem is modified by the evolution and coevolution of the individual species it contains. Understanding how historical conditions have shaped this architecture is vital for understanding system responses to change at scales from the microbial upwards. However, in the absence of a group selection process, the collective behaviours and ecosystem functions exhibited by the whole community cannot be organised or adapted in a Darwinian sense. A long-standing open question thus persists: Are there alternative organising principles that enable us to understand and predict how the coevolution of the component species creates and maintains complex collective behaviours exhibited by the ecosystem as a whole? RESULTS: Here we answer this question by incorporating principles from connectionist learning, a previously unrelated discipline already using well-developed theories on how emergent behaviours arise in simple networks. Specifically, we show conditions where natural selection on ecological interactions is functionally equivalent to a simple type of connectionist learning, 'unsupervised learning', well-known in neural-network models of cognitive systems to produce many non-trivial collective behaviours. Accordingly, we find that a community can self-organise in a well-defined and non-trivial sense without selection at the community level; its organisation can be conditioned by past experience in the same sense as connectionist learning models habituate to stimuli. This conditioning drives the community to form a distributed ecological memory of multiple past states, causing the community to: a) converge to these states from any random initial composition; b) accurately restore historical compositions from small fragments; c) recover a state composition following disturbance; and d) to correctly classify ambiguous initial compositions according to their similarity to learned compositions. We examine how the formation of alternative stable states alters the community's response to changing environmental forcing, and we identify conditions under which the ecosystem exhibits hysteresis with potential for catastrophic regime shifts. CONCLUSIONS: This work highlights the potential of connectionist theory to expand our understanding of evo-eco dynamics and collective ecological behaviours. Within this framework we find that, despite not being a Darwinian unit, ecological communities can behave like connectionist learning systems, creating internal conditions that habituate to past environmental conditions and actively recalling those conditions. REVIEWERS: This article was reviewed by Prof. Ricard V Solé, Universitat Pompeu Fabra, Barcelona and Prof. Rob Knight, University of Colorado, Boulder.