Neural network regression with input uncertainty

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise or corruption. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which allows for input noise given that some model of the noise process exists. In the limit where this noise process is small and symmetric it is shown, using the Laplace approximation, that there is an additional term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable and sampling this jointly with the network's weights, using Markov Chain Monte Carlo methods, it is demonstrated that it is possible to infer the unbiassed regression over the noiseless input.

A novel approach to modelling and exploiting uncertainty in stochastic control systems

We consider an inversion-based neurocontroller for solving control problems of uncertain nonlinear systems. Classical approaches do not use uncertainty information in the neural network models. In this paper we show how we can exploit knowledge of this uncertainty to our advantage by developing a novel robust inverse control method. Simulations on a nonlinear uncertain second order system illustrate the approach.

Conditional distribution modeling for estimating and exploiting uncertainty in control systems

This paper presents a general methodology for estimating and incorporating uncertainty in the controller and forward models for noisy nonlinear control problems. Conditional distribution modeling in a neural network context is used to estimate uncertainty around the prediction of neural network outputs. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localize the possible control solutions to consider. A nonlinear multivariable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non Gaussian distributions of control signal as well as processes with hysteresis.

Handling and communicating uncertainty in chained geospatial web services

Recent developments in service-oriented and distributed computing have created exciting opportunities for the integration of models in service chains to create the Model Web. This offers the potential for orchestrating web data and processing services, in complex chains; a flexible approach which exploits the increased access to products and tools, and the scalability offered by the Web. However, the uncertainty inherent in data and models must be quantified and communicated in an interoperable way, in order for its effects to be effectively assessed as errors propagate through complex automated model chains. We describe a proposed set of tools for handling, characterizing and communicating uncertainty in this context, and show how they can be used to 'uncertainty- enable' Web Services in a model chain. An example implementation is presented, which combines environmental and publicly-contributed data to produce estimates of sea-level air pressure, with estimates of uncertainty which incorporate the effects of model approximation as well as the uncertainty inherent in the observational and derived data.

A robustness framework for monitoring real options under uncertainty

This paper presents a problem structuring methodology to assess real option decisions in the face of unpredictability. Based on principles of robustness analysis and scenario planning, we demonstrate how decision-aiding can facilitate participation in projects setting and achieve effective decision making through the use of real options reasoning. We argue that robustness heuristics developed in earlier studies can be practical proxies for real options performance, hence indicators of efficient flexible planning. The developed framework also highlights how to integrate real options solutions in firms’ strategic plans and operating actions. The use of the methodology in a location decision application is provided for illustration.

Uncertainty and the influence of group norms in the attitude-behaviour relationship

Two studies were conducted to examine the impact of subjective uncertainty on conformity to group norms in the attitude-behaviour context. In both studies, subjective uncertainty was manipulated using a deliberative mindset manipulation (McGregor, Zanna, Holmes, & Spencer, 2001). In Study 1 (N = 106), participants were exposed to either an attitude-congruent or an attitude-incongruent in-group norm. In Study 2(N = 83), participants were exposed to either a congruent, incongruent, or an ambiguous in-group norm. Ranges of attitude-behaviour outcomes, including attitude-intention consistency and change in attitude-certainty, were assessed. In both studies, levels of group-normative behaviour varied as a function of uncertainty condition. In Study 1, conformity to group norms, as evidenced by variations in the level of attitude-intention consistency, was observed only in the high uncertainty condition. In Study 2, exposure to an ambiguous norm had different effects for those in the low and die high uncertainty conditions. In the low uncertainty condition, greatest conformity was observed in the attitude-congruent norm condition compared with an attitude-congruent or ambiguous norm. In contrast, individuals in the high uncertainty condition displayed greatest conformity when exposed to either an attitude-congruent or an ambiguous in-group norm. The implications of these results for the role of subjective uncertainty in social influence processes are discussed. © 2007 The British Psychological Society.

Discriminating depth in corrugated stereo surfaces: facilitation by a pedestal is explained by removal of uncertainty

With luminance gratings, psychophysical thresholds for detecting a small increase in the contrast of a weak ‘pedestal’ grating are 2–3 times lower than for detection of a grating when the pedestal is absent. This is the ‘dipper effect’ – a reliable improvement whose interpretation remains controversial. Analogies between luminance and depth (disparity) processing have attracted interest in the existence of a ‘disparity dipper’. Are thresholds for disparity modulation (corrugated surfaces), facilitated by the presence of a weak disparity-modulated pedestal? We used a 14-bit greyscale to render small disparities accurately, and measured 2AFC discrimination thresholds for disparity modulation (0.3 or 0.6 c/deg) of a random texture at various pedestal levels. In the first experiment, a clear dipper was found. Thresholds were about 2× lower with weak pedestals than without. But here the phase of modulation (0 or 180 deg) was varied from trial to trial. In a noisy signal-detection framework, this creates uncertainty that is reduced by the pedestal, which thus improves performance. When the uncertainty was eliminated by keeping phase constant within sessions, the dipper effect was weak or absent. Monte Carlo simulations showed that the influence of uncertainty could account well for the results of both experiments. A corollary is that the visual depth response to small disparities is probably linear, with no threshold-like nonlinearity.

Seeing light vs dark lines: psychophysical performance is based on separate channels, limited by noise and uncertainty

Visual detection performance (d') is usually an accelerating function of stimulus contrast, which could imply a smooth, threshold-like nonlinearity in the sensory response. Alternatively, Pelli (1985 Journal of the Optical Society of America A 2 1508 - 1532) developed the 'uncertainty model' in which responses were linear with contrast, but the observer was uncertain about which of many noisy channels contained the signal. Such internal uncertainty effectively adds noise to weak signals, and predicts the nonlinear psychometric function. We re-examined these ideas by plotting psychometric functions (as z-scores) for two observers (SAW, PRM) with high precision. The task was to detect a single, vertical, blurred line at the fixation point, or identify its polarity (light vs dark). Detection of a known polarity was nearly linear for SAW but very nonlinear for PRM. Randomly interleaving light and dark trials reduced performance and rendered it non-linear for SAW, but had little effect for PRM. This occurred for both single-interval and 2AFC procedures. The whole pattern of results was well predicted by our Monte Carlo simulation of Pelli's model, with only two free parameters. SAW (highly practised) had very low uncertainty. PRM (with little prior practice) had much greater uncertainty, resulting in lower contrast sensitivity, nonlinear performance, and no effect of external (polarity) uncertainty. For SAW, identification was about v2 better than detection, implying statistically independent channels for stimuli of opposite polarity, rather than an opponent (light - dark) channel. These findings strongly suggest that noise and uncertainty, rather than sensory nonlinearity, limit visual detection.

Exchanging uncertainty: interoperable geostatistics?

Traditionally, geostatistical algorithms are contained within specialist GIS and spatial statistics software. Such packages are often expensive, with relatively complex user interfaces and steep learning curves, and cannot be easily integrated into more complex process chains. In contrast, Service Oriented Architectures (SOAs) promote interoperability and loose coupling within distributed systems, typically using XML (eXtensible Markup Language) and Web services. Web services provide a mechanism for a user to discover and consume a particular process, often as part of a larger process chain, with minimal knowledge of how it works. Wrapping current geostatistical algorithms with a Web service layer would thus increase their accessibility, but raises several complex issues. This paper discusses a solution to providing interoperable, automatic geostatistical processing through the use of Web services, developed in the INTAMAP project (INTeroperability and Automated MAPping). The project builds upon Open Geospatial Consortium standards for describing observations, typically used within sensor webs, and employs Geography Markup Language (GML) to describe the spatial aspect of the problem domain. Thus the interpolation service is extremely flexible, being able to support a range of observation types, and can cope with issues such as change of support and differing error characteristics of sensors (by utilising descriptions of the observation process provided by SensorML). XML is accepted as the de facto standard for describing Web services, due to its expressive capabilities which allow automatic discovery and consumption by ‘naive’ users. Any XML schema employed must therefore be capable of describing every aspect of a service and its processes. However, no schema currently exists that can define the complex uncertainties and modelling choices that are often present within geostatistical analysis. We show a solution to this problem, developing a family of XML schemata to enable the description of a full range of uncertainty types. These types will range from simple statistics, such as the kriging mean and variances, through to a range of probability distributions and non-parametric models, such as realisations from a conditional simulation. By employing these schemata within a Web Processing Service (WPS) we show a prototype moving towards a truly interoperable geostatistical software architecture.

Probabilistic uncertainty in an interoperable framework

This thesis provides an interoperable language for quantifying uncertainty using probability theory. A general introduction to interoperability and uncertainty is given, with particular emphasis on the geospatial domain. Existing interoperable standards used within the geospatial sciences are reviewed, including Geography Markup Language (GML), Observations and Measurements (O&M) and the Web Processing Service (WPS) specifications. The importance of uncertainty in geospatial data is identified and probability theory is examined as a mechanism for quantifying these uncertainties. The Uncertainty Markup Language (UncertML) is presented as a solution to the lack of an interoperable standard for quantifying uncertainty. UncertML is capable of describing uncertainty using statistics, probability distributions or a series of realisations. The capabilities of UncertML are demonstrated through a series of XML examples. This thesis then provides a series of example use cases where UncertML is integrated with existing standards in a variety of applications. The Sensor Observation Service - a service for querying and retrieving sensor-observed data - is extended to provide a standardised method for quantifying the inherent uncertainties in sensor observations. The INTAMAP project demonstrates how UncertML can be used to aid uncertainty propagation using a WPS by allowing UncertML as input and output data. The flexibility of UncertML is demonstrated with an extension to the GML geometry schemas to allow positional uncertainty to be quantified. Further applications and developments of UncertML are discussed.

UncertML: an XML schema for exchanging uncertainty

Authors from Burrough (1992) to Heuvelink et al. (2007) have highlighted the importance of GIS frameworks which can handle incomplete knowledge in data inputs, in decision rules and in the geometries and attributes modelled. It is particularly important for this uncertainty to be characterised and quantified when GI data is used for spatial decision making. Despite a substantial and valuable literature on means of representing and encoding uncertainty and its propagation in GI (e.g.,Hunter and Goodchild 1993; Duckham et al. 2001; Couclelis 2003), no framework yet exists to describe and communicate uncertainty in an interoperable way. This limits the usability of Internet resources of geospatial data, which are ever-increasing, based on specifications that provide frameworks for the ‘GeoWeb’ (Botts and Robin 2007; Cox 2006). In this paper we present UncertML, an XML schema which provides a framework for describing uncertainty as it propagates through many applications, including online risk management chains. This uncertainty description ranges from simple summary statistics (e.g., mean and variance) to complex representations such as parametric, multivariate distributions at each point of a regular grid. The philosophy adopted in UncertML is that all data values are inherently uncertain, (i.e., they are random variables, rather than values with defined quality metadata).

Scenario planning:teaching how to anticipate perceived environmental uncertainty within strategy development

Scenario Planning is a strategy tool with growing popularity in both academia and practical situations. Current practices in the teaching of scenario planning are largely based on existing literature which utilises scenario planning to develop strategies for the future, primarily considering the assessment of perceived macro-external environmental uncertainties. However there is a body of literature hitherto ignored by scenario planning researchers, which suggests that Perceived Environmental Uncertainty (PEU) influences micro-external or industrial environmental as well as the internal environment of the organisation. This paper provides a review of the most dominant theories on scenario planning process, demonstrates the need to consider PEU theory within scenario planning and presents how this can be done. The scope of this paper is to enhance the scenario planning process as a tool taught for Strategy Development. A case vignette is developed based on published scenarios to demonstrate the potential utilisation of the proposed process.

When do conservation planning methods deliver? Quantifying the consequences of uncertainty

The rapid global loss of biodiversity has led to a proliferation of systematic conservation planning methods. In spite of their utility and mathematical sophistication, these methods only provide approximate solutions to real-world problems where there is uncertainty and temporal change. The consequences of errors in these solutions are seldom characterized or addressed. We propose a conceptual structure for exploring the consequences of input uncertainty and oversimpli?ed approximations to real-world processes for any conservation planning tool or strategy. We then present a computational framework based on this structure to quantitatively model species representation and persistence outcomes across a range of uncertainties. These include factors such as land costs, landscape structure, species composition and distribution, and temporal changes in habitat. We demonstrate the utility of the framework using several reserve selection methods including simple rules of thumb and more sophisticated tools such as Marxan and Zonation. We present new results showing how outcomes can be strongly affected by variation in problem characteristics that are seldom compared across multiple studies. These characteristics include number of species prioritized, distribution of species richness and rarity, and uncertainties in the amount and quality of habitat patches. We also demonstrate how the framework allows comparisons between conservation planning strategies and their response to error under a range of conditions. Using the approach presented here will improve conservation outcomes and resource allocation by making it easier to predict and quantify the consequences of many different uncertainties and assumptions simultaneously. Our results show that without more rigorously generalizable results, it is very dif?cult to predict the amount of error in any conservation plan. These results imply the need for standard practice to include evaluating the effects of multiple real-world complications on the behavior of any conservation planning method.

Neural Network Modelling with Input Uncertainty: Theory and Application

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which accounts for input noise provided that a model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method adds an extra term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable, and sampling this jointly with the network’s weights, using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input. This leads to the possibility of training an accurate model of a system using less accurate, or more uncertain, data. This is demonstrated on both the, synthetic, noisy sine wave problem and a real problem of inferring the forward model for a satellite radar backscatter system used to predict sea surface wind vectors.