Predictable Feature Analysis

Every organism in an environment, whether biological, robotic or virtual, must be able to predict certain aspects of its environment in order to survive or perform whatever task is intended. It needs a model that is capable of estimating the consequences of possible actions, so that planning, control, and decision-making become feasible. For scientific purposes, such models are usually created in a problem specific manner using differential equations and other techniques from control- and system-theory. In contrast to that, we aim for an unsupervised approach that builds up the desired model in a self-organized fashion. Inspired by Slow Feature Analysis (SFA), our approach is to extract sub-signals from the input, that behave as predictable as possible. These "predictable features" are highly relevant for modeling, because predictability is a desired property of the needed consequence-estimating model by definition. In our approach, we measure predictability with respect to a certain prediction model. We focus here on the solution of the arising optimization problem and present a tractable algorithm based on algebraic methods which we call Predictable Feature Analysis (PFA). We prove that the algorithm finds the globally optimal signal, if this signal can be predicted with low error. To deal with cases where the optimal signal has a significant prediction error, we provide a robust, heuristically motivated variant of the algorithm and verify it empirically. Additionally, we give formal criteria a prediction-model must meet to be suitable for measuring predictability in the PFA setting and also provide a suitable default-model along with a formal proof that it meets these criteria

Application of an inverse neural network model for the identification of optimal amendment to reduce Copper toxicity in phytoremediated contaminated soils

International audienceArtificial neural network ANN prediction approaches applied to the modeling of soil behavior are often solved in the forward direction, by measuring the response of the soil (outputs) to a given set of soil inputs. Conversely, one may be interested in the assessment of a given set of soil inputs that leads to given (target) soil outputs. This is the inverse of the former problem. In this study, we develop and test an inverse artificial neural network model for the prediction of the optimal soil treatment to reduce copper (Cu) toxicity assessed by a given target concentration of Cu in dwarf bean leaves (BL) from selected soil inputs. In this study the inputs are the soil pH, electrical conductivity (EC), dissolved organic carbon (DOC) and a given target toxicity value of Cu, whereas the output is the best treatment to reduce the given toxicity level. It is shown that the proposed method can successfully identify the best soil treatment from the soil properties (inputs). Two important challenges for optimal treatment prediction using neural networks are the non-uniqueness of the solution of the inverse problem and the inaccuracies in the measurement of the soil properties (inputs). It is shown that the neural network prediction model proposed can overcome both these challenges. It is also shown that the proposed inverse neural network method can potentially be applied with a high level of success to the phytoremediation of contaminated soils. Before large-scale application, further validation is needed by performing several experiments and investigations including additional factors and their combinations to capture the complex soil behavior