Comparing Rough Set Theory with Multiple Regression Analysis as Automated Valuation Methodologies

This paper focuses on the problem of applying rough set theory to mass appraisal. This methodology was first introduced by a Polish mathematician, and has been applied recently as an automated valuation methodology by the author. The method allows the appraiser to estimate a property without defining econometric modeling, although it does not give any quantitative estimation of marginal prices. In a previous paper by the author, data were organized into classes prior to the valuation process, allowing for the if-then, or right “rule” for each property class to be defined. In that work, the relationship between property and class of valued was said to be dichotomic.mass appraisal; property valuation; rough set theory; valued tolerance relation

Rough Set Theory for Real Estate Appraisal: An Application to Directional District of Naples

This paper proposes an application of Rough Set Theory (RST) to the real estate field, in order to highlight its operational potentialities for mass appraisal purposes. RST allows one to solve the appraisal of real estate units regardless of the deterministic relationship between characteristics that contribute to the formation of the property market price and the same real estate prices. RST was applied to a real estate sample (office units located in Directional District of Naples) and was also integrated with a functional extension so-called Valued Tolerance Relation (VTR) in order to improve its flexibility. A multiple regression analysis (MRA) was developed on the same real estate sample with the aim to compare RST and MRA results. The case study is followed by a brief discussion on basic theoretical connotations of this methodology

A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of "continuous" matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities

Teachers' and children's personal epistemologies for moral education: Case studies in early years elementary education

While there is strong interest in teaching values in Australia and internationally there is little focus on young children’s moral values learning in the classroom. Research shows that personal epistemology influences teaching and learning in a range of education contexts, including moral education. This study examines relationships between personal epistemologies (children’s and teachers’), pedagogies, and school contexts for moral learning in two early years classrooms. Interviews with teachers and children and analysis of school policy revealed clear patterns of personal epistemologies and pedagogies within each school. A whole school approach to understanding personal epistemologies and practice for moral values learning is suggested

Computable decision making on the reals and other spaces via partiality and nondeterminism

Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause errors and jeopardize safety. Some programming systems implement exact real arithmetic, which resolves this matter but complicates others, such as decision making. In these systems, it is impossible to compute (total and deterministic) discrete decisions based on connected spaces such as $\mathbb{R}$. We present programming-language semantics based on constructive topology with variants allowing nondeterminism and/or partiality. Either nondeterminism or partiality suffices to allow computable decision making on connected spaces such as $\mathbb{R}$. We then introduce pattern matching on spaces, a language construct for creating programs on spaces, generalizing pattern matching in functional programming, where patterns need not represent decidable predicates and also may overlap or be inexhaustive, giving rise to nondeterminism or partiality, respectively. Nondeterminism and/or partiality also yield formal logics for constructing approximate decision procedures. We implemented these constructs in the Marshall language for exact real arithmetic.Comment: This is an extended version of a paper due to appear in the proceedings of the ACM/IEEE Symposium on Logic in Computer Science (LICS) in July 201

On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality conditions as well as a bound on the optimality gap of feasible candidate solutions are derived. Based on these results, two numerical algorithms are proposed that iteratively solve the system of optimality conditions on a grid of discrete points. Both algorithms use a block coordinate descent strategy and terminate once the optimality gap falls below the desired tolerance. While the first algorithm is conceptually simpler and more efficient, it is not guaranteed to converge for objective functions that are not strictly convex. This shortcoming is overcome in the second algorithm, which uses an additional outer proximal iteration, and, which is proven to converge under mild assumptions. Two examples are given to demonstrate the theoretical usefulness of the optimality conditions as well as the high efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on Signal Processing. In previous versions, the example in Section VI.B contained some mistakes and inaccuracies, which have been fixed in this versio

Competing goals attenuate avoidance behavior in the context of pain

Current fear-avoidance models consider pain-related fear as a crucial factor in the development of chronic pain. However, pain-related fear often occurs in a context of multiple, competing goals. This study investigated whether pain-related fear and avoidance behavior are attenuated when individuals are faced with a pain avoidance goal and another valued but competing goal, operationalized as obtaining a monetary reward. Fifty-five healthy participants moved a joystick toward different targets. In the experimental condition, a movement to one target (conditioned stimulus [CS+]) was followed by a painful unconditioned stimulus (pain-US) and a rewarding unconditioned stimulus (reward-US) on 50% of the trials, whereas the other movement (nonreinforced conditioned stimulus [CS)) movement was not. In the control condition, the CS+ movement was followed by the pain-US only. Results showed that pain-related fear was elevated in response to the CS+ compared to the CS movement, but that it was not influenced by the reward-US. Interestingly, participants initiated a CS+ movement slower than a CS movement in the control condition but not in the experimental condition. Also, in choice trials, participants performed the CS+ movement more frequently in the experimental than in the control condition. These results suggest that the presence of a valued competing goal can attenuate avoidance behavior. Perspective: The current study provides experimental evidence that both pain and competing goals impact on behavioral decision making and avoidance behavior. These results provide experimental support for treatments of chronic pain that include an individual's pursuit of valuable daily life goals, rather than limiting focus to pain reduction only. (C) 2014 by the American Pain Societ

Hybrid automata dicretising agents for formal modelling of robots

Some of the fundamental capabilities required by autonomous vehicles and systems for their intelligent decision making are: modelling of the environment and forming data abstractions for symbolic, logic based reasoning. The paper formulates a discrete agent framework that abstracts and controls a hybrid system that is a composition of hybrid automata modelled continuous individual processes. Theoretical foundations are laid down for a class of general model composition agents (MCAs) with an advanced subclass of rational physical agents (RPAs). We define MCAs as the most basic structures for the description of complex autonomous robotic systems. The RPA’s have logic based decision making that is obtained by an extension of the hybrid systems concepts using a set of abstractions. The theory presented helps the creation of robots with reliable performance and safe operation in their environment. The paper emphasizes the abstraction aspects of the overall hybrid system that emerges from parallel composition of sets of RPAs and MCAs

Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking

Machine-learned models are often described as "black boxes". In many real-world applications however, models may have to sacrifice predictive power in favour of human-interpretability. When this is the case, feature engineering becomes a crucial task, which requires significant and time-consuming human effort. Whilst some features are inherently static, representing properties that cannot be influenced (e.g., the age of an individual), others capture characteristics that could be adjusted (e.g., the daily amount of carbohydrates taken). Nonetheless, once a model is learned from the data, each prediction it makes on new instances is irreversible - assuming every instance to be a static point located in the chosen feature space. There are many circumstances however where it is important to understand (i) why a model outputs a certain prediction on a given instance, (ii) which adjustable features of that instance should be modified, and finally (iii) how to alter such a prediction when the mutated instance is input back to the model. In this paper, we present a technique that exploits the internals of a tree-based ensemble classifier to offer recommendations for transforming true negative instances into positively predicted ones. We demonstrate the validity of our approach using an online advertising application. First, we design a Random Forest classifier that effectively separates between two types of ads: low (negative) and high (positive) quality ads (instances). Then, we introduce an algorithm that provides recommendations that aim to transform a low quality ad (negative instance) into a high quality one (positive instance). Finally, we evaluate our approach on a subset of the active inventory of a large ad network, Yahoo Gemini.Comment: 10 pages, KDD 201