Variable Precision Model Research Articles

Unsupervised Attribute Reduction Algorithm for Mixed Data Based on Fuzzy Optimal Approximation Set

Fuzzy rough set theory has been successfully applied to many attribute reduction methods, in which the lower approximation set plays a pivotal role. However, the definition of lower approximation used has ignored the information conveyed by the upper approximation and the boundary region. This oversight has resulted in an unreasonable relation representation of the target set. Despite the fact that scholars have proposed numerous enhancements to rough set models, such as the variable precision model, none have successfully resolved the issues inherent in the classical models. To address this limitation, this paper proposes an unsupervised attribute reduction algorithm for mixed data based on an improved optimal approximation set. Firstly, the theory of an improved optimal approximation set and its associated algorithm are proposed. Subsequently, we extend the classical theory of optimal approximation sets to fuzzy rough set theory, leading to the development of a fuzzy improved approximation set method. Finally, building on the proposed theory, we introduce a novel, fuzzy optimal approximation-set-based unsupervised attribute reduction algorithm (FOUAR). Comparative experiments conducted with all the proposed algorithms indicate the efficacy of FOUAR in selecting fewer attributes while maintaining and improving the performance of the machine learning algorithm. Furthermore, they highlight the advantage of the improved optimal approximation set algorithm, which offers higher similarity to the target set and provides a more concise expression.

Energy Saving via a Minimal Structure

Not only mathematical statistics, differential equations, and mathematical models were used to analyze and reduce data, but a rough set model is also employed in medical, engineering, and other fields to analyze and reduce them. The goal of this paper is to introduce a minimal structure concept to produce new rough set models and show that it is suitable for analyzing most real-life problems, reduction of attributes, and decision making. We examine the effectiveness of the following method in the problem of electric power generators and decision making. We also offer a comparison of our method and Pawlak’s method. Finally, the variable precision model improves the accuracy of decision making.

An interference model for visual working memory: Applications to the change detection task

Most studies of visual-working memory employ one of two experimental paradigms: change-detection or continuous-stimulus reproduction. In this study, we extended the Interference Model (IM; Oberauer & Lin, 2017), which was designed for continuous reproduction, to the single-probe change-detection task. In continuous reproduction, participants occasionally report the non-target items instead of the target. The presence of non-target response is predicted by the Interference Model, which relies in part on the interference of non-target items to explain the set-size effect. By presenting a probe matching a non-target item, we can investigate the amount of interference from non-target items in change detection. As predicted by the Interference Model, we observed poorer performance in rejecting a probe matching a non-target item compared to a new probe (i.e., a cost due to intrusions from non-targets). We fitted the IM along with the Variable Precision, the Slot-Averaging, and the Neural-Population model to the data from two change-detection experiments. The models were equipped with a Bayesian decision rule based on the one used in Keshvari, van den Berg, and Ma (2013). The Interference Model and the Neural-Population model successfully predicted the set-size effect and the non-target intrusion cost, whereas the Variable Precision (VP) and Slot-Averaging (SA) models failed to predict the intrusion cost at all. Even with additional assumptions enabling VP and SA to produce intrusion costs, the IM still performed better than the competing models quantitatively.

Atypically larger variability of resource allocation accounts for visual working memory deficits in schizophrenia.

Working memory (WM) deficits have been widely documented in schizophrenia (SZ), and almost all existing studies attributed the deficits to decreased capacity as compared to healthy control (HC) subjects. Recent developments in WM research suggest that other components, such as precision, also mediate behavioral performance. It remains unclear how different WM components jointly contribute to deficits in schizophrenia. We measured the performance of 60 SZ (31 females) and 61 HC (29 females) in a classical delay-estimation visual working memory (VWM) task and evaluated several influential computational models proposed in basic science of VWM to disentangle the effect of various memory components. We show that the model assuming variable precision (VP) across items and trials is the best model to explain the performance of both groups. According to the VP model, SZ exhibited abnormally larger variability of allocating memory resources rather than resources or capacity per se. Finally, individual differences in the resource allocation variability predicted variation of symptom severity in SZ, highlighting its functional relevance to schizophrenic pathology. This finding was further verified using distinct visual features and subject cohorts. These results provide an alternative view instead of the widely accepted decreased-capacity theory and highlight the key role of elevated resource allocation variability in generating atypical VWM behavior in schizophrenia. Our findings also shed new light on the utility of Bayesian observer models to characterize mechanisms of mental deficits in clinical neuroscience.

To see, not to see or to see poorly: Perceptual quality and guess rate as a function of electroencephalography (EEG) brain activity in an orientation perception task.

Detection of visual stimuli fluctuates over time, and these fluctuations have been shown to correlate with time domain evoked activity and frequency-domain periodic activity. However, it is unclear if these fluctuations are related to a change in guess rate, perceptual quality or both. Here we determined whether the quality of perception randomly varies across trials or is fixed so that the variability is the same. Then we estimated how perceptual quality and guess rate on an orientation perception task relate to electroencephalography (EEG) activity. Response errors were fitted to variable precision models and the standard mixture model to determine whether perceptual quality is from a varying or fixed distribution. Overall, the best fit was the standard mixture model that assumes that response variability can be defined by a fixed distribution. The power and phase of 2-7 Hz post-target activities were found to vary along with task performance in that more accurate trials had greater power, and the preferred phase differed significantly between accurate and guess trials. Guess rate and σ were significantly lower on trials with high 2- to 3-Hz power than low, and the difference started around 250-ms post-target. These effects coincide with changes in the P3 event-related potential (ERP): There was a more positive deflection in the accurate trials versus guesses. These results suggest that the spread of errors (perceptual quality) can be characterised by a fixed range of values. Where the errors fall within that range is modulated by the post-target power in the lower-frequency bands and their analogous ERPs.

Medical applications via minimal topological structure

It is known that mathematical statics, mathematical modeling, and differential equations are used to give an in-depth understanding of many medical problems. On the edge of the information revolution, minimal structures show some qualitative properties issues that are difficult to deal with it, such as quality of education, nutrition, etc. The aim of this paper is to discuss two medical applications and show that a minimal structure space is suitable for analyzing several real-life problems. Then, the accuracy of the decision-making and attributes reduction of the medical information system are explained and obtained. Furthermore, we introduce a comparison between our approach and Pawlak’s approach to find accuracy for decision-making. Finally, the accuracy of decision-making via a variable precision model is improved.

More than a filter: Feature-based attention regulates the distribution of visual working memory resources.

Across 2 experiments we revisited the filter account of how feature-based attention regulates visual working memory (VWM). Originally drawing from discrete-capacity ("slot") models, the filter account proposes that attention operates like the "bouncer in the brain," preventing distracting information from being encoded so that VWM resources are reserved for relevant information. Given recent challenges to the assumptions of discrete-capacity models, we investigated whether feature-based attention plays a broader role in regulating memory. Both experiments used partial report tasks in which participants memorized the colors of circle and square stimuli, and we provided a feature-based goal by manipulating the likelihood that 1 shape would be probed over the other across a range of probabilities. By decomposing participants' responses using mixture and variable-precision models, we estimated the contributions of guesses, nontarget responses, and imprecise memory representations to their errors. Consistent with the filter account, participants were less likely to guess when the probed memory item matched the feature-based goal. Interestingly, this effect varied with goal strength, even across high probabilities where goal-matching information should always be prioritized, demonstrating strategic control over filter strength. Beyond this effect of attention on which stimuli were encoded, we also observed effects on how they were encoded: Estimates of both memory precision and nontarget errors varied continuously with feature-based attention. The results offer support for an extension to the filter account, where feature-based attention dynamically regulates the distribution of resources within working memory so that the most relevant items are encoded with the greatest precision. (PsycINFO Database Record

More than a filter: Feature-based attention regulates the distribution of visual working memory resources

Across 2 experiments we revisited the filter account of how feature-based attention regulates visual working memory (VWM). Originally drawing from discrete-capacity (slot) models, the filter account proposes that attention operates like the bouncer in the brain, preventing distracting information from being encoded so that VWM resources are reserved for relevant information. Given recent challenges to the assumptions of discrete-capacity models, we investigated whether feature-based attention plays a broader role in regulating memory. Both experiments used partial report tasks in which participants memorized the colors of circle and square stimuli, and we provided a feature-based goal by manipulating the likelihood that 1 shape would be probed over the other across a range of probabilities. By decomposing participants' responses using mixture and variable-precision models, we estimated the contributions of guesses, nontarget responses, and imprecise memory representations to their errors. Consistent with the filter account, participants were less likely to guess when the probed memory item matched the feature-based goal. Interestingly, this effect varied with goal strength, even across high probabilities where goal-matching information should always be prioritized, demonstrating strategic control over filter strength. Beyond this effect of attention on which stimuli were encoded, we also observed effects on how they were encoded: Estimates of both memory precision and nontarget errors varied continuously with feature-based attention. The results offer support for an extension to the filter account, where feature-based attention dynamically regulates the distribution of resources within working memory so that the most relevant items are encoded with the greatest precision. (PsycINFO Database Record

Attention mediates the flexible allocation of visual working memory resources.

Though it is clear that it is impossible to store an unlimited amount of information in visual working memory (VWM), the limiting mechanisms remain elusive. While several models of VWM limitations exist, these typically characterize changes in performance as a function of the number of to-be-remembered items. Here, we examine whether changes in spatial attention could better account for VWM performance, independent of load. Across 2 experiments, performance was better predicted by the prioritization of memory items (i.e., attention) than by the number of items to be remembered (i.e., memory load). This relationship followed a power law, and held regardless of whether performance was assessed based on overall precision or any of 3 measures in a mixture model. Moreover, at large set sizes, even minimally attended items could receive a small proportion of resources, without any evidence for a discrete-capacity on the number of items that could be maintained in VWM. Finally, the observed data were best fit by a variable-precision model in which response error was related to the proportion of resources allocated to each item, consistent with a model of VWM in which performance is determined by the continuous allocation of attentional resources during encoding. (PsycINFO Database Record

Inclusion degree with variable-precision model in analyzing inconsistent decision tables

In this paper, we incorporate the concepts of evidence theory and variable precision rough set model (VP-model) to examine inconsistent decision tables. For the decision classes in a given decision table, we point out the relationship between approximation degree of dependency and the belief functions. We also introduce the notion of weakly discernable decision tables, and show how to obtain the discernibility threshold of a given weakly discernable decision table. We prove that weakly discernibility is a necessary condition of relative consistency in a given decision table.

Discernibility Thresholds and Approximate Dependency in Analysis of Decision Tables

The concept of discernibility thresholds in the variable precision model (VP-model) is presented to classify sets in a nonempty finite universe. Analysis of inconsistent decision table is obtained by using the tools in VP-model. The tools are obtained by the interplay among inclusion error, discernibility threshold dependency and consistency as well as lower and upper approximation with thresholds. We also provide the relationships between the inclusion errors and lower approximations with threshold.

Variable consistency and variable precision models for dominance-based fuzzy rough set analysis of possibilistic information systems

The dominance-based fuzzy rough set approach (DFRSA) is a theoretical framework that can deal with multi-criteria decision analysis of possibilistic information systems. While a set of comprehensive decision rules can be induced from a possibilistic information system by using DFRSA, generation of several intuitively justified rules is sometimes blocked by objects that only partially satisfy the antecedents of the rules. In this paper, we use the variable consistency models and variable precision models of DFRSA to cope with the problem. The models admit rules that are not satisfied by all objects. It is only required that the proportion of objects satisfying the rules must be above a threshold called a consistency level or a precision level. In the presented models, the proportion of objects is represented as a relative cardinality of a fuzzy set with respect to another fuzzy set. We investigate three types of models based on different definitions of fuzzy cardinalities including -counts, possibilistic cardinalities, and probabilistic cardinalities; and the consistency levels or precision levels corresponding to the three types of models are, respectively, scalars, fuzzy numbers, and random variables.

Variability in color working memory precision reflects inherent stimulus properties

State of the art visual working memory models suggest that resources are not only continuous, but also variable across items and trials. The cause of trial-to-trial variability remains unknown, with several possibilities proposed (e.g., doubly stochastic neural representation). One important possibility is that variation is due to the particular stimulus values presented in a trial. To explore this possibility, Experiment 1 used delayed estimation for color, testing participants at a memory load of one, probing each of 180 colors ten times. We found clear differences among these colors in average recall precision. Experiment 2 replicated a study by van de Berg et al. (2012), and fit their variable-precision model to the results. We averaged the model’s precision estimates for each color, and correlated these averages with the values obtained in Experiment 1. The correlation was highly significant, both overall and for each memory load, suggesting that differences among stimulus values account for a large proportion of the trial-to-trial variance. Experiment 3 investigated one reason why responses for certain colors might be more precise than for others. Participants were asked to identify the most prototypical example of each of seven colors by marking a color wheel. The least frequent selections served as good proxies for color category boundaries. We averaged the trial-to-trial variance estimates within each category for Experiment 1; these estimates correlated significantly with estimates derived in the same way for each color category at each memory load in Experiment 2. These results again suggest that trial variability is stimulus driven, perhaps reflecting categorical effects in color perception. This has important implications for modeling visual working memory, primarily, via the opportunity to account for trial variability with independent estimates of stimulus perception. We discuss a number of possible models employing such an approach. Meeting abstract presented at VSS 2013

The Role of Arithmetic in Fast Parallel Matrix Inversion

In the last two decades several NC algorithms for solving basic linear algebraic problems have ap- peared in the literature. This interest was clearly motivated by the emergence of a parallel computing technology and by the wide applicability of matrix computations. The traditionally adopted computation model, however, ignores the arithmetic aspects of the applications, and no analysis is currently available demonstrating the con- crete feasibility of many of the known fast methods. In this paper we give strong evidence to the contrary, on the sole basis of the issue of robustness, indicating that some theoretically brilliant solutions fail the severe test of the "Engineering of Algorithms." We perform a comparative analysis of several well-known numerical matrix inversion algorithms under both fixed- and variable-precision models of arithmetic. We show that, for most methods investigated, a typical input leads to poor numerical performance, and that in the exact-arithmetic set- ting no benefit derives from conditions usually deemed favorable in standard scientific computing. Under these circumstances, the only algorithm admitting sufficiently accurate NC implementations is Newton's iterative method, and the word size required to guarantee worst-case correctness appears to be the critical complexity measure. Our analysis also accounts for the observed instability of the considered superfast methods when implemented with the same floating-point arithmetic that is perfectly adequate for the fixed-precision approach.

Vocabulary mining for information retrieval: rough sets and fuzzy sets

Vocabulary mining in information retrieval refers to the utilization of the domain vocabulary towards improving the user’s query. Most often queries posed to information retrieval systems are not optimal for retrieval purposes. Vocabulary mining allows one to generalize, specialize or perform other kinds of vocabulary-based transformations on the query in order to improve retrieval performance. This paper investigates a new framework for vocabulary mining that derives from the combination of rough sets and fuzzy sets. The framework allows one to use rough set-based approximations even when the documents and queries are described using weighted, i.e., fuzzy representations. The paper also explores the application of generalized rough sets and the variable precision models. The problem of coordination between multiple vocabulary views is also examined. Finally, a preliminary analysis of issues that arise when applying the proposed vocabulary mining framework to the Unified Medical Language System (a state-of-the-art vocabulary system) is presented. The proposed framework supports the systematic study and application of different vocabulary views in information retrieval.

Variable precision rough set model

A generalized model of rough sets called variable precision model (VP-model), aimed at modelling classification problems involving uncertain or imprecise information, is presented. The generalized model inherits all basic mathematical properties of the original model introduced by Pawlak. The main concepts are introduced formally and illustrated with simple examples. The application of the model to analysis of knowledge representation systems is also discussed.