Strong rules for nonconvex penalties and their implications for efficient algorithms in high-dimensional regression

We consider approaches for improving the efficiency of algorithms for fitting nonconvex penalized regression models such as SCAD and MCP in high dimensions. In particular, we develop rules for discarding variables during cyclic coordinate descent. This dimension reduction leads to a substantial improvement in the speed of these algorithms for high-dimensional problems. The rules we propose here eliminate a substantial fraction of the variables from the coordinate descent algorithm. Violations are quite rare, especially in the locally convex region of the solution path, and furthermore, may be easily detected and corrected by checking the Karush-Kuhn-Tucker conditions. We extend these rules to generalized linear models, as well as to other nonconvex penalties such as the $\ell_2$-stabilized Mnet penalty, group MCP, and group SCAD. We explore three variants of the coordinate decent algorithm that incorporate these rules and study the efficiency of these algorithms in fitting models to both simulated data and on real data from a genome-wide association study

Nonlinear Model for Reinforced Concrete under Cyclic Loading

Most of the available shear models for reinforced concrete rely on empirical formulations. In this study, a rational shear stress function is used to define the shear stress–strain envelope for reinforced concrete. Cyclic rules are proposed to define the loading, unloading and reloading relationships for reinforced concrete under shear stress reversals. A normal stress function describing the cyclic relationship of concrete under axial stress is also introduced. The proposed functions are verified using experimental data of reinforced concrete panels tested under monotonic and cyclic loading. Subsequently, the normal and shear stress functions along with their cyclic rules are integrated in a non-linear finite element analysis code. The resulting model accounts for tension stiffening, crack opening and closing, compression hardening and softening, degradation of concrete strength and stiffness in the direction parallel to the crack, compression unloading and reloading, as well as non-linear steel behaviour (strain hardening and Bauschinger effect). The finite element model is then used to analyse two Portland Cement Association shear walls with different geometries tested under cyclic loading. The results show a good agreement between analytical and experimental data. The model showed an excellent capacity of predicting shear deformations of reinforced concrete elements under cyclic loading with minimal computational efforts

Mining process factor causality links with multi-relational associations

International audienceTo make knowledge-supported decisions, industrial actors often need to examine available data for suggestive patterns. As industrial data are typically unlabeled and involve multiple object types, unsupervised multi-relational (MR) data mining methods are particularly suitable for the task. Current MR association miners merely produce singleton-conclusions rules hence might miss multi-way dependencies. Our novel MR miner builds upon a relational extension of concept analysis to extract general associations. While successfully dealing with circularity in data, it avoids producing cyclic rules by limiting the description depth of relational concepts. Our rules' relevance was validated by an application to aluminum die casting

The tone system of Foodo nouns

This thesis presents an autosegmental analysis of the tone system of the nouns of Foodo, a Guang language of Benin. The goal is to give an analysis of the tone system of nouns that will account for all the surface tonal phenomena by positing two underlying tones. Foodo nouns consist of a stem together with its class prefix and/or suffix; while tonal alternations in prefixes are easily explained by two tone rules, the suffixes exhibit rather complex alternations. Many of the theoretical assumptions of lexical phonology, (especially the view that most lexical rules are cyclic and Kiparsky\u27s Elsewhere Condition) allow for a simple and straightforward account of these tonal alternations. This thesis assumes Pulleyblank\u27s (1986:78-82) version of the Association Convention which excludes automatic multiple-linking and automatic spreading. A secondary goal of this thesis is to address certain theoretical issues in light of the analysis contained herein. Chapter 6 shows that cyclic application of rules is necessary in the lexical component of a Foodo grammar, thus lending support to the claim of lexical phonology that rule application in the lexical component may be cyclic. This chapter also discusses the issue of what constitutes a tone-bearing unit (TBU) in the language, and shows that current phonological theory does not provide an adequate element to serve as the TBU in Foodo

Market basket analysis : trend analysis of association rules in different time periods

Dissertation presented as the partial requirement for obtaining a Master's degree in Statistics and Information Management, specialization in Marketing Research e CRMMarket basket analysis (i.e. Data mining technique in the field of marketing) is the method to find the associations between the items / item sets and based on those associations we can analyze the consumer behavior. In this research we have presented the variability of time, because with the change in time the habits or behavior of the customer also changes. For example, people wear warm clothes in winter and light clothes in summer. Similarly, customers purchase behavior also changes with the change in time. We study the problem of discovering association rules that display regular cyclic variation over time. This problem will allow us to access the changing trends in the purchase behavior of customers in a retail market, and we will be able to analyze the results which will display the changing trends of the association rules. In this research we will study the interaction between association rules and time. We worked on transactional data of a Belgian retail company and analyzed the results which will help the company to build up time period specific marketing strategies, promotional strategies, etc. to increase the profit of their company

Evolving temporal fuzzy association rules from quantitative data with a multi-objective evolutionary algorithm

A novel method for mining association rules that are both quantitative and temporal using a multi-objective evolutionary algorithm is presented. This method successfully identifies numerous temporal association rules that occur more frequently in areas of a dataset with specific quantitative values represented with fuzzy sets. The novelty of this research lies in exploring the composition of quantitative and temporal fuzzy association rules and the approach of using a hybridisation of a multi-objective evolutionary algorithm with fuzzy sets. Results show the ability of a multi-objective evolutionary algorithm (NSGA-II) to evolve multiple target itemsets that have been augmented into synthetic datasets

Web Usage Mining with Evolutionary Extraction of Temporal Fuzzy Association Rules

In Web usage mining, fuzzy association rules that have a temporal property can provide useful knowledge about when associations occur. However, there is a problem with traditional temporal fuzzy association rule mining algorithms. Some rules occur at the intersection of fuzzy sets' boundaries where there is less support (lower membership), so the rules are lost. A genetic algorithm (GA)-based solution is described that uses the flexible nature of the 2-tuple linguistic representation to discover rules that occur at the intersection of fuzzy set boundaries. The GA-based approach is enhanced from previous work by including a graph representation and an improved fitness function. A comparison of the GA-based approach with a traditional approach on real-world Web log data discovered rules that were lost with the traditional approach. The GA-based approach is recommended as complementary to existing algorithms, because it discovers extra rules. (C) 2013 Elsevier B.V. All rights reserved