Robust model selection with flexible trimming

The forward search provides data-driven flexible trimming of a C_p statistic for the choice of regression models that reveals the effect of outliers on model selection. An informed robust model choice follows. Even in small samples, the statistic has a null distribution indistinguishable from an F distribution. Limits on acceptable values of the C_p statistic follow. Two examples of widely differing size are discussed. A powerful graphical tool is the generalized candlestick plot, which summarizes the information on all forward searches and on the choice of models. A comparison is made with the use of M-estimation in robust model choice.     

Approximate dynamic programming-based approaches for input-output data-driven control of nonlinear processes

We propose two approximate dynamic programming (ADP)-based strategies for control of nonlinear processes using input-output data. In the first strategy, which we term ‘J-learning,’ one builds an empirical nonlinear model using closed-loop test data and performs dynamic programming with it to derive an improved control policy. In the second strategy, called ‘Q-learning,’ one tries to learn an improved control policy in a model-less manner. Compared to the conventional model predictive control approach, the new approach offers some practical advantages in using nonlinear empirical models for process control. Besides the potential reduction in the on-line computational burden, it offers a convenient way to control the degree of model extrapolation in the calculation of optimal control moves. One major difficulty associated with using an empirical model within the multi-step predictive control setting is that the model can be excessively extrapolated into regions of the state space where identification data were scarce or nonexistent, leading to performances far worse than predicted by the model. Within the proposed ADP-based strategies, this problem is handled by imposing a penalty term designed on the basis of local data distribution. A CSTR example is provided to illustrate the proposed approaches.     

State feedback control of continuous-time T-S fuzzy systems via switched fuzzy controllers

This paper studies the problem of state feedback control of continuous-time T-S fuzzy systems. Switched fuzzy controllers are exploited in the control design, which are switched based on the values of membership functions, and the control scheme is an extension of the parallel distributed compensation (PDC) scheme. Sufficient conditions for designing switched state feedback controllers are obtained with meeting an H_∞ norm bound requirement and quadratic D stability constraints. It is shown that the new control design method provides less conservative results than the corresponding ones via the parallel distributed compensation (PDC) scheme. A numerical example is given to illustrate the effectiveness of the proposed method.     

Fuzzy and possibilistic clustering for fuzzy data

The Fuzzy k-Means clustering model (FkM) is a powerful tool for classifying objects into a set of k homogeneous clusters by means of the membership degrees of an object in a cluster. In FkM, for each object, the sum of the membership degrees in the clusters must be equal to one. Such a constraint may cause meaningless results, especially when noise is present. To avoid this drawback, it is possible to relax the constraint, leading to the so-called Possibilistic k-Means clustering model (PkM). In particular, attention is paid to the case in which the empirical information is affected by imprecision or vagueness. This is handled by means of LR fuzzy numbers. An FkM model for LR fuzzy data is firstly developed and a PkM model for the same type of data is then proposed. The results of a simulation experiment and of two applications to real world fuzzy data confirm the validity of both models, while providing indications as to some advantages connected with the use of the possibilistic approach.     

Modelling series of studies with a common structure

Consider the situation where the Structuration des Tableaux à Trois Indices de la Statistique (STATIS) methodology is applied to a series of studies, each study being represented by data and weight matrices. Relations between studies may be captured by the Hilbert-Schmidt product of these matrices. Specifically, the eigenvalues and eigenvectors of the Hilbert-Schmidt matrix S may be used to obtain a geometrical representation of the studies. The studies in a series may further be considered to have a common structure whenever their corresponding points lie along the first axis. The matrix S can be expressed as the sum of a rank 1 matrix λuu^T with an error matrix E. Therefore, the components of the vector are sufficient to locate the points associated to the studies. Former models for S where vec(E) are mathematically tractable and yet do not take into account the symmetry of the matrix S. Thus a new symmetric model is proposed as well as the corresponding tests for a common structure. It is further shown how to assess the goodness of fit of such models. An application to the human immunodeficiency virus (HIV) infection is used for assessing the proposed model.     

Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems

Verification problems for finite- and infinite-state processes, like model checking and equivalence checking, can effectively be encoded in Parameterised Boolean Equation Systems (PBESs). Solving the PBES then solves the encoded problem. The decidability of solving a PBES depends on the data sorts that occur in the PBES. We describe a pragmatic methodology for solving PBESs, viz., by attempting to instantiate them to the sub-fragment of Boolean Equation Systems (BESs). Unlike solving PBESs, solving BESs is a decidable problem. Based on instantiation, verification using PBESs can effectively be done fully automatically in most practical cases. We demonstrate this by solving several complex verification problems using a prototype implementation of our instantiation technique. In addition, practical issues concerning this implementation are addressed. Furthermore, we illustrate the effectiveness of instantiation as a transformation on PBESs when solving verification problems involving systems of infinite size.     

A discrete-time stable controller for an omni-directional mobile robot based on an approximated model

An adaptive controller based on multi-input fuzzy rules emulated networks (MIFRENs) is introduced for omni-directional mobile robot systems in the discrete-time domain without any kinematic or dynamic models. An approximated model for unknown systems is developed by using two MIFRENs with an online learning algorithm in addition to the stability analysis. The main theorem in this model is proposed to guarantee closed-loop performance and system robustness for all adjustable parameters inside MIFRENs. The system is validated by an experimental setup with a FESTO omni-directional mobile robot called Robotino^®. The proposed algorithm is shown to have superior performance compared to that of an algorithm that uses only an embedded controller. The advantage of the MIFREN initial setting is verified comparing its results with those of a controller that is based on neural networks.     

Model-free Q-learning designs for linear discrete-time zero-sum games with application to H-infinity control

In this paper, the optimal strategies for discrete-time linear system quadratic zero-sum games related to the H-infinity optimal control problem are solved in forward time without knowing the system dynamical matrices. The idea is to solve for an action dependent value function Q(x,u,w) of the zero-sum game instead of solving for the state dependent value function V(x) which satisfies a corresponding game algebraic Riccati equation (GARE). Since the state and actions spaces are continuous, two action networks and one critic network are used that are adaptively tuned in forward time using adaptive critic methods. The result is a Q-learning approximate dynamic programming (ADP) model-free approach that solves the zero-sum game forward in time. It is shown that the critic converges to the game value function and the action networks converge to the Nash equilibrium of the game. Proofs of convergence of the algorithm are shown. It is proven that the algorithm ends up to be a model-free iterative algorithm to solve the GARE of the linear quadratic discrete-time zero-sum game. The effectiveness of this method is shown by performing an H-infinity control autopilot design for an F-16 aircraft.     

Input-output properties of the Page-Hinkley detector

We consider the stochastic input-output properties of a simple non-linear dynamical system, the so-called Page-Hinkley detector, playing a key role in change detection, and also in queuing theory. We show that for L-mixing inputs with negative expectation the output process of this system is L-mixing. The result is applied to get an upper bound for the false alarm rate. The proof is then adapted to get a similar result for the case of random i.i.d. inputs. Possible extensions and open problems are given in the discussion.     

Online computation with advice

We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice is a function, defined by the online algorithm, of the whole request sequence. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical model of complete lack of information regarding the future. We are interested in the impact of such advice on the competitive ratio, and in particular, in the relation between the size b of the advice, measured in terms of bits of information per request, and the (improved) competitive ratio. Since b=0 corresponds to the classical online model, and b=⌈log∣A∣⌉, where A is the algorithm’s action space, corresponds to the optimal (offline) one, our model spans a spectrum of settings ranging from classical online algorithms to offline ones.In this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the k-server problem. For MTS we establish tight (up to constant factors) upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1≤b≤Θ(logn), where n is the number of states in the system: we prove that any randomized online algorithm for MTS has competitive ratio Ω(log(n)/b) and we present a deterministic online algorithm for MTS with competitive ratio O(log(n)/b). For the k-server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k^O(1/b) for any choice of Θ(1)≤b≤logk.     

Hamiltonian connectivity and globally 3∗-connectivity of dual-cube extensive networks

In 2000, Li et al. introduced dual-cube networks, denoted by DC_n for n?1, using the hypercube family Q_n and showed the vertex symmetry and some fault-tolerant hamiltonian properties of DC_n. In this article, we introduce a new family of interconnection networks called dual-cube extensive networks, denoted by DCEN(G). Given any arbitrary graph G, DCEN(G) is generated from G using the similar structure of DC_n. We show that if G is a nonbipartite and hamiltonian connected graph, then DCEN(G) is hamiltonian connected. In addition, if G has the property that for any two distinct vertices u,v of G, there exist three disjoint paths between u and v such that these three paths span the graph G, then DCEN(G) preserves the same property. Furthermore, we prove that the similar results hold when G is a bipartite graph.     

On the hardness of finding near-optimal multicuts in directed acyclic graphs

Given an edge-weighted (di)graph and a list of source-sink pairs of vertices of this graph, the minimum multicut problem consists in selecting a minimum-weight set of edges (or arcs), whose removal leaves no path from each source to the corresponding sink. This is a well-known NP-hard problem, and improving several previous results, we show that it remains APX-hard in unweighted directed acyclic graphs (DAG), even with only two source-sink pairs. This is also true if we remove vertices instead of arcs.     

Supersaturated designs: Are our results significant?

Two-level supersaturated designs (SSDs) are designs that examine more than n−1 factors in n runs. Although SSD literature for both construction and analysis is plentiful, the dearth of actual applications suggests that SSDs are still an unproven tool. Whether using forward selection or all-subsets regression, it is easy to select simple models from SSDs that explain a very large percentage of the total variation. Hence, naive p-values can persuade the user that included factors are indeed active. We propose the use of a global model randomization test in conjunction with all-subsets (or a shrinkage method) to more appropriately select candidate models of interest. For settings where the large number of factors makes repeated use of all-subsets expensive, we propose a short-cut approximation for the p-values. Two state-of-the-art model selection methods that have received considerable attention in recent years, Least Angle Regression and the Dantzig Selector, were likewise supplemented with the global randomization test. Finally, we propose a randomization test for reducing the number of terms in candidate models with small global p-values. Randomization tests effectively emphasize the limitations of SSDs, especially those with a large factor to run size ratio.     

A novel and quick SVM-based multi-class classifier

Use different real positive numbers p_i to represent all kinds of pattern categories, after mapping the inputted patterns into a special feature space by a non-linear mapping, a linear relation between the mapped patterns and numbers p_i is assumed, whose bias and coefficients are undetermined, and the hyper-plane corresponding to zero output of the linear relation is looked as the base hyper-plane. To determine the pending parameters, an objective function is founded aiming to minimize the difference between the outputs of the patterns belonging to a same type and the corresponding p_i, and to maximize the distance between any two different hyper-planes corresponding to different pattern types. The objective function is same to that of support vector regression in form, so the coefficients and bias of the linear relation are calculated by some known methods such as SVM^light approach. Simultaneously, three methods are also given to determine p_i, the best one is to determine them in training process, which has relatively high accuracy. Experiment results of the IRIS data set show that, the accuracy of this method is better than those of many SVM-based multi-class classifiers, and close to that of DAGSVM (decision-directed acyclic graph SVM), emphatically, the recognition speed is the highest.     

A necessary and sufficient condition for parameter insensitive disturbance-rejection problem with state feedback

In this paper a necessary and sufficient condition for a parameter insensitive disturbance-rejection problem with state feedback which was pointed out as an open problem by Bhattacharyya to be solvable is proved. A constructive algorithm of simultaneously (A,B)-invariant subspaces for a finite-number of linear systems and a relationship between simultaneously (A,B)-invariant subspaces and generalized (A,B)-invariant subspaces play an important role to prove the main result.     

Three-dimensional beta shapes

The Voronoi diagram of a point set has been extensively used in various disciplines ever since it was first proposed. Its application realms have been even further extended to estimate the shape of point clouds when Edelsbrunner and Mücke introduced the concept of α-shape based on the Delaunay triangulation of a point set.In this paper, we present the theory of β-shape for a set of three-dimensional spheres as the generalization of the well-known α-shape for a set of points. The proposed β-shape fully accounts for the size differences among spheres and therefore it is more appropriate for the efficient and correct solution for applications in biological systems such as proteins.Once the Voronoi diagram of spheres is given, the corresponding β-shape can be efficiently constructed and various geometric computations on the sphere complex can be efficiently and correctly performed. It turns out that many important problems in biological systems such as proteins can be easily solved via the Voronoi diagram of atoms in proteins and β-shapes transformed from the Voronoi diagram.     

Fitting finite mixtures of generalized linear regressions in R

R package flexmix provides flexible modelling of finite mixtures of regression models using the EM algorithm. Several new features of the software such as fixed and nested varying effects for mixtures of generalized linear models and multinomial regression for a priori probabilities given concomitant variables are introduced. The use of the software in addition to model selection is demonstrated on a logistic regression example.     

A comparison of design and model selection methods for supersaturated experiments

Various design and model selection methods are available for supersaturated designs having more factors than runs but little research is available on their comparison and evaluation. Simulated experiments are used to evaluate the use of E(s²)-optimal and Bayesian D-optimal designs and to compare three analysis strategies representing regression, shrinkage and a novel model-averaging procedure. Suggestions are made for choosing the values of the tuning constants for each approach. Findings include that (i) the preferred analysis is via shrinkage; (ii) designs with similar numbers of runs and factors can be effective for a considerable number of active effects of only moderate size; and (iii) unbalanced designs can perform well. Some comments are made on the performance of the design and analysis methods when effect sparsity does not hold.