Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

A unifying view of multiple kernel learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion’s dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

On the optimality of sample-based estimates of the expectation of the empirical minimizer

We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates expectations to sample averages. Second, we show that these structural upper bounds can be loose, compared to previous bounds. In particular, we demonstrate a class for which the expectation of the empirical minimizer decreases as O(1/n) for sample size n, although the upper bound based on structural properties is Ω(1). Third, we show that this looseness of the bound is inevitable: we present an example that shows that a sharp bound cannot be universally recovered from empirical data.

Classification with a reject option using a hinge loss

We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

A unifying view of multiple kernel learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion's dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

Margin-adaptive model selection in statistical learning

A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning framework. Actually, we consider a weaker version of this condition that allows one to take into account that learning within a small model can be much easier than within a large one. Requiring this “strong margin adaptivity” makes the model selection problem more challenging. We first prove, in a general framework, that some penalization procedures (including local Rademacher complexities) exhibit this adaptivity when the models are nested. Contrary to previous results, this holds with penalties that only depend on the data. Our second main result is that strong margin adaptivity is not always possible when the models are not nested: for every model selection procedure (even a randomized one), there is a problem for which it does not demonstrate strong margin adaptivity.

Some novel techniques of parameter estimation for the dynamical models in biological systems

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

Implementable efficient time and energy consumption trajectories design for an autonomous underwater vehicle

In this paper we consider the implementation of time and energy efficient trajectories onto a test-bed autonomous underwater vehicle. The trajectories are losely connected to the results of the application of the maximum principle to the controlled mechanical system. We use a numerical algorithm to compute efficient trajectories designed using geometric control theory to optimize a given cost function. Experimental results are shown for the time minimization problem.

Optimal sitting and sizing of distributed generators considering plug-in electric vehicles

Some uncertainties such as the stochastic input/output power of a plug-in electric vehicle due to its stochastic charging and discharging schedule, that of a wind unit and that of a photovoltaic generation source, volatile fuel prices and future uncertain load growth, all together could lead to some risks in determining the optimal siting and sizing of distributed generators (DGs) in distributed systems. Given this background, under the chance constrained programming (CCP) framework, a new method is presented to handle these uncertainties in the optimal sitting and sizing problem of DGs. First, a mathematical model of CCP is developed with the minimization of DGs investment cost, operational cost and maintenance cost as well as the network loss cost as the objective, security limitations as constraints, the sitting and sizing of DGs as optimization variables. Then, a Monte Carolo simulation embedded genetic algorithm approach is developed to solve the developed CCP model. Finally, the IEEE 37-node test feeder is employed to verify the feasibility and effectiveness of the developed model and method. This work is supported by an Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) Project on Intelligent Grids Under the Energy Transformed Flagship, and Project from Jiangxi Power Company.

Victims Speak: Comparing Child Sexual Abusers and Their Victims Accounts of Offence Circumstances

This article presents findings from a longitudinal study. The research aimed to explore the effectiveness of a treatment program for offenders which lasted for three years. The research design was structured around the program with interviews and psychometric testing undertaken at key points in time with the same group of respondents. View all notes that sought to evaluate a treatment program for child sexual abusers. A triangulated methodological approach was adopted drawing upon quantitative and qualitative methodological techniques. The focus here is upon one element of this research. 2 2The quantitative element of this research will be published shortly but is referred to in the following reports Davidson 2000, 2003 [research funded by the National Probation Service]. Psychometric testing was undertaken over a four-year period with the men attending the treatment program to explore shifts in the extent of denial, blame attribution, and victim empathy over time. Offender cognitive distortions, general health, and self-esteem were also explored via psychometric testing. An interview-administered survey was undertaken with all sex offenders registered with the Probation Service (those on probation and in custody) in order to gather demographic data, and 117 of 150 offenders responded. View all notes Ninety-one in-depth interviews were conducted over a four-year period with a small, nonrandom sample of twenty-one male offenders who had been convicted of sexual offenses against children. All of the men were subject to probation orders with a psychiatric condition (Criminal Justice Act, 1991). One of the aims of this element of the research was to explore the extent to which evidence of denial could be found in offenders’ accounts of offense circumstance and also to explore the extent to which offenders minimized the nature and extent of abuse perpetrated. Offenders’ accounts of offense circumstances were compared to victim statements, and stark differences emerge. These findings have considerable implications for treatment practice with sex offenders, where victims’ perceptions could be used to directly confront offender denial and minimization.

Improvement of the statutory framework for construction and demolition waste management exemplified in Germany and Australia

Construction and demolition (C&D) waste occupies the largest share of overall waste generation in many countries. However, waste management practices and outcomes may differ between countries. For instance, in Australia, C&D waste recovery is continuously improving during the last years but the amount of C&D waste increases every year, as there has been little improvement in waste avoidance and minimization. In contrast, in Germany, waste generation remains constant over many years despite the continuous economic growth. The waste recycling rate in Germany is one of the highest in the world. However, most waste recycled is from demolition work rather than from waste generated during new construction. In addition, specific laws need to be developed to further reduce landfill of non-recycled waste. Despite of the differences, C&D waste generation and recovery in both countries depend on the effectiveness of the statutory framework, which regulates their waste management practices. This is an issue in other parts of the world as well. Therefore countries can learn from each other to improve their current statutory framework for C&D waste management. By taking Germany and Australia as an example, possible measures to improve current practices of C&D waste management through better statutory tools are identified in this paper. After providing an overview of the statutory framework of both countries and their status in waste generation and recovery, a SWOT analysis is conducted to identify strengths, weaknesses, opportunities and threats of the statutory tools. Recommendations to improve the current statutory frameworks, in order to achieve less waste generation and more waste recovery in the construction industry are provided for the German and Australian government and they can also be transferred to other countries.

Optimal planning of electric-vehicle charging stations in distribution systems

With the progressive exhaustion of fossil energy and the enhanced awareness of environmental protection, more attention is being paid to electric vehicles (EVs). Inappropriate siting and sizing of EV charging stations could have negative effects on the development of EVs, the layout of the city traffic network, and the convenience of EVs' drivers, and lead to an increase in network losses and a degradation in voltage profiles at some nodes. Given this background, the optimal sites of EV charging stations are first identified by a two-step screening method with environmental factors and service radius of EV charging stations considered. Then, a mathematical model for the optimal sizing of EV charging stations is developed with the minimization of total cost associated with EV charging stations to be planned as the objective function and solved by a modified primal-dual interior point algorithm (MPDIPA). Finally, simulation results of the IEEE 123-node test feeder have demonstrated that the developed model and method cannot only attain the reasonable planning scheme of EV charging stations, but also reduce the network loss and improve the voltage profile.

A randomized controlled pilot study comparing aqueous cream with a beeswax and herbal oil cream in the provision of relief from postburn pruritis

Postburn itch is reported to affect up to 87% of the burn population. Although treatments for postburn itch are multimodal, they remain consistently ineffective. However, recent anecdotal evidence from several outpatients at a tertiary referral hospital suggests that a cream combining beeswax and several herbal oils may be effective in the minimization of postburn itch. The aim of this study was to test the efficacy of beeswax and herbal oil cream against the standard treatment of aqueous cream in the provision of relief from the symptoms of postburn itch. A randomized controlled trial compared two groups using a visual analog scale, frequency of cream application, itch recurrence after cream application, use of antipruritic medications, and sleep disturbance to determine the effect of itch severity and duration. Fifty-two participants were enrolled in the study (84% male) with a mean age of 35 years (SD = 16) and mean burn TBSA of 7.2% (SD = 7.7). Study results found that the beeswax and herbal oil cream reduce itch after application more frequently than aqueous cream (P = .001). In addition, when managed with beeswax and herbal oil cream, participants found that their itch recurred later (P ≤ .001) and their use of antipruritic medications was lower (P = .023). Findings of this study suggest beeswax and herbal oil cream to be more effective in the minimization of postburn itch than aqueous cream. Given this, a larger study examining the efficacy of beeswax and herbal oil cream appears warranted.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Molecular dynamics simulation of fracture strength and morphology of defective graphene

Different types of defects can be introduced into graphene during material synthesis, and significantly influence the properties of graphene. In this work, we investigated the effects of structural defects, edge functionalisation and reconstruction on the fracture strength and morphology of graphene by molecular dynamics simulations. The minimum energy path analysis was conducted to investigate the formation of Stone-Wales defects. We also employed out-of-plane perturbation and energy minimization principle to study the possi-ble morphology of graphene nanoribbons with edge-termination. Our numerical results show that the fracture strength of graphene is dependent on defects and environmental temperature. However, pre-existing defects may be healed, resulting in strength recovery. Edge functionalization can induce compressive stress and ripples in the edge areas of gra-phene nanoribbons. On the other hand, edge reconstruction contributed to the tensile stress and curved shape in the graphene nanoribbons.