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.

Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

The Bayesian conditional independence model for measurement error: applications in ecology

The measurement error model is a well established statistical method for regression problems in medical sciences, although rarely used in ecological studies. While the situations in which it is appropriate may be less common in ecology, there are instances in which there may be benefits in its use for prediction and estimation of parameters of interest. We have chosen to explore this topic using a conditional independence model in a Bayesian framework using a Gibbs sampler, as this gives a great deal of flexibility, allowing us to analyse a number of different models without losing generality. Using simulations and two examples, we show how the conditional independence model can be used in ecology, and when it is appropriate.

Under the carpet : the politics and trauma of patient harm

Few studies have investigated iatrogenic outcomes from the viewpoint of patient experience. To address this anomaly, the broad aim of this research is to explore the lived experience of patient harm. Patient harm is defined as major harm to the patient, either psychosocial or physical in nature, resulting from any aspect of health care. Utilising the method of Consensual Qualitative Research (CQR), in-depth interviews are conducted with twenty-four volunteer research participants who self-report having been severely harmed by an invasive medical procedure. A standardised measure of emotional distress, the Impact of Event Scale (IES), is additionally employed for purposes of triangulation. Thematic analysis of transcript data indicate numerous findings including: (i) difficulties regarding patients‘ prior understanding of risks involved with their medical procedure; (ii) the problematic response of the health system post-procedure; (iii) multiple adverse effects upon life functioning; (iv) limited recourse options for patients; and (v) the approach desired in terms of how patient harm should be systemically handled. In addition, IES results indicate a clinically significant level of distress in the sample as a whole. To discuss findings, a cross-disciplinary approach is adopted that draws upon sociology, medicine, medical anthropology, psychology, philosophy, history, ethics, law, and political theory. Furthermore, an overall explanatory framework is proposed in terms of the master themes of power and trauma. In terms of the theme of power, a postmodernist analysis explores the politics of patient harm, particularly the dynamics surrounding the politics of knowledge (e.g., notions of subjective versus objective knowledge, informed consent, and open disclosure). This analysis suggests that patient care is not the prime function of the health system, which appears more focussed upon serving the interests of those in the upper levels of its hierarchy. In terms of the master theme of trauma, current understandings of posttraumatic stress disorder (PTSD) are critiqued, and based on data from this research as well as the international literature, a new model of trauma is proposed. This model is based upon the principle of homeostasis observed in biology, whereby within every cell or organism a state of equilibrium is sought and maintained. The proposed model identifies several bio-psychosocial markers of trauma across its three main phases. These trauma markers include: (i) a profound sense of loss; (ii) a lack of perceived control; (iii) passive trauma processing responses; (iv) an identity crisis; (v) a quest to fully understand the trauma event; (vi) a need for social validation of the traumatic experience; and (vii) posttraumatic adaption with the possibility of positive change. To further explore the master themes of power and trauma, a natural group interview is carried out at a meeting of a patient support group for arachnoiditis. Observations at this meeting and members‘ stories in general support the homeostatic model of trauma, particularly the quest to find answers in the face of distressing experience, as well as the need for social recognition of that experience. In addition, the sociopolitical response to arachnoiditis highlights how public domains of knowledge are largely constructed and controlled by vested interests. Implications of the data overall are discussed in terms of a cultural revolution being needed in health care to position core values around a prime focus upon patients as human beings.

Error analysis and attitude observability of a monocular GPS/visual odometry integrated navigation filter

In this paper, we present a method for the recovery of position and absolute attitude (including pitch, roll and yaw) using a novel fusion of monocular Visual Odometry and GPS measurements in a similar manner to a classic loosely-coupled GPS/INS error state navigation filter. The proposed filter does not require additional restrictions or assumptions such as platform-specific dynamics, map-matching, feature-tracking, visual loop-closing, gravity vector or additional sensors such as an IMU or magnetic compass. An observability analysis of the proposed filter is performed, showing that the scale factor, position and attitude errors are fully observable under acceleration that is non-parallel to velocity vector in the navigation frame. The observability properties of the proposed filter are demonstrated using numerical simulations. We conclude the article with an implementation of the proposed filter using real flight data collected from a Cessna 172 equipped with a downwards-looking camera and GPS, showing the feasibility of the algorithm in real-world conditions.

Feedback information and consumer motivation : the moderation role of positive and negative reference values in self-regulation

Marketers spend considerable resources to motivate people to consume their products and services as a means of goal attainment (Bagozzi and Dholakia, 1999). Why people increase, decrease, or stop consuming some products is based largely on how well they perceive they are doing in pursuit of their goals (Carver and Scheier, 1992). Yet despite the importance for marketers in understanding how current performance influences a consumer’s future efforts, this topic has received little attention in marketing research. Goal researchers generally agree that feedback about how well or how poorly people are doing in achieving their goals affects their motivation (Bandura and Cervone, 1986; Locke and Latham, 1990). Yet there is less agreement about whether positive and negative performance feedback increases or decreases future effort (Locke and Latham, 1990). For instance, while a customer of a gym might cancel his membership after receiving negative feedback about his fitness, the same negative feedback might cause another customer to visit the gym more often to achieve better results. A similar logic can apply to many products and services from the use of cosmetics to investing in mutual funds. The present research offers managers key insights into how to engage customers and keep them motivated. Given that connecting customers with the company is a top research priority for managers (Marketing Science Institute, 2006), this article provides suggestions for performance metrics including four questions that managers can use to apply the findings.

The effect of simulated astigmatic refractive error on reading performance

Background: Few studies have specifically investigated the functional effects of uncorrected astigmatism on measures of reading fluency. This information is important to provide evidence for the development of clinical guidelines for the correction of astigmatism. Methods: Participants included 30 visually normal, young adults (mean age 21.7 ± 3.4 years). Distance and near visual acuity and reading fluency were assessed with optimal spectacle correction (baseline) and for two levels of astigmatism, 1.00DC and 2.00DC, at two axes (90° and 180°) to induce both against-the-rule (ATR) and with-the-rule (WTR) astigmatism. Reading and eye movement fluency were assessed using standardized clinical measures including the test of Discrete Reading Rate (DRR), the Developmental Eye Movement (DEM) test and by recording eye movement patterns with the Visagraph (III) during reading for comprehension. Results: Both distance and near acuity were significantly decreased compared to baseline for all of the astigmatic lens conditions (p < 0.001). Reading speed with the DRR for N16 print size was significantly reduced for the 2.00DC ATR condition (a reduction of 10%), while for smaller text sizes reading speed was reduced by up to 24% for the 1.00DC ATR and 2.00DC condition in both axis directions (p<0.05). For the DEM, sub-test completion speeds were significantly impaired, with the 2.00DC condition affecting both vertical and horizontal times and the 1.00DC ATR condition affecting only horizontal times (p<0.05). Visagraph reading eye movements were not significantly affected by the induced astigmatism. Conclusions: Induced astigmatism impaired performance on selected tests of reading fluency, with ATR astigmatism having significantly greater effects on performance than did WTR, even for relatively small amounts of astigmatic blur of 1.00DC. These findings have implications for the minimal prescribing criteria for astigmatic refractive errors.

Motivational Interviewing (MINT) improves Continuous Positive Airway Pressure (CPAP) acceptance and adherence : a randomised controlled trial

Objective: Adherence to Continuous Positive Airway Pressure Therapy (CPAP) for Obstructive Sleep Apnoea (OSA) is poor. We assessed the effectiveness of a motivational interviewing intervention (MINT) in addition to best practice standard care to improve acceptance and adherence to CPAP therapy in people with a new diagnosis of OSA. Method: 106 Australian adults (69% male) with a new diagnosis of obstructive sleep apnoea and clinical recommendation for CPAP treatment were recruited from a tertiary sleep disorders centre. Participants were randomly assigned to receive either three sessions of a motivational interviewing intervention ‘MINT’ (n=53; mean age=55.4 years), or no intervention ‘Control’ (n=53; mean age=57.74). The primary outcome was the difference between the groups in objective CPAP adherence at 1 month, 2 months, 3 months and 12 months follow-up. Results: Fifty (94%) participants in the MINT group and 50 (94%) of participants in the control group met all inclusion and exclusion criteria and were included in the primary analysis. The hours of CPAP use per night in the MINT group at 3 months was 4.63 hours and 3.16 hours in the control group (p=0.005). This represents almost 50% better adherence in the MINT group relative to the control group. Patients in the MINT group were substantially more likely to accept CPAP treatment. Conclusions: MINT is a brief, manualized, effective intervention which improves CPAP acceptance and objective adherence rates as compared to standard care alone.