On the consistency of multiclass classification methods

Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that not all generalizations preserve the nice property of Bayes consistency. We provide a necessary and sufficient condition for consistency which applies to a large class of multiclass classification methods. The approach is illustrated by applying it to some multiclass methods proposed in the literature.

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.

On the consistency of multiclass classification methods

Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.

Effect of external high pressures on the clay mineral sodium montmorillonite intercalated with methylated octadecylammonium bromide surfactants

Raman microprobe spectra of the clay mineral Wyoming SWy-2-sodium montmorillonite intercalated with the surfactants, methyltrioctadecylammonium bromide (TOMA) dimethyldiotadecylammonium bromide (DODMA) and octadecyl-trimethylammonium bromide (ODTMA), have been measured in the CH2 stretching region at external pressures up to ~40 kbar with the aid of a diamond-anvil cell. In the case of the intercalated clays containing TOMA and DODMA, the Raman data afford evidence for gauche to trans conformational changes in the orientation of the CH2 chains in the surfactants with increasing pressure. These conformational changes are reversed completely upon the release of pressure.

On the natural convection boundary layer adjacent to an inclined flat plate subject to ramp heating

An investigation of the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a temperature boundary condition which follows a ramp function up until some specified time and then remains constant is reported. The development of the flow from start-up to a steadystate has been described based on scaling analyses and verified by numerical simulations. Attention in this study has been given to fluids having a Prandtl number Pr less than unity. The boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

Utility of routine data sources for feedback on the quality of cancer care: an assessment based on clinical practice guidelines

Background Not all cancer patients receive state-of-the-art care and providing regular feedback to clinicians might reduce this problem. The purpose of this study was to assess the utility of various data sources in providing feedback on the quality of cancer care. Methods Published clinical practice guidelines were used to obtain a list of processes-of-care of interest to clinicians. These were assigned to one of four data categories according to their availability and the marginal cost of using them for feedback. Results Only 8 (3%) of 243 processes-of-care could be measured using population-based registry or administrative inpatient data (lowest cost). A further 119 (49%) could be measured using a core clinical registry, which contains information on important prognostic factors (e.g., clinical stage, physiological reserve, hormone-receptor status). Another 88 (36%) required an expanded clinical registry or medical record review; mainly because they concerned long-term management of disease progression (recurrences and metastases) and 28 (11.5%) required patient interview or audio-taping of consultations because they involved information sharing between clinician and patient. Conclusion The advantages of population-based cancer registries and administrative inpatient data are wide coverage and low cost. The disadvantage is that they currently contain information on only a few processes-of-care. In most jurisdictions, clinical cancer registries, which can be used to report on many more processes-of-care, do not cover smaller hospitals. If we are to provide feedback about all patients, not just those in larger academic hospitals with the most developed data systems, then we need to develop sustainable population-based data systems that capture information on prognostic factors at the time of initial diagnosis and information on management of disease progression.