Noise Tolerance under Risk Minimization

In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with the ideal noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper we analyze the noise tolerance properties of risk minimization (under different loss functions), which is a generic method for learning classifiers. We show that risk minimization under 0-1 loss function has impressive noise tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude the paper with some discussion on implications of these theoretical results

Making Risk Minimization Tolerant to Label Noise

In many applications, the training data, from which one needs to learn a classifier, is corrupted with label noise. Many standard algorithms such as SVM perform poorly in presence of label noise. In this paper we investigate the robustness of risk minimization to label noise. We prove a sufficient condition on a loss function for the risk minimization under that loss to be tolerant to uniform label noise. We show that the $0-1$ loss, sigmoid loss, ramp loss and probit loss satisfy this condition though none of the standard convex loss functions satisfy it. We also prove that, by choosing a sufficiently large value of a parameter in the loss function, the sigmoid loss, ramp loss and probit loss can be made tolerant to non-uniform label noise also if we can assume the classes to be separable under noise-free data distribution. Through extensive empirical studies, we show that risk minimization under the $0-1$ loss, the sigmoid loss and the ramp loss has much better robustness to label noise when compared to the SVM algorithm

Effects of osmotic and matric potential on radial growth and accumulation of endogenous reserves in three isolates of Pochonia chlamydosporia

For the first time, the effects of varying osmotic and matric potential on fungal radial growth and accumulation of polyols were studied in three isolates of Pochonia chlamydosporia. Fungal radial growth was measured on potato dextrose agar modified osmotically using potassium chloride or glycerol. PEG 8000 was used to modify matric potential. When plotted, the radii of the colonies were found to grow linearly with time, and regression was applied to estimate the radial growth rate (mm day-1). Samples of fresh mycelia from 25-day-old cultures were collected and the quantity (mg g-1 fresh biomass) of four polyols (glycerol, erythritol, arabitol and mannitol) and one sugar (glucose) was determined using HPLC. Results revealed that fungal radial growth rates decreased with increased osmotic or matric stress. Statistically significant differences in radial growth were found between isolates in response to matric stress (P<0.006) but not in response to osmotic stress (P=0.759). Similarly, differences in the total amounts of polyols accumulated by the fungus were found between isolates in response to matric stress (P<0.001), but not in response to osmotic stress (P=0.952). Under water stress, the fungus accumulated a combination of different polyols important in osmoregulation, which depended on the solute used to generate the stress. Arabitol and glycerol were the main polyols accumulated in osmotically modified media, whereas erythritol was the main polyol that was accumulated in media amended with PEG. The results found that Pochonia chlamydosporia may use different osmoregulation mechanisms to overcome osmotic and matric stresses