Discriminant analysis with a stochastic supervisor

Generalisations of stochastic supervision models

“…On the basis of these assessments (or say probabilistic labels), the statistical classification problem, of fitting a model to the training data and inferring the real labels of the test data, was studied under the nomenclature of stochastic supervision [14][15][16][17][18][19].…”

“…The research of stochastic supervision models for discriminant analysis was pioneered by Aitchison and Begg [14] and Krishnan and Nandy [15]. As with [15] we assume two classes, namely class 1 and class 2, with proportions π 1 and π 2 = 1 − π 1 , respectively.…”

“…The research of stochastic supervision models for discriminant analysis was pioneered by Aitchison and Begg [14] and Krishnan and Nandy [15]. As with [15] we assume two classes, namely class 1 and class 2, with proportions π 1 and π 2 = 1 − π 1 , respectively. In each class, the data available, including both the d-dimensional feature vector x of an instance and its supervisor's assessment z that the instance belongs to class j, follow a class-dependent distribution f j (x, z), for j = 1, 2.…”

“…In [15], the class-dependent joint data-generating distribution f j (x, z) was further factorised as f j (x, z) = f j (x)q j (z), by assuming that the features…”

“…We denote the pdfs of z|y = 1 and z|y = 2 as q 1 (z) and q 2 (z), respectively. That is to say, the model in [15] assumes that the data-generating process in class j follows a Gaussian distribution f j (x) for features x and a Beta distribution q j (z) for assessment z. Although the assessment z is given for each training instance…”