Online Optimization Methods for the Quantification Problem

Abstract

The estimation of class prevalence, i.e., the fraction of a population that belongs to a certain class, is a very useful tool in data analytics and learning, and finds applications in many domains such as sentiment analysis, epidemiology, etc. For example, in sentiment analysis, the objective is often not to estimate whether a specific text conveys a positive or a negative sentiment, but rather estimate the overall distribution of positive and negative sentiments during an event window. A popular way of performing the above task, often dubbed quantification, is to use supervised learning to train a prevalence estimator from labeled data.Contemporary literature cites several performance measures used to measure the success of such prevalence estimators. In this paper we propose the first online stochastic algorithms for directly optimizing these quantificationspecific performance measures. We also provide algorithms that optimize hybrid performance measures that seek to balance quantification and classification performance. Our algorithms present a significant advancement in the theory of multivariate optimization and we show, by a rigorous theoretical analysis, that they exhibit optimal convergence. We also report extensive experiments on benchmark and real data sets which demonstrate that our methods significantly outperform existing optimization techniques used for these performance measures.

Optimizing non-decomposable measures with deep networks

“…The recent years have seen much interest, as well as progress, in training directly with task-specific performance measures in the field of classification and ranking. Some notable works include those of [10,15] that investigate the statistical properties of plug-in classifiers for various non-decomposable objectives including F-measure, and [7,8,12,13] which propose stochastic gradient-style algorithms for optimizing non-decomposable performance measures such as F-measure, KL-divergence, area under the ROC curve (AUC), precision recall curve (AUCPR), recall at fixed precision (R@P), etc. However, all the works cited above focus only on training linear models.…”

“…, (x n , y n )}, denote the sample average asP S (w) = 1 n n i=1 r + (w; x i , y i ) and similarly define N (w),N S (w). Unlike previous work [7,14], we will not restrict ourselves to concave surrogate reward functions. In particular we will utilize the sigmoidal reward, which is widely used as an activation function in neural networks is non-concave: r sigmoid (ŷ, y) = (1 + exp(−y ·ŷ)) −1…”

“…We note that there are several other performance measures that our techniques can handle but which we do not discuss here due to lack of space. These include measures for class-imbalanced classification such as H-mean, G-mean, Jaccard coefficient (see [14]), as well as quantification measures such as Q-measure, NSS and CQB (see [7]).…”

“…The following experiments Figure: [7] show the performance of DAME on the F1-Measure. A naive training with misclassification loss yields extremely poor F-measure performance.…”

Analytic approximate solutions to the chemically reactive solute transfer problem with partial slip in the flow of a viscous fluid over an exponentially stretching sheet with suction/blowing

“…Along with the analytical methods, some computational methods to solve nonlinear problems from engineering and computer sciences have been developed by Li et al [17][18][19][20][21][22][23][24], Guo et al [25], Korda et al [26].…”