Improved Multi-Class Cost-Sensitive Boosting via Estimation of the Minimum-Risk Class

We present a simple unified framework for multi-class cost-sensitive boosting. The minimum-risk class is estimated directly, rather than via an approximation of the posterior distribution. Our method jointly optimizes binary weak learners and their corresponding output vectors, requiring classes to share features at each iteration. By training in a cost-sensitive manner, weak learners are invested in separating classes whose discrimination is important, at the expense of less relevant classification boundaries. Additional contributions are a family of loss functions along with proof that our algorithm is Boostable in the theoretical sense, as well as an efficient procedure for growing decision trees for use as weak learners. We evaluate our method on a variety of datasets: a collection of synthetic planar data, common UCI datasets, MNIST digits, SUN scenes, and CUB-200 birds. Results show state-of-the-art performance across all datasets against several strong baselines, including non-boosting multi-class approaches

On Classification-Calibration of Gamma-Phi Losses

Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration of such losses. In addition, we show that a previously proposed sufficient condition is in fact not sufficient.Comment: 21 page

Improved Multi-Class Cost-Sensitive Boosting via Estimation of the Minimum-Risk Class

We present a simple unified framework for multi-class cost-sensitive boosting. The minimum-risk class is estimated directly, rather than via an approximation of the posterior distribution. Our method jointly optimizes binary weak learners and their corresponding output vectors, requiring classes to share features at each iteration. By training in a cost-sensitive manner, weak learners are invested in separating classes whose discrimination is important, at the expense of less relevant classification boundaries. Additional contributions are a family of loss functions along with proof that our algorithm is Boostable in the theoretical sense, as well as an efficient procedure for growing decision trees for use as weak learners. We evaluate our method on a variety of datasets: a collection of synthetic planar data, common UCI datasets, MNIST digits, SUN scenes, and CUB-200 birds. Results show state-of-the-art performance across all datasets against several strong baselines, including non-boosting multi-class approaches

Rectified softmax loss with all-sided cost sensitivity for age estimation

In Convolutional Neural Network (ConvNet) based age estimation algorithms, softmax loss is usually chosen as the loss function directly, and the problems of Cost Sensitivity (CS), such as class imbalance and misclassification cost difference between different classes, are not considered. Focus on these problems, this paper constructs a rectified softmax loss function with all-sided CS, and proposes a novel cost-sensitive ConvNet based age estimation algorithm. Firstly, a loss function is established for each age category to solve the imbalance of the number of training samples. Then, a cost matrix is defined to reflect the cost difference caused by misclassification between different classes, thus constructing a new cost-sensitive error function. Finally, the above methods are merged to construct a rectified softmax loss function for ConvNet model, and a corresponding Back Propagation (BP) training scheme is designed to enable ConvNet network to learn robust face representation for age estimation during the training phase. Simultaneously, the rectified softmax loss is theoretically proved that it satisfies the general conditions of the loss function used for classification. The effectiveness of the proposed method is verified by experiments on face image datasets of different races. © 2013 IEEE

Boosting Boosting

Machine learning is becoming prevalent in all aspects of our lives. For some applications, there is a need for simple but accurate white-box systems that are able to train efficiently and with little data. "Boosting" is an intuitive method, combining many simple (possibly inaccurate) predictors to form a powerful, accurate classifier. Boosted classifiers are intuitive, easy to use, and exhibit the fastest speeds at test-time when implemented as a cascade. However, they have a few drawbacks: training decision trees is a relatively slow procedure, and from a theoretical standpoint, no simple unified framework for cost-sensitive multi-class boosting exists. Furthermore, (axis-aligned) decision trees may be inadequate in some situations, thereby stalling training; and even in cases where they are sufficiently useful, they don't capture the intrinsic nature of the data, as they tend to form boundaries that overfit. My thesis focuses on remedying these three drawbacks of boosting. Ch.III outlines a method (called QuickBoost) that trains identical classifiers at an order of magnitude faster than before, based on a proof of a bound. In Ch.IV, a unified framework for cost-sensitive multi-class boosting (called REBEL) is proposed, both advancing theory and demonstrating empirical gains. Finally, Ch.V describes a novel family of weak learners (called Localized Similarities) that guarantee theoretical bounds and outperform decision trees and Neural Nets (as well as several other commonly used classification methods) on a range of datasets. The culmination of my work is an easy-to-use, fast-training, cost-sensitive multi-class boosting framework whose functionality is interpretable (since each weak learner is a simple comparison of similarity), and whose performance is better than Neural Networks and other competing methods. It is the tool that everyone should have in their toolbox and the first one they try.</p

Unified Binary and Multiclass Margin-Based Classification

The notion of margin loss has been central to the development and analysis of algorithms for binary classification. To date, however, there remains no consensus as to the analogue of the margin loss for multiclass classification. In this work, we show that a broad range of multiclass loss functions, including many popular ones, can be expressed in the relative margin form, a generalization of the margin form of binary losses. The relative margin form is broadly useful for understanding and analyzing multiclass losses as shown by our prior work (Wang and Scott, 2020, 2021). To further demonstrate the utility of this way of expressing multiclass losses, we use it to extend the seminal result of Bartlett et al. (2006) on classification-calibration of binary margin losses to multiclass. We then analyze the class of Fenchel-Young losses, and expand the set of these losses that are known to be classification-calibrated

Exploring the International Application of Machine Learning in Asset Pricing: An Empirical Study

This thesis delves into the application of machine learning models for predicting cross-sectional returns in diverse markets. Chapter One explores the predictive abilities of XG-Boost, Random Forest, and neural network models in relation to fund performance and fund manager information characteristics. The findings indicate that fund performance characteristics prove to be more informative of future fund performance than the characteristics of fund managers. Chapter Two probes the presence of bimodality in momentum stocks and examines the profitability of deep momentum, a machine learning return prediction model, in the UK, Japan, and South Korea. The findings demonstrate that bimodality is a phenomenon linked to developed markets and can cause losses for JT strategy investors. However, the deep momentum model generates substantial profits in all markets by relieving bimodality in long-short portfolios. Chapter Three investigates the efficacy of the momentum factor in Chinese stock markets. We compare the performance of the traditional linear JT model, the XG-Boost model, the neural network model, and neural network reclassification models as developed by Han (2022). The study finds that machine learning models based on the momentum factor outperform the traditional JT linear regression model, indicating a non-linear relationship between the momentum factor and stock returns in China. Han's reclassification models perform the most strongly after reclassification of the true target distribution within high-return deciles moves from a bimodal shape to a right-skewed distribution. The study also observes a significant positive correlation between the return of the long-only portfolio developed using the momentum factor in the machine learning framework and the size and sentiment index. Overall, this thesis attests to the practicality of machine learning models for predicting cross-sectional returns in various markets, with potentially gainful implications for investors and policymakers

Economics of Conflict and Terrorism

This book contributes to the literature on conflict and terrorism through a selection of articles that deal with theoretical, methodological and empirical issues related to the topic. The papers study important problems, are original in their approach and innovative in the techniques used. This will be useful for researchers in the fields of game theory, economics and political sciences

Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.Comment: 59 page