相关论文: Fundamental Laws of Binary Classification

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…

Many regression problems involve not one but several response variables (y's). Often the responses are suspected to share a common underlying structure, in which case it may be advantageous to share information across them; this is known as…

Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of…

The celebrated minimax principle of Yao (1977) says that for any Boolean-valued function $f$ with finite domain, there is a distribution $\mu$ over the domain of $f$ such that computing $f$ to error $\epsilon$ against inputs from $\mu$ is…

We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…

In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…

In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the…

In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold…

This research seeks to benefit the software engineering society by proposing comparative separation, a novel group fairness notion to evaluate the fairness of machine learning software on comparative judgment test data. Fairness issues have…

We consider neural network training, in applications in which there are many possible classes, but at test-time, the task is a binary classification task of determining whether the given example belongs to a specific class, where the class…

We develop a new classification framework based on the theory of coherent risk measures and systemic risk. The proposed approach is suitable for multi-class problems when the data is noisy, scarce (relative to the dimension of the problem),…

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights…

Similarity learning is a general problem to elicit useful representations by predicting the relationship between a pair of patterns. This problem is related to various important preprocessing tasks such as metric learning, kernel learning,…

We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…

Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching…

When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…

Advances in machine learning technologies have led to increasingly powerful models in particular in the context of big data. Yet, many application scenarios demand for robustly interpretable models rather than optimum model accuracy; as an…

Motivated by the need for, and growing interest in, modeling uncertainty in data, we introduce and study {\em stochastic minimum-norm optimization}. We have an underlying combinatorial optimization problem where the costs involved are {\em…

In this paper, we propose an unconstrained framework for eigenvalue problems in both discrete and continuous settings. We begin our discussion to solve a generalized eigenvalue problem $A{\bf x} = \lambda B{\bf x}$ with two $N\times N$ real…

Traffic signs play a critical role in road safety and traffic management for autonomous driving systems. Accurate traffic sign classification is essential but challenging due to real-world complexities like adversarial examples and…