相关论文: Fundamental Laws of Binary Classification

Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…

We propose a Binary Robust Least Squares (BRLS) model that encompasses key robust least squares formulations, such as those involving uncertain binary labels and adversarial noise constrained within a hypercube. We show that the geometric…

Data-driven decision support tools play an increasingly central role in decision-making across various domains. In this work, we focus on binary classification models for predicting positive-outcome scores and deciding on resource…

A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…

This paper studies the problem of, given the structure of a linear-time invariant system and a set of possible inputs, finding the smallest subset of input vectors that ensures system's structural controllability. We refer to this problem…

This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…

Although kernel methods are widely used in many learning problems, they have poor scalability to large datasets. To address this problem, sketching and stochastic gradient methods are the most commonly used techniques to derive efficient…

Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…

Low rank matrix approximation is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns and provides concise representations for the data. Research on low rank approximation…

Few-shot learning aims to adapt models trained on the base dataset to novel tasks where the categories were not seen by the model before. This often leads to a relatively uniform distribution of feature values across channels on novel…

We propose a novel reduction-to-binary (R2B) approach that enforces demographic parity for multiclass classification with non-binary sensitive attributes via a reduction to a sequence of binary debiasing tasks. We prove that R2B satisfies…

It was recently shown that almost all solutions in the symmetric binary perceptron are isolated, even at low constraint densities, suggesting that finding typical solutions is hard. In contrast, some algorithms have been shown empirically…

Many applications of AI involve scoring individuals using a learned function of their attributes. These predictive risk scores are then used to take decisions based on whether the score exceeds a certain threshold, which may vary depending…

Bin Packing with Minimum Color Fragmentation (BPMCF) is an extension of the Bin Packing Problem in which each item has a size and a color and the goal is to minimize the sum of the number of bins containing items of each color. In this…

The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…

Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

We study the problem of online binary classification where strategic agents can manipulate their observable features in predefined ways, modeled by a manipulation graph, in order to receive a positive classification. We show this setting…

During the last decades, many methods for the analysis of functional data including classification methods have been developed. Nonetheless, there are issues that have not been adressed satisfactorily by currently available methods, as, for…

We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…