Related papers: Generalized Huber Loss for Robust Learning and its…
The loss function is crucial to machine learning, especially in supervised learning frameworks. It is a fundamental component that controls the behavior and general efficacy of learning algorithms. However, despite their widespread use,…
We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In…
We introduce a tunable loss function called $\alpha$-loss, parameterized by $\alpha \in (0,\infty]$, which interpolates between the exponential loss ($\alpha = 1/2$), the log-loss ($\alpha = 1$), and the 0-1 loss ($\alpha = \infty$), for…
We introduce a novel end-to-end approach for learning to cluster in the absence of labeled examples. Our clustering objective is based on optimizing normalized cuts, a criterion which measures both intra-cluster similarity as well as…
As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a parametric setup, it…
This paper explores connections between margin-based loss functions and consistency in binary classification and regression applications. It is shown that a large class of margin-based loss functions for binary classification/regression…
A common goal in statistics and machine learning is estimation of unknowns. Point estimates alone are of little value without an accompanying measure of uncertainty, but traditional uncertainty quantification methods, such as confidence…
In recent years, there has been growing interest in utilizing modern machine learning techniques to learn heuristic functions for forward search algorithms. Despite this, there has been little theoretical understanding of what they should…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
Learning-to-optimize leverages machine learning to accelerate optimization algorithms. While empirical results show tremendous improvements compared to classical optimization algorithms, theoretical guarantees are mostly lacking, such that…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function…
Metric learning has attracted a lot of interest over the last decade, but the generalization ability of such methods has not been thoroughly studied. In this paper, we introduce an adaptation of the notion of algorithmic robustness…
Loss functions play an important role in the training of artificial neural networks (ANNs), and can affect the generalisation ability of the ANN model, among other properties. Specifically, it has been shown that the cross entropy and sum…
We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case of high-dimensional linear regression model selection with…
Federated learning has attracted significant attention as a privacy-preserving framework for training personalised models on multi-source heterogeneous data. However, most existing approaches are unable to handle scenarios where subgroup…
We propose a learning framework for calibrating predictive models to make loss-controlling prediction for exchangeable data, which extends our recently proposed conformal loss-controlling prediction for more general cases. By comparison,…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…