Related papers: Making Convex Loss Functions Robust to Outliers us…

Diffusion models are known to be vulnerable to outliers in training data. In this paper we study an alternative diffusion loss function, which can preserve the high quality of generated data like the original squared $L_{2}$ loss while at…

In the financial field, precise risk assessment tools are essential for decision-making. Recent studies have challenged the notion that traditional network loss functions like Mean Square Error (MSE) are adequate, especially under extreme…

We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$…

We generalized a modified exponentialized estimator by pushing the robust-optimal (RO) index $\lambda$ to $-\infty$ for achieving robustness to outliers by optimizing a quasi-Minimin function. The robustness is realized and controlled…

Knowledge graphs (KGs) represent world's facts in structured forms. KG completion exploits the existing facts in a KG to discover new ones. Translation-based embedding model (TransE) is a prominent formulation to do KG completion. Despite…

This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…

Optimal transport (OT) is known to be sensitive against outliers because of its marginal constraints. Outlier robust OT variants have been proposed based on the definition that outliers are samples which are expensive to move. In this…

In many real-world applications, data usually contain outliers. One popular approach is to use L2,1 norm function as a robust error/loss function. However, the robustness of L2,1 norm function is not well understood so far. In this paper,…

We propose a generalized formulation of the Huber loss. We show that with a suitable function of choice, specifically the log-exp transform; we can achieve a loss function which combines the desirable properties of both the absolute and the…

It has been reported that deep learning models are extremely vulnerable to small but intentionally chosen perturbations of its input. In particular, a deep network, despite its near-optimal accuracy on the clean images, often mis-classifies…

Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy…

We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map),…

We present a "learning to learn" approach for automatically constructing white-box classification loss functions that are robust to label noise in the training data. We parameterize a flexible family of loss functions using Taylor…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Automatic detection of statistical outliers is facilitated through knowledge of the source distribution of regular observations. Since the population distribution is often unknown in practice, one approach is to apply a transformation to…

In the context of regularized loss minimization with polyhedral gauges, we show that for a broad class of loss functions (possibly non-smooth and non-convex) and under a simple geometric condition on the input data it is possible to…

Outlier exposure (OE) is powerful in out-of-distribution (OOD) detection, enhancing detection capability via model fine-tuning with surrogate OOD data. However, surrogate data typically deviate from test OOD data. Thus, the performance of…

We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…

Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light…

We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…