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Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for…
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…
We consider a binary supervised learning classification problem where instead of having data in a finite-dimensional Euclidean space, we observe measures on a compact space $\mathcal{X}$. Formally, we observe data $D_N = (\mu_1, Y_1),…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
Log-linear models are a well-established method for describing statistical dependencies among a set of n random variables. The observed frequencies of the n-tuples are explained by a joint probability such that its logarithm is a sum of…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
Typically, binary classification lens-finding schemes are used to discriminate between lens candidates and non-lenses. However, these models often suffer from substantial false-positive classifications. Such false positives frequently occur…
This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based…
We show that learning can be improved by using loss functions that evolve cyclically during training to emphasize one class at a time. In underparameterized networks, such dynamical loss functions can lead to successful training for…
Loss functions are error metrics that quantify the difference between a prediction and its corresponding ground truth. Fundamentally, they define a functional landscape for traversal by gradient descent. Although numerous loss functions…
Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…
Fine-grained visual categorization (FGVC) is an important but challenging task due to high intra-class variances and low inter-class variances caused by deformation, occlusion, illumination, etc. An attention convolutional binary neural…
Since the rise of deep learning, many computer vision tasks have seen significant advancements. However, the downside of deep learning is that it is very data-hungry. Especially for segmentation problems, training a deep neural net requires…
In deep neural network, the cross-entropy loss function is commonly used for classification. Minimizing cross-entropy is equivalent to maximizing likelihood under assumptions of uniform feature and class distributions. It belongs to…
Multi-class classification is one of the most important tasks in machine learning. In this paper we consider two online multi-class classification problems: classification by a linear model and by a kernelized model. The quality of…
We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…
The adequate use of information measured in a continuous manner along a period of time represents a methodological challenge. In the last decades, most of traditional statistical procedures have been extended for accommodating these…
Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet…
Mixable loss functions are of fundamental importance in the context of prediction with expert advice in the online setting since they characterize fast learning rates. By re-interpreting properness from the point of view of differential…
In functional data analysis, binary classification with one functional covariate has been extensively studied. We aim to fill in the gap of considering multivariate functional covariates in classification. In particular, we propose an…