Related papers: Class Probability Estimation via Differential Geom…
We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
This paper provides both an introduction to and a detailed overview of the principles and practice of classifier calibration. A well-calibrated classifier correctly quantifies the level of uncertainty or confidence associated with its…
The universal-set naive Bayes classifier (UNB)~\cite{Komiya:13}, defined using likelihood ratios (LRs), was proposed to address imbalanced classification problems. However, the LR estimator used in the UNB overestimates LRs for…
Training deep neural networks is known to require a large number of training samples. However, in many applications only few training samples are available. In this work, we tackle the issue of training neural networks for classification…
Recent studies have shown that regularization techniques using soft labels, e.g., label smoothing, Mixup, and CutMix, not only enhance image classification accuracy but also mitigate miscalibration due to overconfident predictions, and…
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…
Imbalanced classification presents a formidable challenge in machine learning, particularly when tabular datasets are plagued by noise and overlapping class boundaries. From a geometric perspective, the core difficulty lies in the…
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable…
There has been considerable effort to better understand the generalization capabilities of deep neural networks both as a means to unlock a theoretical understanding of their success as well as providing directions for further improvements.…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…
This work considers the problem of binary classification: given training data $x_1, \dots, x_n$ from a certain population, together with associated labels $y_1,\dots, y_n \in \left\{0,1 \right\}$, determine the best label for an element $x$…
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…
Preference-based reinforcement learning (PbRL) promises to learn a complex reward function with binary human preference. However, such human-in-the-loop formulation requires considerable human effort to assign preference labels to segment…