Related papers: The DD$^G$-classifier in the functional setting
To mitigate the burden of data labeling, we aim at improving data efficiency for both classification and regression setups in deep learning. However, the current focus is on classification problems while rare attention has been paid to deep…
The concept of deep dictionary learning has been recently proposed. Unlike shallow dictionary learning which learns single level of dictionary to represent the data, it uses multiple layers of dictionaries. So far, the problem could only be…
There are many problems in machine learning and data mining which are equivalent to selecting a non-redundant, high "quality" set of objects. Recommender systems, feature selection, and data summarization are among many applications of…
Matrix completion is one of the key problems in signal processing and machine learning. In recent years, deep-learning-based models have achieved state-of-the-art results in matrix completion. Nevertheless, they suffer from two drawbacks:…
We study supervised multiclass classification for diffusion processes, where each class is characterized by a distinct drift function and trajectories are observed at discrete times. We first derive a multidimensional Bayes rule and then…
Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data…
As a measure for the centrality of a point in a set of multivariate data, statistical depth functions play important roles in multivariate analysis, because one may conveniently construct descriptive as well as inferential procedures…
Deep neural networks (DNNs) have become the technology of choice for realizing a variety of complex tasks. However, as highlighted by many recent studies, even an imperceptible perturbation to a correctly classified input can lead to…
This paper proposes a method to use deep neural networks as end-to-end open-set classifiers. It is based on intra-class data splitting. In open-set recognition, only samples from a limited number of known classes are available for training.…
The Data Clustering (DC) problem is of central importance for the area of Machine Learning (ML), given its usefulness to represent data structural similarities from input spaces. Differently from Supervised Machine Learning (SML), which…
Deep Matching (DM) is a popular high-quality method for quasi-dense image matching. Despite its name, however, the original DM formulation does not yield a deep neural network that can be trained end-to-end via backpropagation. In this…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Multi-label classification has received considerable interest in recent years. Multi-label classifiers have to address many problems including: handling large-scale datasets with many instances and a large set of labels, compensating…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
A long standing problem in visual object categorization is the ability of algorithms to generalize across different testing conditions. The problem has been formalized as a covariate shift among the probability distributions generating the…
Though deep learning has pushed the boundaries of classification forward, in recent years hints of the limits of standard classification have begun to emerge. Problems such as fooling, adding new classes over time, and the need to retrain…
Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown classes. The recently introduced…
Deep learning has achieved remarkable results in many computer vision tasks. Deep neural networks typically rely on large amounts of training data to avoid overfitting. However, labeled data for real-world applications may be limited. By…
Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer…
Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce a class of target functions (single and multi-index Gaussian…