相关论文: Minimax deviation strategies for machine learning …

We show that forms of Bayesian and MDL inference that are often applied to classification problems can be *inconsistent*. This means there exists a learning problem such that for all amounts of data the generalization errors of the MDL…

The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more…

We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…

Machine learning has become one of the main components for task automation in many application domains. Despite the advancements and impressive achievements of machine learning, it has been shown that learning algorithms can be compromised…

The main purpose of this paper is to introduce and study the behavior of minimum {\phi}-divergence estimators as an alternative to the maximum likelihood estimator in latent class models for binary items. As it will become clear below,…

We take a closer look at some theoretical challenges of Machine Learning as a function approximation, gradient descent as the default optimization algorithm, limitations of fixed length and width networks and a different approach to RNNs…

As a promising area in artificial intelligence, a new learning paradigm, called Small Sample Learning (SSL), has been attracting prominent research attention in the recent years. In this paper, we aim to present a survey to comprehensively…

A crucial assumption underlying the most current theory of machine learning is that the training distribution is identical to the test distribution. However, this assumption may not hold in some real-world applications. In this paper, we…

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…

Over the past decade, the field of machine learning has experienced remarkable advancements. While image recognition systems have achieved impressive levels of accuracy, they continue to rely on extensive training datasets. Additionally, a…

Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…

Training a neural network model that can quickly adapt to a new task is highly desirable yet challenging for few-shot learning problems. Recent few-shot learning methods mostly concentrate on developing various meta-learning strategies from…

Much of the teaching of machine learning focuses on iterative hill-climbing approaches and the use of local knowledge to gain information leading to local or global maxima. In this paper we advocate the teaching of alternative methods of…

In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical…

This paper attempts to address the issues of machine learning in its current implementation. It is known that machine learning algorithms require a significant amount of data for training purposes, whereas recent developments in deep…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

Robust low-rank matrix estimation is a topic of increasing interest, with promising applications in a variety of fields, from computer vision to data mining and recommender systems. Recent theoretical results establish the ability of such…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

We propose simple active sampling and reweighting strategies for optimizing min-max fairness that can be applied to any classification or regression model learned via loss minimization. The key intuition behind our approach is to use at…

We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction -- the…