Related papers: Mathematical Perspective of Machine Learning
In the last years decision-focused learning framework, also known as predict-and-optimize, have received increasing attention. In this setting, the predictions of a machine learning model are used as estimated cost coefficients in the…
In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained…
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…
Recent advances unveiled physical neural networks as promising machine learning platforms, offering faster and more energy-efficient information processing. Compared with extensively-studied optical neural networks, the development of…
Despite the high interest for Machine Learning (ML) in academia and industry, many issues related to the application of ML to real-life problems are yet to be addressed. Here we put forward one limitation which arises from a lack of…
Today's telecommunication networks have become sources of enormous amounts of widely heterogeneous data. This information can be retrieved from network traffic traces, network alarms, signal quality indicators, users' behavioral data, etc.…
In recent years, representation learning has become the research focus of the machine learning community. Large-scale neural networks are a crucial step toward achieving general intelligence, with their success largely attributed to their…
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…
We show that many machine-learning algorithms are specific instances of a single algorithm called the \emph{Bayesian learning rule}. The rule, derived from Bayesian principles, yields a wide-range of algorithms from fields such as…
In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
Despite the highest classification accuracy in wide varieties of application areas, artificial neural network has one disadvantage. The way this Network comes to a decision is not easily comprehensible. The lack of explanation ability…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
Recurrent Neural Networks (RNNs) produce state-of-art performance on many machine learning tasks but their demand on resources in terms of memory and computational power are often high. Therefore, there is a great interest in optimizing the…
Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily…
Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…
Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Neural networks are usually trained by some form of stochastic gradient descent (SGD)). A number of strategies are in common use intended to improve SGD optimization, such as learning rate schedules, momentum, and batching. These are…