Related papers: Machine-Learning Mathematical Structures
Conventional Supervised Learning approaches focus on the mapping from input features to output labels. After training, the learnt models alone are adapted onto testing features to predict testing labels in isolation, with training data…
This paper presents a novel approach to machine learning algorithm design based on information theory, specifically mutual information (MI). We propose a framework for learning and representing functional relationships in data using…
Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply…
Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are…
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
In this paper, we propose a supervised dictionary learning algorithm that aims to preserve the local geometry in both dimensions of the data. A graph-based regularization explicitly takes into account the local manifold structure of the…
Due to recent advances - compute, data, models - the role of learning in autonomous systems has expanded significantly, rendering new applications possible for the first time. While some of the most significant benefits are obtained in the…
Recent research put a big effort in the development of deep learning architectures and optimizers obtaining impressive results in areas ranging from vision to language processing. However little attention has been addressed to the need of a…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…
The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This…
Measurements are fundamental to knowledge creation in science, enabling consistent sharing of findings and serving as the foundation for scientific discovery. As machine learning systems increasingly transform scientific fields, the…
Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…
Meta-learning, or "learning to learn," is a subfield of machine learning where the goal is to develop models and algorithms that can learn from various tasks and improve their learning process over time. Unlike traditional machine learning…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
We present an approach to minimally supervised relation extraction that combines the benefits of learned representations and structured learning, and accurately predicts sentence-level relation mentions given only proposition-level…
High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…
We propose a general purpose active learning algorithm for structured prediction, gathering labeled data for training a model that outputs a set of related labels for an image or video. Active learning starts with a limited initial training…