A Comparative Study of Pairwise Learning Methods based on Kernel Ridge Regression

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction or network inference problems. During the last decade kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify existing kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency and spectral filtering properties. Our theoretical results provide valuable insights in assessing the advantages and limitations of existing pairwise learning methods.Comment: arXiv admin note: text overlap with arXiv:1606.0427

An embedding-based distance for temporal graphs

We define a distance between temporal graphs based on graph embeddings built using time-respecting random walks. We study both the case of matched graphs, when there exists a known relation between the nodes, and the unmatched case, when such a relation is unavailable and the graphs may be of different sizes. We illustrate the interest of our distance definition, using both real and synthetic temporal network data, by showing its ability to discriminate between graphs with different structural and temporal properties. Leveraging state-of-the-art machine learning techniques, we propose an efficient implementation of distance computation that is viable for large-scale temporal graphs

A spatial-temporal data mining method for the extraction of vessel traffic patterns using AIS data

Current traffic pattern mining methods fail to incorporate the temporal co-occurrence of traffic characteristics. To address this problem, a new spatial-temporal data mining method is developed involving three steps. Firstly, a three-dimensional traffic tensor is constructed utilizing AIS data. The AIS data is discretized and numbered so that each AIS data entry is represented by a one-dimensional array that includes region, time, ship type, and speed numbers. Then the AIS array is mapped to the three-dimensional ship traffic tensor. Second, non-negative tensor factorization (NTF) is used to break down the tensor into multiple sub-tensors (i.e., traffic patterns). The effect of the tensor rank (i.e., the number of traffic patterns) is discussed, and the appropriate value of the tensor rank is determined. Thirdly, the traffic patterns are derived from the three-dimensional traffic tensor. The ship traffic pattern is subsequently analyzed in accordance with the actual circumstances. To demonstrate the feasibility of the method, 9 traffic patterns are obtained from the AIS data of Tianjin port-Caofeidian waters. These patterns reveal the presentation of the spatio-temporal distribution of traffic activities of different ship types, and the distribution of navigation speed of different ship types in space, that are of strategic values for port planning, and maritime safety and sustainability

Foundational principles for large scale inference: Illustrations through correlation mining

When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset is often variable-rich but sample-starved: a regime where the number $n$ of acquired samples (statistical replicates) is far fewer than the number $p$ of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data." Sample complexity however has received relatively less attention, especially in the setting when the sample size $n$ is fixed, and the dimension $p$ grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. We demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks

An Overview on Application of Machine Learning Techniques in Optical Networks

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. Advanced mathematical tools are required to extract meaningful information from these data and take decisions pertaining to the proper functioning of the networks from the network-generated data. Among these mathematical tools, Machine Learning (ML) is regarded as one of the most promising methodological approaches to perform network-data analysis and enable automated network self-configuration and fault management. The adoption of ML techniques in the field of optical communication networks is motivated by the unprecedented growth of network complexity faced by optical networks in the last few years. Such complexity increase is due to the introduction of a huge number of adjustable and interdependent system parameters (e.g., routing configurations, modulation format, symbol rate, coding schemes, etc.) that are enabled by the usage of coherent transmission/reception technologies, advanced digital signal processing and compensation of nonlinear effects in optical fiber propagation. In this paper we provide an overview of the application of ML to optical communications and networking. We classify and survey relevant literature dealing with the topic, and we also provide an introductory tutorial on ML for researchers and practitioners interested in this field. Although a good number of research papers have recently appeared, the application of ML to optical networks is still in its infancy: to stimulate further work in this area, we conclude the paper proposing new possible research directions

Recommender Systems

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.Comment: 97 pages, 20 figures (To appear in Physics Reports

MetaRec: Meta-Learning Meets Recommendation Systems

Artificial neural networks (ANNs) have recently received increasing attention as powerful modeling tools to improve the performance of recommendation systems. Meta-learning, on the other hand, is a paradigm that has re-surged in popularity within the broader machine learning community over the past several years. In this thesis, we will explore the intersection of these two domains and work on developing methods for integrating meta-learning to design more accurate and flexible recommendation systems. In the present work, we propose a meta-learning framework for the design of collaborative filtering methods in recommendation systems, drawing from ideas, models, and solutions from modern approaches in both the meta-learning and recommendation system literature, applying them to recommendation tasks to obtain improved generalization performance. Our proposed framework, MetaRec, includes and unifies the main state-of-the-art models in recommendation systems, extending them to be flexibly configured and efficiently operate with limited data. We empirically test the architectures created under our MetaRec framework on several recommendation benchmark datasets using a plethora of evaluation metrics and find that by taking a meta-learning approach to the collaborative filtering problem, we observe notable gains in predictive performance