Transfer learning borrows knowledge from a source domain to facilitate learning in a target domain. Two primary issues to be addressed in transfer learning are what and how to transfer. For a pair of domains, adopting different transfer learning algorithms results in different knowledge transferred between them. To discover the optimal transfer learning algorithm that maximally improves the learning performance in the target domain, researchers have to exhaustively explore all existing transfer learning algorithms, which is computationally intractable. As a trade-off, a sub-optimal algorithm is selected, which requires considerable expertise in an ad-hoc way. Meanwhile, it is widely accepted in educational psychology that human beings improve transfer learning skills of deciding what to transfer through meta-cognitive reflection on inductive transfer learning practices. Motivated by this, we propose a novel transfer learning framework known as Learning to Transfer (L2T) to automatically determine what and how to transfer are the best by leveraging previous transfer learning experiences. We establish the L2T framework in two stages: 1) we first learn a reflection function encrypting transfer learning skills from experiences; and 2) we infer what and how to transfer for a newly arrived pair of domains by optimizing the reflection function. Extensive experiments demonstrate the L2T's superiority over several state-of-the-art transfer learning algorithms and its effectiveness on discovering more transferable knowledge.

The analysis of mixed data has been raising challenges in statistics and machine learning. One of two most prominent challenges is to develop new statistical techniques and methodologies to effectively handle mixed data by making the data less heterogeneous with minimum loss of information. The other challenge is that such methods must be able to apply in large-scale tasks when dealing with huge amount of mixed data. To tackle these challenges, we introduce parameter sharing and balancing extensions to our recent model, the mixed-variate restricted Boltzmann machine (MV.RBM) which can transform heterogeneous data into homogeneous representation. We also integrate structured sparsity and distance metric learning into RBM-based models. Our proposed methods are applied in various applications including latent patient profile modelling in medical data analysis and representation learning for image retrieval. The experimental results demonstrate the models perform better than baseline methods in medical data and outperform state-of-the-art rivals in image dataset.

In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a single clustering. The main advantage of these algorithms is that they bring down significantly the computational cost of traditional algorithms, including spectral clustering, semi-definite programs, modularity based methods, likelihood based methods etc., without losing on accuracy and even improving accuracy at times. These algorithms are also, by nature, parallelizable. Thus, exploiting the facts that most traditional algorithms are accurate and the corresponding optimization problems are much simpler in small problems, our divide-and-conquer methods provide an omnibus recipe for scaling traditional algorithms up to large networks. We prove consistency of these algorithms under various subgraph selection procedures and perform extensive simulations and real-data analysis to understand the advantages of the divide-and-conquer approach in various settings.

Revealing a community structure in a network or dataset is a central problem arising in many scientific areas. The modularity function $Q$ is an established measure quantifying the quality of a community, being identified as a set of nodes having high modularity. In our terminology, a set of nodes with positive modularity is called a \textit{module} and a set that maximizes $Q$ is thus called \textit{leading module}. Finding a leading module in a network is an important task, however the dimension of real-world problems makes the maximization of $Q$ unfeasible. This poses the need of approximation techniques which are typically based on a linear relaxation of $Q$, induced by the spectrum of the modularity matrix $M$. In this work we propose a nonlinear relaxation which is instead based on the spectrum of a nonlinear modularity operator $\mathcal M$. We show that extremal eigenvalues of $\mathcal M$ provide an exact relaxation of the modularity measure $Q$, however at the price of being more challenging to be computed than those of $M$. Thus we extend the work made on nonlinear Laplacians, by proposing a computational scheme, named \textit{generalized RatioDCA}, to address such extremal eigenvalues. We show monotonic ascent and convergence of the method. We finally apply the new method to several synthetic and real-world data sets, showing both effectiveness of the model and performance of the method.

Person re-identification (Re-ID) aims at matching images of the same person across disjoint camera views, which is a challenging problem in multimedia analysis, multimedia editing and content-based media retrieval communities. The major challenge lies in how to preserve similarity of the same person across video footages with large appearance variations, while discriminating different individuals. To address this problem, conventional methods usually consider the pairwise similarity between persons by only measuring the point to point (P2P) distance. In this paper, we propose to use deep learning technique to model a novel set to set (S2S) distance, in which the underline objective focuses on preserving the compactness of intra-class samples for each camera view, while maximizing the margin between the intra-class set and inter-class set. The S2S distance metric is consisted of three terms, namely the class-identity term, the relative distance term and the regularization term. The class-identity term keeps the intra-class samples within each camera view gathering together, the relative distance term maximizes the distance between the intra-class class set and inter-class set across different camera views, and the regularization term smoothness the parameters of deep convolutional neural network (CNN). As a result, the final learned deep model can effectively find out the matched target to the probe object among various candidates in the video gallery by learning discriminative and stable feature representations. Using the CUHK01, CUHK03, PRID2011 and Market1501 benchmark datasets, we extensively conducted comparative evaluations to demonstrate the advantages of our method over the state-of-the-art approaches.

There is a pressing need to build an architecture that could subsume these networks undera unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discrete. The second one is how to remove the full-precision hidden weights in the training phase to break the bottlenecks of memory/computation consumption. To address the first issue, we present a multistep neuronal activation discretization method and a derivative approximation technique that enable the implementing the back propagation algorithm on discrete DNNs. While for the second issue, we propose a discrete state transition (DST) methodology to constrain the weights in a discrete space without saving the hidden weights. In this way, we build a unified framework that subsumes the binary or ternary networks as its special cases.More particularly, we find that when both the weights and activations become ternary values, the DNNs can be reduced to gated XNOR networks (or sparse binary networks) since only the event of non-zero weight and non-zero activation enables the control gate to start the XNOR logic operations in the original binary networks. This promises the event-driven hardware design for efficient mobile intelligence. We achieve advanced performance compared with state-of-the-art algorithms. Furthermore,the computational sparsity and the number of states in the discrete space can be flexibly modified to make it suitable for various hardware platforms.

Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their close connection to generalized linear models, it is also natural to incorporate covariate information in them. The current paper presents two universal fitting algorithms for networks with edge covariates: one based on nuclear norm penalization and the other based on projected gradient descent. Both algorithms are motivated by maximizing likelihood for a special class of inner-product models while working simultaneously for a wide range of different latent space models, such as distance models, which allow latent vectors to affect edge formation in flexible ways. These fitting methods, especially the one based on projected gradient descent, are fast and scalable to large networks. We obtain their rates of convergence for both inner-product models and beyond. The effectiveness of the modeling approach and fitting algorithms is demonstrated on five real world network datasets for different statistical tasks, including community detection with and without edge covariates, and network assisted learning.

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also requires the storage of a large matrix in memory. These factors restrict the application of Gaussian Process regression to small and moderate size data sets. We present an algorithm that combines estimates from models developed using subsets of the data obtained in a manner similar to the bootstrap. The sample size is a critical parameter for this algorithm. Guidelines for reasonable choices of algorithm parameters, based on detailed experimental study, are provided. Various techniques have been proposed to scale Gaussian Processes to large scale regression tasks. The most appropriate choice depends on the problem context. The proposed method is most appropriate for problems where an additive model works well and the response depends on a small number of features. The minimax rate of convergence for such problems is attractive and we can build effective models with a small subset of the data. The Stochastic Variational Gaussian Process and the Sparse Gaussian Process are also appropriate choices for such problems. These methods pick a subset of data based on theoretical considerations. The proposed algorithm uses bagging and random sampling. Results from experiments conducted as part of this study indicate that the algorithm presented in this work can be as effective as these methods. Keywords: Big Data, Gaussian Process, Regression 2010 MSC: 00-01, 99-00 1. Introduction Gaussian Processes (GP) are attractive tools to perform supervised learning tasks on complex datasets on which traditional parametric methods may not be effective. They are also easier to use in comparison to alternatives like neural networks ([1]).

We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and $\rm W_{H\alpha}$ vs. [NII]/H$\alpha$ (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLIGHT datasets. We apply a GMM to empirically define classes of galaxies in a three-dimensional space spanned by the $\log$ [OIII]/H$\beta$, $\log$ [NII]/H$\alpha$, and $\log$ EW(H${\alpha}$), optical parameters. The best-fit GMM based on several statistical criteria suggests a solution around four Gaussian components (GCs), which are capable to explain up to 97 per cent of the data variance. Using elements of information theory, we compare each GC to their respective astronomical counterpart. GC1 and GC4 are associated with star-forming galaxies, suggesting the need to define a new starburst subgroup. GC2 is associated with BPT's Active Galaxy Nuclei (AGN) class and WHAN's weak AGN class. GC3 is associated with BPT's composite class and WHAN's strong AGN class. Conversely, there is no statistical evidence -- based on four GCs -- for the existence of a Seyfert/LINER dichotomy in our sample. Notwithstanding, the inclusion of an additional GC5 unravels it. The GC5 appears associated to the LINER and Passive galaxies on the BPT and WHAN diagrams respectively. Subtleties aside, we demonstrate the potential of our methodology to recover/unravel different objects inside the wilderness of astronomical datasets, without lacking the ability to convey physically interpretable results. The probabilistic classifications from the GMM analysis are publicly available within the COINtoolbox (https://cointoolbox.github.io/GMM\_Catalogue/).

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.